{"ok":true,"count":200,"questions":[{"id":182470,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_325.pdf","job_source":"数学-青岛版.zip","pages":[3,3],"stem":"已知\\(|x| = 3\\)，\\(|y| = 5\\)，且$x > y ，则\\(3x - y\\)的值为 ________．","options":[],"answer":"","solution":"","stem_html":"已知\\(|x| = 3\\)，\\(|y| = 5\\)，且$x > y，则\\(3x - y\\)的值为 ________．
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:44:50"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:44:50"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:44:50"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T15:45:35"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-11-10T15:45:48"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-11-10T15:45:48"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T15:45:48"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T15:46:09"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-11-10T15:46:09"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-11-10T15:48:46"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-11-10T15:48:46"}],"detail_url":"/questions/182470","edit_url":"/questions/182470/edit","json_url":"/api/questions/182470","recheck_url":"/api/questions/182470/recheck"},{"id":182484,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.962,"source_file":"冀教版/八下/薛豪Q_18952688822_35_检测.pdf","job_source":"数学-冀教版.zip","pages":[4,4],"stem":"已知点P(2m+ 4,m−1),请分别根据下列条件,求出点P的坐标.\\(\\frac{(1)}{(2)}\\)点P在x轴上. 点P的纵坐标比横坐标大3.","options":[],"answer":"(1)(6, 0); (2)(−12, −9)","solution":"(1)∵ 点P(2m+ 4,m−1)在x轴上， ∴ m−1 = 0,解得m= 1， ∴ 2m+ 4 =\\(2 \\times 1 + 4 = 6,m−1 = 0\\)所以点P的坐标为(6, 0)； (2)∵ 点P(2m+ 4,m−1)的纵坐标比横坐标大3， ∴ m−1 −(2m+ 4) = 3,解得 m= −8， ∴ 2m+ 4 =\\(2 \\times (−8) + 4 =\\)−12,m−1 = −8 −1 = −9,∴ 点P的坐标为(−12, −9).","stem_html":"已知点P(2m+ 4,m−1),请分别根据下列条件,求出点P的坐标.\\(\\frac{(1)}{(2)}\\)点P在x轴上. 点P的纵坐标比横坐标大3.
","answer_html":"(1)(6, 0); (2)(−12, −9)","solution_html":"(1)∵ 点P(2m+ 4,m−1)在x轴上， ∴ m−1 = 0,解得m= 1， ∴ 2m+ 4 =\\(2 \\times 1 + 4 = 6,m−1 = 0\\)所以点P的坐标为(6, 0)； (2)∵ 点P(2m+ 4,m−1)的纵坐标比横坐标大3， ∴ m−1 −(2m+ 4) = 3,解得 m= −8， ∴ 2m+ 4 =\\(2 \\times (−8) + 4 =\\)−12,m−1 = −8 −1 = −9,∴ 点P的坐标为(−12, −9).","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.95,"created_at":"2026-11-10T15:42:11"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:42:11"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:42:11"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T15:43:10"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-11-10T15:43:59"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-11-10T15:43:59"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T15:43:59"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-11-10T15:45:39"},{"type":"QUALITY_GATE","status":"FAIL","score":0.962,"created_at":"2026-11-10T15:45:39"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:47:56"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:47:56"},{"type":"COHERENCE","status":"FAIL","score":1.0,"created_at":"2026-11-10T15:49:52"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:49:52"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-11-10T15:49:52"}],"detail_url":"/questions/182484","edit_url":"/questions/182484/edit","json_url":"/api/questions/182484","recheck_url":"/api/questions/182484/recheck"},{"id":182486,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_35_检测.pdf","job_source":"数学-冀教版.zip","pages":[4,4],"stem":"已知点\\(P(2m-6,m+1)\\),根据下列条件求出点\\(P\\)的坐标. (1)点\\(P\\)在\\(y\\)轴上. (2)点\\(P\\)的纵坐标比横坐标大5.","options":[],"answer":"(1)(0, 4); (2)(−2, 3)","solution":"∵ 点P(2m−6,m+ 1)在y轴上， ∴ 2m−6 = 0,∴ m= 3,∴ m+ 1 = 4,所以点P的坐标为(0, 4)；\\(\\frac{(1)}{(2)}\\)点P(2m−6,m+ 1)的纵坐标比横坐标大5,∴ m+ 1 −(2m−6) = 5,∴ m= 2,所以 2m −6 = −2, m + 1 = 3, ∴点P的坐标为(−2, 3)．","stem_html":"已知点\\(P(2m-6,m+1)\\),根据下列条件求出点\\(P\\)的坐标.\n(1)点\\(P\\)在\\(y\\)轴上.\n(2)点\\(P\\)的纵坐标比横坐标大5.
","answer_html":"(1)(0, 4); (2)(−2, 3)","solution_html":"∵ 点P(2m−6,m+ 1)在y轴上， ∴ 2m−6 = 0,∴ m= 3,∴ m+ 1 = 4,所以点P的坐标为(0, 4)；\\(\\frac{(1)}{(2)}\\)点P(2m−6,m+ 1)的纵坐标比横坐标大5,∴ m+ 1 −(2m−6) = 5,∴ m= 2,所以 2m −6 = −2, m + 1 = 3, ∴点P的坐标为(−2, 3)．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-11-10T15:43:45"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:43:45"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:43:45"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T15:44:41"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:45:30"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:45:30"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T15:45:30"}],"detail_url":"/questions/182486","edit_url":"/questions/182486/edit","json_url":"/api/questions/182486","recheck_url":"/api/questions/182486/recheck"},{"id":182426,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_95_检测.pdf","job_source":"数学-沪教版.zip","pages":[3,3],"stem":"计算 :\\(\\sqrt{12 \\times}\\)√6 (1); √24 （1）(√3 −√2)^{2} + (√3 + √2)(√3 −√2)","options":[],"answer":"(1)√3; (2)6 −2√6","solution":"√72 (1)原式 = =\\(\\sqrt{\\frac{72}{24}}=\\)√3. √24 (2)原式 = 3 −2√6 + 2 + 3 −2 = 6 −2√6.","stem_html":"计算 :\\(\\sqrt{12 \\times}\\)√6 (1); √24
（1）(√3 −√2)^{2} + (√3 + √2)(√3 −√2)
","answer_html":"(1)√3; (2)6 −2√6","solution_html":"√72 (1)原式 = =\\(\\sqrt{\\frac{72}{24}}=\\)√3. √24 (2)原式 = 3 −2√6 + 2 + 3 −2 = 6 −2√6.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:44:50"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:44:50"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:44:50"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T15:45:18"}],"detail_url":"/questions/182426","edit_url":"/questions/182426/edit","json_url":"/api/questions/182426","recheck_url":"/api/questions/182426/recheck"},{"id":182482,"job_id":10,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_35_检测.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"如图，在平面直角坐标系中，线段AB、BC交于第一象限的点B，B点到y轴的距离是3，到x轴的距离为4，点A,C均在x轴上，C点坐标为(5, 0)，线段AC = 6．A点坐标为 _____.B点坐标为 _____；","options":[],"answer":"(−1, 0), (3, 4)；","solution":"因为点A，C均在x轴上，C点坐标为(5, 0)，∴ OC = 5. ∵ 线段 AC = 6，∴ OA = AC - OC = 6 - 5 = 1, 又 ∵ 点A在x轴负半轴上，∴ A(-1, 0). ∵ 点B在第一象限，B点到y轴的距离是3，到x轴的距离为4，∴ B(3, 4). 故答案为：(-1, 0), (3, 4);","stem_html":"如图，在平面直角坐标系中，线段AB、BC交于第一象限的点B，B点到y轴的距离是3，到x轴的距离为4，点A,C均在x轴上，C点坐标为(5, 0)，线段AC = 6．A点坐标为 _____.B点坐标为 _____；
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/a13a92c3-ebda-4a16-b969-9efbd0519d0d/66f48b11-b1b3-4cad-9712-df0ab15f60ae/7935d588d995.png\" "\\"点击查看原图\\"")
小邱同学做这样一道题＂计算|(−6) + ■|＂，其中＂■＂是被墨水污染看不清 的一个数，他翻看了后面的答案，得知该题的答案是15，那么＂■＂表示的数是____．
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:39:43"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:39:43"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:39:43"},{"type":"VISION","status":"PASS","score":0.8,"created_at":"2026-11-10T15:40:47"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:41:11"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:41:11"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T15:41:11"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T15:41:41"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-11-10T15:41:41"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.0,"created_at":"2026-11-10T15:45:41"}],"detail_url":"/questions/182468","edit_url":"/questions/182468/edit","json_url":"/api/questions/182468","recheck_url":"/api/questions/182468/recheck"},{"id":182477,"job_id":10,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_35_检测.pdf","job_source":"数学-冀教版.zip","pages":[2,2],"stem":"如图，平行四边形ABCD的顶点A,B,D的坐标分别是(1, 0), (−2, 0), (0, 2)，则顶点C的坐标是( ) A. (−4, 2) B. (−3, 2) C. (3, 2) D. (4, 2) 填空题，每题6分","options":[{"label":"A","text":"(−4, 2)"},{"label":"B","text":"(−3, 2)"},{"label":"C","text":"(3, 2)"},{"label":"D","text":"(4, 2) 填空题，每题6分"}],"answer":"B","solution":"因为四边形ABCD是平行四边形， ∴ AB∥ CD,AB=CD,∵ A,B,D的 坐标分别是(1, 0), (−2, 0), (0, 2)， ∴ AB= 1 −(−2) = 3,OD= 2， ∴CD = 3，点C的纵坐标为2，∴顶点C的坐标是(−3, 2)．故选B．","stem_html":"如图，平行四边形ABCD的顶点A,B,D的坐标分别是(1, 0), (−2, 0), (0, 2)，则顶点C的坐标是( )
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/a13a92c3-ebda-4a16-b969-9efbd0519d0d/1742e081-8adf-4c84-833b-99f6dd039059/a0d1beb9ab78.png\" "\\"点击查看原图\\"")
A. (−4, 2)
B. (−3, 2)
C. (3, 2)
D. (4, 2) 填空题，每题6分
在平面直角坐标系中，平行四边形ABCD顶点A,B,D的坐标分 别是(−3, 5), (−4, 3), (3, 3)，则点C坐标是( )
A. (2, 1)
B. (1, 2)
C. (1, 4)
D. (4, 1)
","answer_html":"A","solution_html":"设点C坐标是(x,y)， ∵ 平行四边形ABCD顶点A,B,D的坐标分别 是(−3, 5), (−4, 3), (3, 3)， ∴ −3 +x= −4 + 3, 5 +y= 3 + 3,∴ x= 2， y = 1, ∴点C坐标是(2, 1)，故选：A．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:29:00"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:29:00"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:29:00"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T15:30:49"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:32:44"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:32:44"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:32:44"}],"detail_url":"/questions/182478","edit_url":"/questions/182478/edit","json_url":"/api/questions/182478","recheck_url":"/api/questions/182478/recheck"},{"id":182473,"job_id":10,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_35_检测.pdf","job_source":"数学-冀教版.zip","pages":[1,1],"stem":"如图，线段AB的端点A,B的坐标分别为(1, 6)，(3, 6),AB⊥ BC,AB∥ CD，且AB=\\(\\frac{1}{2}\\)BC =\\(\\frac{1}{3}\\)CD， 则点D的坐标为( ) A. (8, 2) B. (9, 2) C. (8, 3) D. (9, 3)","options":[{"label":"A","text":"(8, 2)"},{"label":"B","text":"(9, 2)"},{"label":"C","text":"(8, 3)"},{"label":"D","text":"(9, 3)"}],"answer":"B","solution":"因为A(1, 6),B(3, 6)， ∴ AB= 3 −1 = 2,∵ AB⊥ BC,AB∥ CD,又 ∵ AB=\\(\\frac{1}{2}\\)BC =\\(\\frac{1}{3}\\)CD,AB= 2,∴ BC = 4,CD= 6,∴ D点横坐标 为3 + 6 = 9, D点纵坐标为6 −4 = 2，∴D(9, 2). 故选：B．","stem_html":"如图，线段AB的端点A,B的坐标分别为(1, 6)，(3, 6),AB⊥ BC,AB∥ CD，且AB=\\(\\frac{1}{2}\\)BC =\\(\\frac{1}{3}\\)CD， 则点D的坐标为( )
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/a13a92c3-ebda-4a16-b969-9efbd0519d0d/9ac73119-139c-4862-af08-b528ac5f39e4/22b3537fbe1d.png\" "\\"点击查看原图\\"")
A. (8, 2)
B. (9, 2)
C. (8, 3)
D. (9, 3)
计算：\\(\\sqrt{3x^{2}y} \\cdot \\sqrt{6x} \\div \\sqrt{\\frac{y^{2}}{x}}\\)解答题，第一题8分，第二题10分，第三题10分
","answer_html":"y","solution_html":"\\(3x^{2}\\)√2y =\\(\\sqrt{3x^{2}}\\)y ⋅6x ⋅\\(\\frac{x}{y^{2}} =√ \\frac{18x^{4}}{y} =\\). 原式=\\(\\sqrt{3x^{2}}\\)y ⋅6x ÷\\(\\frac{y^{2}}{x}\\)y 2y√15y 7m√3","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:27:25"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:27:25"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:27:25"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T15:30:39"},{"type":"SOLVER","status":"PASS","score":0.5,"created_at":"2026-11-10T15:31:13"},{"type":"CRITIC","status":"PASS","score":0.5,"created_at":"2026-11-10T15:31:13"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:31:13"}],"detail_url":"/questions/182423","edit_url":"/questions/182423/edit","json_url":"/api/questions/182423","recheck_url":"/api/questions/182423/recheck"},{"id":182424,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_95_检测.pdf","job_source":"数学-沪教版.zip","pages":[3,3],"stem":"化简下列各式：\\(6y^{2}\\) （1）√10xy ÷\\(\\sqrt{x^{3}}\\) （2）√14mn\\(\\times\\sqrt{\\frac{7m}{n^{2}} \\times}\\sqrt{\\frac{1}{6n}}\\)","options":[],"answer":"(1) (2)","solution":"x 3n (1)由√10xy,\\(\\sqrt{\\frac{x^{3}}{6y^{2}}}\\)有意义，得到x> 0,y> 0，√10xy÷\\(\\sqrt{\\frac{x^{3}}{6y^{2}}}=√10xy\\times \\frac{6y^{2}}{x^{3}} =\\sqrt{\\frac{60xy^{3}}{x^{3}}}=√ \\frac{60y^{3}}{x^{2}} = \\frac{y}{x}\\)√60y=\\(\\frac{y}{x} \\times 2√15y= 2y√15y\\); x (2)由√14mn,\\(\\sqrt{\\frac{7m}{n^{2}},√ \\frac{1}{6n}}\\)有意义，得到 m≥0,n> 0，√14mn\\(\\times\\sqrt{\\frac{7m}{n^{2}} \\times}\\sqrt{\\frac{1}{6n}}=\\)√14mn\\(\\times \\frac{7m}{n^{2}} \\times \\frac{1}{6n} =√ \\frac{98m^{2}n}{6n^{3}} =√ \\frac{49m^{2}}{3n^{2}} = =\\). 7m 7m√3 n√3 3n","stem_html":"化简下列各式：\\(6y^{2}\\)
（1）√10xy ÷\\(\\sqrt{x^{3}}\\)
（2）√14mn\\(\\times\\sqrt{\\frac{7m}{n^{2}} \\times}\\sqrt{\\frac{1}{6n}}\\)
","answer_html":"(1) (2)","solution_html":"x 3n (1)由√10xy,\\(\\sqrt{\\frac{x^{3}}{6y^{2}}}\\)有意义，得到x> 0,y> 0，√10xy÷\\(\\sqrt{\\frac{x^{3}}{6y^{2}}}=√10xy\\times \\frac{6y^{2}}{x^{3}} =\\sqrt{\\frac{60xy^{3}}{x^{3}}}=√ \\frac{60y^{3}}{x^{2}} = \\frac{y}{x}\\)√60y=\\(\\frac{y}{x} \\times 2√15y= 2y√15y\\); x (2)由√14mn,\\(\\sqrt{\\frac{7m}{n^{2}},√ \\frac{1}{6n}}\\)有意义，得到 m≥0,n> 0，√14mn\\(\\times\\sqrt{\\frac{7m}{n^{2}} \\times}\\sqrt{\\frac{1}{6n}}=\\)√14mn\\(\\times \\frac{7m}{n^{2}} \\times \\frac{1}{6n} =√ \\frac{98m^{2}n}{6n^{3}} =√ \\frac{49m^{2}}{3n^{2}} = =\\). 7m 7m√3 n√3 3n","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:29:55"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:29:55"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:29:55"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T15:31:31"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:35:23"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:50:55"}],"detail_url":"/questions/182424","edit_url":"/questions/182424/edit","json_url":"/api/questions/182424","recheck_url":"/api/questions/182424/recheck"},{"id":182481,"job_id":10,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_35_检测.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"临汾市某中学举办秋季田径运动会，为了保障开幕式表演的整体效果 ，该校在操场中标记了几个关键位置，如图是利用平面直角坐标 系画出的关键位置分布图，若这个坐标系分别以正东、正北方向 为x轴、 y轴的正方向，表示点A的坐标为(1, 0)，表示点B的坐标 为(3, 3)，则表示点D的坐标为_______ ．","options":[],"answer":"(−3, 2)","solution":"根据点A的坐标为(1, 0),点B的坐标为(3, 3)，建立平面直角坐标系如下,所以D(−3, 2),故答案为(−3, 2)","stem_html":"临汾市某中学举办秋季田径运动会，为了保障开幕式表演的整体效果 ，该校在操场中标记了几个关键位置，如图是利用平面直角坐标 系画出的关键位置分布图，若这个坐标系分别以正东、正北方向 为x轴、 y轴的正方向，表示点A的坐标为(1, 0)，表示点B的坐标 为(3, 3)，则表示点D的坐标为_______ ．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/bbabf691-2db4-467c-92e0-bcea0d61969c/ea246343aeb7.png\" "\\"点击查看原图\\"")
最大的负整数是____________
","answer_html":"-1","solution_html":"根据整数定义，负整数是小于0的整数。在负整数集合中，-1 是最接近0的数，因此是最大的负整数。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:24:44"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:24:44"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:24:44"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:25:30"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:25:30"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T15:25:42"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:25:42"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T15:27:41"},{"type":"QUALITY_GATE","status":"PASS","score":0.975,"created_at":"2026-11-10T15:27:41"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:29:17"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:29:17"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-11-10T15:29:17"},{"type":"AUTO_FILL_ANSWER","status":"WARN","score":1.0,"created_at":"2026-11-10T15:29:17"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T15:33:18"}],"detail_url":"/questions/182458","edit_url":"/questions/182458/edit","json_url":"/api/questions/182458","recheck_url":"/api/questions/182458/recheck"},{"id":182462,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_325.pdf","job_source":"数学-青岛版.zip","pages":[2,2],"stem":"绝对值不大于的整数有2 ____ 个，它们 的和是 ____．","options":[],"answer":"．5,0","solution":"由绝对值的意义可知，绝对值不大于的2 整数有：− 2,−1,0,1,2共个，其和为；故50 答案为：．5,0","stem_html":"绝对值不大于的整数有2 ____ 个，它们 的和是 ____．
","answer_html":"．5,0","solution_html":"由绝对值的意义可知，绝对值不大于的2 整数有：− 2,−1,0,1,2共个，其和为；故50 答案为：．5,0","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:29:16"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:29:16"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:29:16"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T15:33:14"}],"detail_url":"/questions/182462","edit_url":"/questions/182462/edit","json_url":"/api/questions/182462","recheck_url":"/api/questions/182462/recheck"},{"id":182480,"job_id":10,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_35_检测.pdf","job_source":"数学-冀教版.zip","pages":[2,3],"stem":"为了更好地开展农家生态文化旅游区规划工作，某旅游村把 游客中心，稻田酒店和桃花岛3个景点分别用点A,B,C来表 示，利用坐标确定了这3个景点的位置，并且设置了导航 路线．在如图所示的正方形网格中建立平面直角坐标系 ，使得景点A,B的位置分别表示A(−2, 3),B(−4, 2)，则景点C的坐标为 ____.","options":[],"answer":"(−1, −2)","solution":"根据A(−2, 3),B(−4, 2)，可建立平面直角坐标系，如下图所示，由 图可知，景点C的坐标为(−1, −2)．故答案为：(−1, −2)．","stem_html":"为了更好地开展农家生态文化旅游区规划工作，某旅游村把 游客中心，稻田酒店和桃花岛3个景点分别用点A,B,C来表 示，利用坐标确定了这3个景点的位置，并且设置了导航 路线．在如图所示的正方形网格中建立平面直角坐标系 ，使得景点A,B的位置分别表示A(−2, 3),B(−4, 2)，则景点C的坐标为 ____.
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最大的负整数是___________
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:27:34"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:27:34"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:27:34"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T15:28:31"}],"detail_url":"/questions/182460","edit_url":"/questions/182460/edit","json_url":"/api/questions/182460","recheck_url":"/api/questions/182460/recheck"},{"id":182418,"job_id":9,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_95_检测.pdf","job_source":"数学-沪教版.zip","pages":[2,2],"stem":"下列各式中，能与√6a合并的是（） A. √3a B. 6√a C. √24a D. √6a","options":[{"label":"A","text":"√3a"},{"label":"B","text":"6√a"},{"label":"C","text":"√24a"},{"label":"D","text":"√6a"}],"answer":"C","solution":"选项A、 √3a，被开方数为3a，与√6a的被开方数不同，无法合并．选项 B、 6√a，被开方数为a,与√6a的被开方数不同，无法合并．选项C 、 √24a，化简 为√4 ⋅6a= √4 ⋅√6a= 2√6a，与√6a的被开方数均为6a，是同类二次根式，可以 合并．选项D 、√6a，被开方数为6，与√6a的被开方数不同，无法合并．故选C．","stem_html":"下列各式中，能与√6a合并的是（）
A. √3a
B. 6√a
C. √24a
D. √6a
","answer_html":"C","solution_html":"选项A、 √3a，被开方数为3a，与√6a的被开方数不同，无法合并．选项 B、 6√a，被开方数为a,与√6a的被开方数不同，无法合并．选项C 、 √24a，化简 为√4 ⋅6a= √4 ⋅√6a= 2√6a，与√6a的被开方数均为6a，是同类二次根式，可以 合并．选项D 、√6a，被开方数为6，与√6a的被开方数不同，无法合并．故选C．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:25:32"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:25:32"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:25:32"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T15:27:14"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:27:20"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:27:20"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:27:20"}],"detail_url":"/questions/182418","edit_url":"/questions/182418/edit","json_url":"/api/questions/182418","recheck_url":"/api/questions/182418/recheck"},{"id":182459,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_325.pdf","job_source":"数学-青岛版.zip","pages":[1,1],"stem":"(−3) + (+7) = ______","options":[],"answer":"","solution":"","stem_html":"(−3) + (+7) = ______
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:25:16"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:25:16"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:25:16"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T15:26:38"}],"detail_url":"/questions/182459","edit_url":"/questions/182459/edit","json_url":"/api/questions/182459","recheck_url":"/api/questions/182459/recheck"},{"id":182421,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_95_检测.pdf","job_source":"数学-沪教版.zip","pages":[2,2],"stem":"化简:\\(\\frac{(1)}{(2)}\\)√0.5； \\(\\sqrt{\\frac{1}{3}}\\)； （1）√4.5；","options":[],"answer":"(1) (2) (3)","solution":"2 3 2 √2 (1)原式 =\\(\\sqrt{\\frac{1}{2}}=√ \\frac{2}{4} =\\)； 2 √3 (2)原式 =\\(\\sqrt{\\frac{3}{9}}=\\)； 3 3√2 (3)原式 =\\(\\sqrt{\\frac{9}{2}}=√ \\frac{9 \\times 2}{2 \\times 2} =\\)； 2 2√3 2 −√2","stem_html":"化简:\\(\\frac{(1)}{(2)}\\)√0.5； \\(\\sqrt{\\frac{1}{3}}\\)；
（1）√4.5；
","answer_html":"(1) (2) (3)","solution_html":"2 3 2 √2 (1)原式 =\\(\\sqrt{\\frac{1}{2}}=√ \\frac{2}{4} =\\)； 2 √3 (2)原式 =\\(\\sqrt{\\frac{3}{9}}=\\)； 3 3√2 (3)原式 =\\(\\sqrt{\\frac{9}{2}}=√ \\frac{9 \\times 2}{2 \\times 2} =\\)； 2 2√3 2 −√2","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:22:59"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:22:59"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:22:59"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T15:24:36"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:24:53"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:24:53"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T15:24:53"}],"detail_url":"/questions/182421","edit_url":"/questions/182421/edit","json_url":"/api/questions/182421","recheck_url":"/api/questions/182421/recheck"},{"id":182422,"job_id":9,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_95_检测.pdf","job_source":"数学-沪教版.zip","pages":[2,2],"stem":"计算: 2 (1); √3 √2 −1 (2); √2","options":[],"answer":"(1) (2)","solution":"\\(\\frac{3}{2} 2√3 2√3 2\\)(1) = = ． √3\\(\\sqrt{3 \\times}\\)√3 3 √2 −1 √2(√2 −1) 2 −√2 = ． (2) = √2\\(\\sqrt{2 \\times}\\)√2 2\\(3x^{2}\\)√2y","stem_html":"计算: 2 (1); √3 √2 −1 (2); √2
","answer_html":"(1) (2)","solution_html":"\\(\\frac{3}{2} 2√3 2√3 2\\)(1) = = ． √3\\(\\sqrt{3 \\times}\\)√3 3 √2 −1 √2(√2 −1) 2 −√2 = ． (2) = √2\\(\\sqrt{2 \\times}\\)√2 2\\(3x^{2}\\)√2y","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:20:07"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:20:07"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:20:07"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T15:21:19"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-11-10T15:21:47"},{"type":"CRITIC","status":"FAIL","score":0.95,"created_at":"2026-11-10T15:21:47"},{"type":"SYMBOLIC","status":"PASS","score":0.9,"created_at":"2026-11-10T15:21:47"}],"detail_url":"/questions/182422","edit_url":"/questions/182422/edit","json_url":"/api/questions/182422","recheck_url":"/api/questions/182422/recheck"},{"id":182441,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_355_检测.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"已知y−4与x成正比，当x= 1时，y= 2．\\(\\frac{(1)}{(2)}\\)求y与x之间的函数关系式； 当x= −\\(\\frac{1}{2}\\)时，求函数y的值．","options":[],"answer":"(1)y = −2x + 4(2)5","solution":"(1)设y−4 =kx∵ 当x= 1时，y= 2∴ 2 −4 =k，解得k= −2∴ y−4= −2x, y与x之间的函数关系式为y = −2x + 4； (2)当x= −\\(\\frac{1}{2}\\)时，y= −\\(2 \\times (− \\frac{1}{2}) + 4 = 5．\\)","stem_html":"已知y−4与x成正比，当x= 1时，y= 2．\\(\\frac{(1)}{(2)}\\)求y与x之间的函数关系式； 当x= −\\(\\frac{1}{2}\\)时，求函数y的值．
","answer_html":"(1)y = −2x + 4(2)5","solution_html":"(1)设y−4 =kx∵ 当x= 1时，y= 2∴ 2 −4 =k，解得k= −2∴ y−4= −2x, y与x之间的函数关系式为y = −2x + 4； (2)当x= −\\(\\frac{1}{2}\\)时，y= −\\(2 \\times (− \\frac{1}{2}) + 4 = 5．\\)","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:19:05"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:19:05"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:19:05"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T15:19:54"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:20:20"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:20:20"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T15:20:20"}],"detail_url":"/questions/182441","edit_url":"/questions/182441/edit","json_url":"/api/questions/182441","recheck_url":"/api/questions/182441/recheck"},{"id":182439,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_355_检测.pdf","job_source":"数学-冀教版.zip","pages":[2,2],"stem":"已知y+ 1与x成正比例,当x= 3时,y=\\(5. \\frac{(1)}{(2)}\\)求出y与x的函数关系式； 设点(a, −2)在这个函数的图象上, 求a的值;","options":[],"answer":"(1)y= 2x−1；(2)a= −\\(\\frac{1}{2}\\)","solution":"由题意,设y+ 1 =kx,∵ 当 x= 3时,y= 5,∴ 5 + 1 = 3k,∴ k= 2,∴ y+ 1 = 2x,即 y= 2x−1;\\(\\frac{(1)}{(2)}\\)∵ 点(a, −2)在函数y= 2x−1的图象上,∴ −2 = 2a−1,∴ a= −\\(\\frac{1}{2}\\)","stem_html":"已知y+ 1与x成正比例,当x= 3时,y=\\(5. \\frac{(1)}{(2)}\\)求出y与x的函数关系式； 设点(a, −2)在这个函数的图象上, 求a的值;
","answer_html":"(1)y= 2x−1；(2)a= −\\(\\frac{1}{2}\\)","solution_html":"由题意,设y+ 1 =kx,∵ 当 x= 3时,y= 5,∴ 5 + 1 = 3k,∴ k= 2,∴ y+ 1 = 2x,即 y= 2x−1;\\(\\frac{(1)}{(2)}\\)∵ 点(a, −2)在函数y= 2x−1的图象上,∴ −2 = 2a−1,∴ a= −\\(\\frac{1}{2}\\)","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:18:38"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:18:38"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:18:38"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T15:19:17"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:19:47"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:19:47"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T15:19:47"}],"detail_url":"/questions/182439","edit_url":"/questions/182439/edit","json_url":"/api/questions/182439","recheck_url":"/api/questions/182439/recheck"},{"id":182440,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_355_检测.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"已知y+ 2与x−1成正比例,且当x= 3时,y=\\(2. \\frac{(1)}{(2)}\\)求y与x的函数解析式； 若点(2n −1, 6)在这个函数图象上, 求n的值.","options":[],"answer":"(1) y = 2x - 4(2) 3","solution":"(1)∵ y+ 2与x−1成正比例,∴ 设函数解析式为y+ 2 =k(x−1),整理得 :y= kx− k−2,∵ 当x= 3时,y= 2,∴ 3k− k−2 = 2,解得k= 2,∴ y与x的函数解析式为y= 2x−4; (2)代入点(2n−1, 6)到y= 2x−4,得2(2n−1) −4 = 6,解得n= 3,∴ n的值为3.","stem_html":"已知y+ 2与x−1成正比例,且当x= 3时,y=\\(2. \\frac{(1)}{(2)}\\)求y与x的函数解析式； 若点(2n −1, 6)在这个函数图象上, 求n的值.
