data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of tetrahedron PQRS with edge lengths PQ = 4, PR = 5, PS = 6, QR = 3, QS = √37, and RS = 7."
}
] | math | {
"style": "rule",
"ground_truth": "10.25"
} | {
"index": 5900,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of the solid bounded by the surfaces \\(x + z = 6\\), \\(y = \\sqrt{x}\\), \\(y = 2\\sqrt{x}\\), and \\(z = 0\\) using a triple integral."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{48}{5} \\sqrt{6}"
} | {
"index": 5901,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of the solid formed by rotating around the $O Y$ axis the curvilinear trapezoid which is bounded by the hyperbola $x y=2$ and the lines $y_{1}=1, y_{2}=4$, and $y_{3}=0$."
}
] | math | {
"style": "rule",
"ground_truth": "3\\pi"
} | {
"index": 5902,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of the solid of revolution obtained by rotating a right triangle with sides 3, 4, and 5 around one of its legs that form the right angle."
}
] | math | {
"style": "rule",
"ground_truth": "12 \\pi"
} | {
"index": 5903,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of the tetrahedron with vertices at points $A_{1}, A_{2}, A_{3}, A_{4}$ and its height dropped from vertex $A_{4}$ onto the face $A_{1} A_{2} A_{3}$.\n\n$A_{1}(1, 1, 2)$\n\n$A_{2}(-1, 1, 3)$\n\n$A_{3}(2, -2, 4)$\n\n$A_{4}(-1, 0, -2)$"
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{\\frac{35}{2}}"
} | {
"index": 5904,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of the tetrahedron with vertices at points $A_{1}, A_{2}, A_{3}, A_{4}$ and its height, dropped from vertex $A_{4}$ onto the face $A_{1} A_{2} A_{3}$.\n\n$A_{1}(2, -1, -2)$\n\n$A_{2}(1, 2, 1)$\n\n$A_{3}(5, 0, -6)$\n\n$A_{4}(-10, 9, -7)$"
}
] | math | {
"style": "rule",
"ground_truth": "4\\sqrt{14}"
} | {
"index": 5905,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of the tetrahedron with vertices at points \\( A_{1}, A_{2}, A_{3}, A_{4} \\) and its height dropped from the vertex \\( A_{4} \\) onto the face \\( A_{1} A_{2} A_{3} \\).\n\nGiven points:\n\\( A_{1}(1, -1, 1) \\)\n\n\\( A_{2}(-2, 0, 3) \\)\n\n\\( A_{3}(2, ... | math | {
"style": "rule",
"ground_truth": "\\frac{33}{\\sqrt{101}}"
} | {
"index": 5906,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of the tetrahedron with vertices at points \\( A_{1}, A_{2}, A_{3}, A_{4} \\) and its height dropped from the vertex \\( A_{4} \\) to the face \\( A_{1} A_{2} A_{3} \\).\n\n\\( A_{1}(-2, -1, -1) \\)\n\n\\( A_{2}(0, 3, 2) \\)\n\n\\( A_{3}(3, 1, -4) \\)\n\n\\... | math | {
"style": "rule",
"ground_truth": "\\frac{140}{\\sqrt{1021}}"
} | {
"index": 5907,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of the tetrahedron with vertices at points \\( A_{1}, A_{2}, A_{3}, A_{4} \\) and its height dropped from the vertex \\( A_{4} \\) to the face \\( A_{1} A_{2} A_{3} \\).\n\n\\( A_{1}(1, 0, 2) \\)\n\n\\( A_{2}(1, 2, -1) \\)\n\n\\( A_{3}(2, -2, 1) \\)\n\n\\( ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{\\frac{7}{11}}"
} | {
"index": 5908,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of the tetrahedron with vertices at points \\( A_{1}, A_{2}, A_{3}, A_{4} \\) and its height, dropped from vertex \\( A_{4} \\) onto the face \\( A_{1} A_{2} A_{3} \\).\n\n\\( A_{1}(7, 2, 4) \\) \n\\( A_{2}(7, -1, -2) \\) \n\\( A_{3}(3, 3, 1) \\) \n\\( A... | math | {
"style": "rule",
"ground_truth": "21.5"
} | {
"index": 5909,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of the tetrahedron with vertices at points \\( A_{1}, A_{2}, A_{3}, A_{4} \\). Additionally, find its height dropped from vertex \\( A_{4} \\) onto the face \\( A_{1} A_{2} A_{3} \\).\n\nVertices:\n- \\( A_{1}(-1, 2, 4) \\)\n- \\( A_{2}(-1, -2, -4) \\)\n- \... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 5910,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volumes of solids formed by rotating the region bounded by the function graphs about the \\( O y \\) (y-axis).\n\n$$\ny = x^{2} + 1, \\quad y = x, \\quad x = 0, \\quad x = 1\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5\\pi}{6}"
} | {
"index": 5911,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volumes of solids formed by the rotation of regions bounded by the graphs of the functions around the y-axis.\n\n$$\ny=\\arcsin \\frac{x}{5}, y=\\arcsin x, y=\\frac{\\pi}{2}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "6 \\pi^2"
} | {
"index": 5912,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volumes of the bodies bounded by the surfaces.\n\n$$\nz = 2x^2 + 18y^2, \\quad z = 6\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "6\\pi"
