[ { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating001", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (white water tower and sloped roof warehouse) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating001-1-2.png", "Satellite_Image_Matching/SVILocating001-1-3.png", "Satellite_Image_Matching/SVILocating001-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating002", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (church and its front square) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating002-1-1.png", "Satellite_Image_Matching/SVILocating002-1-3.png", "Satellite_Image_Matching/SVILocating002-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, e on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating004", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (yellow banana sculpture) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating004-1-2.png", "Satellite_Image_Matching/SVILocating004-1-3.png", "Satellite_Image_Matching/SVILocating004-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating005", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (white gothic giant structure) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating005-1-3.png", "Satellite_Image_Matching/SVILocating005-1-1.png", "Satellite_Image_Matching/SVILocating005-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating006", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (blue ox and herdsman statue) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating006-1-1.png", "Satellite_Image_Matching/SVILocating006-1-3.png", "Satellite_Image_Matching/SVILocating006-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating007", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (giant elephant statue) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating007-1-3.png", "Satellite_Image_Matching/SVILocating007-1-1.png", "Satellite_Image_Matching/SVILocating007-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions b, e on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating008", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (giant catenary arch) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating008-1-3.png", "Satellite_Image_Matching/SVILocating008-1-1.png", "Satellite_Image_Matching/SVILocating008-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating009", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (giant sheep statue) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating009-1-3.png", "Satellite_Image_Matching/SVILocating009-1-2.png", "Satellite_Image_Matching/SVILocating009-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating010", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (metal facade curved design building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating010-1-1.png", "Satellite_Image_Matching/SVILocating010-1-3.png", "Satellite_Image_Matching/SVILocating010-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating011", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (domed architecture) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating011-1-2.png", "Satellite_Image_Matching/SVILocating011-1-3.png", "Satellite_Image_Matching/SVILocating011-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, e on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating012", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (white classical european architecture) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating012-1-2.png", "Satellite_Image_Matching/SVILocating012-1-1.png", "Satellite_Image_Matching/SVILocating012-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, g on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating013", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (red-roofed church and bell tower) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating013-1-3.png", "Satellite_Image_Matching/SVILocating013-1-1.png", "Satellite_Image_Matching/SVILocating013-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating015", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (cross-shaped building with green roof) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating015-1-3.png", "Satellite_Image_Matching/SVILocating015-1-1.png", "Satellite_Image_Matching/SVILocating015-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating016", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (square building with white circular helipad on rooftop) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating016-1-2.png", "Satellite_Image_Matching/SVILocating016-1-3.png", "Satellite_Image_Matching/SVILocating016-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, e on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating017", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (c-shaped brown roof building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating017-1-1.png", "Satellite_Image_Matching/SVILocating017-1-3.png", "Satellite_Image_Matching/SVILocating017-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating018", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (ornate patterned circular building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating018-1-1.png", "Satellite_Image_Matching/SVILocating018-1-3.png", "Satellite_Image_Matching/SVILocating018-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating019", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (green rectangular building, hat-shaped roof building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating019-1-1.png", "Satellite_Image_Matching/SVILocating019-1-3.png", "Satellite_Image_Matching/SVILocating019-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating020", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (polygonal building assembly) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating020-1-2.png", "Satellite_Image_Matching/SVILocating020-1-1.png", "Satellite_Image_Matching/SVILocating020-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions b, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating021", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (orange roof triangular building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating021-1-3.jpg", "Satellite_Image_Matching/SVILocating021-1-1.png", "Satellite_Image_Matching/SVILocating021-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, e on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating022", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (black single statue) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating022-1-1.png", "Satellite_Image_Matching/SVILocating022-1-3.png", "Satellite_Image_Matching/SVILocating022-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating023", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (colorful