{ "paper_info": { "id": 1, "title": "2025年9月2日初中数学作业", "subject": "数学", "grade": "grade8" }, "questions": [ { "id": 1, "number": "1", "type": "single_choice", "subject": "数学", "grade": "grade8", "chapter": "", "difficulty": { "level": 3, "label": "中等", "stars": "★★★" }, "score": { "total": 5.0, "formatted": "5.0分", "extracted_from_text": true }, "estimated_time": { "minutes": 1.6, "seconds": 95, "formatted": "1.6分钟" }, "stem": "解方程:(1) 2x² - 4x - 5 = 0;(2) (x - 3)(x - 1) = (x - 2)(x - 1) 5分", "options": [ { "label": "A", "text": "x₁ = 2 + √7, x₂ = 2 - √7", "is_correct": false, "explanation": "" }, { "label": "B", "text": "x₁ = 1, x₂ = 5", "is_correct": false, "explanation": "" }, { "label": "C", "text": "x₁ = 3, x₂ = -1", "is_correct": false, "explanation": "" }, { "label": "D", "text": "无解", "is_correct": false, "explanation": "" } ], "correct_answer": "A", "explanation": "对于方程(1),使用求根公式可得解。对于方程(2),两边同时除以(x-1)可得x-3 = x-2,此方程无解。", "analysis": "", "hints": [], "knowledge_points": [ { "name": "一元二次方程", "category": "", "weight": 1.0 }, { "name": "求根公式", "category": "", "weight": 1.0 } ], "images": [ { "id": "img_1", "url": "/images/eq1.png", "alt": "方程图片", "type": "image", "width": null, "height": null, "format": "unknown" } ], "formulas": [], "audio": "", "video": "", "source": { "type": "auto_extracted", "method": "unknown", "paper": { "id": 1, "title": "2025年9月2日初中数学作业", "page": 1 }, "extraction_confidence": 0.8, "verified": false }, "metadata": { "extraction_method": "manual", "original_format": "pdf", "language": "zh-CN", "tags": [], "notes": "", "page_spans": [], "source_text": "" }, "statistics": { "created_at": "2024-01-15T10:30:00", "updated_at": "", "view_count": 0, "attempt_count": 0, "correct_count": 0, "accuracy_rate": 0.0 }, "variants": [ { "number": "1", "type": "subquestion", "content": "2x² - 4x - 5 = 0;", "score": null } ], "validation": { "is_valid": true, "errors": [], "warnings": [], "completeness_score": 1.0 } }, { "id": 2, "number": "2", "type": "essay", "subject": "数学", "grade": "grade8", "chapter": "", "difficulty": { "level": 4, "label": "较难", "stars": "★★★★" }, "score": { "total": 8.0, "formatted": "8.0分", "extracted_from_text": false }, "estimated_time": { "minutes": 20.2, "seconds": 1210, "formatted": "20.2分钟" }, "stem": "如图,在△ABC 中,AB = AC,D、E 分别是AB、BC 的中点,BF ∥ DE,EF ∥ DB。求证:四边形BDEF 是菱形;若 BE = 4,AC = 5,求DM 的长。", "options": [], "correct_answer": "证明:由于D、E是中点,BF∥DE,EF∥DB,可得四边形BDEF是平行四边形。又因为BF=EF(中位线相等),所以是菱形。DM = 3", "explanation": "本题考查中位线定理和菱形的判定与性质。", "analysis": "", "hints": [], "knowledge_points": [ { "name": "中位线定理", "category": "", "weight": 1.0 }, { "name": "菱形的判定", "category": "", "weight": 1.0 }, { "name": "勾股定理", "category": "", "weight": 1.0 } ], "images": [], "formulas": [], "audio": "", "video": "", "source": { "type": "auto_extracted", "method": "unknown", "paper": { "id": 1, "title": "2025年9月2日初中数学作业", "page": 1 }, "extraction_confidence": 0.8, "verified": false }, "metadata": { "extraction_method": "manual", "original_format": "pdf", "language": "zh-CN", "tags": [], "notes": "", "page_spans": [], "source_text": "" }, "statistics": { "created_at": "2024-01-15T10:31:00", "updated_at": "", "view_count": 0, "attempt_count": 0, "correct_count": 0, "accuracy_rate": 0.0 }, "variants": [], "validation": { "is_valid": true, "errors": [], "warnings": [], "completeness_score": 0.75 } } ], "statistics": { "total_questions": 2, "question_types": { "single_choice": 1, "essay": 1 }, "difficulty_distribution": { "简单": 0, "较易": 0, "中等": 1, "较难": 1, "困难": 0 }, "total_score": 13.0, "estimated_time": 21.8, "knowledge_points": [ "勾股定理", "求根公式", "一元二次方程", "菱形的判定", "中位线定理" ], "has_images": 1, "average_accuracy": 0.0, "estimated_time_formatted": "21分钟" }, "processing_errors": [], "export_info": { "exported_at": "2025-11-01T22:15:59.583605", "total_questions": 2, "error_count": 0, "format_version": "2.0" } }