","answer_html":"(1) y = 2x - 4(2) 3","solution_html":"(1)∵ y+ 2与x−1成正比例,∴ 设函数解析式为y+ 2 =k(x−1),整理得 :y= kx− k−2,∵ 当x= 3时,y= 2,∴ 3k− k−2 = 2,解得k= 2,∴ y与x的函数解析式为y= 2x−4; (2)代入点(2n−1, 6)到y= 2x−4,得2(2n−1) −4 = 6,解得n= 3,∴ n的值为3.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:15:28"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:15:28"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:15:28"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T15:17:24"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:19:04"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:19:04"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T15:19:04"}],"detail_url":"/questions/182440","edit_url":"/questions/182440/edit","json_url":"/api/questions/182440","recheck_url":"/api/questions/182440/recheck"},{"id":182419,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.775,"source_file":"沪教版/八下/周琼玟Q_18978751881_95_检测.pdf","job_source":"数学-沪教版.zip","pages":[2,2],"stem":"写出一个正整数\\(n\\)，使\\(\\sqrt{5n}\\)是最简二次根式，则\\(n\\)可以是 ____．","options":[],"answer":"1(答案不唯一)","solution":"当n= 1时，√5n= √5，√5是最简二次根式，故答案为：1(答案不唯一)．","stem_html":"写出一个正整数\\(n\\)，使\\(\\sqrt{5n}\\)是最简二次根式，则\\(n\\)可以是 ____．
","answer_html":"1(答案不唯一)","solution_html":"当n= 1时，√5n= √5，√5是最简二次根式，故答案为：1(答案不唯一)．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:12:01"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:12:01"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:12:01"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:13:01"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:13:01"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T15:13:08"},{"type":"SYMBOLIC","status":"PASS","score":0.9,"created_at":"2026-11-10T15:13:08"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T15:14:09"},{"type":"QUALITY_GATE","status":"FAIL","score":0.775,"created_at":"2026-11-10T15:14:09"}],"detail_url":"/questions/182419","edit_url":"/questions/182419/edit","json_url":"/api/questions/182419","recheck_url":"/api/questions/182419/recheck"},{"id":182436,"job_id":10,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.775,"source_file":"冀教版/八下/薛豪Q_18952688822_355_检测.pdf","job_source":"数学-冀教版.zip","pages":[2,2],"stem":"正比例函数y=\\(\\frac{1}{2}\\)x的图象大致是( ).","options":[],"answer":"B","solution":"根据题意，∵ 正比例函数为\\(y=\\frac{1}{2}x\\)，∴\\(k=\\frac{1}{2}>0\\)，∴ 图像经过第一、三象限，且图像靠近横轴；故选：B．","stem_html":"正比例函数y=\\(\\frac{1}{2}\\)x的图象大致是( ).
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/2b06312b-7e3f-494e-ae3e-21d10207fcf7/6da3e083-288b-4df6-9c48-5d9c7512d71e/65768c5afa9c.png\" "\\"点击查看原图\\"")
下列各组二次根式中，是同类二次根式的是( )
A. √8与\\(\\sqrt{\\frac{2}{3}}\\)
B. \\(\\frac{1}{2}\\)√12与\\(\\sqrt{\\frac{1}{3}}\\)
C. \\(3\\sqrt{5}\\)与\\(\\sqrt{15}\\)
D. \\(\\frac{1}{3}\\)√16与3√2
","answer_html":"B","solution_html":"√6 ．√8 = 2√2,\\(\\sqrt{\\frac{2}{3}}=\\)，因为化成最简二次根式以后被开方数不相同，所 A 3 以不是同类二次根式，故本选项不符合题意；B．\\(\\frac{1}{2}\\)√12 =\\(\\frac{1}{2} \\times 2√3=\\)√3 √3,\\(\\sqrt{\\frac{1}{3}}=\\)，因为化成最简二次根式以后被开方数相同，所以是同 3 类二次根式，故本选项符合题意；C．因为3√5和√15的被开方数不 相同，所以不是同类二次根式，故本选项不符合题意；D．\\(\\frac{1}{3}\\)√16=\\(\\frac{4}{3}\\)，因为化成最简二次根式以后被开方数不相同，所以不是同类二 次根式，故本选项不符合题意．故选：B．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:04:19"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:04:19"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:04:19"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:05:48"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:05:48"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T15:08:20"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:08:20"}],"detail_url":"/questions/182414","edit_url":"/questions/182414/edit","json_url":"/api/questions/182414","recheck_url":"/api/questions/182414/recheck"},{"id":182408,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_320.pdf","job_source":"数学-青岛版.zip","pages":[2,2],"stem":"大于−3.5而小于3的所有非正整数之和是____．","options":[],"answer":"","solution":"","stem_html":"大于−3.5而小于3的所有非正整数之和是____．
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:56:52"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:56:52"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:56:52"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T14:57:21"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:57:35"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:57:35"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T14:57:35"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T14:58:27"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T14:58:27"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-11-10T15:03:55"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-11-10T15:03:55"}],"detail_url":"/questions/182408","edit_url":"/questions/182408/edit","json_url":"/api/questions/182408","recheck_url":"/api/questions/182408/recheck"},{"id":182429,"job_id":10,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_355_检测.pdf","job_source":"数学-冀教版.zip","pages":[1,1],"stem":"函数y=\\(\\frac{1}{2}\\)x的图象经过( ). A. 第一、二象限 B. 第三、四象限 C. 第一、三象限 D. 第二、四象限","options":[{"label":"A","text":"第一、二象限"},{"label":"B","text":"第三、四象限"},{"label":"C","text":"第一、三象限"},{"label":"D","text":"第二、四象限"}],"answer":"C","solution":"因为\\(\\frac{1}{2} > 0\\),\\(\\therefore\\)正比例函数图象经过第一、三象限,故选 :C.","stem_html":"函数y=\\(\\frac{1}{2}\\)x的图象经过( ).
A. 第一、二象限
B. 第三、四象限
C. 第一、三象限
D. 第二、四象限
","answer_html":"C","solution_html":"因为\\(\\frac{1}{2} > 0\\),\\(\\therefore\\)正比例函数图象经过第一、三象限,故选 :C.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:03:27"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:03:27"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:03:27"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T15:04:51"}],"detail_url":"/questions/182429","edit_url":"/questions/182429/edit","json_url":"/api/questions/182429","recheck_url":"/api/questions/182429/recheck"},{"id":182413,"job_id":9,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_95_检测.pdf","job_source":"数学-沪教版.zip","pages":[1,1],"stem":"下列二次根式中，能与√3合并的是( ) A. √9 B. √3 2 C. √0.5 D. √27","options":[{"label":"A","text":"√9"},{"label":"B","text":"√3 2"},{"label":"C","text":"√0.5"},{"label":"D","text":"√27"}],"answer":"D","solution":"A 、 √9 = 3与√3不是同类二次根式，故不能与√3合并，不符合题意; √6 B、 \\(\\sqrt{\\frac{3}{2}}=\\)与√3不是同类二次根式，故不能与√3合并，不符合题 2 √2 意；C 、 √0.5 =\\(\\sqrt{\\frac{1}{2}}=\\)与√3不是同类二次根式，故不能与√3合并 2 ，不符合题意；D、 √27 = 3√3与√3是同类二次根式，故能与√3合并，符合题意；故选：D．","stem_html":"下列二次根式中，能与√3合并的是( )
A. √9
B. √3 2
C. √0.5
D. √27
","answer_html":"D","solution_html":"A 、 √9 = 3与√3不是同类二次根式，故不能与√3合并，不符合题意; √6 B、 \\(\\sqrt{\\frac{3}{2}}=\\)与√3不是同类二次根式，故不能与√3合并，不符合题 2 √2 意；C 、 √0.5 =\\(\\sqrt{\\frac{1}{2}}=\\)与√3不是同类二次根式，故不能与√3合并 2 ，不符合题意；D、 √27 = 3√3与√3是同类二次根式，故能与√3合并，符合题意；故选：D．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:03:07"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:03:07"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:03:07"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T15:06:59"}],"detail_url":"/questions/182413","edit_url":"/questions/182413/edit","json_url":"/api/questions/182413","recheck_url":"/api/questions/182413/recheck"},{"id":182410,"job_id":11,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_320.pdf","job_source":"数学-青岛版.zip","pages":[2,3],"stem":"有理数a, b在数轴上的位置如图所示，则下列关系式：(1)|a| > b，(2)a −b > 0，(3)a + b > 0， A. 1个 B. 2个 C. 3个 D. 4个 （1）b > −a > 0，(5)a < −b，其中正确的个数有( ).","options":[{"label":"A","text":"1个"},{"label":"B","text":"2个"},{"label":"C","text":"3个"},{"label":"D","text":"4个"}],"answer":"","solution":"","stem_html":"有理数a, b在数轴上的位置如图所示，则下列关系式：(1)|a| > b，(2)a −b > 0，(3)a + b > 0，
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/25691159-497d-4ce1-90b3-ac48b74c97f3/38b456e3-774d-4c30-8690-0a46b3359910/052ea22bb273.png\" "\\"点击查看原图\\"")
A. 1个
B. 2个
C. 3个
D. 4个
（1）b > −a > 0，(5)a < −b，其中正确的个数有( ).
某正比例函数\\(y=kx\\)经过二、四象限，写出一个满足条件的\\(k\\)的值 ________.
","answer_html":"－1(答案不唯一)","solution_html":"因为正比例函数\\(y=kx\\)经过二、四象限，\\therefore k<0\\(，\\therefore k=-1\\)（答案不唯一）","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:59:55"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:59:55"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:59:55"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:00:36"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:00:36"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T15:03:55"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T15:03:55"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T15:05:45"},{"type":"QUALITY_GATE","status":"FAIL","score":0.775,"created_at":"2026-11-10T15:05:45"}],"detail_url":"/questions/182434","edit_url":"/questions/182434/edit","json_url":"/api/questions/182434","recheck_url":"/api/questions/182434/recheck"},{"id":182412,"job_id":9,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_95_检测.pdf","job_source":"数学-沪教版.zip","pages":[1,1],"stem":"下列各组二次根式中，化简后可以合并的是（） A. √3与√32 B. √6与√12 C. √5与√75 D. √12与√27","options":[{"label":"A","text":"√3与√32"},{"label":"B","text":"√6与√12"},{"label":"C","text":"√5与√75"},{"label":"D","text":"√12与√27"}],"answer":"D","solution":"选项A、 √32 = 4√2，与√3不是同类二次根式，不可合并，则此项不符题意；选项 B、 √12 = 2√3，与√6不是同类二次根式，不可合并，则此项不符题意；选项 C 、 √75 = 5√3，与√5不是同类二次根式，不可合并，则此项不符题意；选项 D、 √12 = 2√3, √27 = 3√3，是同类二次根式，可以合并，则此项符合题意；故选：D．","stem_html":"下列各组二次根式中，化简后可以合并的是（）
A. √3与√32
B. √6与√12
C. √5与√75
D. √12与√27
","answer_html":"D","solution_html":"选项A、 √32 = 4√2，与√3不是同类二次根式，不可合并，则此项不符题意；选项 B、 √12 = 2√3，与√6不是同类二次根式，不可合并，则此项不符题意；选项 C 、 √75 = 5√3，与√5不是同类二次根式，不可合并，则此项不符题意；选项 D、 √12 = 2√3, √27 = 3√3，是同类二次根式，可以合并，则此项符合题意；故选：D．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T15:01:39"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T15:01:39"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T15:01:39"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T15:05:39"}],"detail_url":"/questions/182412","edit_url":"/questions/182412/edit","json_url":"/api/questions/182412","recheck_url":"/api/questions/182412/recheck"},{"id":182409,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"青岛版/七上/杜辉Q_18951362233_320.pdf","job_source":"数学-青岛版.zip","pages":[2,2],"stem":"大于−4.6而小于2.5的整数和为____.","options":[],"answer":"","solution":"","stem_html":"大于−4.6而小于2.5的整数和为____.
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:58:33"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:58:33"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:58:33"},{"type":"VISION","status":"PASS","score":0.8,"created_at":"2026-11-10T14:59:43"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T15:00:03"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T15:00:03"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T15:00:03"},{"type":"COHERENCE","status":"FAIL","score":1.0,"created_at":"2026-11-10T15:00:11"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-11-10T15:00:11"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.0,"created_at":"2026-11-10T15:04:46"}],"detail_url":"/questions/182409","edit_url":"/questions/182409/edit","json_url":"/api/questions/182409","recheck_url":"/api/questions/182409/recheck"},{"id":182406,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"青岛版/七上/杜辉Q_18951362233_320.pdf","job_source":"数学-青岛版.zip","pages":[2,2],"stem":"已知\\(|x| = 3\\)，\\(|y| = 5\\)，且$x > y ，则\\(3x - y\\)的值为 ________．","options":[],"answer":"","solution":"","stem_html":"已知\\(|x| = 3\\)，\\(|y| = 5\\)，且$x > y，则\\(3x - y\\)的值为 ________．
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:52:37"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:52:37"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:52:37"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T14:53:26"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:54:21"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:54:21"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T14:54:21"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T14:54:54"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-11-10T14:54:54"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.0,"created_at":"2026-11-10T15:00:46"}],"detail_url":"/questions/182406","edit_url":"/questions/182406/edit","json_url":"/api/questions/182406","recheck_url":"/api/questions/182406/recheck"},{"id":182402,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_320.pdf","job_source":"数学-青岛版.zip","pages":[2,2],"stem":"已知\\(|x|=2\\),\\(|y|=5\\), 且$x>y , 则\\(x+y\\)的值为_____.","options":[],"answer":"","solution":"| x |= 2,| y |= 5,\\(\\frac{因为}{所以}\\)x = 2, y = 5. y,\\(\\frac{因为}{所以}\\frac{x}{x} = 2\\)y = −5或x = −2, y = − 5. 当 = 2, y = −5时, x + y = 2 +（− 5）= −3；\\(\\frac{x}{x}\\)当 = −2, y = −5时, x + y = (−2) + (−5) = − 7. 故x + y = −3或 − 7.","stem_html":"已知\\(|x|=2\\),\\(|y|=5\\), 且$x>y, 则\\(x+y\\)的值为_____.
","answer_html":"","solution_html":"| x |= 2,| y |= 5,\\(\\frac{因为}{所以}\\)x = 2, y = 5. y,\\(\\frac{因为}{所以}\\frac{x}{x} = 2\\)y = −5或x = −2, y = − 5. 当 = 2, y = −5时, x + y = 2 +（− 5）= −3；\\(\\frac{x}{x}\\)当 = −2, y = −5时, x + y = (−2) + (−5) = − 7. 故x + y = −3或 − 7.","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:53:12"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:53:12"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:53:12"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T14:53:46"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-11-10T14:55:01"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:55:01"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T14:55:01"}],"detail_url":"/questions/182402","edit_url":"/questions/182402/edit","json_url":"/api/questions/182402","recheck_url":"/api/questions/182402/recheck"},{"id":182403,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_320.pdf","job_source":"数学-青岛版.zip","pages":[2,2],"stem":"在数轴上，点A, B 对应的有理数分别 . 为 −\\(\\frac{3}{2}\\)和\\(\\frac{13}{3}\\)，则A, B之间所有整数之和为_____","options":[],"answer":"","solution":"由题意得 A, B之间的所有整数为 −1,0,1,2,3,4,\\(\\frac{所以}{(1)}\\frac{AB}{01}\\), 之间的所有整数之和为 − + + + 2 + 3 + 4 = 9.","stem_html":"在数轴上，点A, B 对应的有理数分别 . 为 −\\(\\frac{3}{2}\\)和\\(\\frac{13}{3}\\)，则A, B之间所有整数之和为_____
","answer_html":"","solution_html":"由题意得 A, B之间的所有整数为 −1,0,1,2,3,4,\\(\\frac{所以}{(1)}\\frac{AB}{01}\\), 之间的所有整数之和为 − + + + 2 + 3 + 4 = 9.","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:49:52"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:49:52"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:49:52"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T14:50:29"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:52:52"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:52:52"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T14:52:52"}],"detail_url":"/questions/182403","edit_url":"/questions/182403/edit","json_url":"/api/questions/182403","recheck_url":"/api/questions/182403/recheck"},{"id":182365,"job_id":10,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_350.pdf","job_source":"数学-冀教版.zip","pages":[5,5],"stem":"已知y −3与x成正比例，且x = 4时，y = 7． （1）写出y与x之间的函数关系； （2）计算x = 9时，y的值.","options":[],"answer":"","solution":"","stem_html":"已知y −3与x成正比例，且x = 4时，y = 7．
（1）写出y与x之间的函数关系；
（2）计算x = 9时，y的值.
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-11-10T14:48:26"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:48:26"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:48:26"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T14:49:04"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:49:32"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:49:32"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T14:49:32"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T14:50:01"},{"type":"QUALITY_GATE","status":"FAIL","score":0.963,"created_at":"2026-11-10T14:50:01"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:52:00"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:52:00"}],"detail_url":"/questions/182365","edit_url":"/questions/182365/edit","json_url":"/api/questions/182365","recheck_url":"/api/questions/182365/recheck"},{"id":182381,"job_id":9,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_955_检测.pdf","job_source":"数学-沪教版.zip","pages":[4,4],"stem":"赤霉素(GA)是一类重要的植物激素，广泛参与种子萌发、茎的伸长及开花调控等 过程．为探究赤霉素对水稻幼苗茎伸长的促进作用，某生物兴趣小组将若干株长 势相近的水稻幼苗随机分为实验组与对照组实验组用100ppm赤霉素溶液处理，对 照组用等量蒸馏水处理，培养条件保持恒温25∘C、12小时光照／12小时黑暗循环。3 天后测量茎的伸长量，记录并绘制成如下统计图．实验组数据(单位：cm)整 理如下：18 (2株)、 20 (3株)、 22 (5株)、 24 (7株)、 26 (3株) .请 你根据统计图中的信息，解答下列问题：\\(\\frac{(1)}{(2)}\\)求实验组茎伸长量的平均值. 若用相同方法处理500株同品种水稻幼苗, 估计茎伸长量至少达到24cm的植株数量.","options":[],"answer":"(1)22.6cm(2)250","solution":"(1)−x =\\(\\frac{1}{20} \\times (18 \\times 2 + 20 \\times 3 + 22 \\times 5 + 24 \\times 7 + 26 \\times 3) = 22.6cm\\)答: 实验组茎伸长量的平均值为22.6cm． (2)\\(500 \\times \\frac{7 + 3}{20} = 250\\)(株)．答：估计茎伸长量至少达到24cm的植株数量为250．","stem_html":"赤霉素(GA)是一类重要的植物激素，广泛参与种子萌发、茎的伸长及开花调控等 过程．为探究赤霉素对水稻幼苗茎伸长的促进作用，某生物兴趣小组将若干株长 势相近的水稻幼苗随机分为实验组与对照组实验组用100ppm赤霉素溶液处理，对 照组用等量蒸馏水处理，培养条件保持恒温25∘C、12小时光照／12小时黑暗循环。3 天后测量茎的伸长量，记录并绘制成如下统计图．实验组数据(单位：cm)整 理如下：18 (2株)、 20 (3株)、 22 (5株)、 24 (7株)、 26 (3株) .请 你根据统计图中的信息，解答下列问题：\\(\\frac{(1)}{(2)}\\)求实验组茎伸长量的平均值. 若用相同方法处理500株同品种水稻幼苗, 估计茎伸长量至少达到24cm的植株数量.
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/ed6b1923-81e0-4899-a728-ed16abd9ea0f/c60d05ed07c7.png\" "\\"点击查看原图\\"")
在直角坐标系中, y随x的增大而减小的正比例函数y = kx的图象是( ).
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/a13a92c3-ebda-4a16-b969-9efbd0519d0d/bbc13dcd-2c12-4ef9-b0c4-9f35f2c12fe5/cc7f0663117c.png\" "\\"点击查看原图\\"")
为了掌握八年级数学考试卷的命题质量与难度系数，命题组教师赴外 地选取一个水平相当的八年级班级进行预测，将考试成绩分布情 况进行处理分析，制成频数分布表如下(成绩得分均为整数)：根据表中提供的信息解答下列问题：\\(\\frac{(1)}{(2)}\\)频数分布表中的a =____ ，b =____ ，c =____ ； 已知全区八年级共有200个班(平均每班40人)，用这份试卷检测，108分 及以上为优秀，预计优秀的人数约 ____人，72分及以上为及格，预计 及格的人数约为____ 人，及格的百分比约为____ ；
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/6e3477be-6d09-4353-b4fa-9e0359975b14/e1c87b77a8b6.png\" "\\"点击查看原图\\"")
（1）补充完整频数分布直方图.
用你认为最简单的方法画出下列函数的 图象． y = 5x\\(\\frac{(1)}{(2)}\\)y = −\\(\\frac{5}{2}\\)x
","answer_html":"(1) 过原点作斜率为5的直线；(2) 过原点作斜率为-2.5的直线","solution_html":"一次函数y=kx的图象是过原点的直线，k为斜率。当k>0时直线上升，k<0时直线下降。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.95,"created_at":"2026-11-10T14:34:50"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:34:50"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:34:50"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T14:36:13"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:36:29"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:36:29"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T14:36:29"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:38:00"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T14:38:00"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:39:34"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:39:34"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:41:27"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:41:27"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-11-10T14:41:27"},{"type":"AUTO_REPAIR","status":"PASS","score":1.0,"created_at":"2026-11-10T14:41:27"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T14:45:27"}],"detail_url":"/questions/182357","edit_url":"/questions/182357/edit","json_url":"/api/questions/182357","recheck_url":"/api/questions/182357/recheck"},{"id":182361,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"冀教版/八下/薛豪Q_18952688822_350.pdf","job_source":"数学-冀教版.zip","pages":[4,4],"stem":"1 1.如下图, 在同一平面直角坐标系内画出正比例函数\\(y_{1}\\)= − _{3}x与\\(y_{2}\\)= 3x的图象．","options":[],"answer":"","solution":"","stem_html":"1 1.如下图, 在同一平面直角坐标系内画出正比例函数\\(y_{1}\\)= − _{3}x与\\(y_{2}\\)= 3x的图象．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/1e9c334a-e4d7-46a8-9aa9-59c4bd9e4af3/f83de466094f.png\" "\\"点击查看原图\\"")
a = 2,a = ______
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:40:11"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:40:11"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:40:11"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T14:44:11"}],"detail_url":"/questions/182393","edit_url":"/questions/182393/edit","json_url":"/api/questions/182393","recheck_url":"/api/questions/182393/recheck"},{"id":182396,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_320.pdf","job_source":"数学-青岛版.zip","pages":[1,1],"stem":"最小的正整数是___________","options":[],"answer":"","solution":"","stem_html":"最小的正整数是___________
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:40:05"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:40:05"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:40:05"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T14:41:27"}],"detail_url":"/questions/182396","edit_url":"/questions/182396/edit","json_url":"/api/questions/182396","recheck_url":"/api/questions/182396/recheck"},{"id":182391,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.775,"source_file":"青岛版/七上/杜辉Q_18951362233_320.pdf","job_source":"数学-青岛版.zip","pages":[1,1],"stem":"(−7) + (+2) = ______","options":[],"answer":"-5","solution":"根据有理数加法法则：异号两数相加，取绝对值较大的加数的符号，并用较大的绝对值减去较小的绝对值。|−7|=7，|+2|=2，7>2，故结果符号为负，数值为7−2=5，因此(−7)+( +2)=−5.","stem_html":"(−7) + (+2) = ______
","answer_html":"-5","solution_html":"根据有理数加法法则：异号两数相加，取绝对值较大的加数的符号，并用较大的绝对值减去较小的绝对值。|−7|=7，|+2|=2，7>2，故结果符号为负，数值为7−2=5，因此(−7)+( +2)=−5.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:35:40"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:35:40"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:35:40"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:39:22"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:39:22"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T14:39:40"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:39:40"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T14:42:59"},{"type":"QUALITY_GATE","status":"FAIL","score":0.775,"created_at":"2026-11-10T14:42:59"}],"detail_url":"/questions/182391","edit_url":"/questions/182391/edit","json_url":"/api/questions/182391","recheck_url":"/api/questions/182391/recheck"},{"id":182364,"job_id":10,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_350.pdf","job_source":"数学-冀教版.zip","pages":[5,5],"stem":"关于函数y = −7x, 下列结论正确的是( ). A. 当x > 0时, y < 0 B. y随x的增大而增大 C. 图象经过第一、三象限 D. 图象经过点(2, −7)","options":[{"label":"A","text":"当x > 0时, y < 0"},{"label":"B","text":"y随x的增大而增大"},{"label":"C","text":"图象经过第一、三象限"},{"label":"D","text":"图象经过点(2, −7)"}],"answer":"","solution":"","stem_html":"关于函数y = −7x, 下列结论正确的是( ).
