{
  "homeworkId": "hw-001",
  "title": "数学函数与导数练习",
  "totalScore": 100,
  "avgScore": 78,
  "maxScore": 98,
  "minScore": 45,
  "submitCount": 42,
  "questions": [
    {
      "questionId": "q-001",
      "questionText": "求函数 f(x) = x² + 2x 在 x=1 处的导数值",
      "questionType": "short-answer",
      "correctRate": 0.85,
      "referenceAnswer": "f'(x) = 2x + 2，f'(1) = 4",
      "knowledgePoints": ["导数定义", "求导法则"]
    },
    {
      "questionId": "q-002",
      "questionText": "下列哪个函数是奇函数？",
      "questionType": "single-choice",
      "correctRate": 0.92,
      "referenceAnswer": "f(x) = x³",
      "knowledgePoints": ["奇偶函数", "函数性质"]
    },
    {
      "questionId": "q-003",
      "questionText": "计算定积分 ∫₀¹ (x² + 1) dx 的值",
      "questionType": "short-answer",
      "correctRate": 0.71,
      "referenceAnswer": "∫₀¹ (x² + 1) dx = [x³/3 + x]₀¹ = 1/3 + 1 = 4/3",
      "knowledgePoints": ["定积分", "牛顿-莱布尼茨公式"]
    },
    {
      "questionId": "q-004",
      "questionText": "讨论函数 f(x) = x³ - 3x + 1 的单调性与极值",
      "questionType": "essay",
      "correctRate": 0.54,
      "referenceAnswer": "f'(x) = 3x² - 3，令 f'(x)=0 得 x=±1。x<-1 或 x>1 时单调递增，-1<x<1 时单调递减。x=-1 处取极大值 f(-1)=3，x=1 处取极小值 f(1)=-1",
      "knowledgePoints": ["导数应用", "单调性", "极值"]
    },
    {
      "questionId": "q-005",
      "questionText": "已知 f(x) = ln(x+1)，求 f''(x)",
      "questionType": "fill-blank",
      "correctRate": 0.68,
      "referenceAnswer": "f'(x) = 1/(x+1)，f''(x) = -1/(x+1)²",
      "knowledgePoints": ["复合函数求导", "高阶导数"]
    }
  ]
}
