eval/test_problems.json

[
  {
    "id": 1,
    "topic": "algebra",
    "difficulty": "easy",
    "question": "Solve the equation x^2 - 5x + 6 = 0",
    "expected_answer": "x = 2, x = 3",
    "expected_topic": "algebra"
  },
  {
    "id": 2,
    "topic": "algebra",
    "difficulty": "medium",
    "question": "Find the sum of roots of 2x^2 - 7x + 3 = 0",
    "expected_answer": "7/2",
    "expected_topic": "algebra"
  },
  {
    "id": 3,
    "topic": "algebra",
    "difficulty": "medium",
    "question": "If the roots of x^2 + px + q = 0 are in the ratio 2:3, and their sum is 10, find p and q.",
    "expected_answer": "p = -10, q = 24",
    "expected_topic": "algebra"
  },
  {
    "id": 4,
    "topic": "algebra",
    "difficulty": "hard",
    "question": "Find the minimum value of x + 1/x for x > 0",
    "expected_answer": "2",
    "expected_topic": "algebra"
  },
  {
    "id": 5,
    "topic": "algebra",
    "difficulty": "medium",
    "question": "Evaluate: log_2(8) + log_3(27) - log_5(25)",
    "expected_answer": "4",
    "expected_topic": "algebra"
  },
  {
    "id": 6,
    "topic": "algebra",
    "difficulty": "hard",
    "question": "Find the number of terms in the expansion of (x + y)^10",
    "expected_answer": "11",
    "expected_topic": "algebra"
  },
  {
    "id": 7,
    "topic": "algebra",
    "difficulty": "medium",
    "question": "Find the sum of the first 20 terms of the arithmetic progression 3, 7, 11, 15, ...",
    "expected_answer": "820",
    "expected_topic": "algebra"
  },
  {
    "id": 8,
    "topic": "probability",
    "difficulty": "easy",
    "question": "A fair coin is tossed 3 times. What is the probability of getting exactly 2 heads?",
    "expected_answer": "3/8",
    "expected_topic": "probability"
  },
  {
    "id": 9,
    "topic": "probability",
    "difficulty": "medium",
    "question": "A bag contains 5 red and 3 blue balls. Two balls are drawn without replacement. Find the probability that both are red.",
    "expected_answer": "5/14",
    "expected_topic": "probability"
  },
  {
    "id": 10,
    "topic": "probability",
    "difficulty": "medium",
    "question": "In how many ways can 5 people be arranged in a circle?",
    "expected_answer": "24",
    "expected_topic": "probability"
  },
  {
    "id": 11,
    "topic": "probability",
    "difficulty": "hard",
    "question": "A test has a 95% true positive rate and 10% false positive rate. If 1% of the population has the disease, what is the probability that a person who tests positive actually has the disease?",
    "expected_answer": "0.0876 or approximately 8.76%",
    "expected_topic": "probability"
  },
  {
    "id": 12,
    "topic": "probability",
    "difficulty": "medium",
    "question": "Find P(X >= 1) where X follows Binomial(5, 0.3)",
    "expected_answer": "1 - (0.7)^5 = 0.83193",
    "expected_topic": "probability"
  },
  {
    "id": 13,
    "topic": "probability",
    "difficulty": "easy",
    "question": "How many ways can you choose 3 items from 10?",
    "expected_answer": "120",
    "expected_topic": "probability"
  },
  {
    "id": 14,
    "topic": "calculus",
    "difficulty": "easy",
    "question": "Find the derivative of f(x) = x^3 + 2x^2 - 5x + 1",
    "expected_answer": "3x^2 + 4x - 5",
    "expected_topic": "calculus"
  },
  {
    "id": 15,
    "topic": "calculus",
    "difficulty": "medium",
    "question": "Evaluate the limit: lim(x->0) sin(3x)/x",
    "expected_answer": "3",
    "expected_topic": "calculus"
  },
  {
    "id": 16,
    "topic": "calculus",
    "difficulty": "medium",
    "question": "Find the integral of (2x + 3)dx from 0 to 4",
    "expected_answer": "28",
    "expected_topic": "calculus"
  },
  {
    "id": 17,
    "topic": "calculus",
    "difficulty": "hard",
    "question": "Find the maximum value of f(x) = -x^2 + 6x - 5",
    "expected_answer": "4",
    "expected_topic": "calculus"
  },
  {
    "id": 18,
    "topic": "calculus",
    "difficulty": "medium",
    "question": "Find dy/dx if y = e^(2x) * sin(x)",
    "expected_answer": "e^(2x)(2sin(x) + cos(x))",
    "expected_topic": "calculus"
  },
  {
    "id": 19,
    "topic": "calculus",
    "difficulty": "hard",
    "question": "Evaluate lim(x->0) (e^x - 1 - x) / x^2",
    "expected_answer": "1/2",
    "expected_topic": "calculus"
  },
  {
    "id": 20,
    "topic": "calculus",
    "difficulty": "medium",
    "question": "Find the area under the curve y = x^2 from x = 0 to x = 3",
    "expected_answer": "9",
    "expected_topic": "calculus"
  },
  {
    "id": 21,
    "topic": "linear_algebra",
    "difficulty": "easy",
    "question": "Find the determinant of the matrix [[2, 3], [1, 4]]",
    "expected_answer": "5",
    "expected_topic": "linear_algebra"
  },
  {
    "id": 22,
    "topic": "linear_algebra",
    "difficulty": "medium",
    "question": "Find the dot product of vectors a = (1, 2, 3) and b = (4, 5, 6)",
    "expected_answer": "32",
    "expected_topic": "linear_algebra"
  },
  {
    "id": 23,
    "topic": "linear_algebra",
    "difficulty": "medium",
    "question": "Find the cross product of vectors a = (1, 0, 0) and b = (0, 1, 0)",
    "expected_answer": "(0, 0, 1)",
    "expected_topic": "linear_algebra"
  },
  {
    "id": 24,
    "topic": "linear_algebra",
    "difficulty": "hard",
    "question": "For what value of k does the system x + y = 2, 2x + 2y = k have infinitely many solutions?",
    "expected_answer": "k = 4",
    "expected_topic": "linear_algebra"
  },
  {
    "id": 25,
    "topic": "linear_algebra",
    "difficulty": "medium",
    "question": "Find the inverse of the matrix [[1, 2], [3, 4]]",
    "expected_answer": "[[-2, 1], [3/2, -1/2]]",
    "expected_topic": "linear_algebra"
  }
]