} | {
"index": 5913,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volumes of the solids formed by rotating the regions bounded by the graphs of the functions around the y-axis.\n\n$$\ny = \\arcsin x, \\quad y = \\arccos x, \\quad y = 0\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{2}"
} | {
"index": 5914,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the whole number remainder when 987,670 is divided by 128."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 5915,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the winning rate per game; \nList all possible outcomes; \nCalculate the probability of satisfying the condition \"$a+b+c+d \\leqslant 2$\"."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{11}{16}"
} | {
"index": 5916,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate to 3 decimal places the following expressions:\n\n1. \n\n$$\n\\frac{2 \\sqrt{3}}{\\sqrt{3}-\\sqrt{2}}\n$$\n\n2. \n\n$$\n\\frac{(3+\\sqrt{3})(1+\\sqrt{5})}{(5+\\sqrt{5})(1+\\sqrt{3})}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "0.775"
} | {
"index": 5917,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate using a simple method:<br/>$(1)100.2\\times 99.8$;<br/>$(2)103^{2}$."
}
] | math | {
"style": "rule",
"ground_truth": "10609"
} | {
"index": 5918,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate using factorization:<br/>$(1)\\frac{2021×2023}{2022^2-1}$;<br/>$(2)2\\times 101^{2}+2\\times 101\\times 98+2\\times 49^{2}$."
}
] | math | {
"style": "rule",
"ground_truth": "45000"
} | {
"index": 5919,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate using your preferred method!\n\n100 - 54 - 46 \n234 - (134 + 45) \n125 × 7 × 8 \n15 × (61 - 45) \n318 ÷ 6 + 165."
}
] | math | {
"style": "rule",
"ground_truth": "218"
} | {
"index": 5920,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate using your preferred method: \n(1) $42.67-(12.95-7.33)$ \n(2) $\\left[8.4-8.4\\times(3.12-3.7)\\right]\\div0.42$ \n(3) $5.13\\times0.23+8.7\\times0.513-5.13$ \n(4) $6.66\\times222+3.33\\times556$"
}
] | math | {
"style": "rule",
"ground_truth": "3330"
} | {
"index": 5921,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:\n\n1. $(1)(\\sqrt{2}+2)^{2}$\n2. $(2)(\\sqrt{3}-\\sqrt{8})-\\frac{1}{2}(\\sqrt{18}+\\sqrt{12})$"
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{7\\sqrt{2}}{2}"
} | {
"index": 5922,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:\n\n1. $(2\\frac{3}{5})^{0} + 2^{-2}\\cdot(2\\frac{1}{4})^{-\\frac{1}{2}} + (\\frac{25}{36})^{0.5} + \\sqrt{(-2)^{2}}$;\n2. $\\frac{1}{2}\\log\\frac{32}{49} - \\frac{4}{3}\\log\\sqrt{8} + \\log\\sqrt{245}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 5923,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:\n$$\n202.2 \\times 89.8 - 20.22 \\times 186 + 2.022 \\times 3570 - 0.2022 \\times 16900\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "18198"
} | {
"index": 5924,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:\n$$\n\\left(10^{4}-9^{4}+8^{4}-7^{4}+\\cdots+2^{4}-1^{4}\\right)+\\left(10^{2}+9^{2}+5 \\times 8^{2}+5 \\times 7^{2}+9 \\times 6^{2}+9 \\times 5^{2}+13 \\times 4^{2}+13 \\times 3^{2}\\right) =\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "7615"
} | {
"index": 5925,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: \n\n$$\\frac{\\left(1+\\frac{1}{2}\\right)^{2} \\times\\left(1+\\frac{1}{3}\\right)^{2} \\times\\left(1+\\frac{1}{4}\\right)^{2} \\times\\left(1+\\frac{1}{5}\\right)^{2} \\times \\cdots \\times\\left(1+\\frac{1}{10}\\right)^{2}}{\\left(1-\\frac{1}{2^{2}}\\right) \\ti... | math | {
"style": "rule",
"ground_truth": "55"
} | {
"index": 5926,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: \n(1) $2\\log_{2}{10}+\\log_{2}{0.04}$ \n(2) $(\\log_{4}{3}+\\log_{8}{3})\\cdot(\\log_{3}{5}+\\log_{9}{5})\\cdot(\\log_{5}{2}+\\log_{25}{2})$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{15}{8}"
} | {
"index": 5927,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $$\\frac {1}{2}\\log_{2}3 \\cdot \\frac {1}{2}\\log_{9}8 = \\_\\_\\_\\_\\_\\_ ．$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {3}{8}"
} | {
"index": 5928,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $$\\frac {\\cos 2^\\circ}{\\sin 47^\\circ} + \\frac {\\cos 88^\\circ}{\\sin 133^\\circ}$$."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"index": 5929,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $(-2)^{2}+\\sqrt{(-3)^{2}}-\\sqrt[3]{27}+|\\sqrt{3}-2|$."