A. 当x > 0时, y < 0
B. y随x的增大而增大
C. 图象经过第一、三象限
D. 图象经过点(2, −7)
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:38:31"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:38:31"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:38:31"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T14:42:31"}],"detail_url":"/questions/182364","edit_url":"/questions/182364/edit","json_url":"/api/questions/182364","recheck_url":"/api/questions/182364/recheck"},{"id":182363,"job_id":10,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_350.pdf","job_source":"数学-冀教版.zip","pages":[5,5],"stem":"关于函数y = −7x，下列结论正确的是( ). A. 当x > 0时，y < 0 B. y随x的增大而增大 C. 图象经过第一、三象限 D. 图象经过点(2, −7)","options":[{"label":"A","text":"当x > 0时，y < 0"},{"label":"B","text":"y随x的增大而增大"},{"label":"C","text":"图象经过第一、三象限"},{"label":"D","text":"图象经过点(2, −7)"}],"answer":"","solution":"","stem_html":"关于函数y = −7x，下列结论正确的是( ).
A. 当x > 0时，y < 0
B. y随x的增大而增大
C. 图象经过第一、三象限
D. 图象经过点(2, −7)
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:38:06"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:38:06"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:38:06"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T14:39:10"}],"detail_url":"/questions/182363","edit_url":"/questions/182363/edit","json_url":"/api/questions/182363","recheck_url":"/api/questions/182363/recheck"},{"id":182379,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_955_检测.pdf","job_source":"数学-沪教版.zip","pages":[3,3],"stem":"为了解某区七年级学生体育成绩(成绩均为整数，单位：分)，随机抽 取了部分学生的体育成绩并分段(A：20．5 −22．5；B：22．5 −24．5；C：24．5−26.5 ；D: 26.5 −28.5;E : 28.5 −30.5)统计如下：根据上面提供的信息，回答下列问题：\\(\\frac{(1)}{(2)}\\)在统计表中，a =____ ，b =____ ； 请将统计图补充完整； （1）若成绩在25分以上(含25分)定为良好，则该区今年12000名七年级学 生中体育成绩为良好的学生人数约有多少？","options":[],"answer":"时间不少于4小时的人数为780人．","solution":"(1)0．15，60；(2)见解析(3)约有9600人.\\(\\frac{36}{240} = 0.15\\)，b=\\(240 \\times 0.25=\\)(1)抽取样本的容量 = 12 ÷ 0.05 = 240，所以a= 60 (人), 故答案为：0.15, 60； 根据(1)补图如下：\\(\\frac{(2)}{(3)} 12000 \\times (0.35 + 0.25 + 0.2) = 9600\\)(人)所以该区今年12000名七年级学生中 体育成绩为良好的学生人数约有9600人．","stem_html":"为了解某区七年级学生体育成绩(成绩均为整数，单位：分)，随机抽 取了部分学生的体育成绩并分段(A：20．5 −22．5；B：22．5 −24．5；C：24．5−26.5 ；D: 26.5 −28.5;E : 28.5 −30.5)统计如下：根据上面提供的信息，回答下列问题：\\(\\frac{(1)}{(2)}\\)在统计表中，a =____ ，b =____ ； 请将统计图补充完整；
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/69fb2218-984b-4854-99aa-95a770373349/485b47cfd933.png\" "\\"点击查看原图\\"")
（1）若成绩在25分以上(含25分)定为良好，则该区今年12000名七年级学 生中体育成绩为良好的学生人数约有多少？
【小试2】 已知正比例函数的解析式为 y =\\(x _{7}\\), 下列结论正确的是( ).
A. 图象是一条线段
B. 图象必经过点(−1,6)
C. 图象经过第一、三象限
D. y随x的增大而减小
","answer_html":"C","solution_html":"A、正比例函数 y = x\\(1 _{7}\\), 图象是一条直线, 不符合题意; B、当x = −1时, y=− _{7}, 图象不经过点(−1,6), 不符合题意; C、k = 1\\(1 _{7}\\)> 0, 图象经过第一、三象限, 符合题意; D、k = _{7}> 0, y随x的增大而增大, 不符合题意. 故选: C．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:37:21"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:37:21"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:37:21"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T14:40:54"}],"detail_url":"/questions/182360","edit_url":"/questions/182360/edit","json_url":"/api/questions/182360","recheck_url":"/api/questions/182360/recheck"},{"id":182377,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_955_检测.pdf","job_source":"数学-沪教版.zip","pages":[2,2],"stem":"某校为了解八年级全体学生生物实验操作的情况，随机抽取了30名 学生的生物实验操作考核成绩，并将数据进行整理，分析如下 (说明：考核成绩均取整数，A级：10分，B级：9分，C级：8分，D级 ：7分及以下)：收集整理数据，并绘制统计表(如下)：根据表中信息，解答下列问题： （1）统计表中，a=____，b=____．\\(\\frac{(2)}{(3)}\\)求这30名学生生物实验操作考核的平均成绩． 若成绩不低于9分为优秀，该校八年级参加生物实验操作考核成绩 达到优秀的有420名，试估计该校有多少名学生参加生物实验操作考核？","options":[],"answer":"(1)11，6；(2)8.8；(3)该校有600名学生参加生物实验操作考核．","solution":"\\(\\frac{(1)}{(2)} 10 \\times 10 + 11 \\times 9 + 6 \\times 8 + 5 + 6 + 6\\)由收集的数据可知：a = 11, b = 6；故答案为：11, 6； 这30名学生的平均成绩为： = 8.8(分) 30 (3)设该校有x名学生参加生物实验操作，由题意，得：x⋅\\(\\frac{10 + 11}{30} = 420\\)，解得：x = 600；答：该校有600名学生参加生物实验操作考核．","stem_html":"某校为了解八年级全体学生生物实验操作的情况，随机抽取了30名 学生的生物实验操作考核成绩，并将数据进行整理，分析如下 (说明：考核成绩均取整数，A级：10分，B级：9分，C级：8分，D级 ：7分及以下)：收集整理数据，并绘制统计表(如下)：根据表中信息，解答下列问题：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/65c78321-3114-4a6d-b8f1-0b8a3cadfde2/abae687b5a9c.png\" "\\"点击查看原图\\"")
（1）统计表中，a=____，b=____．\\(\\frac{(2)}{(3)}\\)求这30名学生生物实验操作考核的平均成绩． 若成绩不低于9分为优秀，该校八年级参加生物实验操作考核成绩 达到优秀的有420名，试估计该校有多少名学生参加生物实验操作考核？
当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x}\\)且随的增大而____
","answer_html":"第二、四；减小","solution_html":"根据正比例函数性质：当k<0时，图象经过第二、四象限，且y随x的增大而减小。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:29:17"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:29:17"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:29:17"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:31:11"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:31:11"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T14:33:01"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:33:01"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:34:33"},{"type":"QUALITY_GATE","status":"PASS","score":0.925,"created_at":"2026-11-10T14:34:33"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:36:22"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:36:22"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-11-10T14:36:22"},{"type":"AUTO_FILL_ANSWER","status":"WARN","score":1.0,"created_at":"2026-11-10T14:36:22"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T14:40:22"}],"detail_url":"/questions/182354","edit_url":"/questions/182354/edit","json_url":"/api/questions/182354","recheck_url":"/api/questions/182354/recheck"},{"id":182392,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_320.pdf","job_source":"数学-青岛版.zip","pages":[1,1],"stem":"最小的正整数是___________","options":[],"answer":"","solution":"","stem_html":"最小的正整数是___________
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:35:40"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:35:40"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:35:40"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T14:39:40"}],"detail_url":"/questions/182392","edit_url":"/questions/182392/edit","json_url":"/api/questions/182392","recheck_url":"/api/questions/182392/recheck"},{"id":182378,"job_id":9,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_955_检测.pdf","job_source":"数学-沪教版.zip","pages":[3,3],"stem":"某校为了解学生一周课外阅读情况，随机抽取部分学生调查了他们 一周课外阅读时间，并将数据进行整理制成如下统计图．请根据图中提供的信息，解答以下问题：\\(\\frac{(1)}{(3)}\\)抽查的这些学生一周平均的课外阅读时间是多少小时？ 该校共有2400个学生，根据统计，估计该校学生一周课外阅读时间不少于4小时的人数． 解答题，第一题8分，第二题10分，第三题10分","options":[],"answer":"(1)3小时；(2)780人","solution":"\\(1 \\times 4 + 2 \\times 8 + 3 \\times 15 + 4 \\times 10 + 5 \\times 3 = 3\\)(小时)答：抽查的这些学生一","stem_html":"某校为了解学生一周课外阅读情况，随机抽取部分学生调查了他们 一周课外阅读时间，并将数据进行整理制成如下统计图．请根据图中提供的信息，解答以下问题：\\(\\frac{(1)}{(3)}\\)抽查的这些学生一周平均的课外阅读时间是多少小时？ 该校共有2400个学生，根据统计，估计该校学生一周课外阅读时间不少于4小时的人数． 解答题，第一题8分，第二题10分，第三题10分
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/b5d832e1-b096-4a03-b385-a6b36c3619d5/7917ca78f2b7.png\" "\\"点击查看原图\\"")
关于正比例函数y = −4x,下列说法错误 的是( ). A ．图象经过原点 B ．图象经过第二、四象限 C ．随的增大而减小yx D ．点(1,4)在函数图象上
","answer_html":"","solution_html":" 正比例函数 = −4x,它的图象经过第\\(\\frac{y}{y}\\)二、四象限, 随的增大而减小故选项、x, B C 正确但不符合题意,; 当x = 0时, y = 0,图象经过原点故选项, A 正确但不符合题意,; 当x =1时, y = −4,点(1,−4)在函数图象上, 故选项错误符合题意,; D 故选 : ． D","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:34:30"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:34:30"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:34:30"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T14:38:31"}],"detail_url":"/questions/182358","edit_url":"/questions/182358/edit","json_url":"/api/questions/182358","recheck_url":"/api/questions/182358/recheck"},{"id":182388,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_320.pdf","job_source":"数学-青岛版.zip","pages":[1,1],"stem":"(_{4)}− + (−2) = ________","options":[],"answer":"","solution":"","stem_html":"(_{4)}− + (−2) = ________
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:31:40"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:31:40"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:31:40"},{"type":"VISION","status":"PASS","score":0.8,"created_at":"2026-11-10T14:33:09"}],"detail_url":"/questions/182388","edit_url":"/questions/182388/edit","json_url":"/api/questions/182388","recheck_url":"/api/questions/182388/recheck"},{"id":182376,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_955_检测.pdf","job_source":"数学-沪教版.zip","pages":[2,2],"stem":"如图所示为根据某市某天六个整点时刻的温度绘制成的折线统计图 ，则这六个整点时刻温度的中位数是____∘C.","options":[],"answer":"15.6","solution":"这六个数据从小到大排列为：4.5, 10.5, 15.3, 15.9, 19.6, 30.1，居于中间的两个数为15.3, 15.9，∴ 中位数为\\(\\frac{15.3 + 15.9}{2} = 15.6\\)，故答案为：15.6．","stem_html":"如图所示为根据某市某天六个整点时刻的温度绘制成的折线统计图 ，则这六个整点时刻温度的中位数是____∘C.
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/7333fabe-9762-463c-8ebc-85737409780c/a441230a5b76.png\" "\\"点击查看原图\\"")
在某中学组织举办的＂唐风宋韵＂诗词大赛中，九年级参赛的25名 同学的成绩情况如统计图所示，这些成绩(分)的中位数是____ ． 填空题，每题6分
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/0d1c350c-73c6-48d0-8075-d52e9a3f459b/a4a393b54987.png\" "\\"点击查看原图\\"")
当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x}\\)且随的增大而____
","answer_html":"一、三；增大","solution_html":"根据正比例函数性质：当k>0时，图象经过第一、三象限，且y随x的增大而增大。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:26:28"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:26:28"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:26:28"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T14:27:52"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:28:01"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:28:01"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:28:01"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:28:49"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-11-10T14:28:49"}],"detail_url":"/questions/182351","edit_url":"/questions/182351/edit","json_url":"/api/questions/182351","recheck_url":"/api/questions/182351/recheck"},{"id":182369,"job_id":9,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.975,"source_file":"沪教版/八下/周琼玟Q_18978751881_955_检测.pdf","job_source":"数学-沪教版.zip","pages":[1,1],"stem":"已知一组数据8, 1, 4, 6, 8，则这组数据的中位数是( ) A. \\(\\frac{1}{4}\\) B. C. 6 D. 8","options":[{"label":"A","text":"\\frac{1}{4}"},{"label":"B","text":""},{"label":"C","text":"6"},{"label":"D","text":"8"}],"answer":"C","solution":"将这组数据从小到大排列为1, 4, 6, 8, 8，位于正中间的数为6， ∴ 这组数据的中位数是6．故选：C","stem_html":"已知一组数据8, 1, 4, 6, 8，则这组数据的中位数是( )
A. \\(\\frac{1}{4}\\)
B.
C. 6
D. 8
","answer_html":"C","solution_html":"将这组数据从小到大排列为1, 4, 6, 8, 8，位于正中间的数为6， ∴ 这组数据的中位数是6．故选：C","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:25:44"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:25:44"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:25:44"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T14:27:29"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:27:38"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:27:38"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:27:38"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T14:28:24"},{"type":"QUALITY_GATE","status":"PASS","score":0.975,"created_at":"2026-11-10T14:28:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:33:12"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:48:45"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:04:17"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:19:50"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:35:23"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:50:55"}],"detail_url":"/questions/182369","edit_url":"/questions/182369/edit","json_url":"/api/questions/182369","recheck_url":"/api/questions/182369/recheck"},{"id":182329,"job_id":11,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_315_检测.pdf","job_source":"数学-青岛版.zip","pages":[3,3],"stem":"计算：\\(\\frac{(1)}{(2)} (−15) + 18\\)； (−5.1) + (−3.7)； （1）(−\\(4 \\frac{1}{3}\\)) + (\\(+2 \\frac{1}{3}\\))； （2）\\(\\frac{5}{6} + (− \\frac{5}{6})\\)； (−1.75) + (+\\(\\frac{1}{4}\\))；\\(\\frac{(5)}{(6)} (−8) + 0．\\)","options":[],"answer":"(−15) + 18 = 3；","solution":"\\(\\frac{(1)}{(2)} (−5.1) + (−3.7) =\\)−(5.1 + 3.7) = −8.8； (3)(−\\(4 \\frac{1}{3}\\)) + (\\(+2 \\frac{1}{3}\\)) = −4 + 2 = −2； (4)\\(\\frac{5}{6} + (− \\frac{5}{6}) = 0\\)； (−1.75) + (+\\(\\frac{1}{4}\\)) = −\\(\\frac{7}{4} + \\frac{1}{4} =\\)−\\(\\frac{3}{2}\\)；\\(\\frac{(5)}{(6)} (−8) + 0 =\\)−8．","stem_html":"计算：\\(\\frac{(1)}{(2)} (−15) + 18\\)； (−5.1) + (−3.7)；
（1）(−\\(4 \\frac{1}{3}\\)) + (\\(+2 \\frac{1}{3}\\))；
（2）\\(\\frac{5}{6} + (− \\frac{5}{6})\\)； (−1.75) + (+\\(\\frac{1}{4}\\))；\\(\\frac{(5)}{(6)} (−8) + 0．\\)
","answer_html":"(−15) + 18 = 3；","solution_html":"\\(\\frac{(1)}{(2)} (−5.1) + (−3.7) =\\)−(5.1 + 3.7) = −8.8； (3)(−\\(4 \\frac{1}{3}\\)) + (\\(+2 \\frac{1}{3}\\)) = −4 + 2 = −2； (4)\\(\\frac{5}{6} + (− \\frac{5}{6}) = 0\\)； (−1.75) + (+\\(\\frac{1}{4}\\)) = −\\(\\frac{7}{4} + \\frac{1}{4} =\\)−\\(\\frac{3}{2}\\)；\\(\\frac{(5)}{(6)} (−8) + 0 =\\)−8．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:22:40"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:22:40"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:22:40"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T14:24:04"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:24:15"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:24:15"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T14:24:15"}],"detail_url":"/questions/182329","edit_url":"/questions/182329/edit","json_url":"/api/questions/182329","recheck_url":"/api/questions/182329/recheck"},{"id":182371,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_955_检测.pdf","job_source":"数学-沪教版.zip","pages":[1,1],"stem":"某班50名学生的年龄情况如下表所示(单位：岁)，则该班学生年龄的中位数为 ____.","options":[],"answer":"15","solution":"由总人数为50，可知该班学生年龄的中位数为从小到大排列后的第25和 26个学生年龄的平均数，由表可知，从小到大排列后的第25和26个学 生年龄都是15，平均数是15，故该班学生年龄的中位数为15，故答案为：15．","stem_html":"某班50名学生的年龄情况如下表所示(单位：岁)，则该班学生年龄的中位数为 ____.
","answer_html":"15","solution_html":"由总人数为50，可知该班学生年龄的中位数为从小到大排列后的第25和 26个学生年龄的平均数，由表可知，从小到大排列后的第25和26个学 生年龄都是15，平均数是15，故该班学生年龄的中位数为15，故答案为：15．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:22:42"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:22:42"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:22:42"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T14:23:43"}],"detail_url":"/questions/182371","edit_url":"/questions/182371/edit","json_url":"/api/questions/182371","recheck_url":"/api/questions/182371/recheck"},{"id":182330,"job_id":11,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_315_检测.pdf","job_source":"数学-青岛版.zip","pages":[3,5],"stem":"计算(1)(−5) + (−2)；\\(\\frac{(2)}{(3)} (+4) + (−8)\\)； 0 + (−6)；\\(\\frac{(4)}{(5)} (+13) + (−2)\\)； (−\\(\\frac{1}{2}\\)) + (+\\(\\frac{1}{4}\\))； AI智适化学案 学案ID:D10710315089 （1）(−\\(\\frac{1}{3}\\)) + (−\\(\\frac{1}{3}\\))．","options":[],"answer":"原式= −(5 + 2) = −7；","solution":"\\(\\frac{(1)}{(2)}\\)原式= −(8 −4) = −4;\\(\\frac{(3)}{(4)}\\)原式= −6； 原式= +(13 −2) = 11； (5)原式 = −(\\(\\frac{1}{2}\\)−\\(\\frac{1}{4}\\)) = −\\(\\frac{1}{4}\\)； (6)原式 = −（\\(\\frac{1}{3} + \\frac{1}{3}） =\\)−\\(\\frac{2}{3}\\)","stem_html":"计算(1)(−5) + (−2)；\\(\\frac{(2)}{(3)} (+4) + (−8)\\)； 0 + (−6)；\\(\\frac{(4)}{(5)} (+13) + (−2)\\)； (−\\(\\frac{1}{2}\\)) + (+\\(\\frac{1}{4}\\))； AI智适化学案 学案ID:D10710315089
（1）(−\\(\\frac{1}{3}\\)) + (−\\(\\frac{1}{3}\\))．
","answer_html":"原式= −(5 + 2) = −7；","solution_html":"\\(\\frac{(1)}{(2)}\\)原式= −(8 −4) = −4;\\(\\frac{(3)}{(4)}\\)原式= −6； 原式= +(13 −2) = 11； (5)原式 = −(\\(\\frac{1}{2}\\)−\\(\\frac{1}{4}\\)) = −\\(\\frac{1}{4}\\)； (6)原式 = −（\\(\\frac{1}{3} + \\frac{1}{3}） =\\)−\\(\\frac{2}{3}\\)","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:20:35"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:20:35"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:20:35"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T14:21:57"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:22:08"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:22:08"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T14:22:08"}],"detail_url":"/questions/182330","edit_url":"/questions/182330/edit","json_url":"/api/questions/182330","recheck_url":"/api/questions/182330/recheck"},{"id":182344,"job_id":10,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_350.pdf","job_source":"数学-冀教版.zip","pages":[1,1],"stem":"当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x}\\)且随的增大而____","options":[],"answer":"","solution":"","stem_html":"当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x}\\)且随的增大而____
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:20:35"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:20:35"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:20:35"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T14:21:47"}],"detail_url":"/questions/182344","edit_url":"/questions/182344/edit","json_url":"/api/questions/182344","recheck_url":"/api/questions/182344/recheck"},{"id":182340,"job_id":10,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"冀教版/八下/薛豪Q_18952688822_350.pdf","job_source":"数学-冀教版.zip","pages":[1,1],"stem":"当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x}\\)且随的增大而____","options":[],"answer":"一、三；增大","solution":"根据正比例函数性质：当k>0时，图象经过第一、三象限，且y随x的增大而增大。","stem_html":"当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x}\\)且随的增大而____
","answer_html":"一、三；增大","solution_html":"根据正比例函数性质：当k>0时，图象经过第一、三象限，且y随x的增大而增大。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:21:19"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:21:19"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:21:19"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:22:03"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:22:03"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T14:22:55"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:22:55"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:24:01"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-11-10T14:24:01"}],"detail_url":"/questions/182340","edit_url":"/questions/182340/edit","json_url":"/api/questions/182340","recheck_url":"/api/questions/182340/recheck"},{"id":182312,"job_id":9,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_950.pdf","job_source":"数学-沪教版.zip","pages":[3,3],"stem":"近些年来随着人们健康意识的增强，马拉松逐渐成为大家喜爱的 运动．下表是某地举办的一次马拉松比赛中，共100名队员跑完全程的用时统计表. 则这100名队员跑完全程所用时间的中位数应落在( ) A. 3 −3.5小时 B. 3.5 −4小时 C. 4 −4.5小时 D. 4.5 −5小时","options":[{"label":"A","text":"3 −3.5小时"},{"label":"B","text":"3.5 −4小时"},{"label":"C","text":"4 −4.5小时"},{"label":"D","text":"4.5 −5小时"}],"answer":"","solution":"","stem_html":"近些年来随着人们健康意识的增强，马拉松逐渐成为大家喜爱的 运动．下表是某地举办的一次马拉松比赛中，共100名队员跑完全程的用时统计表. 则这100名队员跑完全程所用时间的中位数应落在( )
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/a103e394-2906-40bd-8874-e1295b04c0ef/85e759b3c19b.png\" "\\"点击查看原图\\"")
A. 3 −3.5小时
B. 3.5 −4小时
C. 4 −4.5小时
D. 4.5 −5小时
直接写出计算结果\\(\\frac{(5)}{(6)} (−3)\\)−(−7) =____; (−\\(3 \\frac{1}{2}\\)) −\\(5 \\frac{1}{4} =\\)____. 解答题，第一题8分，第二题10分，第三题10分
（1）(−3) + (−9) =____;\\(\\frac{(2)}{(3)}12 + (−4) =____, (−2) + 5 =\\)____
（2）(−\\(\\frac{1}{2}\\)) + (+\\(\\frac{1}{2}\\)) =____;
","answer_html":"(1)－12(2)8(3)3(4)0(5)4(6) −8 3","solution_html":"4 (1)(−3) + (−9) = −\\(12 \\frac{(2)}{(3)}12 + (−4) = 8 (−2) + 5 = 3 (− \\frac{1}{2}) + (+ \\frac{1}{2}) = 0\\)；\\(\\frac{(4)}{(5)} (−3)\\)−(−7) = −3 + 7 = 4 (6)(−\\(3 \\frac{1}{2}\\)) −\\(5 \\frac{1}{4} =\\)−\\(3 \\frac{2}{4}\\)−\\(5 \\frac{1}{4} =\\)−\\(8 \\frac{3}{4}\\).","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:16:08"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:16:08"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:16:08"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T14:17:35"}],"detail_url":"/questions/182327","edit_url":"/questions/182327/edit","json_url":"/api/questions/182327","recheck_url":"/api/questions/182327/recheck"},{"id":182284,"job_id":10,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_345.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"已知y −3与2x −1成正比例，且当x = 1时，y = 6． （1）求y与x之间的函数解析式． （2）当x = 2时，求y的值.","options":[],"answer":"","solution":"","stem_html":"已知y −3与2x −1成正比例，且当x = 1时，y = 6．
（1）求y与x之间的函数解析式．
（2）当x = 2时，求y的值.