artistic architecture) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating023-1-1.png", "Satellite_Image_Matching/SVILocating023-1-2.png", "Satellite_Image_Matching/SVILocating023-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating024", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (beatles memorial statue) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating024-1-2.png", "Satellite_Image_Matching/SVILocating024-1-3.png", "Satellite_Image_Matching/SVILocating024-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating025", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (equestrian statue) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating025-1-2.png", "Satellite_Image_Matching/SVILocating025-1-1.png", "Satellite_Image_Matching/SVILocating025-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating026", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (art gallery) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating026-1-2.png", "Satellite_Image_Matching/SVILocating026-1-1.png", "Satellite_Image_Matching/SVILocating026-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, e on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating027", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (irregular silver concert hall) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating027-1-1.png", "Satellite_Image_Matching/SVILocating027-1-3.png", "Satellite_Image_Matching/SVILocating027-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating028", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (red wall white station with clock tower) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating028-1-2.png", "Satellite_Image_Matching/SVILocating028-1-1.png", "Satellite_Image_Matching/SVILocating028-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions f, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating029", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (stadium) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating029-1-2.png", "Satellite_Image_Matching/SVILocating029-1-1.png", "Satellite_Image_Matching/SVILocating029-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating031", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (boat dock) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating031-1-2.png", "Satellite_Image_Matching/SVILocating031-1-3.png", "Satellite_Image_Matching/SVILocating031-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions b, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating033", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (gothic tower monument) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating033-1-2.png", "Satellite_Image_Matching/SVILocating033-1-1.png", "Satellite_Image_Matching/SVILocating033-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions b, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating034", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (sydney opera house) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating034-1-2.png", "Satellite_Image_Matching/SVILocating034-1-1.png", "Satellite_Image_Matching/SVILocating034-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating035", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (irregular circular building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating035-1-3.png", "Satellite_Image_Matching/SVILocating035-1-2.png", "Satellite_Image_Matching/SVILocating035-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating036", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (red roof building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating036-1-3.png", "Satellite_Image_Matching/SVILocating036-1-1.png", "Satellite_Image_Matching/SVILocating036-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating037", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (green sloped roof building and metal lookout tower) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating037-1-3.png", "Satellite_Image_Matching/SVILocating037-1-2.jpg", "Satellite_Image_Matching/SVILocating037-1-1.jpg" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, g on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating038", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (green roof architecture) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating038-1-1.jpg", "Satellite_Image_Matching/SVILocating038-1-2.png", "Satellite_Image_Matching/SVILocating038-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, f on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating039", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (fountain and statue monument) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating039-1-1.png", "Satellite_Image_Matching/SVILocating039-1-3.png", "Satellite_Image_Matching/SVILocating039-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating040", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (multi-story building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating040-1-1.jpg", "Satellite_Image_Matching/SVILocating040-1-2.jpg", "Satellite_Image_Matching/SVILocating040-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating041", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (circular building appearance) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating041-1-2.png", "Satellite_Image_Matching/SVILocating041-1-1.png", "Satellite_Image_Matching/SVILocating041-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating042", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (saint peter's university) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating042-1-1.png", "Satellite_Image_Matching/SVILocating042-1-2.png", "Satellite_Image_Matching/SVILocating042-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating043", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (white memorial pillar, red sloped roof building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating043-1-3.jpg", "Satellite_Image_Matching/SVILocating043-1-2.jpg", "Satellite_Image_Matching/SVILocating043-1-1.jpg" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating044", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (brown triangular pyramid art installation) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating044-1-1.png", "Satellite_Image_Matching/SVILocating044-1-2.png", "Satellite_Image_Matching/SVILocating044-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, e on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating045", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (red frame art installation) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating045-1-1.png", "Satellite_Image_Matching/SVILocating045-1-2.png", "Satellite_Image_Matching/SVILocating045-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions b, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating046", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (white steel frame water tower and sloped roof house) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating046-1-1.png", "Satellite_Image_Matching/SVILocating046-1-3.png", "Satellite_Image_Matching/SVILocating046-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating047", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (red curved brick wall) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating047-1-2.png", "Satellite_Image_Matching/SVILocating047-1-1.png", "Satellite_Image_Matching/SVILocating047-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating048", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (curved irregular glass facade) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating048-1-3.png", "Satellite_Image_Matching/SVILocating048-1-2.png", "Satellite_Image_Matching/SVILocating048-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, f on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating049", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (irregular curved structure) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating049-1-2.png", "Satellite_Image_Matching/SVILocating049-1-3.png", "Satellite_Image_Matching/SVILocating049-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions b, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating050", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (railway overpass and red-roofed two-story building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating050-1-1.png", "Satellite_Image_Matching/SVILocating050-1-3.png", "Satellite_Image_Matching/SVILocating050-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions b, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating051", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (hollow bottom water tower and cylindrical ground device) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating051-1-3.png", "Satellite_Image_Matching/SVILocating051-1-1.png", "Satellite_Image_Matching/SVILocating051-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating052", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (high-voltage transmission towers and large warehouse-like low buildings) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating052-1-2.png", "Satellite_Image_Matching/SVILocating052-1-3.png", "Satellite_Image_Matching/SVILocating052-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating053", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (orange-red pyramid tower and rectangular factory building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating053-1-1.png", "Satellite_Image_Matching/SVILocating053-1-3.png", "Satellite_Image_Matching/SVILocating053-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating054", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (arc-shaped building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating054-1-1.png", "Satellite_Image_Matching/SVILocating054-1-3.png", "Satellite_Image_Matching/SVILocating054-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating055", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (milan cathedral) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating055-1-1.png", "Satellite_Image_Matching/SVILocating055-1-3.png", "Satellite_Image_Matching/SVILocating055-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating056", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (gray-roof temple and surrounding courtyard) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating056-1-1.png", "Satellite_Image_Matching/SVILocating056-1-2.png", "Satellite_Image_Matching/SVILocating056-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating057", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (cologne cathedral) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating057-1-2.png", "Satellite_Image_Matching/SVILocating057-1-3.png", "Satellite_Image_Matching/SVILocating057-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating058", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (high-rise with glass curtain wall) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating058-1-1.png", "Satellite_Image_Matching/SVILocating058-1-2.png", "Satellite_Image_Matching/SVILocating058-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating059", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (rectangular industrial building with multiple green roofs and rectangular sections) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating059-1-2.png", "Satellite_Image_Matching/SVILocating059-1-3.png", "Satellite_Image_Matching/SVILocating059-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating060", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (victorian square with square building and clock tower) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating060-1-2.png", "Satellite_Image_Matching/SVILocating060-1-1.png", "Satellite_Image_Matching/SVILocating060-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating061", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (arched building with unique roof ends) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating061-1-3.png", "Satellite_Image_Matching/SVILocating061-1-2.png", "Satellite_Image_Matching/SVILocating061-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating062", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (large white-roofed blue-black wall building \nsmall white-roofed white wall building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating062-1-3.png", "Satellite_Image_Matching/SVILocating062-1-1.png", "Satellite_Image_Matching/SVILocating062-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, f on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating063", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (circular building and road center sculpture) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating063-1-1.png", "Satellite_Image_Matching/SVILocating063-1-3.png", "Satellite_Image_Matching/SVILocating063-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, f on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating064", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (camouflaged plane in circular area) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating064-1-1.png", "Satellite_Image_Matching/SVILocating064-1-3.png", "Satellite_Image_Matching/SVILocating064-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions b, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating065", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (green dome rectangular building with plaza sculpture) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating065-1-2.png", "Satellite_Image_Matching/SVILocating065-1-1.png", "Satellite_Image_Matching/SVILocating065-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions b, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating066", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (curved glass building ensemble) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating066-1-2.png", "Satellite_Image_Matching/SVILocating066-1-3.png", "Satellite_Image_Matching/SVILocating066-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating067", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (curved roof with linear enclosure modern architecture) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating067-1-1.png", "Satellite_Image_Matching/SVILocating067-1-3.png", "Satellite_Image_Matching/SVILocating067-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions b, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating069", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (silver cross-shaped building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating069-1-1.png", "Satellite_Image_Matching/SVILocating069-1-2.png", "Satellite_Image_Matching/SVILocating069-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating070", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (bell tower and annex) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating070-1-1.png", "Satellite_Image_Matching/SVILocating070-1-3.png", "Satellite_Image_Matching/SVILocating070-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating071", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (white high-rise building and its sky bridge) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating071-1-2.png", "Satellite_Image_Matching/SVILocating071-1-1.png", "Satellite_Image_Matching/SVILocating071-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating072", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (skyscraper and its irregular ground floor) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating072-1-2.png", "Satellite_Image_Matching/SVILocating072-1-1.png", "Satellite_Image_Matching/SVILocating072-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating074", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (cruciform church) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating074-1-1.png", "Satellite_Image_Matching/SVILocating074-1-3.png", "Satellite_Image_Matching/SVILocating074-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions f, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating075", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (stockholm city hall) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating075-1-1.png", "Satellite_Image_Matching/SVILocating075-1-2.png", "Satellite_Image_Matching/SVILocating075-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating076", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (open-air music) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating076-1-2.png", "Satellite_Image_Matching/SVILocating076-1-3.png", "Satellite_Image_Matching/SVILocating076-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating077", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (lotte tower) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating077-1-2.png", "Satellite_Image_Matching/SVILocating077-1-1.png", "Satellite_Image_Matching/SVILocating077-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, f on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating078", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (skyscraper building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating078-1-1.png", "Satellite_Image_Matching/SVILocating078-1-2.png", "Satellite_Image_Matching/SVILocating078-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, f on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating079", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (large supermarket with white roof) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating079-1-3.png", "Satellite_Image_Matching/SVILocating079-1-1.png", "Satellite_Image_Matching/SVILocating079-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions f, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating080", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (large building with white roof) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating080-1-1.png", "Satellite_Image_Matching/SVILocating080-1-2.png", "Satellite_Image_Matching/SVILocating080-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, f on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating081", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (rectangular building with blue roof) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating081-1-1.png", "Satellite_Image_Matching/SVILocating081-1-2.png", "Satellite_Image_Matching/SVILocating081-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating082", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (2-floor L-shaped building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating082-1-2.png", "Satellite_Image_Matching/SVILocating082-1-1.png", "Satellite_Image_Matching/SVILocating082-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, f on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating083", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (silver building complex) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating083-1-1.png", "Satellite_Image_Matching/SVILocating083-1-3.png", "Satellite_Image_Matching/SVILocating083-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, e on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating084", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (education tower) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating084-1-1.png", "Satellite_Image_Matching/SVILocating084-1-2.png", "Satellite_Image_Matching/SVILocating084-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating085", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (Osaka prefectural police headquarters) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating085-1-1.png", "Satellite_Image_Matching/SVILocating085-1-3.png", "Satellite_Image_Matching/SVILocating085-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating086", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (unique