}
] | math | {
"style": "rule",
"ground_truth": "6 - \\sqrt{3}"
} | {
"index": 5930,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $(10 \\times 19 \\times 20 \\times 53 \\times 100 + 601) \\div 13 = \\ ?$"
}
] | math | {
"style": "rule",
"ground_truth": "1549277"
} | {
"index": 5931,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $(128)^{\\frac{7}{3}}$"
}
] | math | {
"style": "rule",
"ground_truth": "65536 \\cdot \\sqrt[3]{2}"
} | {
"index": 5932,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $(243)^{\\frac35}$"
}
] | math | {
"style": "rule",
"ground_truth": "27"
} | {
"index": 5933,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $(\\sqrt{3}+\\sqrt{2})(\\sqrt{3}-\\sqrt{2})^{2}=\\_\\_\\_\\_\\_\\_$."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}-\\sqrt{2}"
} | {
"index": 5934,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $-\\sqrt{4}+|-\\sqrt{2}-1|+(\\pi -2013)^{0}-(\\frac{1}{5})^{0}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2} - 1"
} | {
"index": 5935,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $-{1^{2022}}+{({\\frac{1}{3}})^{-2}}+|{\\sqrt{3}-2}|$."
}
] | math | {
"style": "rule",
"ground_truth": "10-\\sqrt{3}"
} | {
"index": 5936,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $-{1^{2023}}+|{\\sqrt{3}-2}|-3\\tan60°$."
}
] | math | {
"style": "rule",
"ground_truth": "1 - 4\\sqrt{3}"
} | {
"index": 5937,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $1.23 \\times 67 + 8.2 \\times 12.3 - 90 \\times 0.123$"
}
] | math | {
"style": "rule",
"ground_truth": "172.2"
} | {
"index": 5938,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $5 \\times 13 \\times 31 \\times 73 \\times 137$"
}
] | math | {
"style": "rule",
"ground_truth": "20152015"
} | {
"index": 5939,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $9-8+7\\times6+5-4\\times3+2-1$"
}
] | math | {
"style": "rule",
"ground_truth": "37"
} | {
"index": 5940,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $99\\times 101=\\_\\_\\_\\_\\_\\_$."
}
] | math | {
"style": "rule",
"ground_truth": "9999"
} | {
"index": 5941,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $\\frac53\\times\\frac{6}{10}\\times\\frac{15}{9}\\times\\frac{12}{20}\\times\\frac{25}{15}\\times\\frac{18}{30}\\times\\frac{35}{21}\\times\\frac{24}{40}$"
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 5942,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $\\frac{145}{273} \\times 2 \\frac{173}{245} \\div 21 \\frac{13}{15}=$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7395}{112504}"
} | {
"index": 5943,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $\\frac{7}{4} \\times \\frac{8}{14} \\times \\frac{14}{8} \\times \\frac{16}{40} \\times \\frac{35}{20} \\times \\frac{18}{45} \\times \\frac{49}{28} \\times \\frac{32}{64}$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{49}{200}"
} | {
"index": 5944,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $\\frac{{\\cos190°(1+\\sqrt{3}\\tan10°)}}{{\\sin290°\\sqrt{1-\\cos40°}}}=\\_\\_\\_\\_\\_\\_$."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}"
} | {
"index": 5945,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $\\left(-2\\right)^{0}-3\\tan 30^{\\circ}-|\\sqrt{3}-2|$."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 5946,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $\\sqrt[3]{27}+|-\\sqrt{2}|+2\\sqrt{2}-(-\\sqrt{4})$."