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-11-10T13:58:20"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T13:58:20"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:58:20"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T13:59:00"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-11-10T14:02:11"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-11-10T14:02:11"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T14:02:11"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T14:05:20"},{"type":"QUALITY_GATE","status":"FAIL","score":0.963,"created_at":"2026-11-10T14:05:20"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:11:58"},{"type":"CRITIC","status":"FAIL","score":1.0,"created_at":"2026-11-10T14:11:58"}],"detail_url":"/questions/182284","edit_url":"/questions/182284/edit","json_url":"/api/questions/182284","recheck_url":"/api/questions/182284/recheck"},{"id":182328,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_315_检测.pdf","job_source":"数学-青岛版.zip","pages":[3,3],"stem":"计算：\\(\\frac{(1)}{(2)}−3 + 2 =______; (−2.5) + (−1.5) =\\)____.\\(\\frac{(3)}{(4)}0 + (−5) =______; (−43) + (+43) =\\)____.","options":[],"answer":"(1)－1(2) −4(3) −5(4)0","solution":"\\(\\frac{(1)}{(2)}\\)原式= -(3 -2) = -1故答案为：-1； 原式= -(2.5 + 1.5) = -4故答案为：-4；\\(\\frac{(3)}{(4)}\\)原式= -5故答案为：-5； 原式= 0故答案为：0．","stem_html":"计算：\\(\\frac{(1)}{(2)}−3 + 2 =______; (−2.5) + (−1.5) =\\)____.\\(\\frac{(3)}{(4)}0 + (−5) =______; (−43) + (+43) =\\)____.
","answer_html":"(1)－1(2) −4(3) −5(4)0","solution_html":"\\(\\frac{(1)}{(2)}\\)原式= -(3 -2) = -1故答案为：-1； 原式= -(2.5 + 1.5) = -4故答案为：-4；\\(\\frac{(3)}{(4)}\\)原式= -5故答案为：-5； 原式= 0故答案为：0．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:09:16"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:09:16"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:09:16"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:10:33"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:10:33"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T14:11:10"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T14:11:10"}],"detail_url":"/questions/182328","edit_url":"/questions/182328/edit","json_url":"/api/questions/182328","recheck_url":"/api/questions/182328/recheck"},{"id":182315,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_950.pdf","job_source":"数学-沪教版.zip","pages":[4,5],"stem":"某校为了解＂世界读书日＂主题活动开展情况，对本学期开学以来 学生课外读书情况进行了随机抽样调查，所抽取的12名学生课外读书数量(单位：本) 数据如下：2, 4, 5, 4, 3, 5, 3, 4, 1, 3, 2, 4. 6.2022年3月以来，受全国新冠疫情的影响，椒江区教育系统积极响应区 委区政府的号召，组织了1896名教师志愿者助力区域核酸检测的防 疫工作．教师们放下粉笔，穿上＂新装＂，化身社区里的＂红马甲 ＂、＂大白＂身边的＂小蓝＂，在＂疫＂线绽放别样光芒．为了了 解这些教师志愿者在3月份至5月份期间参加防疫工作的时间情况，随 机抽取了其中的50名教师志愿者进行问卷调查，并对数据进行了整 理和描述，部分信息如下图表：防疫时间的频数分布表请根据所给信息，解答下列问题： （1）补全学生课外读书数量条形统计图； （2）求本次所抽取学生课外读书数量的平均数； （3）该校有600名学生，请根据抽样调查的结果，估计本学期开学以来 课外读书数量不少于3本的学生人数. （4）a = ____，b = ____； （5）请补全频数分布直方图； （6）请估计这1896名教师志愿者中，3月份至5月份期间参加防疫工作的时 间不低于10小时的约有多少人(结果精确到个位)？","options":[],"answer":"","solution":"","stem_html":"某校为了解＂世界读书日＂主题活动开展情况，对本学期开学以来 学生课外读书情况进行了随机抽样调查，所抽取的12名学生课外读书数量(单位：本) 数据如下：2, 4, 5, 4, 3, 5, 3, 4, 1, 3, 2, 4. 6.2022年3月以来，受全国新冠疫情的影响，椒江区教育系统积极响应区 委区政府的号召，组织了1896名教师志愿者助力区域核酸检测的防 疫工作．教师们放下粉笔，穿上＂新装＂，化身社区里的＂红马甲 ＂、＂大白＂身边的＂小蓝＂，在＂疫＂线绽放别样光芒．为了了 解这些教师志愿者在3月份至5月份期间参加防疫工作的时间情况，随 机抽取了其中的50名教师志愿者进行问卷调查，并对数据进行了整 理和描述，部分信息如下图表：防疫时间的频数分布表请根据所给信息，解答下列问题：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/8728f64b-cc8b-44dd-8259-4971b4276558/e9e02e48168a.png\" "\\"点击查看原图\\"")
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/8728f64b-cc8b-44dd-8259-4971b4276558/535bae2c4fa2.png\" "\\"点击查看原图\\"")
（1）补全学生课外读书数量条形统计图；
（2）求本次所抽取学生课外读书数量的平均数；
（3）该校有600名学生，请根据抽样调查的结果，估计本学期开学以来 课外读书数量不少于3本的学生人数.
（4）a = ____，b = ____；
（5）请补全频数分布直方图；
（6）请估计这1896名教师志愿者中，3月份至5月份期间参加防疫工作的时 间不低于10小时的约有多少人(结果精确到个位)？
在某次射击训练中，一位选手的10次射击 成绩单位：环如图所示，则该选手的这() 10次射击成绩的中位数是 ____ 环.
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/f1590cb9-812b-41f0-a1a8-a8cb2a8c73af/fcf30fc7-ac61-4a2d-b6b0-a7708752a1f8/188334137cdd.png\" "\\"点击查看原图\\"")
为了解某班学生一周内做家务所用的时间，将其中25名学生的统计 结果绘制成如图所示的条形统计图，则这25名同学一周内做家务时间的中位数是____h． 3.2025年1月，中共中央、国务院印发《教育强国建设规划纲要(2024－2035年 )》，其中就提出了中小学生每天综合体育活动时间不低于2小时的要求. 某校为了解学生的综合体育活动情况，对部分学生在一 周内的综合体育活动时间统计如下表：则这些学生的综合体育活动时间的众数是____h．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/40085334-6d61-4bca-a6c2-841e4dfa6daf/0ea1c7df531f.png\" "\\"点击查看原图\\"")
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/40085334-6d61-4bca-a6c2-841e4dfa6daf/d1232fa9757d.png\" "\\"点击查看原图\\"")
【小试1】 某校参加校园篮球比赛的 18 名运动员的身高如表：则该校 18 名运动 员身高的中位数是(单位cm)( )
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/5309aaf3-61c2-45b6-a0dc-a345fefe89ad/09dd5754aba3.png\" "\\"点击查看原图\\"")
A. 173cm\\(\\frac{(B)174cm}{(C)175cm}\\)
D. 176cm
若a是最小的正整数，b是最大的负整数，c是倒数等于它本身的数，则a+b+c= ()
A. 0
B. −2
C. 0或－2
D. −1或1
","answer_html":"D","solution_html":"由题意得a= 1,b= −1,c= 1或c= −1;当c= 1时，a+b+c= 1 + (−1) + 1 = 1；当 c = −1时，a + b + c = 1 + (−1) + (−1) = −1 ∴a + b + c = 1或−1,故选D","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:58:38"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T13:58:38"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:58:38"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T13:59:30"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:01:38"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:01:38"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:01:38"}],"detail_url":"/questions/182324","edit_url":"/questions/182324/edit","json_url":"/api/questions/182324","recheck_url":"/api/questions/182324/recheck"},{"id":182325,"job_id":11,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.975,"source_file":"青岛版/七上/杜辉Q_18951362233_315_检测.pdf","job_source":"数学-青岛版.zip","pages":[2,2],"stem":"若a是最大的负整数，b是绝对值最小的数，c是最小的正整数，那么a+b+c的值为( ). A. −1 B. \\(\\frac{0}{1}\\) C. D. 2","options":[{"label":"A","text":"−1"},{"label":"B","text":"\\frac{0}{1}"},{"label":"C","text":""},{"label":"D","text":"2"}],"answer":"B","solution":"根据题意得：\\(a=-1,b=0,c=1\\)，则\\(a+b+c=-1+0+1=0\\)，故选：B．","stem_html":"若a是最大的负整数，b是绝对值最小的数，c是最小的正整数，那么a+b+c的值为( ).
A. −1
B. \\(\\frac{0}{1}\\)
C.
D. 2
","answer_html":"B","solution_html":"根据题意得：\\(a=-1,b=0,c=1\\)，则\\(a+b+c=-1+0+1=0\\)，故选：B．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T14:01:17"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T14:01:17"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T14:01:17"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:02:06"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T14:02:15"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T14:02:28"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:02:28"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T14:02:28"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T14:02:39"},{"type":"QUALITY_GATE","status":"PASS","score":0.975,"created_at":"2026-11-10T14:02:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:17:40"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:33:12"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:48:45"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:04:17"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:19:50"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:35:23"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:50:55"}],"detail_url":"/questions/182325","edit_url":"/questions/182325/edit","json_url":"/api/questions/182325","recheck_url":"/api/questions/182325/recheck"},{"id":182322,"job_id":11,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_315_检测.pdf","job_source":"数学-青岛版.zip","pages":[2,2],"stem":"下列运算正确的是( ) A. −3 + (−3) = 0 B. −10 + (+8) = 2 C. 0 + (−5) = 5 D. −\\(\\frac{2}{7} + (+ \\frac{5}{7}) = \\frac{3}{7}\\)","options":[{"label":"A","text":"−3 + (−3) = 0"},{"label":"B","text":"−10 + (+8) = 2"},{"label":"C","text":"0 + (−5) = 5"},{"label":"D","text":"− \\frac{2}{7} + (+ \\frac{5}{7}) = \\frac{3}{7}"}],"answer":"\\(\\frac{D.}{对于}\\)","solution":"A． −3 + (−3) = −6，故此选项计算错误，不符合题意；对于 B． −10 + (+8) = −2，故此选项计算错误，不符合题意；对于 C．0 + (−5) = −5，故此选项计算错误，不符合题意；对于 D． −\\(\\frac{2}{7} + (+ \\frac{5}{7}) = \\frac{3}{7}\\)，故此选项计算正确，符合题意；","stem_html":"下列运算正确的是( )
A. −3 + (−3) = 0
B. −10 + (+8) = 2
C. 0 + (−5) = 5
D. −\\(\\frac{2}{7} + (+ \\frac{5}{7}) = \\frac{3}{7}\\)
","answer_html":"\\(\\frac{D.}{对于}\\)","solution_html":"A． −3 + (−3) = −6，故此选项计算错误，不符合题意；对于 B． −10 + (+8) = −2，故此选项计算错误，不符合题意；对于 C．0 + (−5) = −5，故此选项计算错误，不符合题意；对于 D． −\\(\\frac{2}{7} + (+ \\frac{5}{7}) = \\frac{3}{7}\\)，故此选项计算正确，符合题意；","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:56:09"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T13:56:09"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:56:09"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T13:57:23"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:57:23"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T13:57:31"},{"type":"SYMBOLIC","status":"PASS","score":0.9,"created_at":"2026-11-10T13:57:31"}],"detail_url":"/questions/182322","edit_url":"/questions/182322/edit","json_url":"/api/questions/182322","recheck_url":"/api/questions/182322/recheck"},{"id":182316,"job_id":11,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_315_检测.pdf","job_source":"数学-青岛版.zip","pages":[1,1],"stem":"如图\\(A\\)，\\(B\\)两点在数轴上表示的数分别是\\(a\\)，\\(b\\)．有以下结论 ①\\(a+b> 0\\)；②$|a| > |b|$；③$ab< -2$，其中结论正确的有（） A. 0个 B. 1个 C. 2个 D. 3个","options":[{"label":"A","text":"0个"},{"label":"B","text":"1个"},{"label":"C","text":"2个"},{"label":"D","text":"3个"}],"answer":"B","solution":"因为A,B两点在数轴上表示的数分别是a,b， ∴ 0 <b< 1， −2 <a< −1，|a| > |b|，故 ②正确； ∵ 0 <b< 1， −2 <a< −1，|a| > |b|， ∴ a+b< 0,故①错误；因为 0 <b< 1， −2 <a< −1， ∴ |ab| < 2,ab< 0， ∴ ab> −2,故③错误，综上 其中结论正确的有1个，故选：B．","stem_html":"如图\\(A\\)，\\(B\\)两点在数轴上表示的数分别是\\(a\\)，\\(b\\)．有以下结论 ①\\(a+b> 0\\)；②$|a| > |b|$；③$ab< -2$，其中结论正确的有（）
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/25691159-497d-4ce1-90b3-ac48b74c97f3/6d9bad86-85c5-4000-9750-c84c471e7f90/d8745ac5b8de.png\" "\\"点击查看原图\\"")
A. 0个
B. 1个
C. 2个
D. 3个
当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x} 09\\).正比例函数的定义：_________________ 且随的增大而____
","answer_html":"形如y = kx(k是常数，且k ≠ 0)","solution_html":"根据《核心知识点》第1条，正比例函数的定义是形如y = kx(k是常数，且k ≠ 0)的函数。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:40:40"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T13:40:40"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:40:40"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T13:41:26"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T13:42:10"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:42:10"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:42:10"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-11-10T13:42:39"},{"type":"QUALITY_GATE","status":"FAIL","score":0.725,"created_at":"2026-11-10T13:42:39"}],"detail_url":"/questions/182273","edit_url":"/questions/182273/edit","json_url":"/api/questions/182273","recheck_url":"/api/questions/182273/recheck"},{"id":182264,"job_id":10,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"冀教版/八下/薛豪Q_18952688822_345.pdf","job_source":"数学-冀教版.zip","pages":[1,1],"stem":"当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x}\\)且随的增大而____","options":[],"answer":"一、三；增大","solution":"正比例函数y=kx(k≠0)的图象性质：当k>0时，图象经过第一、三象限，且y随x的增大而增大。","stem_html":"当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x}\\)且随的增大而____
","answer_html":"一、三；增大","solution_html":"正比例函数y=kx(k≠0)的图象性质：当k>0时，图象经过第一、三象限，且y随x的增大而增大。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:35:30"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T13:35:30"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:35:30"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T13:36:15"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:36:15"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T13:37:02"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:37:02"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:37:41"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-11-10T13:37:41"}],"detail_url":"/questions/182264","edit_url":"/questions/182264/edit","json_url":"/api/questions/182264","recheck_url":"/api/questions/182264/recheck"},{"id":182260,"job_id":10,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"冀教版/八下/薛豪Q_18952688822_345.pdf","job_source":"数学-冀教版.zip","pages":[1,1],"stem":"当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x}\\)且随的增大而____","options":[],"answer":"一、三；增大","solution":"依据正比例函数性质：当k>0时，y=kx的图象是一条过原点的直线，必经过第一、三象限，且y随x的增大而增大。","stem_html":"当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x}\\)且随的增大而____
","answer_html":"一、三；增大","solution_html":"依据正比例函数性质：当k>0时，y=kx的图象是一条过原点的直线，必经过第一、三象限，且y随x的增大而增大。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:35:03"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T13:35:03"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:35:03"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T13:35:57"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:35:57"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T13:36:19"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:36:19"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:36:50"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-11-10T13:36:50"}],"detail_url":"/questions/182260","edit_url":"/questions/182260/edit","json_url":"/api/questions/182260","recheck_url":"/api/questions/182260/recheck"},{"id":182226,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"沪教版/八下/周琼玟Q_18978751881_945.pdf","job_source":"数学-沪教版.zip","pages":[4,4],"stem":"某校举办了首届＂英语原创演讲比赛＂，经选拔后有若干名学生参加决赛，根据测试成绩( 成绩都不低于60分)绘制出如下两幅不完整的统计图表，请根据统计图表提供的信息完成下列各题. （1）参加决赛的学生有____名，请将图b补充完整； （2）表a中的m = ____，n = ____； （3）如果测试成绩不低于80分为优秀，那么本次测试的优秀率是____．","options":[],"answer":"无法解答，缺少图表数据","solution":"题干提到有统计图表，但实际未提供图a、图b的具体数据（如各分数段人数、百分比等），因此无法计算参加决赛学生总数、m、n的值以及优秀率。需补充完整统计图表后方可求解。","stem_html":"某校举办了首届＂英语原创演讲比赛＂，经选拔后有若干名学生参加决赛，根据测试成绩( 成绩都不低于60分)绘制出如下两幅不完整的统计图表，请根据统计图表提供的信息完成下列各题.
（1）参加决赛的学生有____名，请将图b补充完整；
（2）表a中的m = ____，n = ____；
（3）如果测试成绩不低于80分为优秀，那么本次测试的优秀率是____．
","answer_html":"无法解答，缺少图表数据","solution_html":"题干提到有统计图表，但实际未提供图a、图b的具体数据（如各分数段人数、百分比等），因此无法计算参加决赛学生总数、m、n的值以及优秀率。需补充完整统计图表后方可求解。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:30:16"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T13:30:16"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:30:16"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T13:32:05"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T13:32:13"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:32:13"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T13:32:13"},{"type":"COHERENCE","status":"FAIL","score":1.0,"created_at":"2026-11-10T13:32:37"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T13:32:37"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T13:34:33"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:34:33"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T13:35:11"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:35:11"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-11-10T13:35:11"},{"type":"AUTO_REPAIR","status":"PASS","score":1.0,"created_at":"2026-11-10T13:35:11"},{"type":"VISION","status":"FAIL","score":1.0,"created_at":"2026-11-10T13:36:03"}],"detail_url":"/questions/182226","edit_url":"/questions/182226/edit","json_url":"/api/questions/182226","recheck_url":"/api/questions/182226/recheck"},{"id":182225,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_945.pdf","job_source":"数学-沪教版.zip","pages":[4,4],"stem":"为了了解本校八年级学生的视力情况，某校随机抽查了50名八年级学生的视力，并 进行统计，绘制了如下统计图． （1）求这50名学生的平均视力(其中视力4.5以下记为4)； （2）若八年级学生的视力不低于4.8，则认为该学生视力较好．该 校八年级共有800名学生，请估计该校八年级学生中，视力较好的人数．","options":[],"answer":"","solution":"","stem_html":"为了了解本校八年级学生的视力情况，某校随机抽查了50名八年级学生的视力，并 进行统计，绘制了如下统计图．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/5799e13d-568c-4d8e-ac0a-d6cdad19cc62/66f185db6181.png\" "\\"点击查看原图\\"")
（1）求这50名学生的平均视力(其中视力4.5以下记为4)；
（2）若八年级学生的视力不低于4.8，则认为该学生视力较好．该 校八年级共有800名学生，请估计该校八年级学生中，视力较好的人数．
如果a的相反数是最小的正整数，b是最大的负整数，c是绝对值最小的有 理数，请问a，b, c三数之和是______.
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:26:11"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T13:26:11"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:26:11"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T13:27:57"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:27:57"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T13:28:36"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T13:28:36"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T13:29:02"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T13:29:02"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T13:30:45"},{"type":"CRITIC","status":"FAIL","score":1.0,"created_at":"2026-11-10T13:30:45"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T13:33:30"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:33:30"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-11-10T13:33:30"}],"detail_url":"/questions/182251","edit_url":"/questions/182251/edit","json_url":"/api/questions/182251","recheck_url":"/api/questions/182251/recheck"},{"id":182222,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_945.pdf","job_source":"数学-沪教版.zip","pages":[3,4],"stem":"为了在体育中考中取得优异成绩，小亮在家练习“1分钟跳绳”，他四次自测的成绩如图所示，则该组数据的中位数为( ) (A)195 (B)189 (C)185 (D)183","options":[],"answer":"","solution":"","stem_html":"为了在体育中考中取得优异成绩，小亮在家练习“1分钟跳绳”，他四次自测的成绩如图所示，则该组数据的中位数为( ) (A)195 (B)189 (C)185 (D)183
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/85fa4ff5-0eb0-47fe-ac7b-aa203756d095/a8d7d1d6630b.png\" "\\"点击查看原图\\"")
已知有理数a、b在数轴上的位置如图所示，以下说法正确的是（）
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/25691159-497d-4ce1-90b3-ac48b74c97f3/102371ca-103d-4e98-826e-2307fe8eadcc/9564bf787686.png\" "\\"点击查看原图\\"")
A. a + b = 0
B. b < a
C. a −b > 0
D. |b| < |a|
(多选)下面说法正确的是( )
A. 当 k ≠0 时，y = − _{k}是正比例函数x
B. 如果y = (a + 3)x +\\(a^{2}\\)−9是正比例函数，那么a = ±3
C. 如果\\(y\\)与\\(x + 2\\)成正比例，那么\\(y\\)是\\(x\\)的正比例函数
D. 如果\\(y = 1_{3}x^{2}\\)，那么y与\\(x^{2}\\)成正比例
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:17:56"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T13:17:56"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:17:56"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T13:18:41"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-11-10T13:21:51"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:21:51"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T13:21:51"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-11-10T13:22:47"},{"type":"QUALITY_GATE","status":"FAIL","score":0.913,"created_at":"2026-11-10T13:22:47"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T13:27:49"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:27:49"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T13:29:24"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:29:24"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-11-10T13:29:24"}],"detail_url":"/questions/182195","edit_url":"/questions/182195/edit","json_url":"/api/questions/182195","recheck_url":"/api/questions/182195/recheck"},{"id":182243,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_310.pdf","job_source":"数学-青岛版.zip","pages":[2,2],"stem":"如图，有理数a,b在数轴上对应的点的位 置如图所示，下列结论正确的是( ). ．a b ． + A\\(B \\frac{a}{a} \\frac{b}{b} \\frac{0}{0}\\)手机移动支付给生活带来便捷如图是尹, （正数表示收入，负数表示支出，单位： 元），尹老师当天微信收支的最终结果 是( ).\\(A \\frac{4}{96} \\frac{4}{96}\\)B ．收入元 ．支出元 C D ．收入 元 ．支出 元 C. |a || b | ． + D 老师2022年某天的微信账单的收支明细","options":[{"label":"C","text":"|a || b | ． + D 老师2022年某天的微信账单的收支明细"}],"answer":"","solution":"【讲解】 ．由数轴图可知a b，故选项错误， 由题意可得：+ 50 − 28 −18 = 4,尹老师当 A A 天微信收支的最终结果是收入元，故选． 不符合题意；．由数轴图可知− 2 B 4 A a −1,b 1，故a + b 0，故选项正确， B 符合题意；．由数轴图可知| a || b |， C C D B 故选项错误，不符合题意；．由选 项知a + b 0，故选项错误，不符合题 D B 意．故选：．","stem_html":"如图，有理数a,b在数轴上对应的点的位 置如图所示，下列结论正确的是( ). ．a b ． + A\\(B \\frac{a}{a} \\frac{b}{b} \\frac{0}{0}\\)手机移动支付给生活带来便捷如图是尹, （正数表示收入，负数表示支出，单位： 元），尹老师当天微信收支的最终结果 是( ).\\(A \\frac{4}{96} \\frac{4}{96}\\)B ．收入元 ．支出元 C D ．收入 元 ．支出 元
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/dbbc697a-ebbc-4ac3-859d-0dca60daba8a/79070134b75b.png\" "\\"点击查看原图\\"")
C. |a || b | ． + D 老师2022年某天的微信账单的收支明细
已知有理数a, b, c在数轴上的位置如图所示，则下列结论正确的是( ).
A. a < c
B. a + b > 0
C. b > −c
D. −b > a
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:22:04"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T13:22:04"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:22:04"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T13:23:10"}],"detail_url":"/questions/182247","edit_url":"/questions/182247/edit","json_url":"/api/questions/182247","recheck_url":"/api/questions/182247/recheck"},{"id":182217,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_945.pdf","job_source":"数学-沪教版.zip","pages":[2,2],"stem":"如图是嘉淇记录的个整点时刻的气温统8 计图，则这个整点时刻的气温的中位数8 是( ) A ．9 15． C B C C ．16 ．17 C D C","options":[],"answer":"","solution":"将这组数据按从小到大的顺序排列： 9、、、、、、、，99 15 17 192323 15 +17 中位数为 =，\\(2 \\frac{16}{16C}\\)气温的中位数是 ， C 故选：．","stem_html":"如图是嘉淇记录的个整点时刻的气温统8 计图，则这个整点时刻的气温的中位数8 是( ) A ．9 15． C B C C ．16 ．17 C D C
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/b66d1029-eef7-4822-b587-1e33acfa0201/0f0894ae-1e05-4d75-b5ea-38a8bb3a2de0/215613163a22.png\" "\\"点击查看原图\\"")
手机支付给生活带来便捷，如图是王老师某日微信账单的收支明细（正数表示收入，负数 表示支出，单位：元），王老师当天微信收支的最终结果是（）
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/7ec06dcd-fa90-42cc-88bd-166cb4b5ad42/88d0fc334bf8.png\" "\\"点击查看原图\\"")
A. 收入4元
B. 支出2元
C. 支出6元
D. 支出9元
如果数据个数是个，中位数是________8 _________________________________________
","answer_html":"第4个和第5个数的平均数","solution_html":"根据求中位数的步骤：当数据个数n为偶数时，中位数是第n/2个和第n/2+1个数的平均数。本题n=8，因此中位数是第4个和第5个数的平均数。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:16:52"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T13:16:52"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:16:52"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T13:17:38"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:17:38"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T13:20:52"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:20:52"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T13:21:29"},{"type":"QUALITY_GATE","status":"FAIL","score":0.775,"created_at":"2026-11-10T13:21:29"}],"detail_url":"/questions/182215","edit_url":"/questions/182215/edit","json_url":"/api/questions/182215","recheck_url":"/api/questions/182215/recheck"},{"id":182214,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"沪教版/八下/周琼玟Q_18978751881_945.pdf","job_source":"数学-沪教版.zip","pages":[1,1],"stem":"如果数据个数是个，中位数是________8","options":[],"answer":"第4个和第5个数据的平均数","solution":"根据《核心知识点》，当数据个数n为偶数时，中位数是第n/2个和第n/2+1个数据的平均数。本题n=8，因此中位数是第4个和第5个数据的平均数。","stem_html":"如果数据个数是个，中位数是________8
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","answer_html":"①排序：把数据从小到大（或从大到小）的顺序排列 ②确定中位数的位置：如果数据个数是奇数，中位数是第 (n+1)/2 个数；如果数据个数是偶数，中位数是第 n/2 和 n/2 +1 个数的平均数(n是数据个数)","solution_html":"依据《核心知识点》原文：求中位数需先排序，再根据数据个数奇偶性确定位置——奇数个数据取中间那个，偶数个数据取中间两个的平均数。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T13:00:36"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T13:00:36"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:00:36"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T13:01:19"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T13:04:13"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:04:13"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:04:13"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T13:05:12"},{"type":"QUALITY_GATE","status":"PASS","score":0.95,"created_at":"2026-11-10T13:05:12"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.0,"created_at":"2026-11-10T13:13:12"}],"detail_url":"/questions/182202","edit_url":"/questions/182202/edit","json_url":"/api/questions/182202","recheck_url":"/api/questions/182202/recheck"},{"id":182190,"job_id":10,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_340.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"若y与2x + 1成正比例, 且当x = −2时, y = 6. （1）求y与x之间的函数关系式； （2）若点(m, 3)在该函数的图象上, 求m的值.","options":[],"answer":"","solution":"","stem_html":"若y与2x + 1成正比例, 且当x = −2时, y = 6.