architectural complex) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating086-1-2.png", "Satellite_Image_Matching/SVILocating086-1-3.png", "Satellite_Image_Matching/SVILocating086-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating087", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (white roof buildings) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating087-1-2.png", "Satellite_Image_Matching/SVILocating087-1-1.png", "Satellite_Image_Matching/SVILocating087-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, f on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating088", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (church) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating088-1-1.png", "Satellite_Image_Matching/SVILocating088-1-3.png", "Satellite_Image_Matching/SVILocating088-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating089", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (basilica of the holy apostles) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating089-1-2.png", "Satellite_Image_Matching/SVILocating089-1-1.png", "Satellite_Image_Matching/SVILocating089-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions f, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating090", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (gymnasium and apartment building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating090-1-2.png", "Satellite_Image_Matching/SVILocating090-1-1.png", "Satellite_Image_Matching/SVILocating090-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating091", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (conical architecture) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating091-1-1.png", "Satellite_Image_Matching/SVILocating091-1-2.png", "Satellite_Image_Matching/SVILocating091-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, e on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating092", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (agbata) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating092-1-2.png", "Satellite_Image_Matching/SVILocating092-1-1.png", "Satellite_Image_Matching/SVILocating092-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions g, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating093", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (group of architecture) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating093-1-1.png", "Satellite_Image_Matching/SVILocating093-1-3.png", "Satellite_Image_Matching/SVILocating093-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions f, d on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating094", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (monumental arch) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating094-1-1.png", "Satellite_Image_Matching/SVILocating094-1-2.png", "Satellite_Image_Matching/SVILocating094-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions g, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating095", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (arched building with glass) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating095-1-2.png", "Satellite_Image_Matching/SVILocating095-1-1.png", "Satellite_Image_Matching/SVILocating095-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, b on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating097", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (blue roof train station and its station square) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating097-1-3.png", "Satellite_Image_Matching/SVILocating097-1-1.png", "Satellite_Image_Matching/SVILocating097-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating098", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (black-roof building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating098-1-2.png", "Satellite_Image_Matching/SVILocating098-1-3.png", "Satellite_Image_Matching/SVILocating098-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions f, g on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating099", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (pointed structure) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating099-1-3.png", "Satellite_Image_Matching/SVILocating099-1-2.png", "Satellite_Image_Matching/SVILocating099-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating100", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (memorial hall) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating100-1-1.png", "Satellite_Image_Matching/SVILocating100-1-3.png", "Satellite_Image_Matching/SVILocating100-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating101", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (pointed roof) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating101-1-1.png", "Satellite_Image_Matching/SVILocating101-1-3.png", "Satellite_Image_Matching/SVILocating101-1-2.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions e, g on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating102", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (pointed roof) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating102-1-2.png", "Satellite_Image_Matching/SVILocating102-1-3.png", "Satellite_Image_Matching/SVILocating102-1-1.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, e on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating103", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (L-shape building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating103-1-1.png", "Satellite_Image_Matching/SVILocating103-1-2.png", "Satellite_Image_Matching/SVILocating103-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, f on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating104", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (red brick building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating104-1-2.png", "Satellite_Image_Matching/SVILocating104-1-1.png", "Satellite_Image_Matching/SVILocating104-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions f, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating105", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (communication tower and glass curtain wall building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating105-1-2.png", "Satellite_Image_Matching/SVILocating105-1-1.png", "Satellite_Image_Matching/SVILocating105-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions c, a on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating106", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (red sloped roof low building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating106-1-1.png", "Satellite_Image_Matching/SVILocating106-1-2.png", "Satellite_Image_Matching/SVILocating106-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions a, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating107", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (gray arched roof complex) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating107-1-1.png", "Satellite_Image_Matching/SVILocating107-1-2.png", "Satellite_Image_Matching/SVILocating107-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions b, c on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } }, { "id": "Spatial_Reasoning/Satellite_Image_Matching/SVILocating109", "system_prompt": "", "prompt": "- I have provided you with 3 photos, including two ground-level photos and one satellite map. The main buildings in the ground-level photos 1 and 2 (gray roof building) are marked with red boxes in the satellite image.