个人项目
  1. 批改
个人项目
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  • 示例项目
    • 查询宠物详情
      GET
    • 新建宠物信息
      POST
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      PUT
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      DELETE
    • 根据状态查找宠物列表
      GET
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    • 大学搜题
      POST
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    • 文档内容提取
      POST
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      POST
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    • 运行工作流
      POST
    • 查询工作流运行记录
      GET
    • 运行agent
      POST
    • 获取工作流执行结果
      GET
  • 批改
    • 批量运行批改
      POST
    • 根据批次批量评估批改结果
      POST
    • 查询批改结果
      POST
    • 批量添加题目
      POST
    • 导入批改数据
      POST
    • 报表
      POST
    • 模型ocr
      POST
    • 批量运行模型ocr
      POST
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      POST
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      POST
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      POST
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  1. 批改

批量添加题目

开发中
POST
http://localhost:7005/correct-question/add_questions

请求参数

Body 参数application/json

示例
[
    {
        "question_type": "选择题",
        "question_index": 1,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/684_WX20250424-161855@2x.png",
        "student_answers": [
            "B"
        ],
        "correct_answers": [
            "D"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 2,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/87_WX20250424-161902@2x.png",
        "student_answers": [
            "A"
        ],
        "correct_answers": [
            "C"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 3,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/282_WX20250424-161910@2x.png",
        "student_answers": [
            "C"
        ],
        "correct_answers": [
            "D"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 4,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/438_WX20250424-161917@2x.png",
        "student_answers": [
            "D"
        ],
        "correct_answers": [
            "A"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 5,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/511_WX20250424-161956.png",
        "student_answers": [
            "A"
        ],
        "correct_answers": [
            "C"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 6,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/356_WX20250424-162004@2x.png",
        "student_answers": [
            "B"
        ],
        "correct_answers": [
            "B"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 7,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/595_WX20250424-162010@2x.png",
        "student_answers": [
            "D"
        ],
        "correct_answers": [
            "A"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 8,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/971_WX20250424-162016@2x.png",
        "student_answers": [
            "C"
        ],
        "correct_answers": [
            "C"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 9,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/104_WX20250424-162024@2x.png",
        "student_answers": [
            "A"
        ],
        "correct_answers": [
            "A"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 10,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/621_WX20250424-162103.png",
        "student_answers": [
            "C"
        ],
        "correct_answers": [
            "C"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 11,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/699_WX20250424-162109@2x.png",
        "student_answers": [
            "$ \\text{x不等于1} $"
        ],
        "correct_answers": [
            "x≠1"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 12,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/36_WX20250424-162116@2x.png",
        "student_answers": [
            "$ a(x+2)(x-2) $"
        ],
        "correct_answers": [