}
] | math | {
"style": "rule",
"ground_truth": "5 + 3\\sqrt{2}"
} | {
"index": 5947,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $\\sqrt{25}-\\left(-1\\right)^{2}+|2-\\sqrt{5}|$."
}
] | math | {
"style": "rule",
"ground_truth": "2+\\sqrt{5}"
} | {
"index": 5948,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $\\sqrt{27} - 2\\cos 30^{\\circ} + \\left(\\frac{1}{2}\\right)^{-2} - |1 - \\sqrt{3}|$"
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3} + 5"
} | {
"index": 5949,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: ${2}^{0}-|-3|+(-\\frac{1}{2})=\\_\\_\\_\\_\\_\\_$."
}
] | math | {
"style": "rule",
"ground_truth": "-2\\frac{1}{2}"
} | {
"index": 5950,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $|1-\\sqrt{2}|+(\\frac{1}{2})^{-2}-\\left(\\pi -2023\\right)^{0}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2} + 2"
} | {
"index": 5951,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $|\\sqrt{3}-2|+(\\pi -\\sqrt{10})^{0}-\\sqrt{12}$."
}
] | math | {
"style": "rule",
"ground_truth": "3-3\\sqrt{3}"
} | {
"index": 5952,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: $|\\sqrt{8}-2|+(\\pi -2023)^{0}+(-\\frac{1}{2})^{-2}-2\\cos 60^{\\circ}$."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}+2"
} | {
"index": 5953,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: (1) $( \\frac {3}{2})^{-2}-(-4.5)^{0}-( \\frac {8}{27})^{ \\frac {2}{3}}$; \n(2) $\\frac {2}{3}\\text{lg}8+\\text{lg}25-3^{2\\log_{3}5}+16^{ \\frac {3}{4}}$."
}
] | math | {
"style": "rule",
"ground_truth": "-15"
} | {
"index": 5954,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: (1) $(\\sqrt[3]{1.5} \\times \\sqrt[6]{12})^{2} + 8{1}^{0.75} - (-\\frac{1}{4})^{-2} - 5 \\times 0.12{5}^{0}$; (2) $\\lg 25 + \\lg 2 \\cdot \\lg 50 + (\\lg 2)^{2} - e^{3\\ln 2}$."
}
] | math | {
"style": "rule",
"ground_truth": "-6"
} | {
"index": 5955,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: \\( 1 \\times 2 - 3 \\times 4 + 5 \\times 6 - 7 \\times 8 + \\cdots + 2015 \\times 2016 \\)"
}
] | math | {
"style": "rule",
"ground_truth": "-2033136"
} | {
"index": 5956,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: \\( 4\\left(\\sin ^{3} \\frac{49 \\pi}{48} \\cos \\frac{49 \\pi}{16} + \\cos ^{3} \\frac{49 \\pi}{48} \\sin \\frac{49 \\pi}{16}\\right) \\cos \\frac{49 \\pi}{12} \\)."
}
] | math | {
"style": "rule",
"ground_truth": "0.75"
} | {
"index": 5957,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: \\( 8.0 \\dot{\\dot{1}} + 7.1 \\dot{2} + 6.2 \\dot{3} + 5.3 \\dot{4} + 4.4 \\dot{5} + 3.5 \\dot{6} + 2.6 \\dot{7} + 1.7 \\dot{8} = \\)"
}
] | math | {
"style": "rule",
"ground_truth": "39.2"
} | {
"index": 5958,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: \\((56 \\times 0.57 \\times 0.85) \\div(2.8 \\times 19 \\times 1.7) =\\)"
}
] | math | {
"style": "rule",
"ground_truth": "0.3"
} | {
"index": 5959,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: \\(\\frac{1}{2 \\cos \\frac{2 \\pi}{7}}+\\frac{1}{2 \\cos \\frac{4 \\pi}{7}}+\\frac{1}{2 \\cos \\frac{6 \\pi}{7}}\\)."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"index": 5960,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: \\(\\frac{2 \\times 4.6 \\times 9 + 4 \\times 9.2 \\times 18}{1 \\times 2.3 \\times 4.5 + 3 \\times 6.9 \\times 13.5} =\\)"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{18}{7}"
} | {
"index": 5961,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: \\(\\left(2 \\frac{2}{3} \\times\\left(\\frac{1}{3}-\\frac{1}{11}\\right) \\div\\left(\\frac{1}{11}+\\frac{1}{5}\\right)\\right) \\div \\frac{8}{27} = 7 \\underline{1}\\)."