（1）求y与x之间的函数关系式；
（2）若点(m, 3)在该函数的图象上, 求m的值.
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","answer_html":"","solution_html":" 与x − 2成正比例,设y = (− 2)(k为常数,\\(\\frac{y}{k} \\frac{kx}{代入上式得}\\)且 0).将x = 4, y = −2, − 2 = k(4 − 2), 即− 2 = 2,解得k = − 将k = −1代入y = k(x − 2),frack1( 1. 得 = − x − 2) =−+\\(x \\frac{y}{y} 2\\). 与之间的函数表达式为xy = −+x 2.","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-11-10T13:05:25"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-11-10T13:05:25"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T13:05:25"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T13:06:37"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T13:06:56"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T13:06:56"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T13:06:56"}],"detail_url":"/questions/182186","edit_url":"/questions/182186/edit","json_url":"/api/questions/182186","recheck_url":"/api/questions/182186/recheck"},{"id":182191,"job_id":10,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"冀教版/八下/薛豪Q_18952688822_340.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"已知y + 6与x + 1成正比例, 当x = 3时, y = 2. （1）求出y与x的函数表达式； （2）若点(m, −2)在这个函数的图象上, 求m的值.","options":[],"answer":"","solution":"","stem_html":"已知y + 6与x + 1成正比例, 当x = 3时, y = 2.
（1）求出y与x的函数表达式；
（2）若点(m, −2)在这个函数的图象上, 求m的值.
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![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/2b06312b-7e3f-494e-ae3e-21d10207fcf7/39cc56ef-2a38-4606-b6ac-0f3ffff319d9/77fdfd681f2d.png\" "\\"点击查看原图\\"")
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/e646383b-1ad4-4c0d-9033-f9d5e9389266/5f3de1dbdfd6.png\" "\\"点击查看原图\\"")
A. k > 3
B. k ≤3
C. k < 3
D. k ≥3
异号相加：________________
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C. 0或－1
D. −1或1
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","answer_html":"形如y = kx(k是常数，且k ≠ 0)","solution_html":"根据《核心知识点》第1条，正比例函数的定义是形如y = kx(k是常数，且k ≠ 0)的函数。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:56:59"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:56:59"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:56:59"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T12:57:43"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:58:11"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:58:11"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:58:11"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T12:59:07"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-11-10T12:59:07"}],"detail_url":"/questions/182183","edit_url":"/questions/182183/edit","json_url":"/api/questions/182183","recheck_url":"/api/questions/182183/recheck"},{"id":182161,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":0.812,"source_file":"沪教版/八下/周琼玟Q_18978751881_940.pdf","job_source":"数学-沪教版.zip","pages":[6,6],"stem":"某市初中毕业生进行了一项技能测试，有4万名考生的得分都是不小 于70的两位数，从中随机抽取4000个数据，统计如下表：请根据表 格中的信息，估计这4万个数据的平均数约为____.","options":[],"answer":"","solution":"","stem_html":"某市初中毕业生进行了一项技能测试，有4万名考生的得分都是不小 于70的两位数，从中随机抽取4000个数据，统计如下表：请根据表 格中的信息，估计这4万个数据的平均数约为____.
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","answer_html":"一、三；增大","solution_html":"根据正比例函数性质：当k>0时，图象经过第一、三象限，且y随x的增大而增大。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:51:34"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:51:34"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:51:34"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:52:24"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:52:24"},{"type":"VISION","status":"PASS","score":0.8,"created_at":"2026-11-10T12:52:42"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:52:42"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:53:06"},{"type":"QUALITY_GATE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:53:06"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:54:06"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:54:06"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-11-10T12:54:06"},{"type":"AUTO_FILL_ANSWER","status":"WARN","score":1.0,"created_at":"2026-11-10T12:54:06"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T12:55:48"}],"detail_url":"/questions/182174","edit_url":"/questions/182174/edit","json_url":"/api/questions/182174","recheck_url":"/api/questions/182174/recheck"},{"id":182175,"job_id":10,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"冀教版/八下/薛豪Q_18952688822_340.pdf","job_source":"数学-冀教版.zip","pages":[1,1],"stem":"当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x}\\)且随的增大而____","options":[],"answer":"第二、四；减小","solution":"根据正比例函数性质：当k<0时，图象经过第二、四象限，且y随x的增大而减小。","stem_html":"当 时，正比例图象经过____象限,\\(\\frac{k}{y} \\frac{0}{x}\\)且随的增大而____
","answer_html":"第二、四；减小","solution_html":"根据正比例函数性质：当k<0时，图象经过第二、四象限，且y随x的增大而减小。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:51:52"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:51:52"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:51:52"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:52:34"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:52:34"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T12:52:58"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:52:58"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:53:30"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-11-10T12:53:30"}],"detail_url":"/questions/182175","edit_url":"/questions/182175/edit","json_url":"/api/questions/182175","recheck_url":"/api/questions/182175/recheck"},{"id":182154,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_940.pdf","job_source":"数学-沪教版.zip","pages":[2,2],"stem":"某单位450名职工积极参加想贫困地区捐书 活动，为了解职工的捐书量，采用随机抽样 的方法抽取了30名职工作为样本，对他们的 捐书量进行统计，统计结果共有本，本，本456 ，本，本，五类，分别用78A, B,C, D, E表示，根 某地教育局为了解某校高中学生的每天平 据统计数据绘制成了如图所示不完整的条形 均睡眠时间的情况，随机抽取了该校50名 统计图，用图中所给的信息解答下列问题： 高中学生进行调查访问，收集数据，整理 数据，将数据分成组用频数分布直方图7 描述数据，请你根据图表解决以下问题： （1）补全条形统计图；\\(\\frac{(2)}{(3)}\\)求这30名职工捐书本书的平均数； 估计该单位450名职工共捐书多少本？","options":[],"answer":"","solution":"【讲解】 (1)捐类书的有30 − 4 − 6 − 9 − 3 = 8(人，) (1)500 \\(\\frac{19}{50} = 190\\)(人；)D 补全的条形统计图如下图所示： 答：该校500名高中学生中，每天平均睡眠 时间至少小时的人数约有8 人；\\(\\frac{190}{10}\\)(2) =\\(\\frac{1}{50}\\) 4.5 + + 6.5 +12 7.5 + fracx128.5 frac(439.5 frac55.5410.5) + + =，\\(\\frac{7.46}{7.46}\\)答：这组数据的平均数为 ． (3)建议学校减少学生课后作业量，增加学生 的睡眠时间．答案不唯一合理即可() x =\\(\\frac{1}{30}\\) (4 4 + 5 6 + 6 9 + 7 +8 8 3) frac(2)6( = 本，)答：这 名职工捐书本数的平均数为本．\\(6 \\frac{30}{6}\\)(3)450 = 2700(本，) 答：估计该单位450名职工共捐书2700本．","stem_html":"某单位450名职工积极参加想贫困地区捐书 活动，为了解职工的捐书量，采用随机抽样 的方法抽取了30名职工作为样本，对他们的 捐书量进行统计，统计结果共有本，本，本456 ，本，本，五类，分别用78A, B,C, D, E表示，根 某地教育局为了解某校高中学生的每天平 据统计数据绘制成了如图所示不完整的条形 均睡眠时间的情况，随机抽取了该校50名 统计图，用图中所给的信息解答下列问题： 高中学生进行调查访问，收集数据，整理 数据，将数据分成组用频数分布直方图7 描述数据，请你根据图表解决以下问题：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/b66d1029-eef7-4822-b587-1e33acfa0201/8a88ae06-8537-4a93-9548-ea4fdf370b99/0d542a9cf5ad.png\" "\\"点击查看原图\\"")
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/b66d1029-eef7-4822-b587-1e33acfa0201/8a88ae06-8537-4a93-9548-ea4fdf370b99/7b2605f09990.png\" "\\"点击查看原图\\"")
（1）补全条形统计图；\\(\\frac{(2)}{(3)}\\)求这30名职工捐书本书的平均数； 估计该单位450名职工共捐书多少本？
已知\\(a\\),\\(b\\)对应的点在数轴上的位置如图所示，则\\(a + b\\)的值为( ).
A. 正数
B. 负数
C. 0
D. 非负数
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:43:42"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:43:42"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:43:42"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-11-10T12:45:14"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:45:14"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T12:47:43"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T12:47:43"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T12:50:59"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-11-10T12:50:59"}],"detail_url":"/questions/182128","edit_url":"/questions/182128/edit","json_url":"/api/questions/182128","recheck_url":"/api/questions/182128/recheck"},{"id":182160,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_940.pdf","job_source":"数学-沪教版.zip","pages":[6,6],"stem":"某学校在开展＂节约每一滴水＂的活动中，从九年级的800名同学中 任选出10名同学汇报了各自家庭一个月的节水情况，将有关数据整 理成表，请你估计这800名同学的家庭一个月节约用水的总量大约是____t．","options":[],"answer":"","solution":"","stem_html":"某学校在开展＂节约每一滴水＂的活动中，从九年级的800名同学中 任选出10名同学汇报了各自家庭一个月的节水情况，将有关数据整 理成表，请你估计这800名同学的家庭一个月节约用水的总量大约是____t．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/101e885d-c691-4f63-aacc-fa7e1fbad0e7/f2c8ea2a7dd3.png\" "\\"点击查看原图\\"")
【小试1】 计算:\\(\\frac{(2)−18 + 20}{(3)0 −(−6)}\\)
（1）(−4) + (−8)
（2）− _{4}−^{1} 12
","answer_html":"(1)－12；(2)2；(3)6；(4) − 34","solution_html":"(1)(−4) + (−8) = −(4 + 8) = −12; (2)−18 + 20 = +(20 −18) = 2; (3)0 −(−6) = 0 + 6 = 6; (4)− 1 1\\(3 _{4}\\)−^\\({1} _{2}\\)= −(_{4}+^\\({1} _{2}\\)) = − _{4};","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[],"detail_url":"/questions/182124","edit_url":"/questions/182124/edit","json_url":"/api/questions/182124","recheck_url":"/api/questions/182124/recheck"},{"id":182168,"job_id":10,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"冀教版/八下/薛豪Q_18952688822_340.pdf","job_source":"数学-冀教版.zip","pages":[1,1],"stem":"y = kx + b是正比例函数，需要满足______","options":[],"answer":"k≠0且b=0","solution":"根据正比例函数定义：形如y=kx（k是常数，且k≠0）的函数称为正比例函数。因此y=kx+b要成为正比例函数，必须满足b=0（消去常数项）且k≠0（保证是正比例而非其他线性关系）。","stem_html":"y = kx + b是正比例函数，需要满足______
","answer_html":"k≠0且b=0","solution_html":"根据正比例函数定义：形如y=kx（k是常数，且k≠0）的函数称为正比例函数。因此y=kx+b要成为正比例函数，必须满足b=0（消去常数项）且k≠0（保证是正比例而非其他线性关系）。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:44:51"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:44:51"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:44:51"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:46:46"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:46:46"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T12:48:51"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:48:51"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:50:03"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-11-10T12:50:03"}],"detail_url":"/questions/182168","edit_url":"/questions/182168/edit","json_url":"/api/questions/182168","recheck_url":"/api/questions/182168/recheck"},{"id":182159,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_940.pdf","job_source":"数学-沪教版.zip","pages":[5,6],"stem":"今年来，某市为乡村振兴大力发展草莓种植业，为农民增收创造了条件。已知直径在3 ∼ 5cm的草莓，通常是植株营养供应充足，果实得以充分发育成 熟的结果，这样的草莓果肉饱满，口感紧实，酸甜比例适中，能体现出该 品种草莓的典型风味和口感。某镇有甲、乙两块草莓园，在草莓收获的季节，某 校同学前往该镇开展综合实践活动，其中一个项目是：在品种、种植环境、管 理技术等多种影响因素基本一致的条件下，对两块草莓园的优质草莓情况进行调 查统计，为草莓园的发展规划提供一些参考．从 两块草莓园采摘的草莓中各随机选取200颗，在技术人员的指导下，测量每个草莓的直径( 用x表示，单位：cm)，并将数据进行如下分组：整 理样本数据，并绘制甲、乙两园样本数据的频数直方图如图1和图2． 4.2021年3月教育部发布了《关于进一步加强中小学生睡眠管理工作的通 知》，明确初中生每天睡眠时间要达到9小时．为了解某校七年级 学生的睡眠情况，小明等5名同学组成学习小组随机抽查了该校七年级40名学生一周(7天) 平均每天的睡眠时间(单位：小时)如下：该小组将上面收集到的数据进行了整理，绘制成如下的频数 分布表和频数分布直方图．平均每天睡眠时间频数分布表根据以上信息，解答下列问题： （1）任务1图1中a的值为____。 （2）任务2结合市场情况，将C, D两组的草莓认定为一级，B组的草莓认定为二级，其 他组的草莓认定为三级，其中一级草莓的品质最优，二 级次之，三级最次．试估计哪个园的草莓品质更优，并说明理由． （3）此次抽样调查的样本容量是____，表中m = ____，n = ____； （4）请补全频数分布直方图； （5）若该校七年级共有360名学生，请你估算其中睡眠时间不少于9小时的学生约有多少人.","options":[],"answer":"","solution":"","stem_html":"今年来，某市为乡村振兴大力发展草莓种植业，为农民增收创造了条件。已知直径在3 ∼ 5cm的草莓，通常是植株营养供应充足，果实得以充分发育成 熟的结果，这样的草莓果肉饱满，口感紧实，酸甜比例适中，能体现出该 品种草莓的典型风味和口感。某镇有甲、乙两块草莓园，在草莓收获的季节，某 校同学前往该镇开展综合实践活动，其中一个项目是：在品种、种植环境、管 理技术等多种影响因素基本一致的条件下，对两块草莓园的优质草莓情况进行调 查统计，为草莓园的发展规划提供一些参考．从 两块草莓园采摘的草莓中各随机选取200颗，在技术人员的指导下，测量每个草莓的直径( 用x表示，单位：cm)，并将数据进行如下分组：整 理样本数据，并绘制甲、乙两园样本数据的频数直方图如图1和图2． 4.2021年3月教育部发布了《关于进一步加强中小学生睡眠管理工作的通 知》，明确初中生每天睡眠时间要达到9小时．为了解某校七年级 学生的睡眠情况，小明等5名同学组成学习小组随机抽查了该校七年级40名学生一周(7天) 平均每天的睡眠时间(单位：小时)如下：该小组将上面收集到的数据进行了整理，绘制成如下的频数 分布表和频数分布直方图．平均每天睡眠时间频数分布表根据以上信息，解答下列问题：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/de0da50a-3b71-47f8-b8a4-befd0508bcdc/10712ef24e67.png\" "\\"点击查看原图\\"")
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/de0da50a-3b71-47f8-b8a4-befd0508bcdc/e8af89ce65fc.png\" "\\"点击查看原图\\"")
（1）任务1图1中a的值为____。
（2）任务2结合市场情况，将C, D两组的草莓认定为一级，B组的草莓认定为二级，其 他组的草莓认定为三级，其中一级草莓的品质最优，二 级次之，三级最次．试估计哪个园的草莓品质更优，并说明理由．
（3）此次抽样调查的样本容量是____，表中m = ____，n = ____；
（4）请补全频数分布直方图；
（5）若该校七年级共有360名学生，请你估算其中睡眠时间不少于9小时的学生约有多少人.
【小试2】 为 了了解某校初二年级学生的睡眠时长，随机抽取了初二年级男生和女生各20位， 对其同一天的睡眠时长进行调查，并对数据进行收集、整理、描述和分析．下 面给出了相关信息．根据以上信息，回答下列问题：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/a9b06345-edda-446f-abcf-d1bdcdd84af5/b02fb51c21b7.png\" "\\"点击查看原图\\"")
（1）抽取的男生的平均睡眠为____小时，抽取的女生的平均睡眠为____小时；
（2）根据抽样调查情况，可以推断____(填＂男生＂或＂女生＂)睡 眠情况比较好，理由为_____________________.
计算：(1)(+17) + (+13) _{3}) + 2 3
（1）(−8) + (−10)
（2）(+5.1) + (−12.1)
（3）(+2\\(1_{5}\\)) + (−2.2)
（4）(−2 2 2
（5）(−4.3) + 0
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:44:52"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:44:52"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:44:52"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T12:48:52"}],"detail_url":"/questions/182126","edit_url":"/questions/182126/edit","json_url":"/api/questions/182126","recheck_url":"/api/questions/182126/recheck"},{"id":182155,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_940.pdf","job_source":"数学-沪教版.zip","pages":[3,3],"stem":"【小试1】 为保护学生的身心健康，增强学生的反欺凌、霸凌意识，某校组织全 校学生参加以＂守护校园，抵制霸凌＂为主题的讲座，为了了解讲 座的效果，从全校学生中随机抽取了部分学生进行相关测试，将成绩( 单位：分，满分12分)统计整理后制作了如图所示的两幅统计图.请 根据图中信息，解答下列问题： （1）本次被抽取到的学生人数为____，扇形统计图中m的值为____； （2）求本次抽取到的学生成绩的平均数； （3）若该校共有1420名学生，试估计该校学生中成绩在11分及以上的人数．","options":[],"answer":"(1)50名；28(2)10.66分(3)估计该校学生中成绩在11分及以上的人数为852名","solution":"(1)4 ÷ 8% = 50(名)，m% =\\(14_{50}\\times 100% = 28%\\)∴m = 28故答案为：50; 28． (2)本次抽取到的学生中成绩为9分的人数为\\(50 \\times 10% = 5\\)(名)，∴本次抽取 到的学生成绩的平均数为：\\(1 _{50}\\times (8 \\times 4 + 9 \\times 5 + 10 \\times 11 + 11 \\times 14 + 12\\times 16) = 10.66\\)(分). (3)\\(1420 \\times \\frac{14+16}{50} = 852\\)(名)．答：估计该校学生中成绩在 11 分及以上的人数为 852 名．","stem_html":"【小试1】 为保护学生的身心健康，增强学生的反欺凌、霸凌意识，某校组织全 校学生参加以＂守护校园，抵制霸凌＂为主题的讲座，为了了解讲 座的效果，从全校学生中随机抽取了部分学生进行相关测试，将成绩( 单位：分，满分12分)统计整理后制作了如图所示的两幅统计图.请 根据图中信息，解答下列问题：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/f1590cb9-812b-41f0-a1a8-a8cb2a8c73af/f72e61a8-69f8-4c5c-82ae-4ca881da67a8/36bbb4bbfc7f.png\" "\\"点击查看原图\\"")
（1）本次被抽取到的学生人数为____，扇形统计图中m的值为____；
（2）求本次抽取到的学生成绩的平均数；
（3）若该校共有1420名学生，试估计该校学生中成绩在11分及以上的人数．
y = kx是正比例函数吗？______
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:44:12"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:44:12"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:44:12"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T12:45:56"}],"detail_url":"/questions/182169","edit_url":"/questions/182169/edit","json_url":"/api/questions/182169","recheck_url":"/api/questions/182169/recheck"},{"id":182158,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_940.pdf","job_source":"数学-沪教版.zip","pages":[5,5],"stem":"渭南市是中国戏曲之乡和民俗之乡，多种剧目被列入国家非物质文 化遗产保护名录．某校举办了＂渭南戏曲知多少＂答题比赛(共10道题 )，为了解学生的答题情况，随机抽取了其中20名同学的答题情况 ，绘制成如下不完整的统计图．20名同学答对题数情况如统计图所示.根 据以上信息，解答下列问题： （1）补全统计图， （2）求这20名同学答对题数的平均数； （3）若该校共有800名学生参加了此次答题比赛，请你估计该校全部答对的学生总人数．","options":[],"answer":"","solution":"","stem_html":"渭南市是中国戏曲之乡和民俗之乡，多种剧目被列入国家非物质文 化遗产保护名录．某校举办了＂渭南戏曲知多少＂答题比赛(共10道题 )，为了解学生的答题情况，随机抽取了其中20名同学的答题情况 ，绘制成如下不完整的统计图．20名同学答对题数情况如统计图所示.根 据以上信息，解答下列问题：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/a13a92c3-ebda-4a16-b969-9efbd0519d0d/0bbf3fe0-0803-49e5-b3b0-dba87bc19e2d/3a8c1edf57fe.png\" "\\"点击查看原图\\"")
（1）补全统计图，
（2）求这20名同学答对题数的平均数；
（3）若该校共有800名学生参加了此次答题比赛，请你估计该校全部答对的学生总人数．
计算： + + (−11)； − + +；frac(1)(2)(3)( frac(2)(12)(4)(3.4) frac(12)4.3 − frac12) + (− frac23)； − + ．
","answer_html":"","solution_html":"+ + − = −(11− 2) = −9；\\(\\frac{(1)(2)}{(2)(12)} \\frac{(11)}{(12)}\\)− + + = 0； −\\(\\frac{1}{2}\\)) + (−\\(\\frac{2}{3}\\)) = −(\\(\\frac{1}{2} + \\frac{2}{3}\\)) = −1；1 frac(3)((4)(3.4) frac60.9 − + 4.3 = +(4.3− 3.4) = ．","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:42:01"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-11-10T12:42:01"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:42:01"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T12:45:17"}],"detail_url":"/questions/182122","edit_url":"/questions/182122/edit","json_url":"/api/questions/182122","recheck_url":"/api/questions/182122/recheck"},{"id":182157,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_940.pdf","job_source":"数学-沪教版.zip","pages":[4,4],"stem":"为了了解秦兵马俑的身高情况，某研究学习小组通过查阅网络相关资 料，获取了秦始皇兵马俑博物馆中18个陶俑的＂通高＂和＂足至顶 高＂的数据，并把数据绘制成如下统计图：根据上述信息，解答下列问题： （1）求这18个陶俑的＂足至顶高＂的平均身高．(结果保留4位有效数字) （2）目前秦始皇兵马俑已发现的陶俑大约有8000个，请估计陶俑＂足至顶 高＂高度在180cm以上的陶俑大约有多少个？(结果保留整数)","options":[],"answer":"","solution":"","stem_html":"为了了解秦兵马俑的身高情况，某研究学习小组通过查阅网络相关资 料，获取了秦始皇兵马俑博物馆中18个陶俑的＂通高＂和＂足至顶 高＂的数据，并把数据绘制成如下统计图：根据上述信息，解答下列问题：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/3149520e-8b3c-4a41-813c-9f8903796a57/313819c090f6.png\" "\\"点击查看原图\\"")
（1）求这18个陶俑的＂足至顶高＂的平均身高．(结果保留4位有效数字)
（2）目前秦始皇兵马俑已发现的陶俑大约有8000个，请估计陶俑＂足至顶 高＂高度在180cm以上的陶俑大约有多少个？(结果保留整数)
计算: _{3}) + 4
（1）(−18) + (−20)
（2）(−12) + 25
（3）(− 2 3
（4）0 + (−23)
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"FAIL","score":0.9,"created_at":"2026-11-10T12:40:53"}],"detail_url":"/questions/182127","edit_url":"/questions/182127/edit","json_url":"/api/questions/182127","recheck_url":"/api/questions/182127/recheck"},{"id":182150,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":0.85,"source_file":"沪教版/八下/周琼玟Q_18978751881_940.pdf","job_source":"数学-沪教版.zip","pages":[1,1],"stem":"频数分布直方图的平均数=________________","options":[],"answer":"\\(\\frac{\\sum (组中值 \\times 频数)}{\\sum 频数}\\)","solution":"根据《核心知识点》第2条，频数分布直方图求平均数的步骤为：先确定各组组中值，再提取对应频数，计算总数量（组中值\\(\\times\\)频数之和）与总频数（频数之和），最后用总数量除以总频数得到平均数。","stem_html":"频数分布直方图的平均数=________________
","answer_html":"\\(\\frac{\\sum (组中值 \\times 频数)}{\\sum 频数}\\)","solution_html":"根据《核心知识点》第2条，频数分布直方图求平均数的步骤为：先确定各组组中值，再提取对应频数，计算总数量（组中值\\(\\times\\)频数之和）与总频数（频数之和），最后用总数量除以总频数得到平均数。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:35:19"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:35:19"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:35:19"},{"type":"VISION","status":"FAIL","score":0.5,"created_at":"2026-11-10T12:36:02"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:37:11"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:37:11"},{"type":"SYMBOLIC","status":"PASS","score":0.9,"created_at":"2026-11-10T12:37:11"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T12:37:36"},{"type":"QUALITY_GATE","status":"FAIL","score":0.85,"created_at":"2026-11-10T12:37:36"}],"detail_url":"/questions/182150","edit_url":"/questions/182150/edit","json_url":"/api/questions/182150","recheck_url":"/api/questions/182150/recheck"},{"id":182099,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_335_检测.pdf","job_source":"数学-冀教版.zip","pages":[4,4],"stem":"已知y−1与x+ 3成正比例，当x= −1时，y= 3．\\(\\frac{(1)}{(2)}\\)求出y与x的函数关系式； 设点(a, −2)在这个函数的图象上，求a的值．","options":[],"answer":"","solution":"","stem_html":"已知y−1与x+ 3成正比例，当x= −1时，y= 3．\\(\\frac{(1)}{(2)}\\)求出y与x的函数关系式； 设点(a, −2)在这个函数的图象上，求a的值．
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:30:58"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:30:58"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:30:58"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T12:31:35"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:32:09"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:32:09"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:32:09"}],"detail_url":"/questions/182099","edit_url":"/questions/182099/edit","json_url":"/api/questions/182099","recheck_url":"/api/questions/182099/recheck"},{"id":182095,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.955,"source_file":"冀教版/八下/薛豪Q_18952688822_335_检测.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"已知y与x+ 2成正比例，当x= 2时y= 4．\\(\\frac{(1)}{(2)}\\)求y关于x的函数表达式； 若点P(−6, m + 4)在该函数图象上，求m的值．","options":[],"answer":"(1) y = x + 2; (2) m = -2","solution":"由正比例关系设 y = k(x+2)，代入 x=2, y=4 得 4 = k(4) ⇒ k=1，故 y = x+2。将 P(−6, m+4) 代入得 m+4 = −6+2 = −4 ⇒ m = −8？等等，−6+2=−4，所以 m+4=−4 ⇒ m=−8。但来源答案写 m=−2，矛盾。","stem_html":"已知y与x+ 2成正比例，当x= 2时y= 4．\\(\\frac{(1)}{(2)}\\)求y关于x的函数表达式； 若点P(−6, m + 4)在该函数图象上，求m的值．
","answer_html":"(1) y = x + 2; (2) m = -2","solution_html":"由正比例关系设 y = k(x+2)，代入 x=2, y=4 得 4 = k(4) ⇒ k=1，故 y = x+2。将 P(−6, m+4) 代入得 m+4 = −6+2 = −4 ⇒ m = −8？等等，−6+2=−4，所以 m+4=−4 ⇒ m=−8。但来源答案写 m=−2，矛盾。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:24:57"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:24:57"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:24:57"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T12:25:39"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-11-10T12:28:31"},{"type":"CRITIC","status":"FAIL","score":0.95,"created_at":"2026-11-10T12:28:31"},{"type":"COHERENCE","status":"FAIL","score":0.2,"created_at":"2026-11-10T12:28:31"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:28:31"},{"type":"QUALITY_GATE","status":"FAIL","score":0.955,"created_at":"2026-11-10T12:28:31"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:35:22"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:35:22"},{"type":"COHERENCE","status":"FAIL","score":0.2,"created_at":"2026-11-10T12:35:22"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:35:22"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-11-10T12:35:22"}],"detail_url":"/questions/182095","edit_url":"/questions/182095/edit","json_url":"/api/questions/182095","recheck_url":"/api/questions/182095/recheck"},{"id":182085,"job_id":10,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_335_检测.pdf","job_source":"数学-冀教版.zip","pages":[1,1],"stem":"若y−1与2x+ 3成正比例，且x= 2时，y= 15，则y关于x的函数解析式为( ) A. y = 2x + 3 B. y = 4x + 7 C. y = 2x + 2 D. y = 2x + 15","options":[{"label":"A","text":"y = 2x + 3"},{"label":"B","text":"y = 4x + 7"},{"label":"C","text":"y = 2x + 2"},{"label":"D","text":"y = 2x + 15"}],"answer":"B","solution":"由题意，设y−1 =k(2x+ 3)， ∵ x= 2时,y= 15,∴ 15 −1 =k(\\(2\\times 2 + 3\\)),解 得：k = 2；∴y −1 = 2(2x + 3), ∴y = 4x + 7; 故选B．","stem_html":"若y−1与2x+ 3成正比例，且x= 2时，y= 15，则y关于x的函数解析式为( )
A. y = 2x + 3
B. y = 4x + 7
C. y = 2x + 2
D. y = 2x + 15
","answer_html":"B","solution_html":"由题意，设y−1 =k(2x+ 3)， ∵ x= 2时,y= 15,∴ 15 −1 =k(\\(2\\times 2 + 3\\)),解 得：k = 2；∴y −1 = 2(2x + 3), ∴y = 4x + 7; 故选B．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:28:24"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:28:24"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:28:24"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T12:29:58"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:30:18"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:30:18"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:30:18"}],"detail_url":"/questions/182085","edit_url":"/questions/182085/edit","json_url":"/api/questions/182085","recheck_url":"/api/questions/182085/recheck"},{"id":182097,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_335_检测.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"已知函数\\(y = (m - 2)x^{m^{2} - 3} + 4 + n\\)． (1) 当$m, n$为何值时，\\(y\\)是\\(x\\)的一次函数，并写出关系式？ (2) 当$m, n$为何值时，\\(y\\)是\\(x\\)的正比例函数，并写出关系式？","options":[],"answer":"","solution":"","stem_html":"已知函数\\(y = (m - 2)x^{m^{2} - 3} + 4 + n\\)．\n(1) 当$m, n$为何值时，\\(y\\)是\\(x\\)的一次函数，并写出关系式？\n(2) 当$m, n$为何值时，\\(y\\)是\\(x\\)的正比例函数，并写出关系式？
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:27:18"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:27:18"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:27:18"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T12:29:03"}],"detail_url":"/questions/182097","edit_url":"/questions/182097/edit","json_url":"/api/questions/182097","recheck_url":"/api/questions/182097/recheck"},{"id":182138,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_940.pdf","job_source":"数学-沪教版.zip","pages":[1,1],"stem":"加权平均数=_____________________","options":[],"answer":"","solution":"","stem_html":"加权平均数=_____________________
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:21:17"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:21:17"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:21:17"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T12:22:00"}],"detail_url":"/questions/182138","edit_url":"/questions/182138/edit","json_url":"/api/questions/182138","recheck_url":"/api/questions/182138/recheck"},{"id":182094,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_335_检测.pdf","job_source":"数学-冀教版.zip","pages":[2,2],"stem":"经验表明，种子在发芽阶段，适当的光照时长对种子发芽的数量有 一定的影响.通过对某种植物种子进行光照时长研究，发现这种 植物的种子发芽数量y(颗)是光照时长x(小时)的一次函数.已知 当光照时长为2h时，该植物种子有5颗发芽；光照时长为8h时，该植物种子有11颗发芽.\\(\\frac{(1)}{(2)}\\)求y与x之间的函数表达式； 当该植物种子有27颗发芽时，光照时长是多少？","options":[],"answer":"","solution":"","stem_html":"经验表明，种子在发芽阶段，适当的光照时长对种子发芽的数量有 一定的影响.通过对某种植物种子进行光照时长研究，发现这种 植物的种子发芽数量y(颗)是光照时长x(小时)的一次函数.已知 当光照时长为2h时，该植物种子有5颗发芽；光照时长为8h时，该植物种子有11颗发芽.\\(\\frac{(1)}{(2)}\\)求y与x之间的函数表达式； 当该植物种子有27颗发芽时，光照时长是多少？
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:17:43"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:17:43"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:17:43"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:19:18"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:19:18"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T12:19:31"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:19:31"}],"detail_url":"/questions/182094","edit_url":"/questions/182094/edit","json_url":"/api/questions/182094","recheck_url":"/api/questions/182094/recheck"},{"id":182093,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_335_检测.pdf","job_source":"数学-冀教版.zip","pages":[2,2],"stem":"某水果超市在元旦期间进行苹果优惠促销活动，苹果的标价为每千 克5元，如果一次性购买4kg以上的苹果，超过4kg的部分按标价6折 售卖.其中x(单位：kg)表示购买苹果的重量，y(单位：元)表示付款金额．\\(\\frac{(1)}{(2)}\\)当一次性购买4kg以上苹果时，请写出y与x之间的函数关系式； 文文妈妈在该超市购买了8kg苹果，应该付多少元？","options":[],"answer":"","solution":"","stem_html":"某水果超市在元旦期间进行苹果优惠促销活动，苹果的标价为每千 克5元，如果一次性购买4kg以上的苹果，超过4kg的部分按标价6折 售卖.其中x(单位：kg)表示购买苹果的重量，y(单位：元)表示付款金额．\\(\\frac{(1)}{(2)}\\)当一次性购买4kg以上苹果时，请写出y与x之间的函数关系式； 文文妈妈在该超市购买了8kg苹果，应该付多少元？
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:17:08"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:17:08"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:17:08"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T12:18:30"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:18:50"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:18:50"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T12:18:50"}],"detail_url":"/questions/182093","edit_url":"/questions/182093/edit","json_url":"/api/questions/182093","recheck_url":"/api/questions/182093/recheck"},{"id":182101,"job_id":11,"qa_status":"QUARANTINED","question_type":"knowledge","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":1.0,"source_file":"青岛版/七上/杜辉Q_18951362233_305.pdf","job_source":"数学-青岛版.zip","pages":[1,1],"stem":"有理数的除法法则： ①同号相加：同号相加，符号不变，绝对值相加. ①两数相除，同号得正，异号得负 ②异号相加：取绝对值较大的加数的符号，并用 ②0 除以任何一个不为0 的数，都得0 较大的绝对值减去较小的绝对值 ③除以一个不为0 的数，等于乘这个数的倒数 ③一个数与0 相加，仍得这个数.","options":[],"answer":"","solution":"","stem_html":"有理数的除法法则： ①同号相加：同号相加，符号不变，绝对值相加. ①两数相除，同号得正，异号得负 ②异号相加：取绝对值较大的加数的符号，并用 ②0 除以任何一个不为0 的数，都得0 较大的绝对值减去较小的绝对值 ③除以一个不为0 的数，等于乘这个数的倒数 ③一个数与0 相加，仍得这个数.
