[
{
"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)"
]
}
]
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)"
]
}
]'
{}