}
] | math | {
"style": "rule",
"ground_truth": "7 \\frac{1}{2}"
} | {
"index": 5962,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate: \\(\\left[\\left(11 \\frac{1}{9}-3 \\frac{2}{5} \\times 1 \\frac{2}{17}\\right)-8 \\frac{2}{5} \\div 3.6\\right] \\div 2 \\frac{6}{25}\\)."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{20}{9}"
} | {
"index": 5963,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)(1\\frac{3}{4}-\\frac{3}{8}+\\frac{5}{6})÷(-\\frac{1}{24})$;<br/>$(2)-2^2+(-4)÷2×\\frac{1}{2}+|-3|$."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"index": 5964,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)(\\frac{5}{7})×(-4\\frac{2}{3})÷1\\frac{2}{3}$;<br/>$(2)(-2\\frac{1}{7})÷(-1.2)×(-1\\frac{2}{5})$."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{5}{2}"
} | {
"index": 5965,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)(\\sqrt{3})^2+|1-\\sqrt{3}|+\\sqrt[3]{-27}$;<br/>$(2)(\\sqrt{12}-\\sqrt{\\frac{1}{3}})×\\sqrt{6}$."
}
] | math | {
"style": "rule",
"ground_truth": "5\\sqrt{2}"
} | {
"index": 5966,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)(\\sqrt{50}-\\sqrt{8})÷\\sqrt{2}$;<br/>$(2)\\sqrt{\\frac{3}{4}}×\\sqrt{2\\frac{2}{3}}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"index": 5967,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)(\\sqrt{\\frac{1}{3}})^{2}+\\sqrt{0．{3}^{2}}-\\sqrt{\\frac{1}{9}}$;<br/>$(2)(\\sqrt{6}-\\sqrt{\\frac{1}{2}})-(\\sqrt{24}+2\\sqrt{\\frac{2}{3}})$;<br/>$(3)(\\frac{\\sqrt{32}}{3}-4\\sqrt{\\frac{1}{2}}+3\\sqrt{27})÷2\\sqrt{2}$;<br/>$(4)(\\sqrt{3}+\\sqrt{2}-1)(\\... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}"
} | {
"index": 5968,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-1^{2023}+8×(-\\frac{1}{2})^{3}+|-3|$;<br/>$(2)(-25)×\\frac{3}{2}-(-25)×\\frac{5}{8}+(-25)÷8($simplified calculation)."
}
] | math | {
"style": "rule",
"ground_truth": "-25"
} | {
"index": 5969,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-1^{2023}-\\sqrt{2\\frac{1}{4}}+\\sqrt[3]{-1}+\\frac{1}{2}$;<br/>$(2)2\\sqrt{3}+|1-\\sqrt{3}|-\\left(-1\\right)^{2022}+2$."
}
] | math | {
"style": "rule",
"ground_truth": "3\\sqrt{3}"
} | {
"index": 5970,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-3+5-\\left(-2\\right)$;<br/>$(2)-6÷\\frac{1}{4}×(-4)$;<br/>$(3)(\\frac{5}{6}-\\frac{3}{4}+\\frac{1}{3})×(-24)$;<br/>$(4)-1^{2023}-[4-(-3)^2]÷(\\frac{2}{7}-1)$."
}
] | math | {
"style": "rule",
"ground_truth": "-8"
} | {
"index": 5971,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-3+8-15-6$;<br/>$(2)-35\\div \\left(-7\\right)\\times (-\\frac{1}{7})$;<br/>$(3)-2^{2}-|2-5|\\div \\left(-3\\right)$;<br/>$(4)(\\frac{1}{2}+\\frac{5}{6}-\\frac{7}{12})×(-24)$;<br/>$(5)(-99\\frac{6}{11})×22$."
}
] | math | {
"style": "rule",
"ground_truth": "-2190"
} | {
"index": 5972,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-3+\\left(-9\\right)+10-\\left(-18\\right)$;<br/>$(2)12÷2×(-\\frac{1}{2})-75÷(-5)$;<br/>$(3)-4^3-2×(-5)^2+6÷(-\\frac{1}{3})^2$;<br/>$(4)(-1\\frac{1}{4}-1\\frac{5}{6}+2\\frac{8}{9})÷(-\\frac{1}{6})^2$."
}
] | math | {
"style": "rule",
"ground_truth": "-7"
} | {
"index": 5973,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-4\\times 9$;<br/>$(2)10-14-\\left(-5\\right)$;<br/>$(3)-3×(-\\frac{1}{3})^3$;<br/>$(4)-56+(-8)×(\\frac{1}{8})$."
