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新增解答题拍照判分:百炼 Qwen-VL 按评分点逐点判分,无 API Key 时演示判分回退;混合卷按真实分值加权计分;判分照片与评分点进错题本;补齐历史迁移缺口(0005 模板生效方式/0006 五张缺失表+grammar_progress point_id)

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Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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jacobxu666
2026-08-17 16:24:23 +08:00
co-authored by Claude Opus 4.8
parent 4033abc21d
commit f80a931ef0
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{
"papers": [
{
"id": "g7s1-m00-entrance",
"grade": "g7",
"semester": "s1",
"month": 0,
"examType": "entrance",
"title": "初一入学分班考数学模拟卷(含解答题)",
"region": "通用",
"year": 2026,
"fullScore": 100,
"sourceUrl": "",
"summary": "按真实分班考卷面结构组卷:填空 8 题×3 分、选择 6 题×3 分、计算解答 4 题×5 分、应用解答 4 题共 38 分,满分 100 分。题目取自本地教研素材的经典分班考题型(鸡兔同笼、工程、分数百分数、行程等),经双模型独立验算;因抓取受限未用原卷页面转录。解答题需纸上手写后拍照,由 AI 按评分点逐步判分。",
"questions": [
{
"type": "fill",
"stem": "24 和 36 的最大公因数是____。",
"answers": [
"12"
],
"explain": "24=2×2×2×3,36=2×2×3×3,公有质因数相乘:2×2×3=12。",
"points": 3
},
{
"type": "fill",
"stem": "8 和 12 的最小公倍数是____。",
"answers": [
"24"
],
"explain": "8=2×2×2,12=2×2×3,最小公倍数=2×2×2×3=24。",
"points": 3
},
{
"type": "fill",
"stem": "一根绳子长 20 米,用去它的 3/5,还剩____米。",
"answers": [
"8"
],
"explain": "用去 20×3/5=12 米,还剩 20-12=8 米(或 20×(1-3/5)=20×2/5=8 米)。",
"points": 3
},
{
"type": "fill",
"stem": "一个两位数,个位上的数字是十位上数字的 3 倍,且两个数位上的数字之和是 8,这个两位数是____。",
"answers": [
"26"
],
"explain": "设十位为 a,则个位为 3a,a+3a=8,a=2,个位是 6,这个数是 26。",
"points": 3
},
{
"type": "fill",
"stem": "一个数除以 5,商是 8,余数是 2,这个数是____。",
"answers": [
"42"
],
"explain": "被除数=商×除数+余数=8×5+2=42。",
"points": 3
},
{
"type": "fill",
"stem": "按规律填数:1,1,2,3,5,8,____。",
"answers": [
"13"
],
"explain": "从第三项起,每个数等于前两个数的和:5+8=13。",
"points": 3
},
{
"type": "fill",
"stem": "把 120 按 2:3 分成两份,较大的一份是____。",
"answers": [
"72"
],
"explain": "总份数 2+3=5,较大一份占 3/5:120×3/5=72。",
"points": 3
},
{
"type": "fill",
"stem": "一个圆的周长是 31.4 厘米,它的直径是____厘米。(π 取 3.14)",
"answers": [
"10"
],
"explain": "直径=周长÷π=31.4÷3.14=10 厘米。",
"points": 3
},
{
"type": "choice",
"stem": "1 元和 5 元的纸币共 12 张,合计 28 元,其中 5 元纸币有( )张。",
"options": [
"A. 3",