            "a(x﹣2)(x+2)"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 13,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/905_WX20250424-162121@2x.png",
        "student_answers": [
            "2.5"
        ],
        "correct_answers": [
            "2.5"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 14,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/514_WX20250424-162126@2x.png",
        "student_answers": [
            "3"
        ],
        "correct_answers": [
            "4"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 15,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/744_WX20250424-162133@2x.png",
        "student_answers": [
            "$ 2\\sqrt{3} $"
        ],
        "correct_answers": [
            "$ 2\\sqrt{3} $"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 16,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/966_WX20250424-162140@2x.png",
        "student_answers": [
            "3"
        ],
        "correct_answers": [
            "3"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 17,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/583_WX20250424-162147@2x.png",
        "student_answers": [
            "$ 2\\sqrt{3} $"
        ],
        "correct_answers": [
            "$ 2\\sqrt{5} $"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 18,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/758_WX20250424-162229.png",
        "student_answers": [
            "$ 50^{\\circ} $"
        ],
        "correct_answers": [
            "60"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 19,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/152_WX20250424-162237@2x.png",
        "student_answers": [
            "10"
        ],
        "correct_answers": [
            "3或$\\sqrt{41} $"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 20,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/977_WX20250424-162245@2x.png",
        "student_answers": [
            "8"
        ],
        "correct_answers": [
            "$ 4\\sqrt{6} $"
        ]
    },
    {
        "question_type": "解答题",
        "question_index": 21,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/404_WX20250424-162255@2x.png",
        "student_answers": [
            "$ x^{2}-2x+x-2=0\\\\x^{2}-x-2=0\\\\(x+1)(x-2)=0\\\\x_{1}=-1或x_{2}=2 $",
            ""
        ],
        "correct_answers": [
            "$ x_{1} =2,x_{2} =﹣1 $",
            "$x_{1} =4+\\sqrt{33} ,x_{2} =4-\\sqrt{33} $\n"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 22,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/93_WX20250424-162309@2x.png",
        "student_answers": [
            ""
        ],
        "correct_answers": [
            "作图题"
        ]
    },
    {
        "question_type": "解答题",
        "question_index": 23,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/990_WX20250424-162421.png",
        "student_answers": [
            "30",
            "80",
            "$ \\begin{aligned}AE&=\\sqrt{AB^{2}-BE^{2}}\\\\&=\\sqrt{3^{2}-(\\frac{3}{2})^{2}}\\\\&=\\frac{3\\sqrt{3}}{2}\\end{aligned} $\n"
        ],
        "correct_answers": [
            "60",
            "30",
            "$ \\frac{3\\sqrt{3} }{2} $"
        ]
    },
    {
        "question_type": "解答题",
        "question_index": 24,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/540_WX20250509-171358.png",
        "student_answers": [
            "$ (1)证\\because DE//AC,CE//BD\\therefore CCED是平方因边形\\\\\\because AC,BD相交于O\\\\\\therefore AC=BD,OC=\\frac{1}{2}AC,OD=\\frac{1}{2}BD\\therefore OC=OD\\therefore OCED是菱形 $",
            "$ \\begin{aligned}&(20)\\because\\angle ADD=120^{\\circ}\\therefore\\angle ADB=60^{\\circ}\\\\&\\because AO=BD\\therefore\\Delta AOB是本边三角形\\\\&\\therefore AO=BO=AB=4\\\\&BC=\\sqrt{AB^{2}A^{2}}=\\sqrt{44+18}=4\\sqrt{3}\\\\&\\therefore SDEBOEO=AAAE=16\\sqrt{3}\\\\&\\therefore SDOO=\\frac{1}{4}SDOCO=\\frac{1}{4}SDOCO=\\frac{1}{4}SDOCO=\\frac{1}{4}SDOCO=\\frac{1}{4}SDOCEO=2\\times4\\sqrt{3}=6\\sqrt{3}\\therefore BOCEDEEEB\\therefore SOCEO=2SOOO=2\\times4\\sqrt{3}=6\\sqrt{3}\\end{aligned} $"
        ],
        "correct_answers": [
            "证明:∵DE∥AC,CE∥BD,\n∴四边形OCED是平行四边形,\n∵矩形ABCD的对角线AC,BD相交于点O,\n∴AC=BD,OC=$\\frac{1}{2} $AC,OD=$\\frac{1}{2} $,\n∴OC=OD,\n∴四边形OCED是菱形",