}
] | math | {
"style": "rule",
"ground_truth": "-57"
} | {
"index": 5974,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-4^2÷(-32)×(\\frac{2}{3})^2$;<br/>$(2)(-1)^{10}÷2+(-\\frac{1}{2})^3×16$;<br/>$(3)\\frac{12}{7}×(\\frac{1}{2}-\\frac{2}{3})÷\\frac{5}{14}×1\\frac{1}{4}$;<br/>$(4)1\\frac{1}{3}×[1-(-4)^2]-(-2)^3÷\\frac{4}{5}$."
}
] | math | {
"style": "rule",
"ground_truth": "-10"
} | {
"index": 5975,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-6-3+\\left(-7\\right)-\\left(-2\\right)$;<br/>$(2)\\left(-1\\right)^{2023}+5\\times \\left(-2\\right)-12\\div \\left(-4\\right)$."
}
] | math | {
"style": "rule",
"ground_truth": "-8"
} | {
"index": 5976,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-7+13-6+20$;<br/>$(2)-2^{3}+\\left(2-3\\right)-2\\times \\left(-1\\right)^{2023}$."
}
] | math | {
"style": "rule",
"ground_truth": "-7"
} | {
"index": 5977,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-9+5-\\left(-12\\right)+\\left(-3\\right)$;<br/>Calculate:<br/>$(2)-(+1.5)-(-4\\frac{1}{4})+3.75-(-8\\frac{1}{2})$;<br/>$(3)$Read the following solution process and answer the question:<br/>Calculate:$\\left(-15\\right)\\div (-\\frac{1}{2}×\\frac{25}{3}$）$÷\\... | math | {
"style": "rule",
"ground_truth": "\\frac{108}{5}"
} | {
"index": 5978,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)2(\\sqrt{3}-\\sqrt{5})+3(\\sqrt{3}+\\sqrt{5})$;<br/>$(2)-{1}^{2}-|1-\\sqrt{3}|+\\sqrt[3]{8}-(-3)×\\sqrt{9}$."
}
] | math | {
"style": "rule",
"ground_truth": "11 - \\sqrt{3}"
} | {
"index": 5979,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)3-\\left(-2\\right)$;<br/>$(2)\\left(-4\\right)\\times \\left(-3\\right)$;<br/>$(3)0\\div \\left(-3\\right)$;<br/>$(4)|-12|+\\left(-4\\right)$;<br/>$(5)\\left(+3\\right)-14-\\left(-5\\right)+\\left(-16\\right)$;<br/>$(6)(-5)÷(-\\frac{1}{5})×(-5)$;<br/>$(7)-24... | math | {
"style": "rule",
"ground_truth": "-399\\frac{3}{4}"
} | {
"index": 5980,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)4.7+\\left(-2.5\\right)-\\left(-5.3\\right)-7.5$;<br/>$(2)18+48\\div \\left(-2\\right)^{2}-\\left(-4\\right)^{2}\\times 5$;<br/>$(3)-1^{4}+\\left(-2\\right)^{2}\\div 4\\times [5-\\left(-3\\right)^{2}]$;<br/>$(4)(-19\\frac{15}{16})×8$ (Solve using a simple met... | math | {
"style": "rule",
"ground_truth": "-159\\frac{1}{2}"
} | {
"index": 5981,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)64.83-5\\frac{18}{19}+35.17-44\\frac{1}{19}$;<br/>$(2)(+2.5)+(-3\\frac{1}{3})-(-1)$;<br/>$(3)\\frac{(0.125+\\frac{3}{5})×\\frac{33}{87}}{12.1×\\frac{1}{11}$;<br/>$(4)41\\frac{1}{3}×\\frac{3}{4}+52\\frac{1}{2}÷1\\frac{1}{4}+63\\frac{3}{5}×\\frac{5}{6}$;<br/>$(... | math | {
"style": "rule",
"ground_truth": "4044\\frac{2022}{2023}"
} | {
"index": 5982,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)\\frac{2}{5}-\\frac{1}{5}\\times \\left(-5\\right)+\\frac{3}{5}$;<br/>$(2)-2^{2}-\\left(-3\\right)^{3}\\div 3\\times \\frac{1}{3}$."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 5983,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)\\frac{\\sqrt{20}+\\sqrt{5}}{\\sqrt{5}}-2$;<br/>$(2)\\sqrt[3]{-8}+5\\sqrt{\\frac{1}{10}}-\\sqrt{10}+\\sqrt{4}$;<br/>$(3)(\\sqrt{3}-\\sqrt{2})^2•(5+2\\sqrt{6})$;<br/>$(4)(π-3.14)^0+\\frac{1}{2+\\sqrt{3}}+(-\\frac{1}{3})^{-1}+|1-\\sqrt{3}|$."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 5984,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)\\frac{\\sqrt{8}-\\sqrt{24}}{\\sqrt{2}}+|1-\\sqrt{3}|$;<br/>$(2)(\\frac{1}{2})^{-1}-2cos30°+|2-\\sqrt{3}|-(2\\sqrt{2}+1)^{0}$."