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-11-10T12:14:21"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:14:21"},{"type":"VISION","status":"FAIL","score":0.9,"created_at":"2026-11-10T12:15:58"},{"type":"QUALITY_GATE","status":"FAIL","score":1.0,"created_at":"2026-11-10T12:15:58"}],"detail_url":"/questions/182101","edit_url":"/questions/182101/edit","json_url":"/api/questions/182101","recheck_url":"/api/questions/182101/recheck"},{"id":182083,"job_id":9,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_935_检测.pdf","job_source":"数学-沪教版.zip","pages":[4,4],"stem":"一个班有50名学生，一次考试成绩(单位：分)的分布情况如下表所示：\\(\\frac{(1)}{(2)}\\)填写表中＂组中值＂一栏的空白； 求该班本次考试的平均成绩．","options":[],"answer":"这组红包金额数据的平均数为33元。","solution":"(1)54.5，64.5，74.5，84.5，94.5；(2)77.3分. (1)\\(\\frac{1}{2} \\times (49.5 + 59.5) = 54.5\\)，\\(\\frac{1}{2} \\times (59.5 + 69.5) = 64.5\\)，\\(\\frac{1}{2} \\times (69.5 + 79.5)= 74.5\\)，\\(\\frac{1}{2} \\times (79.5 + 89.5) = 84.5\\)，\\(\\frac{1}{2} \\times (89.5 + 99.5) = 94.5\\)，故 答案为：54.5，64.5，74.5，84.5，94.5． (2)总成绩为：\\(54.5 \\times 4 + 64.5 \\times 8 + 74.5 \\times 14 + 84.5 \\times 18 + 94.5 \\times 6= 3865\\)(分).3865 ÷ (4 + 14 + 8 + 18 + 6) = 77.3(分).答：本次考试的平均成绩是77.3分．","stem_html":"一个班有50名学生，一次考试成绩(单位：分)的分布情况如下表所示：\\(\\frac{(1)}{(2)}\\)填写表中＂组中值＂一栏的空白； 求该班本次考试的平均成绩．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/b8090d7b-cae2-431f-b528-e600c89ea924/8d3c259bb7be.png\" "\\"点击查看原图\\"")
如果a的相反数是最小的正整数，b是最大的负整数，c是绝对值最小的有 理数，请问a，b, c三数之和是______.
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:02:42"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T12:02:42"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:02:42"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:03:25"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:03:25"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T12:04:25"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T12:04:25"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T12:05:57"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T12:05:57"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:10:57"},{"type":"CRITIC","status":"FAIL","score":1.0,"created_at":"2026-11-10T12:10:57"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T12:13:49"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:13:49"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-11-10T12:13:49"}],"detail_url":"/questions/182068","edit_url":"/questions/182068/edit","json_url":"/api/questions/182068","recheck_url":"/api/questions/182068/recheck"},{"id":182082,"job_id":9,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"沪教版/八下/周琼玟Q_18978751881_935_检测.pdf","job_source":"数学-沪教版.zip","pages":[4,4],"stem":"春节期间为了表达美好的祝福，抢微信红包成为了人们最喜欢的 活动之一．某中学九年级六班班长对全班学生在春节期间所抢的 红包金额进行统计，并绘制成了统计图．请根据相关信息，解答 下列问题：求统计的这组红包金额数据的平均数．","options":[],"answer":"33元","solution":"因为−x =\\(10 \\times 4 + 20 \\times 6 + 30 \\times 12 + 40 \\times 10 + 50 \\times 8 = 33\\)(元)所以 40 这组红包金额数据的平均数为33元。","stem_html":"春节期间为了表达美好的祝福，抢微信红包成为了人们最喜欢的 活动之一．某中学九年级六班班长对全班学生在春节期间所抢的 红包金额进行统计，并绘制成了统计图．请根据相关信息，解答 下列问题：求统计的这组红包金额数据的平均数．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/b66d1029-eef7-4822-b587-1e33acfa0201/107821c8-3cb9-4a67-b40a-ceda15b2f257/200b4258930a.png\" "\\"点击查看原图\\"")
为了鉴定某种灯泡的质量，对其中20个灯泡的使用寿命进行测量，结 果如下表，请填上组中值再求这些灯泡的平均使用寿命．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/e8b5b3ba-7eea-4845-aeae-282b4740c74f/b6c2f8ef3041.png\" "\\"点击查看原图\\"")
某公司开展了以亲近自然、劳逸结合、强健体魄、增强凝聚力为主题 的工会健步走活动．王伟所在的部门共20人，将这20人某一天行走 的步数进行统计，绘制了如下的统计表：根据上述信息，解答下列问题：\\(\\frac{(1)}{(2)}\\)a =_____ ； 求这20人一天行走的平均步数. 10.2023年10月26日，神舟十七号发射成功，三位宇航员将在太空驻留约 6个月．某校为了调查本校学生对航空航天知识的知识情况，开展 了航空航天知识竞赛，从参赛学生中随机抽取若干名学生的成绩进 行统计，得到如下不完整的统计图表：请根据图表信息解答下列问题：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/ba4c8bb9-b438-488c-9d5d-8cd376315d0f/668cc5170910.png\" "\\"点击查看原图\\"")
（1）求\\(a\\)，\\(b\\)，\\(c\\)的值；\\(\\frac{(2)}{(3)}\\)补全频数分布直方图；估计此次航天知识竞赛的平均成绩.
某校八年级(1)班20名学生某次数学测验的成绩统计如表：\\(\\frac{(1)}{(2)}\\)若这20名学生成绩的平均数为82分，求x和y的值． 在(1)的条件下，求这20名学生本次测验成绩的众数和中位数．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/2b88cf0e-bf37-4fa5-af19-f35038eb9d6b/bb05d38112ce.png\" "\\"点击查看原图\\"")
下列各式运算正确的是( ).
A. (−2) −(−2) = 0
B. 0 + (−4) = 4
C. (− 1 1\\(2 _{5}\\)) = −15 \\(frac_3\\)) + (−_2) + (−
D. (− 1\\(1 _{2}\\)) = 0
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T12:01:51"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-11-10T12:01:51"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T12:01:51"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T12:02:37"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T12:03:03"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T12:03:03"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T12:03:03"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T12:03:29"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-11-10T12:03:29"}],"detail_url":"/questions/182065","edit_url":"/questions/182065/edit","json_url":"/api/questions/182065","recheck_url":"/api/questions/182065/recheck"},{"id":182033,"job_id":10,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"冀教版/八下/薛豪Q_18952688822_330.pdf","job_source":"数学-冀教版.zip","pages":[4,4],"stem":"下列说法中正确的是( ) A. y = px是正比例函数 B. 如果y = (d −1)x +\\(d^{2}\\)−1是正比例函数，那么d = ±1 C. 如果y与x −3成正比例，那么y是x的正比例函数 D. 如果y =\\(3x^{5}\\)，那么y与\\(x^{5}\\)成正比例","options":[{"label":"A","text":"y = px是正比例函数"},{"label":"B","text":"如果y = (d −1)x + d^{2} −1是正比例函数，那么d = ±1"},{"label":"C","text":"如果y与x −3成正比例，那么y是x的正比例函数"},{"label":"D","text":"如果y = 3x^{5} ，那么y与 x^{5} 成正比例"}],"answer":"","solution":"","stem_html":"下列说法中正确的是( )
A. y = px是正比例函数
B. 如果y = (d −1)x +\\(d^{2}\\)−1是正比例函数，那么d = ±1
C. 如果y与x −3成正比例，那么y是x的正比例函数
D. 如果y =\\(3x^{5}\\)，那么y与\\(x^{5}\\)成正比例
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:52:04"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:52:04"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:52:04"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T11:53:11"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T11:55:45"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:55:45"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T11:55:45"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T11:56:20"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T11:56:20"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.0,"created_at":"2026-11-10T12:01:34"}],"detail_url":"/questions/182033","edit_url":"/questions/182033/edit","json_url":"/api/questions/182033","recheck_url":"/api/questions/182033/recheck"},{"id":182077,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"沪教版/八下/周琼玟Q_18978751881_935_检测.pdf","job_source":"数学-沪教版.zip","pages":[2,2],"stem":"植物兴趣小组进行辣椒种植实验．移栽时，兴趣小组记录了每一棵辣 椒苗的高度(单位：cm)，绘制了如图所示的直方统计图，这批辣椒 苗的平均高度是____ cm．(结果保留一位小数)","options":[],"answer":"5.1","solution":"\\(3.5 \\times 2 + 4.5 \\times 6 + 5.5 \\times 5 + 6.5 \\times 3\\)辣椒苗的平均高度 = ≈5.1(cm)，故答案为：5.1． 16","stem_html":"植物兴趣小组进行辣椒种植实验．移栽时，兴趣小组记录了每一棵辣 椒苗的高度(单位：cm)，绘制了如图所示的直方统计图，这批辣椒 苗的平均高度是____ cm．(结果保留一位小数)
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/a3e04980-fe95-4c65-8e62-8878e51256a2/71b5eb3970b9.png\" "\\"点击查看原图\\"")
下列计算中，正确的是( ). ．2+ (−3) = −5 6．+ (−1) = 7 A B ．(−3) + (−9) =12 ．(−7) + 4 = −3 C D
","answer_html":"","solution_html":"、2+ (−3) = −1，原题计算错误； A 、6+ (−1) = 5，原题计算错误； B 、(−3) + (−9) = −12，原题计算错误； C 、(−7) + 4 = −3，原题计算正确． D D 故选：．","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:51:51"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:51:51"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:51:51"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T11:52:57"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:52:57"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T11:53:00"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T11:53:00"},{"type":"COHERENCE","status":"FAIL","score":1.0,"created_at":"2026-11-10T11:54:42"},{"type":"QUALITY_GATE","status":"FAIL","score":0.963,"created_at":"2026-11-10T11:54:42"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T11:56:10"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:56:10"},{"type":"COHERENCE","status":"FAIL","score":1.0,"created_at":"2026-11-10T11:59:56"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T11:59:56"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-11-10T11:59:56"}],"detail_url":"/questions/182061","edit_url":"/questions/182061/edit","json_url":"/api/questions/182061","recheck_url":"/api/questions/182061/recheck"},{"id":182078,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_935_检测.pdf","job_source":"数学-沪教版.zip","pages":[2,2],"stem":"西安，这座见证了千年历史的城市，以其深厚的文化底蕴和丰富的 旅游资源吸引着各地游客.某景区管理处为了解景区的服务质量，现 从该景区8月份某天的游客中随机抽取200名游客对景区的服务质量进行 评分，评分结果用x(单位：分)表示，将全部评分结果按以下四组 进行整理，并绘制了如下不完整的统计图表：请根据上述信息，解答下列问题：\\(\\frac{(1)}{(2)}\\)m =____ ； 求所抽取游客评分的平均分数.","options":[],"answer":"(1)40; (2)85分","solution":"\\(\\frac{(1)}{(2)}\\)抽取总人数为200人. 故m = 200 −16 −94 −50 = 40人．故答案为：40；\\(\\frac{1100 + 3000 + 8000 + 4900}{200} = 85\\)(分)； ∴ 所抽取游客评分的平均分数为85分．","stem_html":"西安，这座见证了千年历史的城市，以其深厚的文化底蕴和丰富的 旅游资源吸引着各地游客.某景区管理处为了解景区的服务质量，现 从该景区8月份某天的游客中随机抽取200名游客对景区的服务质量进行 评分，评分结果用x(单位：分)表示，将全部评分结果按以下四组 进行整理，并绘制了如下不完整的统计图表：请根据上述信息，解答下列问题：\\(\\frac{(1)}{(2)}\\)m =____ ； 求所抽取游客评分的平均分数.
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/8f81845d-34e4-4c8f-acb0-097e23d7e77a/5deed859c1ff.png\" "\\"点击查看原图\\"")
对一组数据整理如下表，估计这组数据的平均数为 ____. 填空题，每题6分
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/e0901573-f954-490f-9527-7cbfcb22ba44/9a3f33723e75.png\" "\\"点击查看原图\\"")
已知y = (m −1)x2−|m|+ n + 4．
（1）当m, n取何值时，y是x的一次函数？
（2）当m, n取何值时，y是x的正比例函数？
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:46:32"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:46:32"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:46:32"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T11:47:59"}],"detail_url":"/questions/182035","edit_url":"/questions/182035/edit","json_url":"/api/questions/182035","recheck_url":"/api/questions/182035/recheck"},{"id":182028,"job_id":10,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_330.pdf","job_source":"数学-冀教版.zip","pages":[2,2],"stem":"若函数 = 3x + 5，函数\\(y_{2}\\)= 2x − 5，且\\(\\frac{y_{1}}{y_{2}}\\)y =\\(y_{1}\\)+，则下列说法错误的是( ) A ．是的正比例函数yx B ．是的一次函数yx C ．不是的正比例函数\\(y_{1}\\)x D ．是关于的正比例函数\\(y_{2}\\)x","options":[],"answer":"","solution":"Q = 3 + 5, = x − 5， y = + \\(y_2fracy_1\\)(3 fracx5) \\(fracy_2\\)x frac25) \\(fracy_1\\)5 = x + + (2 − = 5x, A、y = x是 B 正比例函数，正确，不符合题意；、 y = 5x是一次函数，正确，不符合题 意；、\\(y_{1}\\)= 3x + 5有常数项，不是正5 C 比例函数，正确，不符合题意；、\\(y_{2}\\)D = 2x − 5有常数项 − 5，不是正比例函数， D 错误，符合题意；故选：．","stem_html":"若函数 = 3x + 5，函数\\(y_{2}\\)= 2x − 5，且\\(\\frac{y_{1}}{y_{2}}\\)y =\\(y_{1}\\)+，则下列说法错误的是( ) A ．是的正比例函数yx B ．是的一次函数yx C ．不是的正比例函数\\(y_{1}\\)x D ．是关于的正比例函数\\(y_{2}\\)x
","answer_html":"","solution_html":"Q = 3 + 5, = x − 5， y = +\\(y_2fracy_1\\)(3 fracx5) \\(fracy_2\\)x frac25) \\(fracy_1\\)5 =x + + (2 − = 5x, A、y = x是 B 正比例函数，正确，不符合题意；、 y = 5x是一次函数，正确，不符合题 意；、\\(y_{1}\\)= 3x + 5有常数项，不是正5 C 比例函数，正确，不符合题意；、\\(y_{2}\\)D = 2x − 5有常数项 − 5，不是正比例函数， D 错误，符合题意；故选：．","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:40:48"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-11-10T11:40:48"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:40:48"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T11:42:20"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T11:44:48"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:44:48"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T11:44:48"}],"detail_url":"/questions/182028","edit_url":"/questions/182028/edit","json_url":"/api/questions/182028","recheck_url":"/api/questions/182028/recheck"},{"id":182072,"job_id":9,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_935_检测.pdf","job_source":"数学-沪教版.zip","pages":[1,1],"stem":"学校为了解八年级(一)班学生一周内坐公交车的情况，统计了八年 级(一)班50名学生一周内坐公交车的次数如图所示．则八年级(一)班 学生平均一周内坐公交车的次数为( ) A. 4次 B. 6次 C. 8次 D. 10次","options":[{"label":"A","text":"4次"},{"label":"B","text":"6次"},{"label":"C","text":"8次"},{"label":"D","text":"10次"}],"answer":"C","solution":"由题意可得：\\(\\frac{1}{50} (5 \\times 4 + 10 \\times 6 + 15 \\times 8 + 20 \\times 10) = 8\\)(次)．故选：C． 25∘C(单位不写不扣分)","stem_html":"学校为了解八年级(一)班学生一周内坐公交车的情况，统计了八年 级(一)班50名学生一周内坐公交车的次数如图所示．则八年级(一)班 学生平均一周内坐公交车的次数为( )
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/3df0ac15-f58e-4918-a300-8704fffa71ae/7127a117f27a.png\" "\\"点击查看原图\\"")
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/3df0ac15-f58e-4918-a300-8704fffa71ae/6934d89ecfe5.png\" "\\"点击查看原图\\"")
A. 4次
B. 6次
C. 8次
D. 10次
某班数学兴趣小组调查了全班50名学生每周做家务的时间，根据调 查所得的数据制成如图所示的条形统计图(部分)，已知全班50名学 生每周做家务的时间均为0.5, 1, 1.5, 2(单位：小时)中的一个，则该班 学生每周做家务时间的平均数(单位：小时)为( )
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/aee09174-2125-4fcd-9058-a38151ffbd9a/dcd5a74a21ec.png\" "\\"点击查看原图\\"")
A. 0.88
B. 0.98
C. 1
D. 13
下表是小叶同学根据某地一周的气温测量数据制作成的统计表，则 这一周的气温测量数的平均数是____．
","answer_html":"25∘C(单位不写不扣分)","solution_html":"\\(25 \\times 3 + 23 \\times 1 + 20 \\times 1 + 27 \\times 1 + 30 \\times 1 = 25(∘C)\\)，故 这一周的气温测量数的平均数是 3 + 1 + 1 + 1 + 1 答案为：25∘C．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:43:27"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:43:27"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:43:27"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T11:45:20"}],"detail_url":"/questions/182074","edit_url":"/questions/182074/edit","json_url":"/api/questions/182074","recheck_url":"/api/questions/182074/recheck"},{"id":182034,"job_id":10,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_330.pdf","job_source":"数学-冀教版.zip","pages":[4,4],"stem":"下列说法中正确的有( )①当 k ≠0 时, y = − _{k}是正比例函数；②如果y = (a + 3)x +\\(a^{2}\\)−x 9是正比例函数，那么a = ±3；③如果y与x + 2成正比例, 那么y是x的正比例函数；④如果y =\\(1 _{3}x^{2}\\), 那么y与\\(x^{2}\\)成正比例. A. 4个 B. 3个 C. 2个 D. 1个","options":[{"label":"A","text":"4个"},{"label":"B","text":"3个"},{"label":"C","text":"2个"},{"label":"D","text":"1个"}],"answer":"","solution":"","stem_html":"下列说法中正确的有( )①当 k ≠0 时, y = − _{k}是正比例函数；②如果y = (a + 3)x +\\(a^{2}\\)−x 9是正比例函数，那么a = ±3；③如果y与x + 2成正比例, 那么y是x的正比例函数；④如果y =\\(1 _{3}x^{2}\\), 那么y与\\(x^{2}\\)成正比例.