            "$2S_{\\bigtriangleup OCD } =2\\times 4\\sqrt{3} =8\\sqrt{3} $"
        ]
    },
    {
        "question_type": "解答题",
        "question_index": 25,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/179_WX20250424-162701.png",
        "student_answers": [
            "$\\bigtriangleup BOE$",
            "$\\frac{3}{4} $",
            "$\\frac{\\sqrt{2} }{2} $",
            "$ BE+DF=\\sqrt{2}OC $",
            "$ BP^{2}+DQ^{2}=PQ^{2} $"
        ],
        "correct_answers": [
            "$\\bigtriangleup BEO$",
            "$\\frac{1}{4} $",
            "$\\frac{\\sqrt{2} }{2} $",
            "$ BE+DF=\\sqrt{2}OC $",
            "$ BP^{2}+DQ^{2}=PQ^{2} $"
        ]
    },
    {
        "question_type": "解答题",
        "question_index": 26,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/576_WX20250424-162723@2x.png",
        "student_answers": [
            "$ (1)在正方形ABCO中各角为90^{\\circ}LBPO=LABP+\\angle BAP,\\angle CFE=\\angle FAO+\\angle AOF,\\angle BPD=\\angle CFE\\\\\\therefore\\angle ABP=\\angle FAD\\therefore\\angle FAP+\\angle BPE=90^{\\circ}\\therefore\\angle AHP=180^{\\circ}-\\angle FAD-\\angle BPE=90^{\\circ}\\therefore EF\\bot BP $",
            "$ DG=9\\sqrt{5} $"
        ],
        "correct_answers": [
            "在正方形ABCD中,∠ABC=∠BAD=∠ADC=90°,\n∵∠BPD=∠ABP+∠BAP,∠CFE=∠FAD+∠ADF,\n∠BPD=∠CFE,\n∴∠ABP=∠FAD,\n又∵∠ABP+∠BPE=90°,\n∴∠FAD+∠BPE=90°,\n∴∠AHP=180°﹣∠FAD﹣∠BPE=90°,\n即EF⊥BP",
            "证明:过点A作AM∥EF交CD于点M,如图2,",
            "∴∠AMF=∠EFC,\n∵AB∥CD,\n∴四边形AEFM是平行四边形,\n∴AE=FM,\n又∵∠BPD=∠CFE,\n∴∠AMF=∠BPD,\n∴∠AMD=∠BPA,\n在△AMD和△BPA中,\n$\\left\\{\\begin{matrix}\n  \\angle AMD=\\angle BPA\n  &  & \\\\\\angle ADM=\\angle BAP\n\\\\AD=BA\n\\end{matrix}\\right.$,\n∴△AMD≌△BPA(AAS),\n∴MD=PA,\n又∵AE=FM,\n∴DF=FM+MD=AE+AP,\n即AE+AP=DF",
            "$9\\sqrt{5} $"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 27,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/241_WX20250424-162833@2x.png",
        "student_answers": [
            "(0,3)",
            "(3,0)",
            "$ S=\\begin{cases}-\\frac{3}{2}t+\\frac{9}{2}(0<t<3)\\\\\\frac{3}{2}t-\\frac{9}{2}(t>3)\\end{cases} $",
            "$ Q点生标(4,-3) $",
            ""
        ],
        "correct_answers": [
            "(0,3)",
            "(3,0)",
            "$ S=\\begin{cases}-\\frac{3}{2}t+\\frac{9}{2}(0<t<3)\\\\\\frac{3}{2}t-\\frac{9}{2}(t>3)\\end{cases} $",
            "Q(4,3)"
        ]
    }
]

请求示例代码

Shell
JavaScript
Java
Swift
Go
PHP
Python
HTTP
C
C#
Objective-C
Ruby
OCaml
Dart
R
请求示例请求示例
Shell
JavaScript
Java
Swift
curl --location --request POST 'http://localhost:7005/correct-question/add_questions' \
--header 'Content-Type: application/json' \
--data-raw '[
    {
        "question_type": "选择题",
        "question_index": 1,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/684_WX20250424-161855@2x.png",
        "student_answers": [
            "B"
        ],
        "correct_answers": [
            "D"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 2,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/87_WX20250424-161902@2x.png",
        "student_answers": [
            "A"
        ],
        "correct_answers": [
            "C"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 3,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/282_WX20250424-161910@2x.png",
        "student_answers": [
            "C"
        ],
        "correct_answers": [
            "D"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 4,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/438_WX20250424-161917@2x.png",
        "student_answers": [
            "D"
        ],
        "correct_answers": [
            "A"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 5,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/511_WX20250424-161956.png",
        "student_answers": [
            "A"
        ],
        "correct_answers": [
            "C"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 6,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/356_WX20250424-162004@2x.png",
        "student_answers": [
            "B"
        ],
        "correct_answers": [