"B. 4",
"C. 5",
"D. 6"
],
"answer": 1,
"explain": "设 5 元 x 张,则 1 元 (12-x) 张:5x+(12-x)=28,4x=16,x=4。",
"points": 3
},
{
"type": "choice",
"stem": "一件衣服原价 200 元,打七五折出售,现价是( )元。",
"options": [
"A. 50",
"B. 150",
"C. 160",
"D. 175"
],
"answer": 1,
"explain": "七五折即按原价的 75% 出售:200×75%=150 元。",
"points": 3
},
{
"type": "choice",
"stem": "路程一定,行驶的速度和所需的时间( )。",
"options": [
"A. 成正比例",
"B. 成反比例",
"C. 不成比例"
],
"answer": 1,
"explain": "速度×时间=路程(一定),乘积一定,成反比例。",
"points": 3
},
{
"type": "choice",
"stem": "下面各数中,是质数的是( )。",
"options": [
"A. 51",
"B. 91",
"C. 97",
"D. 117"
],
"answer": 2,
"explain": "51=3×17,91=7×13,117=3×39=9×13,都不是质数;97 只有 1 和它本身两个因数,是质数。",
"points": 3
},
{
"type": "choice",
"stem": "一个圆的半径扩大到原来的 2 倍,它的面积扩大到原来的( )倍。",
"options": [
"A. 2",
"B. 4",
"C. 6",
"D. 8"
],
"answer": 1,
"explain": "面积=πr²,半径扩大 2 倍,面积扩大 2²=4 倍。",
"points": 3
},
{
"type": "choice",
"stem": "爸爸今年 40 岁,儿子今年 12 岁,( )年后爸爸的年龄是儿子的 3 倍。",
"options": [
"A. 1",
"B. 2",
"C. 3",
"D. 4"
],
"answer": 1,
"explain": "设 x 年后:40+x=3×(12+x),40+x=36+3x,2x=4,x=2。",
"points": 3
},
{
"type": "solve",
"stem": "用简便方法计算:25×32×125",
"points": 5,
"reference": "25×32×125\n=25×(4×8)×125(把 32 拆成 4×8)\n=(25×4)×(8×125)(乘法交换律、结合律)\n=100×1000\n=100000",
"rubric": [
{
"point": "把 32 拆成 4×8,并合理运用乘法交换律/结合律重组算式",
"score": 2
},
{
"point": "正确算出 25×4=100 与 8×125=1000",
"score": 2
},
{
"point": "得出正确结果 100000",
"score": 1
}
],
"explain": "看到 25 想 4,看到 125 想 8:把 32 拆成 4×8,凑成 25×4 与 8×125 两组整百整千。"
},
{
"type": "solve",
"stem": "用简便方法计算:3/4×5/6+5/6×1/4",
"points": 5,
"reference": "3/4×5/6+5/6×1/4\n=5/6×(3/4+1/4)(乘法分配律逆用)\n=5/6×1\n=5/6",
"rubric": [
{
"point": "发现公因数 5/6,逆用乘法分配律写成 5/6×(3/4+1/4)",
"score": 2
},
{
"point": "正确算出 3/4+1/4=1",
"score": 1
},
{
"point": "得出正确结果 5/6",
"score": 2
}
],
"explain": "两个乘积都有因数 5/6,逆用分配律:5/6×(3/4+1/4)=5/6×1=5/6。"
},
{
"type": "solve",
"stem": "解方程:3x+5=2x+9",
"points": 5,
"reference": "3x+5=2x+9\n3x-2x=9-5(两边同时减 2x、减 5)\nx=4",
"rubric": [
{
"point": "正确移项(含未知数的项移到一边,常数项移到另一边,变号正确)",
"score": 2
},
{
"point": "得出 x=4",
"score": 2
},
{
"point": "写出结论或代入检验",
"score": 1
}
],
"explain": "移项:3x-2x=9-5,即 x=4。检验:左边=3×4+5=17,右边=2×4+9=17,相等。"
},
{