A. 4个
B. 3个
C. 2个
D. 1个
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:43:02"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:43:02"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:43:02"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T11:46:27"}],"detail_url":"/questions/182034","edit_url":"/questions/182034/edit","json_url":"/api/questions/182034","recheck_url":"/api/questions/182034/recheck"},{"id":182032,"job_id":10,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_330.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"声音在空气中的传播速度 y(\\(\\,\\mathrm{m/s}\\)) 随气温 x(∘C) 的变化而变化．下 表给出了一组不同气温下声音传播的速度： （1）当x的值为35时，求对应的y的值； （2）求y与x的关系式．","options":[],"answer":"","solution":"","stem_html":"声音在空气中的传播速度 y(\\(\\,\\mathrm{m/s}\\)) 随气温 x(∘C) 的变化而变化．下 表给出了一组不同气温下声音传播的速度：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/a13a92c3-ebda-4a16-b969-9efbd0519d0d/166982ef-8370-46de-99dd-2763a88997e1/b08691e86f23.png\" "\\"点击查看原图\\"")
（1）当x的值为35时，求对应的y的值；
（2）求y与x的关系式．
某种储蓄罐的质量为50克，投入若干枚某种一元硬币以后，储蓄罐和硬币的总质量y(单位：克) 与硬币数量x(单位：枚)的关系如下表：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/a13a92c3-ebda-4a16-b969-9efbd0519d0d/0ca3dd5a-a7ec-44f0-b450-9837e9094053/a5718fe7095c.png\" "\\"点击查看原图\\"")
（1）求y与x之间的函数关系式(x为正整数)；
（2）当投入的硬币数量为6枚时，储蓄罐和硬币的总质量为____克；
已知等腰三角形 的周长为，设腰\\(12 \\frac{ABC}{BC}\\)AB长为，底边x 长为．\\(y \\frac{(1)}{(2)}\\)求关于的函数表达式．yx 当腰长为时，求底边的长．4
","answer_html":"","solution_html":"(1) Q 等腰三角形 的周长为，腰AB\\(\\frac{ABC}{长为} \\frac{12}{x}\\)长为，底边xBC y = 12 − 2，根据 − x 三角形三边关系可知：\\(\\frac{12}{12} \\frac{2}{2}\\frac{x}{x} \\frac{2}{0}\\)解得： − 3 x 6， = 12 − 2x(3 x 6);\\(\\frac{y}{代入}\\)把x = = 12 − 2x得：\\(\\frac{(2)}{y} \\frac{4}{2} \\frac{y}{4} = 12\\)− =，\\(\\frac{4}{4}\\)当腰长为时，底边的长为．4","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:39:50"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:39:50"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:39:50"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T11:41:07"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T11:41:22"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:41:22"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T11:41:22"}],"detail_url":"/questions/182027","edit_url":"/questions/182027/edit","json_url":"/api/questions/182027","recheck_url":"/api/questions/182027/recheck"},{"id":182029,"job_id":10,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_330.pdf","job_source":"数学-冀教版.zip","pages":[2,2],"stem":"【小试1】 某风景区集体门票的收费标准是：20人以内(含20人)，每人50元； 超过20人的，超过的部分，每人40元． （1）写出门票收费y(元)与游览人数x(人)之间的关系式； （2）701班班主任带领45名学生去该风景区游览，购买门票共需要多 少元？","options":[],"answer":"(1)y = {50x(0 ≤x ≤20)","solution":"40x + 200(x > 20) (2)2040元 (1)当0 ≤x ≤20时，y = 50x；当x > 20时，y = 40(x −20) +\\(20\\times 50=40x + 200\\)(其中x是整数 )，综上所述，门票费y(元)与游览人数x(人)之间的关系式为：y = {50x(0 ≤x ≤20) 40x + 200(x > 20)； (2)老师和学生的总人数为：45 + 1 = 46(人)，当x = 46时，y = 40x+200 =\\(40\\times 46 + 200 = 2040\\)(元 ). 答：购买门票共需要2040元．","stem_html":"【小试1】 某风景区集体门票的收费标准是：20人以内(含20人)，每人50元； 超过20人的，超过的部分，每人40元．
（1）写出门票收费y(元)与游览人数x(人)之间的关系式；
（2）701班班主任带领45名学生去该风景区游览，购买门票共需要多 少元？
","answer_html":"(1)y = {50x(0 ≤x ≤20)","solution_html":"40x + 200(x > 20) (2)2040元 (1)当0 ≤x ≤20时，y = 50x；当x > 20时，y = 40(x −20) +\\(20\\times 50=40x + 200\\)(其中x是整数 )，综上所述，门票费y(元)与游览人数x(人)之间的关系式为：y = {50x(0 ≤x ≤20) 40x + 200(x > 20)； (2)老师和学生的总人数为：45 + 1 = 46(人)，当x = 46时，y = 40x+200 =\\(40\\times 46 + 200 = 2040\\)(元 ). 答：购买门票共需要2040元．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:38:32"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:38:32"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:38:32"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T11:39:56"}],"detail_url":"/questions/182029","edit_url":"/questions/182029/edit","json_url":"/api/questions/182029","recheck_url":"/api/questions/182029/recheck"},{"id":182000,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_930.pdf","job_source":"数学-沪教版.zip","pages":[4,4],"stem":"如图，某学校抽查了10名八年级学生的数学期中成绩，则这10名学生的数学平均成绩为( )\\(\\frac{(A)88}{(B)87} \\frac{(C)86}{(D)85} 6.2018\\)年10月28日，江西省第十五届运动会在景德镇开幕，来自梨树园小学的 80名同学参加了开幕式表演，他们用葫芦丝合奏了《我在景德镇等你》，他 们当中男同学人数的2倍比女同学人数的3倍少15人. （1）男、女同学各有多少人？ （2）若这80名同学学习葫芦丝的平均时间为14.25个月，其中女同学学习葫芦丝 的平均时间为12个月，则男同学学习葫芦丝的平均时间是多少个月？","options":[],"answer":"","solution":"","stem_html":"如图，某学校抽查了10名八年级学生的数学期中成绩，则这10名学生的数学平均成绩为( )\\(\\frac{(A)88}{(B)87} \\frac{(C)86}{(D)85} 6.2018\\)年10月28日，江西省第十五届运动会在景德镇开幕，来自梨树园小学的 80名同学参加了开幕式表演，他们用葫芦丝合奏了《我在景德镇等你》，他 们当中男同学人数的2倍比女同学人数的3倍少15人.
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/fa0cc763-ea5a-4b62-8e57-d9170cc20e5e/798729164d97.png\" "\\"点击查看原图\\"")
（1）男、女同学各有多少人？
（2）若这80名同学学习葫芦丝的平均时间为14.25个月，其中女同学学习葫芦丝 的平均时间为12个月，则男同学学习葫芦丝的平均时间是多少个月？
在一次演讲比赛中，参赛的20名学生成绩统计如图，则这20名学生成绩的平均数是____．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/f1590cb9-812b-41f0-a1a8-a8cb2a8c73af/6a2a80a0-88f1-4a78-b309-67edc9185833/ce30c0f48879.png\" "\\"点击查看原图\\"")
为了了解400名八年级男生的身体发育情况，随机抽取了100名八年级 男生进行身高测量，得到统计表：估计该校八年级男生的平均身高为____cm.
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/0730e009-323e-4266-a4b5-e0e85b030b36/5c5fcb41d92f.png\" "\\"点击查看原图\\"")
把下列各数填在相应的括号里 −3, 23\\(3 _{5}\\), 7,3.14,2025, −\\(3 _{4}\\), 0, −5%,\\(\\pi\\)整数集合：{ . . . } 分数集合：{ . . . }有理数集合：{ . . . }非负整数集合：{ . . . }
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:17:35"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:17:35"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:17:35"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T11:20:22"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T11:21:25"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:21:25"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T11:21:25"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T11:22:38"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-11-10T11:22:38"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.0,"created_at":"2026-11-10T11:30:29"}],"detail_url":"/questions/181966","edit_url":"/questions/181966/edit","json_url":"/api/questions/181966","recheck_url":"/api/questions/181966/recheck"},{"id":181995,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_930.pdf","job_source":"数学-沪教版.zip","pages":[3,3],"stem":"【小试2】 某校为了了解该校学生在家做家务的情况，随机调查了50名学生，得 到他们在一周内做家务所用时间的情况如下表所示，则可以估计该校 学生平均每人在一周内做家务所用时间是____小时. (同一组中的数 据用这组数据的组中值作代表)","options":[],"answer":"","solution":"","stem_html":"【小试2】 某校为了了解该校学生在家做家务的情况，随机调查了50名学生，得 到他们在一周内做家务所用时间的情况如下表所示，则可以估计该校 学生平均每人在一周内做家务所用时间是____小时. (同一组中的数 据用这组数据的组中值作代表)
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/aa652241-c57c-4505-93dc-55507bca60f1/d17073d80bca.png\" "\\"点击查看原图\\"")
某灯泡厂为测试一批节能灯的使用寿命， 从中随机抽查了100个节能灯，它们的使 用寿命如下表所示： 则这批节能灯的平均使用寿命是____小时.
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/a13a92c3-ebda-4a16-b969-9efbd0519d0d/c55f4dd7-1369-4e1c-8d7b-4c1714137361/0c871e377cba.png\" "\\"点击查看原图\\"")
某超市2025年1－6月份的营业额与2024年同月营业额相比，其增长率 如下表所示．请根据表格信息回答下列问题：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/25691159-497d-4ce1-90b3-ac48b74c97f3/4d213a39-0d04-445a-a1ca-6692fc90e70f/fe4fc65811bd.png\" "\\"点击查看原图\\"")
（1）该超市2025年1－6月份的营业额与2024年同月营业额相比，哪几个月是增长的？
（2）2025年1月和4月相比2024年同月营业额的增长率是负数分别表示什么意义？
射击比赛中，某选手的10次射击成绩如表所示： 则该选手的平均成绩是____ 环．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/a13a92c3-ebda-4a16-b969-9efbd0519d0d/ff553019-e739-4ee2-86b7-56d31c4bad79/a0ba857c4611.png\" "\\"点击查看原图\\"")
观察下面各数：−1, +2, −3, +4, −5, +6, −7, +8, −9, ⋯⋯．
（1）写出这列数中的第100个数和第2025个数．
（2）在前2025个数中，正数和负数分别有多少个？
（3）2035是否在这列数中？若在，请写出2035是第几个数；若不在，请说明理由．
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:18:02"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:18:02"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:18:02"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T11:18:59"}],"detail_url":"/questions/181969","edit_url":"/questions/181969/edit","json_url":"/api/questions/181969","recheck_url":"/api/questions/181969/recheck"},{"id":181967,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_30.pdf","job_source":"数学-青岛版.zip","pages":[3,3],"stem":"把下列各数的序号分别填入相应的大括号内：①10%②−1\\(1 _{2}\\)③−2④101⑤− 15⑥0⑦2．010010001⑧\\(\\pi⑨ 22_{7}\\)正有理数集合：{______. . . }整数集合：{___________. . . }非负数集合： {___________. . . }","options":[],"answer":"","solution":"","stem_html":"把下列各数的序号分别填入相应的大括号内：①10%②−1\\(1 _{2}\\)③−2④101⑤− 15⑥0⑦2．010010001⑧\\(\\pi⑨ 22_{7}\\)正有理数集合：{______. . . }整数集合：{___________. . . }非负数集合： {___________. . . }
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:17:52"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:17:52"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:17:52"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T11:18:43"}],"detail_url":"/questions/181967","edit_url":"/questions/181967/edit","json_url":"/api/questions/181967","recheck_url":"/api/questions/181967/recheck"},{"id":181961,"job_id":11,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_30.pdf","job_source":"数学-青岛版.zip","pages":[2,2],"stem":"把下列各数填入相应的集合内： 5,\\(\\frac{1}{6},98%,2 \\frac{5}{8}\\)−\\(\\frac{1}{3}\\)−325,0,100.2, −0.12, 0.1, −51%,. 2 正有理数集合 :{ }; 负有理数集合 :{ }; 负整数集合 :{ }; 非负整数集合 :{ }.","options":[],"answer":"","solution":"正有理数集合：{5,\\(\\frac{1}{6},98%,2 \\frac{5}{8},100.2,0.1,\\)}； 负有理数集合：{− 1 ,325,0.12,51%−−−，；} 3 负整数集合：{−325, }； 非负整数集合：{5,0， }.","stem_html":"把下列各数填入相应的集合内： 5,\\(\\frac{1}{6},98%,2 \\frac{5}{8}\\)−\\(\\frac{1}{3}\\)−325,0,100.2, −0.12, 0.1, −51%,. 2 正有理数集合 :{ }; 负有理数集合 :{ }; 负整数集合 :{ }; 非负整数集合 :{ }.
","answer_html":"","solution_html":"正有理数集合：{5,\\(\\frac{1}{6},98%,2 \\frac{5}{8},100.2,0.1,\\)}； 负有理数集合：{− 1 ,325,0.12,51%−−−，；} 3 负整数集合：{−325, }； 非负整数集合：{5,0， }.","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:11:00"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:11:00"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:11:00"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T11:14:39"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:14:39"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T11:14:48"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T11:14:48"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T11:16:17"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-11-10T11:16:17"}],"detail_url":"/questions/181961","edit_url":"/questions/181961/edit","json_url":"/api/questions/181961","recheck_url":"/api/questions/181961/recheck"},{"id":181963,"job_id":11,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_30.pdf","job_source":"数学-青岛版.zip","pages":[2,3],"stem":"将下列各数填入适当的括号内：\\(\\pi, 5, 2 6 _{3}\\)−3,8.9,19, − _{7}, −3.14,0有 理数集：{ . . . }; 整数集：{ . . . }; 非正数集：{ . . . }; 2 6 将下列各数填入适当的括号内：π, 5, , −3,8.9,19, − , −3.14,0有 3 7 理数集：{ . . . }; 整数集：{ . . . }; 非正数集：{ . . . }; Col1","options":[],"answer":"","solution":"","stem_html":"将下列各数填入适当的括号内：\\(\\pi, 5, 2 6 _{3}\\)−3,8.9,19, − _{7}, −3.14,0有 理数集：{ . . . }; 整数集：{ . . . }; 非正数集：{ . . . };
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/25691159-497d-4ce1-90b3-ac48b74c97f3/978b2222-4c99-40f1-b9ce-abad09181734/6a4726ac1fd2.png\" "\\"点击查看原图\\"")
\n \n \n | 2 6\n将下列各数填入适当的括号内：π, 5, , −3,8.9,19, − , −3.14,0有\n3 7\n理数集：{ . . . }; 整数集：{ . . . }; 非正数集：{ . . . }; | \n Col1 | \n
\n \n \n \n
请写出一个小于2的正分数：____．
","answer_html":"1/2","solution_html":"题目要求写出一个小于2的正分数。正分数是指大于0的分数，而1/2是一个大于0且小于2的分数，因此1/2是一个符合条件的答案。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:09:43"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:09:43"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:09:43"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T11:10:26"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:10:26"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T11:10:50"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T11:10:50"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T11:11:20"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T11:11:20"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T11:12:39"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:12:39"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:13:44"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:13:44"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-11-10T11:13:44"},{"type":"AUTO_REPAIR","status":"PASS","score":1.0,"created_at":"2026-11-10T11:13:44"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T11:17:44"}],"detail_url":"/questions/181965","edit_url":"/questions/181965/edit","json_url":"/api/questions/181965","recheck_url":"/api/questions/181965/recheck"},{"id":181925,"job_id":10,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_325.pdf","job_source":"数学-冀教版.zip","pages":[2,2],"stem":"【小试1】 等腰三角形周长为20cm，底边长ycm与腰长xcm之间的函数关系是 ( ) A. y = 20 −2x(0 < x < 10) B. y = 20 −2x(5 < x < 10) C. y = 10 −x(5 < x < 10) D. y = 10 −0.5x(10 < x < 20)","options":[{"label":"A","text":"y = 20 −2x(0 < x < 10)"},{"label":"B","text":"y = 20 −2x(5 < x < 10)"},{"label":"C","text":"y = 10 −x(5 < x < 10)"},{"label":"D","text":"y = 10 −0.5x(10 < x < 20)"}],"answer":"B","solution":"因为2x + y = 20，∴y = 20 −2x, 则20 −2x > 0, 解得：x < 10，由两边之和大于第三边，得x + x > 20 −2x，解得：x > 5，综上可得：y=20 −2x(5 < x < 10)故选B．","stem_html":"【小试1】 等腰三角形周长为20cm，底边长ycm与腰长xcm之间的函数关系是 ( )
A. y = 20 −2x(0 < x < 10)
B. y = 20 −2x(5 < x < 10)
C. y = 10 −x(5 < x < 10)
D. y = 10 −0.5x(10 < x < 20)
","answer_html":"B","solution_html":"因为2x + y = 20，∴y = 20 −2x, 则20 −2x > 0, 解得：x < 10，由两边之和大于第三边，得x + x > 20 −2x，解得：x > 5，综上可得：y=20 −2x(5 < x < 10)故选B．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:07:26"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:07:26"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:07:26"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T11:08:17"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T11:08:53"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:08:53"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:08:53"}],"detail_url":"/questions/181925","edit_url":"/questions/181925/edit","json_url":"/api/questions/181925","recheck_url":"/api/questions/181925/recheck"},{"id":181930,"job_id":10,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_325.pdf","job_source":"数学-冀教版.zip","pages":[4,4],"stem":"已知y + 3与x −1成正比例，且x = 2时，y = 2． （1）求y关于x的函数关系式． （2）判断点(−1, −5)是不是上述函数图象上的点，说明理由．","options":[],"answer":"","solution":"","stem_html":"已知y + 3与x −1成正比例，且x = 2时，y = 2．
（1）求y关于x的函数关系式．
（2）判断点(−1, −5)是不是上述函数图象上的点，说明理由．
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:02:06"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:02:06"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:02:06"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T11:03:30"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-11-10T11:03:44"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T11:03:44"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T11:03:44"}],"detail_url":"/questions/181930","edit_url":"/questions/181930/edit","json_url":"/api/questions/181930","recheck_url":"/api/questions/181930/recheck"},{"id":181931,"job_id":10,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_325.pdf","job_source":"数学-冀教版.zip","pages":[4,4],"stem":"函数y = (m −2)x +\\(m^{2}\\)−4(m为常数)． （1）当m取何值时，y是x的正比例函数？ （2）当m取何值时，y是x的一次函数？","options":[],"answer":"","solution":"","stem_html":"函数y = (m −2)x +\\(m^{2}\\)−4(m为常数)．
（1）当m取何值时，y是x的正比例函数？
（2）当m取何值时，y是x的一次函数？
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:03:34"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:03:34"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:03:34"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T11:05:03"}],"detail_url":"/questions/181931","edit_url":"/questions/181931/edit","json_url":"/api/questions/181931","recheck_url":"/api/questions/181931/recheck"},{"id":181929,"job_id":10,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_325.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"已知y与4x −2成正比例，且x = 1时，y = −4． （1）求y与x的函数关系式． （2）当x = 2时，y的值为多少？当y = 6时，x的值为多少？","options":[],"answer":"","solution":"","stem_html":"已知y与4x −2成正比例，且x = 1时，y = −4．
（1）求y与x的函数关系式．
（2）当x = 2时，y的值为多少？当y = 6时，x的值为多少？
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T11:03:05"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T11:03:05"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T11:03:05"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T11:04:07"}],"detail_url":"/questions/181929","edit_url":"/questions/181929/edit","json_url":"/api/questions/181929","recheck_url":"/api/questions/181929/recheck"},{"id":181957,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_30.pdf","job_source":"数学-青岛版.zip","pages":[2,2],"stem":"有理数的分类：_____________","options":[],"answer":"","solution":"","stem_html":"有理数的分类：_____________
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:59:00"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:59:00"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:59:00"},{"type":"VISION","status":"PASS","score":0.8,"created_at":"2026-11-10T10:59:39"}],"detail_url":"/questions/181957","edit_url":"/questions/181957/edit","json_url":"/api/questions/181957","recheck_url":"/api/questions/181957/recheck"},{"id":181923,"job_id":10,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_325.pdf","job_source":"数学-冀教版.zip","pages":[2,2],"stem":"已知长方形的周长为30,一边长为 cm，\\(\\frac{cm}{y} \\frac{x}{x}\\)与其相邻的另一边长为 cm，则与之y 间的函数解析式为( )\\(\\frac{30}{x} \\frac{x}{x}\\)．y = ．y = 30 − A\\(B \\frac{x}{30}\\)．y = − 2 ．y = 15 − C D","options":[],"answer":"","solution":"Q 矩形的周长是 cm，矩形的一组邻\\(\\frac{30}{Q} \\frac{边的和为}{边长为}\\frac{15}{cm}\\)cm，一边长为xcm，另一 y ． y = 15 − x,故选． D","stem_html":"已知长方形的周长为30,一边长为 cm，\\(\\frac{cm}{y} \\frac{x}{x}\\)与其相邻的另一边长为 cm，则与之y 间的函数解析式为( )\\(\\frac{30}{x} \\frac{x}{x}\\)．y = ．y = 30 − A\\(B \\frac{x}{30}\\)．y = − 2 ．y = 15 − C D
","answer_html":"","solution_html":"Q 矩形的周长是 cm，矩形的一组邻\\(\\frac{30}{Q} \\frac{边的和为}{边长为}\\frac{15}{cm}\\)cm，一边长为xcm，另一 y ． y = 15 − x,故选． D","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:53:33"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:53:33"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:53:33"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:54:13"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:54:13"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T10:54:54"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T10:54:54"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-11-10T10:56:00"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T10:56:00"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:57:48"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:57:48"}],"detail_url":"/questions/181923","edit_url":"/questions/181923/edit","json_url":"/api/questions/181923","recheck_url":"/api/questions/181923/recheck"},{"id":181952,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"青岛版/七上/杜辉Q_18951362233_30.pdf","job_source":"数学-青岛版.zip","pages":[2,2],"stem":"有理数：__________________","options":[],"answer":"可以写成分数形式的数","solution":"根据《核心知识点》第7条，有理数的定义是‘可以写成分数形式的数’。这一定义涵盖了整数（可视为分母为1的分数）和有限小数、无限循环小数等。","stem_html":"有理数：__________________
","answer_html":"可以写成分数形式的数","solution_html":"根据《核心知识点》第7条，有理数的定义是‘可以写成分数形式的数’。这一定义涵盖了整数（可视为分母为1的分数）和有限小数、无限循环小数等。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:51:43"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:51:43"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:51:43"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:53:30"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:53:30"},{"type":"VISION","status":"PASS","score":0.8,"created_at":"2026-11-10T10:55:01"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:55:01"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:55:48"},{"type":"QUALITY_GATE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:55:48"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:57:30"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:57:30"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-11-10T10:57:30"},{"type":"AUTO_FILL_ANSWER","status":"WARN","score":1.0,"created_at":"2026-11-10T10:57:30"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T11:01:30"}],"detail_url":"/questions/181952","edit_url":"/questions/181952/edit","json_url":"/api/questions/181952","recheck_url":"/api/questions/181952/recheck"},{"id":181924,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_325.pdf","job_source":"数学-冀教版.zip","pages":[2,2],"stem":"已知 −1与x +1成正比例，当x = −2时，\\(\\frac{y}{4}\\)y = ．\\(\\frac{(1)}{(2)} \\frac{x}{P}\\)求出与的函数关系式；y 判断点 (−−1,1)是否在函数图像上?","options":[],"answer":"","solution":"Q −1与x + 成正比例， y −= frac(1)kx fracy1) frac1x frac11 (+ ，代入 = −2, = 4得，−= \\(\\frac{y}{3} \\frac{4}{1}\\) k −+(21)，解得k = −， y −= −3(x +1)， 整理得： = −3 − 2； \\(\\frac{y}{1} \\frac{x}{y}\\)(2)当 = − 时， = −−3(1) − 2 = 1 −1， \\(\\frac{x}{P}\\) 点 (−−1,1)不在函数图像上．","stem_html":"已知 −1与x +1成正比例，当x = −2时，\\(\\frac{y}{4}\\)y = ．\\(\\frac{(1)}{(2)} \\frac{x}{P}\\)求出与的函数关系式；y 判断点 (−−1,1)是否在函数图像上?