}
] | math | {
"style": "rule",
"ground_truth": "3 - 2\\sqrt{3}"
} | {
"index": 5985,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(1)\\left(-12\\right)-5+\\left(-14\\right)-\\left(-39\\right)$;<br/>$(2)-2^{2}\\times 5-\\left(-12\\right)\\div 4-4$."
}
] | math | {
"style": "rule",
"ground_truth": "-21"
} | {
"index": 5986,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate:<br/>$(Ⅰ)(1\\frac{9}{16})^{0.5}+0.01^{-1}+(2\\frac{10}{27})^{-\\frac{2}{3}}-2π^0+\\frac{3}{16}$;<br/>$(Ⅱ)\\log _{2}(4\\times 8^{2})+\\log _{3}18-\\log _{3}2+\\log _{4}3\\times \\log _{3}16$."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 5987,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Call a $3$-digit number geometric if it has $3$ distinct digits which, when read from left to right, form a geometric sequence. Find the difference between the largest and smallest geometric numbers."
}
] | math | {
"style": "rule",
"ground_truth": "840"
} | {
"index": 5988,
"solution": "The smallest geometric number is $124$ because $123$ and any number containing a zero does not work. $964$ is the largest geometric number because the middle digit cannot be 8 or 7. Subtracting the numbers gives $\\boxed{840}.$\n ~IceMatrix\n ~Shreyas S"
} |
DeepScaleR | [
{
"role": "user",
"content": "Call a $7$-digit telephone number $d_1d_2d_3-d_4d_5d_6d_7$ memorable if the prefix sequence $d_1d_2d_3$ is exactly the same as either of the sequences $d_4d_5d_6$ or $d_5d_6d_7$ (possibly both). Assuming that each $d_i$ can be any of the ten decimal digits $0, 1, 2, \\ldots, 9$... | math | {
"style": "rule",
"ground_truth": "19990"
} | {
"index": 5989,
"solution": "To solve this problem, we need to count the number of memorable telephone numbers based on the given conditions. A memorable telephone number is defined as $d_1d_2d_3-d_4d_5d_6d_7$ where the sequence $d_1d_2d_3$ matches either $d_4d_5d_6$ or $d_5d_6d_7$.\n\n1. **Counting the total poss... |
DeepScaleR | [
{
"role": "user",
"content": "Call a fraction $\\frac{a}{b}$, not necessarily in the simplest form, special if $a$ and $b$ are positive integers whose sum is $15$. How many distinct integers can be written as the sum of two, not necessarily different, special fractions?"
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 5990,
"solution": "1. **Identify Special Fractions**: A fraction $\\frac{a}{b}$ is special if $a+b=15$ where $a$ and $b$ are positive integers. The possible pairs $(a, b)$ are:\n - $(1, 14), (2, 13), (3, 12), (4, 11), (5, 10), (6, 9), (7, 8), (8, 7), (9, 6), (10, 5), (11, 4), (12, 3), (13, 2), (14, 1)$... |
DeepScaleR | [
{
"role": "user",
"content": "Call a lattice point visible if the line segment connecting the point and the origin does not pass through another lattice point. Given a positive integer \\(k\\), denote by \\(S_{k}\\) the set of all visible lattice points \\((x, y)\\) such that \\(x^{2}+y^{2}=k^{2}\\). Let \\... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 5991,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Call a number feared if it contains the digits 13 as a contiguous substring and fearless otherwise. (For example, 132 is feared, while 123 is fearless.) Compute the smallest positive integer $n$ such that there exists a positive integer $a<100$ such that $n$ and $n+10 a$ are fe... | math | {
"style": "rule",
"ground_truth": "1287"
} | {
"index": 5992,
"solution": "First of all, note that we cannot have $n, n+a, \\ldots, n+10 a$ be less than 1000, since we cannot have fearless numbers have 13 as their last two digits since $a<100$, and $129,130,131, \\ldots, 139$ doesn't work as 139 is feared. Thus, we must utilize numbers of the form $13 x y$, w... |
DeepScaleR | [
{
"role": "user",
"content": "Call a number prime-looking if it is composite but not divisible by $2, 3,$ or $5.$ The three smallest prime-looking numbers are $49, 77$, and $91$. There are $168$ prime numbers less than $1000$. How many prime-looking numbers are there less than $1000$?"