"type": "solve",
"stem": "计算:4.8÷(1.2×2)+3.5",
"points": 5,
"reference": "4.8÷(1.2×2)+3.5\n=4.8÷2.4+3.5(先算括号里的)\n=2+3.5\n=5.5",
"rubric": [
{
"point": "按运算顺序先算括号内 1.2×2=2.4",
"score": 1
},
{
"point": "正确算出 4.8÷2.4=2",
"score": 2
},
{
"point": "得出正确结果 5.5",
"score": 2
}
],
"explain": "运算顺序:先括号,再乘除,最后加减。4.8÷2.4=2,2+3.5=5.5。"
},
{
"type": "solve",
"stem": "笼子里有鸡和兔共 35 只,数一数共有 94 条腿。鸡和兔各有多少只?",
"points": 8,
"reference": "假设全是鸡:35×2=70(条腿)\n比实际少:94-70=24(条腿)\n每把一只鸡换成兔多 2 条腿:24÷2=12(只)\n兔有 12 只,鸡有 35-12=23(只)\n答:鸡有 23 只,兔有 12 只。",
"rubric": [
{
"point": "方法正确完整(假设法、方程法等任一种,数量关系列对)",
"score": 3
},
{
"point": "求出兔 12 只",
"score": 3
},
{
"point": "求出鸡 23 只并写出答句",
"score": 2
}
],
"explain": "鸡兔同笼经典题:假设全是鸡得 70 条腿,差的 24 条腿由每只换兔补 2 条,兔=24÷2=12 只。也可设兔 x 只:4x+2(35-x)=94。"
},
{
"type": "solve",
"stem": "一件工作,甲单独做 20 天完成,乙单独做 30 天完成。两人合作,多少天可以完成?",
"points": 10,
"reference": "把工作总量看作 1。\n甲每天完成 1/20,乙每天完成 1/30。\n两人每天共完成:1/20+1/30=3/60+2/60=5/60=1/12\n完成天数:1÷1/12=12(天)\n答:两人合作 12 天可以完成。",
"rubric": [
{
"point": "设工作总量为 1,正确表示甲、乙工作效率 1/20 与 1/30",
"score": 3
},
{
"point": "正确求出效率和 1/20+1/30=1/12",
"score": 4
},
{
"point": "得出 12 天并写出答句",
"score": 3
}
],
"explain": "工程问题:工作总量÷效率和=合作时间。1÷(1/20+1/30)=1÷1/12=12 天。"
},
{
"type": "solve",
"stem": "商店运来一批水果,上午卖出总数的 1/3,下午卖出总数的 1/4,还剩 50 千克。这批水果共有多少千克?",
"points": 10,
"reference": "把水果总数看作单位“1”。\n50 千克对应的分率:1-1/3-1/4=12/12-4/12-3/12=5/12\n总数:50÷5/12=50×12/5=120(千克)\n答:这批水果共有 120 千克。",
"rubric": [
{
"point": "找准单位“1”,正确求出 50 千克对应的分率 1-1/3-1/4=5/12",
"score": 4
},
{
"point": "正确列式 50÷5/12 并计算",
"score": 3
},
{
"point": "得出 120 千克并写出答句",
"score": 3
}
],
"explain": "分数应用题:已知剩余量求单位“1”,用除法。剩余对应分率 5/12,总数=50÷5/12=120 千克。"
},
{
"type": "solve",
"stem": "甲、乙两地相距 480 千米,一辆客车从甲地出发,每小时行 60 千米;同时一辆货车从乙地出发,每小时行 40 千米,两车相向而行。经过几小时两车相遇?相遇时客车行了多少千米?",
"points": 10,
"reference": "速度和:60+40=100(千米/时)\n相遇时间:480÷100=4.8(小时)\n客车行驶路程:60×4.8=288(千米)\n答:经过 4.8 小时两车相遇,相遇时客车行了 288 千米。",
"rubric": [
{
"point": "正确求出速度和 60+40=100 千米/时",
"score": 2
},
{
"point": "得出相遇时间 480÷100=4.8 小时",
"score": 4
},
{
"point": "得出客车行了 288 千米并写出答句",
"score": 4
}
],
"explain": "相遇问题:相遇时间=总路程÷速度和=480÷100=4.8 小时;客车路程=60×4.8=288 千米。"
}
]
}
]
}