\n- Please determine from which numbered positions in the satellite image photos 1 and 2 were taken. Analyze first, then provide your answer.\n- The answer format should be as follows: Photos 1 and 2 correspond to positions x and x on the map, respectively.", "image_list": [ "Satellite_Image_Matching/SVILocating109-1-2.png", "Satellite_Image_Matching/SVILocating109-1-1.png", "Satellite_Image_Matching/SVILocating109-1-3.png" ], "ground_truth": { "answer": "Photos 1, 2 correspond to positions d, f on the map, respectively", "rationale": "" }, "judge_system_prompt": "You are a grading teacher tasked with reviewing and scoring student answers based on the reference answer. During the grading process, you must adhere to the following important points:\n\n- The scoring is based solely on the correctness of the student’s final answer compared to the reference answer. There is no need to assess whether the intermediate steps in the solution are correct. \n- First, extract the final answer provided by the student and display it in your analysis result. Then, judge the correctness of the extracted answer based on the reference answer. \n- Assign a score based on your analysis. When explaining the scoring analysis, the explanation should be broken down logically into sections. At the end of your explanation, summarize the analysis and format it as: \"In conclusion, the student’s answer should receive x points\" (where x indicates the specific score awarded). \n- Keep your explanation concise, limited to 200 words. \n- Provide the final score in \"JSON\" format using a code block.\n\nYour output format should be: \n[Scoring analysis]: \n[Score]: x points \n[JSON]: \n```json\n{\n \"answer_score\": [[score]]\n}\n```\n\n### Scoring Criteria:\n[Score Levels]:\nThe final answer is assessed according to the reference answer key and assigned one of two levels: \n- 1 Point: Maximum score. \n- 0 Points: Minimum score. (Even if the answer would merit less than 0 points, apply 0 as the lowest score.) \n\n[Detailed Explanation]:\n- 1 Point: \n - The student's final answer matches the reference answer exactly. \n - For questions with multiple subparts, all subparts must be correct to receive 1 point. \n - If the student’s answer is mathematically equivalent to the reference answer (e.g., if the student writes 1+1/2x while the reference answer is 1+0.5x, this is acceptable as 1/2=0.5 and earns full credit. \n- 0 Points:\n - The student’s final answer does not match the reference answer. \n - The student’s answer is empty. \n\nExample 1: \n\n: \nXiao Ming decides to host a party. If he has 5 tables and each table is paired with 10 chairs, how many more chairs than tables does he have? \n\n: 45 \n\n: \nXiao Ming has $5$ tables, and each table is paired with $10$ chairs. So, he has a total of $5\\times10=50$ chairs. \nThe number of chairs minus the number of tables is $50-5=45$. \nThus, Xiao Ming has $45$ more chairs than tables. \n\n[Scoring analysis]: \nThe student’s final answer is that there are 45 more chairs than tables. \nThe reference answer is 45. \nThe two answers are consistent, so the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 2: \n\n: \nBox A contains 42 oranges, and Box B contains 18 oranges. If the same number of oranges is removed from both boxes such that the remaining oranges in Box A are 9 times those in Box B, how many oranges remain in each box? \n\n: 27, 3 \n\n: \nLet the number of oranges removed from each box be \\(x\\). \nAccording to the problem, the remaining oranges in Box A are 9 times those in Box B. This gives the equation: \n\n(42 - x) = (18 - x) * 9 \n\nExpanding the equation: \n42 - x = 162 - 9x. \n\nRearranging terms: \n9x - x = 162 - 42.\n\nSimplifying: \n8x = 120. \n\nSolving for x: \nx = 120 / 8 \nx = 15. \n\nNow, calculate the remaining oranges: \nBox A: 42 - 15 = 27, \nBox B: 18 - 15 = 3. \n\nVerify the result: \nCheck whether the remaining oranges in Box A are 9 times those in Box B: \n27 = 3 * 9\n27 = 27\n\nThus, the solution satisfies the problem conditions. The final answer is: \nBox A has 27 oranges remaining, and Box B has 3 oranges remaining. \n\n[Scoring analysis]: \nThe student’s final answers are 27 for Box A and 3 for Box B. \nThe reference answers are 27 and 3. \nThe student’s answers match the reference answers. Therefore, the student earns 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```\n\nExample 3: \n\n: \nWhat is the value of sin(105°)? \n\n: \\(\\frac{\\sqrt{2} + \\sqrt{6}}{4}\\) \n\n: \nTo calculate sin(105°), we can use the trigonometric addition formula and properties of angles greater than 90°. 105° can be expressed as 45° + 60°. \nThe formula for sine of a sum is: \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B). \n\nThus: \nsin(105°) = sin(45° + 60°)\n= sin(45°)cos(60°) + cos(45°)sin(60°)\nWe know: \nsin(45°) = cos(45°) = √2/2\nsin(60°) = √3/2\ncos(60°) = 1/2\nSubstituting these values: \nsin(105°) = (√2/2)(1/2) + (√2/2)(√3/2)\n= √2/4 + √6/4\n= (√2 + √6) / 4. \n\nThus, sin(105°) 's exact value is (√2 + √6) / 4. \n\n[Scoring analysis]: \nThe student’s final answer is (√2 + √6) / 4. \nThe reference answer is \\\\frac{\\\\sqrt6+\\\\sqrt2}{4}, expressed in LaTeX format. Both answers are mathematically equivalent as\\\\frac{\\\\sqrt6+\\\\sqrt2}{4}=(√6 + √2)/4=(√2 + √6)/4. \nTherefore, the student’s answer is correct, and they earn 1 point. \n\n[Score]: 1 point \n[JSON]: \n```json\n{\n \"answer_score\": [[1]]\n}\n```", "judge_prompt_template": ":\n{prompt}\n\n:\n{response_reference}\n\n:\n{response}", "extra": { "difficulty": "", "Category": "Spatial Reasoning", "Subtask": "Satellite Image Matching", "tags": [], "metadata": { "source": "" } } } ]