[
  {
    "ces_question_format": "1.0",
    "site": "math",
    "question_type": "text",
    "question_title": "Derivative of a polynomial",
    "question_content": "Let $f(x) = a x^2 + b x$. Find $f'(x)$ and $f'(1)$.\n\n$f'(x) = $ \\ans{A}, $f'(1) = $ \\ans{B}",
    "question_variable": "a=1,...,5\nb=-3,-2,-1,1,2,3",
    "question_answer": "A=2*a*x+b\nB=2*a+b",
    "evaluation_method": 0,
    "score": 2,
    "question_hint": "$(x^n)' = n x^{n-1}$",
    "q_solution_explanation": "$f'(x) = 2ax + b$, so $f'(1) = 2a + b$."
  },
  {
    "ces_question_format": "1.0",
    "site": "math",
    "question_type": "select",
    "question_title": "Limit",
    "question_content": "Find $\\displaystyle \\lim_{x \\to 0} \\frac{\\sin x}{x}$.",
    "answer_candidate": [
      "0",
      "1",
      "$\\infty$",
      "The limit does not exist"
    ],
    "question_answer": "1",
    "score": 1
  }
]