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 5993,
"solution": "1. **Identify the total number of integers less than 1000**: \n There are 999 integers from 1 to 999.\n\n2. **Calculate the number of prime numbers less than 1000**:\n It is given that there are 168 prime numbers less than 1000.\n\n3. **Exclude the primes 2, 3, and 5 from the count... |
DeepScaleR | [
{
"role": "user",
"content": "Call a permutation $a_1, a_2, \\ldots, a_n$ of the integers $1, 2, \\ldots, n$ quasi-increasing if $a_k \\leq a_{k+1} + 2$ for each $1 \\leq k \\leq n-1$. For example, 53421 and 14253 are quasi-increasing permutations of the integers $1, 2, 3, 4, 5$, but 45123 is not. Find the ... | math | {
"style": "rule",
"ground_truth": "486"
} | {
"index": 5994,
"solution": "The simple recurrence can be found.\n When inserting an integer $n$ into a string with $n - 1$ integers, we notice that the integer $n$ has 3 spots where it can go: before $n - 1$, before $n - 2$, and at the very end.\n EXAMPLE: Putting 4 into the string 123: 4 can go before the 2: 142... |
DeepScaleR | [
{
"role": "user",
"content": "Call a polygon normal if it can be inscribed in a unit circle. How many non-congruent normal polygons are there such that the square of each side length is a positive integer?"
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 5995,
"solution": "The side lengths of the polygon can only be from the set $\\{1, \\sqrt{2}, \\sqrt{3}, 2\\}$, which take up $60^{\\circ}, 90^{\\circ}, 120^{\\circ}, 180^{\\circ}$ of the circle respectively. By working modulo 60 degrees we see that $\\sqrt{2}$ must be used an even number of times. We no... |
DeepScaleR | [
{
"role": "user",
"content": "Call a positive integer $N \\geq 2$ \"special\" if for every $k$ such that $2 \\leq k \\leq N, N$ can be expressed as a sum of $k$ positive integers that are relatively prime to $N$ (although not necessarily relatively prime to each other). How many special integers are there l... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"index": 5996,
"solution": "We claim that all odd numbers are special, and the only special even number is 2. For any even $N>2$, the numbers relatively prime to $N$ must be odd. When we consider $k=3$, we see that $N$ can't be expressed as a sum of 3 odd numbers. Now suppose that $N$ is odd, and we look at the b... |
DeepScaleR | [
{
"role": "user",
"content": "Call a positive integer $N$ a 7-10 double if the digits of the base-$7$ representation of $N$ form a base-$10$ number that is twice $N$. For example, $51$ is a 7-10 double because its base-$7$ representation is $102$. What is the largest 7-10 double?"
}
] | math | {
"style": "rule",
"ground_truth": "315"
} | {
"index": 5997,
"solution": "Since this is an AIME problem, the maximum number of digits the 7-10 double can have is 3. Let the number be \\[abc\\] in base 7. Then the number in expanded form is \\[49a+7b+c\\] in base 7 and \\[100a+10b+c\\] in base 10. Since the number in base 7 is half the number in base 10, we g... |
DeepScaleR | [
{
"role": "user",
"content": "Call a positive integer $n$ $k$-pretty if $n$ has exactly $k$ positive divisors and $n$ is divisible by $k$. For example, $18$ is $6$-pretty. Let $S$ be the sum of positive integers less than $2019$ that are $20$-pretty. Find $\\tfrac{S}{20}$."
}
] | math | {
"style": "rule",
"ground_truth": "472"
} | {
"index": 5998,
"solution": "For $n$ to have exactly $20$ positive divisors, $n$ can only take on certain prime factorization forms: namely, $p^{19}, p^9q, p^4q^3, p^4qr$. No number that is a multiple of $20$ can be expressed in the first form, and the only integer divisible by $20$ that has the second form is $2^... |
DeepScaleR | [
{
"role": "user",
"content": "Call a positive integer $n$ extra-distinct if the remainders when $n$ is divided by $2, 3, 4, 5,$ and $6$ are distinct. Find the number of extra-distinct positive integers less than $1000$."
}
] | math | {
"style": "rule",
"ground_truth": "049"
} | {
"index": 5999,
"solution": "Because the LCM of all of the numbers we are dividing by is $60$, we know that all of the remainders are $0$ again at $60$, meaning that we have a cycle that repeats itself every $60$ numbers.\n After listing all of the remainders up to $60$, we find that $35$, $58$, and $59$ are extra... |
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