            "B"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 7,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/595_WX20250424-162010@2x.png",
        "student_answers": [
            "D"
        ],
        "correct_answers": [
            "A"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 8,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/971_WX20250424-162016@2x.png",
        "student_answers": [
            "C"
        ],
        "correct_answers": [
            "C"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 9,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/104_WX20250424-162024@2x.png",
        "student_answers": [
            "A"
        ],
        "correct_answers": [
            "A"
        ]
    },
    {
        "question_type": "选择题",
        "question_index": 10,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/621_WX20250424-162103.png",
        "student_answers": [
            "C"
        ],
        "correct_answers": [
            "C"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 11,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/699_WX20250424-162109@2x.png",
        "student_answers": [
            "$ \\text{x不等于1} $"
        ],
        "correct_answers": [
            "x≠1"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 12,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/36_WX20250424-162116@2x.png",
        "student_answers": [
            "$ a(x+2)(x-2) $"
        ],
        "correct_answers": [
            "a(x﹣2)(x+2)"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 13,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/905_WX20250424-162121@2x.png",
        "student_answers": [
            "2.5"
        ],
        "correct_answers": [
            "2.5"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 14,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/514_WX20250424-162126@2x.png",
        "student_answers": [
            "3"
        ],
        "correct_answers": [
            "4"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 15,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/744_WX20250424-162133@2x.png",
        "student_answers": [
            "$ 2\\sqrt{3} $"
        ],
        "correct_answers": [
            "$ 2\\sqrt{3} $"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 16,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/966_WX20250424-162140@2x.png",
        "student_answers": [
            "3"
        ],
        "correct_answers": [
            "3"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 17,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/583_WX20250424-162147@2x.png",
        "student_answers": [
            "$ 2\\sqrt{3} $"
        ],
        "correct_answers": [
            "$ 2\\sqrt{5} $"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 18,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/758_WX20250424-162229.png",
        "student_answers": [
            "$ 50^{\\circ} $"
        ],
        "correct_answers": [
            "60"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 19,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/152_WX20250424-162237@2x.png",
        "student_answers": [
            "10"
        ],
        "correct_answers": [
            "3或$\\sqrt{41} $"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 20,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/977_WX20250424-162245@2x.png",
        "student_answers": [
            "8"
        ],
        "correct_answers": [
            "$ 4\\sqrt{6} $"
        ]
    },
    {
        "question_type": "解答题",
        "question_index": 21,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/404_WX20250424-162255@2x.png",
        "student_answers": [
            "$ x^{2}-2x+x-2=0\\\\x^{2}-x-2=0\\\\(x+1)(x-2)=0\\\\x_{1}=-1或x_{2}=2 $",
            ""
        ],
        "correct_answers": [
            "$ x_{1} =2,x_{2} =﹣1 $",
            "$x_{1} =4+\\sqrt{33} ,x_{2} =4-\\sqrt{33} $\n"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 22,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/93_WX20250424-162309@2x.png",
        "student_answers": [
            ""
        ],
        "correct_answers": [
            "作图题"
        ]
    },
    {
        "question_type": "解答题",
        "question_index": 23,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/990_WX20250424-162421.png",
        "student_answers": [
            "30",
            "80",
            "$ \\begin{aligned}AE&=\\sqrt{AB^{2}-BE^{2}}\\\\&=\\sqrt{3^{2}-(\\frac{3}{2})^{2}}\\\\&=\\frac{3\\sqrt{3}}{2}\\end{aligned} $\n"
        ],
        "correct_answers": [
            "60",
            "30",
            "$ \\frac{3\\sqrt{3} }{2} $"
        ]
    },
    {
        "question_type": "解答题",
        "question_index": 24,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/540_WX20250509-171358.png",
        "student_answers": [
            "$ (1)证\\because DE//AC,CE//BD\\therefore CCED是平方因边形\\\\\\because AC,BD相交于O\\\\\\therefore AC=BD,OC=\\frac{1}{2}AC,OD=\\frac{1}{2}BD\\therefore OC=OD\\therefore OCED是菱形 $",
            "$ \\begin{aligned}&(20)\\because\\angle ADD=120^{\\circ}\\therefore\\angle ADB=60^{\\circ}\\\\&\\because AO=BD\\therefore\\Delta AOB是本边三角形\\\\&\\therefore AO=BO=AB=4\\\\&BC=\\sqrt{AB^{2}A^{2}}=\\sqrt{44+18}=4\\sqrt{3}\\\\&\\therefore SDEBOEO=AAAE=16\\sqrt{3}\\\\&\\therefore SDOO=\\frac{1}{4}SDOCO=\\frac{1}{4}SDOCO=\\frac{1}{4}SDOCO=\\frac{1}{4}SDOCO=\\frac{1}{4}SDOCEO=2\\times4\\sqrt{3}=6\\sqrt{3}\\therefore BOCEDEEEB\\therefore SOCEO=2SOOO=2\\times4\\sqrt{3}=6\\sqrt{3}\\end{aligned} $"
        ],
        "correct_answers": [
            "证明:∵DE∥AC,CE∥BD,\n∴四边形OCED是平行四边形,\n∵矩形ABCD的对角线AC,BD相交于点O,\n∴AC=BD,OC=$\\frac{1}{2} $AC,OD=$\\frac{1}{2} $,\n∴OC=OD,\n∴四边形OCED是菱形",
            "$2S_{\\bigtriangleup OCD } =2\\times 4\\sqrt{3} =8\\sqrt{3} $"
        ]
    },
    {
        "question_type": "解答题",
        "question_index": 25,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/179_WX20250424-162701.png",
        "student_answers": [
            "$\\bigtriangleup BOE$",
            "$\\frac{3}{4} $",
            "$\\frac{\\sqrt{2} }{2} $",
            "$ BE+DF=\\sqrt{2}OC $",
            "$ BP^{2}+DQ^{2}=PQ^{2} $"
        ],
        "correct_answers": [
            "$\\bigtriangleup BEO$",
            "$\\frac{1}{4} $",
            "$\\frac{\\sqrt{2} }{2} $",
            "$ BE+DF=\\sqrt{2}OC $",
            "$ BP^{2}+DQ^{2}=PQ^{2} $"
        ]
    },
    {
        "question_type": "解答题",
        "question_index": 26,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/576_WX20250424-162723@2x.png",
        "student_answers": [
            "$ (1)在正方形ABCO中各角为90^{\\circ}LBPO=LABP+\\angle BAP,\\angle CFE=\\angle FAO+\\angle AOF,\\angle BPD=\\angle CFE\\\\\\therefore\\angle ABP=\\angle FAD\\therefore\\angle FAP+\\angle BPE=90^{\\circ}\\therefore\\angle AHP=180^{\\circ}-\\angle FAD-\\angle BPE=90^{\\circ}\\therefore EF\\bot BP $",
            "$ DG=9\\sqrt{5} $"
        ],
        "correct_answers": [
            "在正方形ABCD中,∠ABC=∠BAD=∠ADC=90°,\n∵∠BPD=∠ABP+∠BAP,∠CFE=∠FAD+∠ADF,\n∠BPD=∠CFE,\n∴∠ABP=∠FAD,\n又∵∠ABP+∠BPE=90°,\n∴∠FAD+∠BPE=90°,\n∴∠AHP=180°﹣∠FAD﹣∠BPE=90°,\n即EF⊥BP",
            "证明:过点A作AM∥EF交CD于点M,如图2,",
            "∴∠AMF=∠EFC,\n∵AB∥CD,\n∴四边形AEFM是平行四边形,\n∴AE=FM,\n又∵∠BPD=∠CFE,\n∴∠AMF=∠BPD,\n∴∠AMD=∠BPA,\n在△AMD和△BPA中,\n$\\left\\{\\begin{matrix}\n  \\angle AMD=\\angle BPA\n  &  & \\\\\\angle ADM=\\angle BAP\n\\\\AD=BA\n\\end{matrix}\\right.$,\n∴△AMD≌△BPA(AAS),\n∴MD=PA,\n又∵AE=FM,\n∴DF=FM+MD=AE+AP,\n即AE+AP=DF",
            "$9\\sqrt{5} $"
        ]
    },
    {
        "question_type": "填空题",
        "question_index": 27,
        "paper_id": 1,
        "question_url": "https://img.qiaoxuesi.com/upfiles/241_WX20250424-162833@2x.png",
        "student_answers": [
            "(0,3)",
            "(3,0)",
            "$ S=\\begin{cases}-\\frac{3}{2}t+\\frac{9}{2}(0<t<3)\\\\\\frac{3}{2}t-\\frac{9}{2}(t>3)\\end{cases} $",
            "$ Q点生标(4,-3) $",
            ""
        ],
        "correct_answers": [
            "(0,3)",
            "(3,0)",
            "$ S=\\begin{cases}-\\frac{3}{2}t+\\frac{9}{2}(0<t<3)\\\\\\frac{3}{2}t-\\frac{9}{2}(t>3)\\end{cases} $",
            "Q(4,3)"
        ]
    }
]'

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修改于 2025-08-12 08:56:39
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