","answer_html":"","solution_html":"Q −1与x + 成正比例， y −=frac(1)kx fracy1) frac1x frac11 (+，代入 = −2, = 4得，−= \\(\\frac{y}{3} \\frac{4}{1}\\) k −+(21)，解得k = −， y −= −3(x +1)， 整理得： = −3 − 2； \\(\\frac{y}{1} \\frac{x}{y}\\)(2)当 = − 时， = −−3(1) − 2 = 1 −1， \\(\\frac{x}{P}\\) 点 (−−1,1)不在函数图像上．","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:56:54"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-11-10T10:56:54"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:56:54"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T10:58:30"}],"detail_url":"/questions/181924","edit_url":"/questions/181924/edit","json_url":"/api/questions/181924","recheck_url":"/api/questions/181924/recheck"},{"id":181976,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_930.pdf","job_source":"数学-沪教版.zip","pages":[1,1],"stem":"加权平均数=_____________________","options":[],"answer":"","solution":"","stem_html":"加权平均数=_____________________
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:55:37"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:55:37"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:55:37"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T10:57:32"}],"detail_url":"/questions/181976","edit_url":"/questions/181976/edit","json_url":"/api/questions/181976","recheck_url":"/api/questions/181976/recheck"},{"id":181928,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_325.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"一个弹簧原长10cm，每挂1kg重物，弹簧伸长0.5cm，设重物质量为 x(kg)，弹簧总长为y(cm)，写出y与x的函数关系式。","options":[],"answer":"","solution":"","stem_html":"一个弹簧原长10cm，每挂1kg重物，弹簧伸长0.5cm，设重物质量为 x(kg)，弹簧总长为y(cm)，写出y与x的函数关系式。
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-11-10T10:55:34"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:55:34"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:55:34"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T10:57:10"}],"detail_url":"/questions/181928","edit_url":"/questions/181928/edit","json_url":"/api/questions/181928","recheck_url":"/api/questions/181928/recheck"},{"id":181946,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"青岛版/七上/杜辉Q_18951362233_30.pdf","job_source":"数学-青岛版.zip","pages":[1,1],"stem":"有理数的分类：________________ 05.0 是正数吗？__________________","options":[],"answer":"04. 有理数的分类：正有理数、零、负有理数 05. 0 是正数吗？不是","solution":"根据《核心知识点》第8条，有理数分为正有理数、零、负有理数三类。第3条明确指出'0既不是正数，也不是负数'，因此0不是正数。","stem_html":"有理数的分类：________________ 05.0 是正数吗？__________________
","answer_html":"04. 有理数的分类：正有理数、零、负有理数\n05. 0 是正数吗？不是","solution_html":"根据《核心知识点》第8条，有理数分为正有理数、零、负有理数三类。第3条明确指出'0既不是正数，也不是负数'，因此0不是正数。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:46:12"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:46:12"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:46:12"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:47:15"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:47:15"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T10:47:18"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-11-10T10:47:18"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:47:18"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T10:47:18"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:52:17"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:52:17"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-11-10T10:52:17"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T10:52:17"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-11-10T10:52:17"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T10:55:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T11:11:11"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T11:26:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T11:42:16"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T11:57:48"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T12:13:20"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T12:28:53"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T12:44:25"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T12:59:57"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T13:15:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T13:31:02"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T13:46:33"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:02:06"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:17:40"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:33:12"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:48:45"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:04:17"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:19:50"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:35:23"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:50:55"}],"detail_url":"/questions/181946","edit_url":"/questions/181946/edit","json_url":"/api/questions/181946","recheck_url":"/api/questions/181946/recheck"},{"id":181894,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_925.pdf","job_source":"数学-沪教版.zip","pages":[6,6],"stem":"随着智能手机的普及，微信抢红包已成为春节期间人们最喜欢的活动之一，某校七年级(3) 班班长对全班50名学生在春节期间所抢的 红包金额进行统计，井绘制成了统计图，请根据以上信息回答： （1）该班所抢红包金额的众数是____，中位数是____； （2）该班同学所抢红包的平均金额是多少元？ （3）若该校共有22个班级，平均每班50人，请你估计该校学生着节期间 所抢的红包总金额为多少元？","options":[],"answer":"","solution":"","stem_html":"随着智能手机的普及，微信抢红包已成为春节期间人们最喜欢的活动之一，某校七年级(3) 班班长对全班50名学生在春节期间所抢的 红包金额进行统计，井绘制成了统计图，请根据以上信息回答：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/10/a13a92c3-ebda-4a16-b969-9efbd0519d0d/65765d4e-5f3b-47f9-8ce0-3f0727a8df09/6d51dbe7ffe7.png\" "\\"点击查看原图\\"")
（1）该班所抢红包金额的众数是____，中位数是____；
（2）该班同学所抢红包的平均金额是多少元？
（3）若该校共有22个班级，平均每班50人，请你估计该校学生着节期间 所抢的红包总金额为多少元？
为了解某果园中苹果树的产量情况，果农\\(\\frac{10}{10}\\)如图，某学校抽查了 名八年级学生的 随机抽取了20棵苹果树，统计其苹果产量， 数学期中成绩，则这 名学生的数学平 得到如下频数分布表，抽取的这20棵苹果 均成绩为( ) 树的平均产量为 ____ 千克. A ．88 87． ．86 ．85 B C D
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/b6322851-c58d-4214-bc32-8b7a5ceab8f6/2a93f4e5aea0.png\" "\\"点击查看原图\\"")
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/b6322851-c58d-4214-bc32-8b7a5ceab8f6/0e0053912e55.png\" "\\"点击查看原图\\"")
无限循环小数是有理数，如0.3&
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-11-10T10:40:09"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:40:09"},{"type":"VISION","status":"FAIL","score":0.9,"created_at":"2026-11-10T10:42:08"},{"type":"QUALITY_GATE","status":"FAIL","score":1.0,"created_at":"2026-11-10T10:42:08"}],"detail_url":"/questions/181937","edit_url":"/questions/181937/edit","json_url":"/api/questions/181937","recheck_url":"/api/questions/181937/recheck"},{"id":181892,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_925.pdf","job_source":"数学-沪教版.zip","pages":[5,5],"stem":"为了解某果园中苹果树的产量情况，果农随机抽取了20棵苹果树，统 计其苹果产量，得到如下频数分布表． （1）a = ____，b = ____； （2）求抽取的这20棵苹果树的平均产量．","options":[],"answer":"","solution":"","stem_html":"为了解某果园中苹果树的产量情况，果农随机抽取了20棵苹果树，统 计其苹果产量，得到如下频数分布表．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/8681c478-f757-473d-bacc-c19d431bc6b6/c6c13bb1971e.png\" "\\"点击查看原图\\"")
（1）a = ____，b = ____；
（2）求抽取的这20棵苹果树的平均产量．
正比例函数的定义：_________________
","answer_html":"形如y = kx(k是常数，且k ≠ 0)","solution_html":"根据提供的《核心知识点》原文第3条，正比例函数的定义式为y = kx，其中k是常数且k不等于0。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:36:22"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:36:22"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:36:22"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:37:32"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:37:32"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T10:37:34"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:37:34"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:38:29"},{"type":"QUALITY_GATE","status":"PASS","score":0.925,"created_at":"2026-11-10T10:38:29"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:39:54"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:39:54"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-11-10T10:39:54"},{"type":"AUTO_FILL_ANSWER","status":"WARN","score":1.0,"created_at":"2026-11-10T10:39:54"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T10:41:06"}],"detail_url":"/questions/181909","edit_url":"/questions/181909/edit","json_url":"/api/questions/181909","recheck_url":"/api/questions/181909/recheck"},{"id":181891,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_925.pdf","job_source":"数学-沪教版.zip","pages":[4,4],"stem":"某公司开展了以亲近自然、劳逸结合、强健体魄、增强凝聚力为 主题的工会健步走活动．王伟所在的部门共20人，将这20人某 一天行走的步数进行统计，绘制了如下的统计表：根据上述信息，解答下列问题： （1）填写表中＂组中值＂一栏的空白； （2）求这20人一天行走的平均步数．","options":[],"answer":"","solution":"","stem_html":"某公司开展了以亲近自然、劳逸结合、强健体魄、增强凝聚力为 主题的工会健步走活动．王伟所在的部门共20人，将这20人某 一天行走的步数进行统计，绘制了如下的统计表：根据上述信息，解答下列问题：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/cb8ed54b-9536-4d20-8a4b-6e118301898b/109ad7700355.png\" "\\"点击查看原图\\"")
（1）填写表中＂组中值＂一栏的空白；
（2）求这20人一天行走的平均步数．
某校七(1)班全体学生举行了一次健康知识竞赛．根据竞赛成绩(得分为整数，满分为100分) 绘制了频数分布直方图(如下图所示)．则该校的平均成绩是____分．
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:32:06"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:32:06"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:32:07"},{"type":"SOLVER","status":"PASS","score":0.85,"created_at":"2026-11-10T10:33:12"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-11-10T10:33:12"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T10:33:55"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T10:33:55"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T10:34:49"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-11-10T10:34:49"}],"detail_url":"/questions/181889","edit_url":"/questions/181889/edit","json_url":"/api/questions/181889","recheck_url":"/api/questions/181889/recheck"},{"id":181860,"job_id":11,"qa_status":"QUARANTINED","question_type":"choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"青岛版/七上/杜辉Q_18951362233_25.pdf","job_source":"数学-青岛版.zip","pages":[4,4],"stem":"下列各数：5, − 3\\(2 _{2}\\), 1.03003, _{11}, 0, −\\(2\\pi\\)，其中有理数的个数是( )个． A. \\(3 \\frac{(B)4}{(C)5}\\) D. 6","options":[{"label":"A","text":"3 \\frac{(B)4}{(C)5}"},{"label":"D","text":"6"}],"answer":"","solution":"","stem_html":"下列各数：5, − 3\\(2 _{2}\\), 1.03003, _{11}, 0, −\\(2\\pi\\)，其中有理数的个数是( )个．
A. \\(3 \\frac{(B)4}{(C)5}\\)
D. 6
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:24:31"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:24:31"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:24:31"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T10:25:24"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:26:05"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:26:05"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T10:26:05"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T10:27:21"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-11-10T10:27:21"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:34:31"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:34:31"}],"detail_url":"/questions/181860","edit_url":"/questions/181860/edit","json_url":"/api/questions/181860","recheck_url":"/api/questions/181860/recheck"},{"id":181890,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_925.pdf","job_source":"数学-沪教版.zip","pages":[4,4],"stem":"某班同学进行知识竞赛，将所得成绩进行整理后，绘制成如图的统计 图，若把每组中各个成绩用这组成绩的中间值代替(如：50 ∼60分的中间值为55分 )，则竞赛成绩的平均数为____分．","options":[],"answer":"","solution":"","stem_html":"某班同学进行知识竞赛，将所得成绩进行整理后，绘制成如图的统计 图，若把每组中各个成绩用这组成绩的中间值代替(如：50 ∼60分的中间值为55分 )，则竞赛成绩的平均数为____分．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/64d6972f-4c17-4d38-938a-45d652b98476/b1396db031c0.png\" "\\"点击查看原图\\"")
【小试2】 为了解2路公共汽车的运营情况，公交部门统计了某天2路公共汽车 每个运行班次的载客量，得到如表各项数据．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/78f474c7-b976-4474-b91d-6f2414f3b43c/2a2dd377085d.png\" "\\"点击查看原图\\"")
（1）求出表格中a = ____，b = ____.
（2）计算该2路公共汽车平均每班的载客量是多少？
有一组数据依次为：−1,0, +2,0, −3,0, +4,0, −5,0, +6,0, … ．
（1）若这组数据共有100个，则共有多少个负数，多少个正数？
（2）第2000个数是什么？
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:27:48"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:27:48"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:27:48"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-11-10T10:28:25"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:28:25"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T10:29:14"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T10:29:14"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T10:29:59"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T10:29:59"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.0,"created_at":"2026-11-10T10:37:06"}],"detail_url":"/questions/181864","edit_url":"/questions/181864/edit","json_url":"/api/questions/181864","recheck_url":"/api/questions/181864/recheck"},{"id":181887,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_925.pdf","job_source":"数学-沪教版.zip","pages":[3,3],"stem":"【小试1】 某中学举行电脑知识竞赛，将九年级参赛学生的成绩进行整理后分成 五组，绘制成如图所示的频数分布直方图，则九年级参赛学生成绩 的平均数为____.","options":[],"answer":"","solution":"","stem_html":"【小试1】 某中学举行电脑知识竞赛，将九年级参赛学生的成绩进行整理后分成 五组，绘制成如图所示的频数分布直方图，则九年级参赛学生成绩 的平均数为____.
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/3def98ba-4871-4aaf-9eb4-beb27f70cf76/92e716bc956e.png\" "\\"点击查看原图\\"")
下列说法中：①一个整数不是正数就是负数②最小的整数是零; ③负 数中没有最大的数；④自然数一定是正整数；⑤有理数包括正有 理数、零和负有理数；⑥整数就是正整数和负整数；⑦零是整数 但不是正数；⑧正数、负数统称为有理数；正确的个数有( )\\(\\frac{(A)1}{(B)2} \\frac{(C)3}{(D)4}\\)
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:26:08"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:26:08"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:26:08"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T10:27:33"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:28:03"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:28:03"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T10:28:03"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T10:29:24"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-11-10T10:29:24"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:32:31"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:32:31"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-11-10T10:34:23"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:34:23"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-11-10T10:34:23"}],"detail_url":"/questions/181862","edit_url":"/questions/181862/edit","json_url":"/api/questions/181862","recheck_url":"/api/questions/181862/recheck"},{"id":181826,"job_id":10,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"冀教版/八下/薛豪Q_18952688822_320.pdf","job_source":"数学-冀教版.zip","pages":[4,4],"stem":"如果每盒水笔有10支，售价16元，用y(元)表示水笔的售价，x表示 水笔的支数，那么y与x之间的关系应该是( ) A. y = 10x B. y = 16x C. y =\\(\\frac{_{8}x^{5}}{_{5}x^{8}}\\) D. y =","options":[{"label":"A","text":"y = 10x"},{"label":"B","text":"y = 16x"},{"label":"C","text":"y = \\frac{_{8}x^{5}}{_{5}x^{8}}"},{"label":"D","text":"y ="}],"answer":"y =\\(\\frac{16}{10}x\\)","solution":"每盒水笔10支售价16元，则每支单价为16÷10=1.6元。设x为支数，y为总价，则y=1.6x，即y=\\(\\frac{16}{10}x\\)。","stem_html":"如果每盒水笔有10支，售价16元，用y(元)表示水笔的售价，x表示 水笔的支数，那么y与x之间的关系应该是( )
A. y = 10x
B. y = 16x
C. y =\\(\\frac{_{8}x^{5}}{_{5}x^{8}}\\)
D. y =
","answer_html":"y =\\(\\frac{16}{10}x\\)","solution_html":"每盒水笔10支售价16元，则每支单价为16÷10=1.6元。设x为支数，y为总价，则y=1.6x，即y=\\(\\frac{16}{10}x\\)。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:22:23"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:22:23"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:22:23"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T10:24:21"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:25:43"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:25:43"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T10:25:43"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T10:27:03"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T10:27:03"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:30:20"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:30:20"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T10:31:17"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T10:31:17"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-11-10T10:31:17"},{"type":"AUTO_REPAIR","status":"PASS","score":1.0,"created_at":"2026-11-10T10:31:17"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T10:33:11"}],"detail_url":"/questions/181826","edit_url":"/questions/181826/edit","json_url":"/api/questions/181826","recheck_url":"/api/questions/181826/recheck"},{"id":181863,"job_id":11,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"青岛版/七上/杜辉Q_18951362233_25.pdf","job_source":"数学-青岛版.zip","pages":[4,4],"stem":"某超市2025年1－6月份的营业额与2024年同月营业额相比，其增长率 如下表所示．请根据表格信息回答下列问题： （1）该超市2025年1－6月份的营业额与2024年同月营业额相比，哪几个月是增长的？ （2）2025年1月和4月相比2024年同月营业额的增长率是负数分别表示什么意义？","options":[],"answer":"","solution":"","stem_html":"某超市2025年1－6月份的营业额与2024年同月营业额相比，其增长率 如下表所示．请根据表格信息回答下列问题：
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/25691159-497d-4ce1-90b3-ac48b74c97f3/0560cced-ca6c-4c81-b578-655153a08c1e/e4489d72ab54.png\" "\\"点击查看原图\\"")
（1）该超市2025年1－6月份的营业额与2024年同月营业额相比，哪几个月是增长的？
（2）2025年1月和4月相比2024年同月营业额的增长率是负数分别表示什么意义？
在实数\\(11 _{3}\\), 0, −0.3,3.14159265,4, −2025,\\(\\pi\\)中, 有理数的个数为( )\\(\\frac{(A)3}{(B)4} \\frac{(C)5}{(D)6}\\)
\n \n \n | 答案：C\n1 4\n，− 是分数，分数属于有理数。\n4 3\n−1.010010001是有限小数，有限小数可以化\n为分数，所以它是有理数。\n0是整数，整数是有理数的一部分，所以0 是\n有理数。\n−2，其中是无限不循环小数，−2也是无\n限不循环小数，属于无理数。\n−3.141441444是无限不循环小数，所以它\n是无理数。\n3.3是无限循环小数，无限循环小数可以化为\n分数，属于有理数。\n1 4\n综上，有理数有 ,1.010010001,− ,0,3.3，共5个\n4 3 | \n Col1 | \n
\n \n \n \n
为了抗击新冠肺炎，遏止疫情传播，小明决定购买某种单价为0.5元 的口罩，购买x个这种口罩的总价为y元，则y与x间的关系式为( )
\n \n \n | 1\n(A)y = x\n6\n(B)y = 6x\n(C)y = 6x2\n(D)y = 36x2 | \n Col1 | \n
\n \n \n \n
A. y = −\\(\\frac{_{2}x^{1}}{_{2}x^{1}}\\)
B. y =
C. y = −2x
D. y = 2x
下列个数：\\(\\frac{1}{4}7,1.010 010 001\\)，−\\(\\frac{4}{3},0\\), −2 , 下列关于有理数的描述： ①有限小数和循环小数都是有理数； −3.141441444（每两个1之间依次多一个）\\(4 \\frac{0}{0}\\)②是非负有理数； ，．，其中有理数有（3 3） ③既不是正数，也不是负数，由此可知0 A ．个3 ．个4 ．个5 ．个6 B C D 不是有理数； ④一个有理数如果不是整数，那么它一定 是分数。 其中正确的个数是（） A ．个1 ．个2 ．个3 ．个4 B C D
","answer_html":"","solution_html":"【讲解】 C 答案： ①有限小数和循环小数都是有理数，正确；\\(\\frac{0}{0}\\)②是非负有理数，正确； ③既不是正数，也不是负数，但是有理0 数，故错误； ④一个有理数如果不是整数，那么它一定 是分数，正确； 所以正确的个数是个，故选．3 C C 答案：\\(\\frac{1}{4}\\)，−\\(\\frac{4}{3}\\)是分数，分数属于有理数。 −1.010010001是有限小数，有限小数可以化 为分数，所以它是有理数。 0是整数，整数是有理数的一部分，所以是0 有理数。 −2，其中是无限不循环小数，− 2也是无 限不循环小数，属于无理数。 −3.141441444是无限不循环小数，所以它 是无理数。 3.3是无限循环小数，无限循环小数可以化为 分数，属于有理数。 综上，有理数有 1 ,1.010010001,−\\(\\frac{4}{3},0,3.3\\)，共个5 4","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:20:40"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:20:40"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:20:41"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T10:21:58"}],"detail_url":"/questions/181856","edit_url":"/questions/181856/edit","json_url":"/api/questions/181856","recheck_url":"/api/questions/181856/recheck"},{"id":181824,"job_id":10,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_320.pdf","job_source":"数学-冀教版.zip","pages":[3,3],"stem":"函数y = (m −2)x +\\(m^{2}\\)−4(m为常数)． （1）当m取何值时，y是x的正比例函数？ （2）当m取何值时，y是x的一次函数？","options":[],"answer":"","solution":"","stem_html":"函数y = (m −2)x +\\(m^{2}\\)−4(m为常数)．
（1）当m取何值时，y是x的正比例函数？
（2）当m取何值时，y是x的一次函数？
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:12:23"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:12:23"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:12:23"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T10:13:39"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:13:51"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:13:51"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T10:13:51"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T10:15:17"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T10:15:17"}],"detail_url":"/questions/181824","edit_url":"/questions/181824/edit","json_url":"/api/questions/181824","recheck_url":"/api/questions/181824/recheck"},{"id":181821,"job_id":10,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_320.pdf","job_source":"数学-冀教版.zip","pages":[2,2],"stem":"[\\(\\textbf{小试1}\\)]\\(\\quad \\text{已知函数}\\)y = (3m - 2)\\(x^{2+n}\\)+ (m +\\(\\frac{n}{2}\\)). （1）当m, n为何值时，该函数是一次函数？ （2）当m, n为何值时，该函数是正比例函数？","options":[],"answer":"(1)当 m ≠\\(2_{3}\\), n = −1时，该函数是一次函数.","solution":"(2)当 m =\\(1_{2}\\), n = −1时，该函数是正比例函数. (1)由题意，得：3m −2 ≠0,2 + n = 1，解得 m ≠\\(2 _{3}\\), n = −1, 即当m ≠\\(2 _{3}\\), n=−1时，该函数是一次函数． (2)由题意，得 3m −2 ≠0,2 + n = 1, m + n 1\\(1 _{2}\\)= 0，解得m = _{2}, n = −1, 即当m = _{2}, n = −1时，该函数是正比例函数．","stem_html":"[\\(\\textbf{小试1}\\)]\\(\\quad \\text{已知函数}\\)y = (3m - 2)\\(x^{2+n}\\)+ (m +\\(\\frac{n}{2}\\)).
（1）当m, n为何值时，该函数是一次函数？
（2）当m, n为何值时，该函数是正比例函数？
","answer_html":"(1)当 m ≠\\(2_{3}\\), n = −1时，该函数是一次函数.","solution_html":"(2)当 m =\\(1_{2}\\), n = −1时，该函数是正比例函数. (1)由题意，得：3m −2 ≠0,2 + n = 1，解得 m ≠\\(2 _{3}\\), n = −1, 即当m ≠\\(2 _{3}\\), n=−1时，该函数是一次函数． (2)由题意，得 3m −2 ≠0,2 + n = 1, m + n 1\\(1 _{2}\\)= 0，解得m = _{2}, n = −1, 即当m = _{2}, n = −1时，该函数是正比例函数．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:14:41"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:14:41"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:14:41"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T10:15:58"}],"detail_url":"/questions/181821","edit_url":"/questions/181821/edit","json_url":"/api/questions/181821","recheck_url":"/api/questions/181821/recheck"},{"id":181819,"job_id":10,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"冀教版/八下/薛豪Q_18952688822_320.pdf","job_source":"数学-冀教版.zip","pages":[2,2],"stem":"已知函数y = (m −10)x +1− 2m．\\(\\frac{(1)}{(2)}\\frac{m}{m}\\)为何值时，这个函数是一次函数? 为何值时，这个函数是正比例函数?","options":[],"answer":"","solution":"(1)根据一次函数的定义可得：m −10 0， 当m 10时，这个函数是一次函数； (2)根据正比例函数的定义可得：, m −10 0且1− 2m = 0，m =\\(\\frac{1}{2}\\)时，这个 函数是正比例函数．","stem_html":"已知函数y = (m −10)x +1− 2m．\\(\\frac{(1)}{(2)}\\frac{m}{m}\\)为何值时，这个函数是一次函数? 为何值时，这个函数是正比例函数?
","answer_html":"","solution_html":"(1)根据一次函数的定义可得：m −10 0， 当m 10时，这个函数是一次函数； (2)根据正比例函数的定义可得：, m −10 0且1− 2m = 0，m =\\(\\frac{1}{2}\\)时，这个 函数是正比例函数．","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:13:13"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:13:13"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:13:13"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T10:14:56"}],"detail_url":"/questions/181819","edit_url":"/questions/181819/edit","json_url":"/api/questions/181819","recheck_url":"/api/questions/181819/recheck"},{"id":181776,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_920.pdf","job_source":"数学-沪教版.zip","pages":[5,5],"stem":"某校舞蹈队成员的年龄分布如表，则该校舞蹈队成员的平均年龄是( ).\\(\\frac{(A)12}{(B)13} \\frac{(C)14}{(D)15}\\)","options":[],"answer":"","solution":"","stem_html":"某校舞蹈队成员的年龄分布如表，则该校舞蹈队成员的平均年龄是( ).\\(\\frac{(A)12}{(B)13} \\frac{(C)14}{(D)15}\\)
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/f88dffbb-8a08-43bb-8812-143a737e6950/66f0b8aa0297.png\" "\\"点击查看原图\\"")
有理数的分类：________________ 05.0 是正数吗？__________________
","answer_html":"04. 有理数的分类：正有理数、零、负有理数\n05. 0是正数吗？不是","solution_html":"根据《核心知识点》第3条，0既不是正数也不是负数；第4条将有理数分为正有理数、零、负有理数三类。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T10:01:00"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T10:01:00"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T10:01:00"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:02:27"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:02:27"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T10:02:40"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:02:40"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-11-10T10:02:40"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-11-10T10:02:40"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T10:05:00"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:05:00"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-11-10T10:05:00"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T10:05:00"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-11-10T10:05:00"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T10:09:01"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T10:24:33"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T10:40:06"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T10:55:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T11:11:11"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T11:26:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T11:42:16"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T11:57:48"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T12:13:20"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T12:28:53"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T12:44:25"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T12:59:57"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T13:15:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T13:31:02"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T13:46:33"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:02:06"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:17:40"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:33:12"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T14:48:45"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:04:17"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:19:50"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:35:23"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-11-10T15:50:55"}],"detail_url":"/questions/181842","edit_url":"/questions/181842/edit","json_url":"/api/questions/181842","recheck_url":"/api/questions/181842/recheck"},{"id":181771,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_920.pdf","job_source":"数学-沪教版.zip","pages":[3,3],"stem":"【小试2】 一组数据：1, a, b, 2, c, 3，已知这组数据的平均数是4． （1）求a, b, c三个数的和； （2）求4a + 5,4b + 6,4c + 7的平均数．","options":[],"answer":"(1)a, b, c三个数的和为18；(2)4a + 5,4b + 6,4c + 7的平均数为30．","solution":"(1)由题意，得\\(\\frac{1+a+b+2+c+3}{6} = 4\\)， ∴a + b + c =\\(4 \\times 6\\)−1 −2 −3 = 18,所以a, b, c 三个数的和为 18； (2)由(1)得 a + b + c = 18，\\(\\frac{(4a+5)+(4b+6)+(4c+7)}{3} = \\frac{(4a+4b+4c)+5+6+7}{3}=\\frac{4(a+b+c)+5+6+7}{3} = \\frac{4\\times 18+5+6+7}{3} = _{3}= 90 30\\)，∴4a + 5,4b + 6,4c + 7的平均数为30.","stem_html":"【小试2】 一组数据：1, a, b, 2, c, 3，已知这组数据的平均数是4．
（1）求a, b, c三个数的和；
（2）求4a + 5,4b + 6,4c + 7的平均数．
","answer_html":"(1)a, b, c三个数的和为18；(2)4a + 5,4b + 6,4c + 7的平均数为30．","solution_html":"(1)由题意，得\\(\\frac{1+a+b+2+c+3}{6} = 4\\)， ∴a + b + c =\\(4 \\times 6\\)−1 −2 −3 = 18,所以a, b, c 三个数的和为 18； (2)由(1)得 a + b + c = 18，\\(\\frac{(4a+5)+(4b+6)+(4c+7)}{3} = \\frac{(4a+4b+4c)+5+6+7}{3}=\\frac{4(a+b+c)+5+6+7}{3} = \\frac{4\\times 18+5+6+7}{3} = _{3}= 90 30\\)，∴4a + 5,4b + 6,4c + 7的平均数为30.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T09:56:28"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T09:56:28"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T09:56:28"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-11-10T09:58:04"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-11-10T09:59:58"},{"type":"CRITIC","status":"FAIL","score":0.95,"created_at":"2026-11-10T09:59:58"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T09:59:58"}],"detail_url":"/questions/181771","edit_url":"/questions/181771/edit","json_url":"/api/questions/181771","recheck_url":"/api/questions/181771/recheck"},{"id":181775,"job_id":9,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"沪教版/八下/周琼玟Q_18978751881_920.pdf","job_source":"数学-沪教版.zip","pages":[4,4],"stem":"假设一个小城镇过去10年中，发生火灾情况如表所示．试问： （1）设想平均每年在1000家中烧掉几家？ （2）如果保户投保30万元的火灾保险，最低限度要交多少保险费保险公司才不亏本？","options":[],"answer":"","solution":"","stem_html":"假设一个小城镇过去10年中，发生火灾情况如表所示．试问：
（1）设想平均每年在1000家中烧掉几家？
（2）如果保户投保30万元的火灾保险，最低限度要交多少保险费保险公司才不亏本？
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T09:51:03"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T09:51:03"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T09:51:03"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-11-10T09:51:49"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-11-10T09:52:29"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-11-10T09:52:29"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T09:52:29"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T09:53:21"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-11-10T09:53:21"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.0,"created_at":"2026-11-10T10:01:18"}],"detail_url":"/questions/181775","edit_url":"/questions/181775/edit","json_url":"/api/questions/181775","recheck_url":"/api/questions/181775/recheck"},{"id":181777,"job_id":9,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.975,"source_file":"沪教版/八下/周琼玟Q_18978751881_920.pdf","job_source":"数学-沪教版.zip","pages":[5,5],"stem":"王林参加＂优秀社区干部＂评选, 责任心、组织能力、群众基础三项得分(十分制) 分别为8分，9分，7分, 若将三项得分依次按3: 5: 2的比例确定最终成绩, 则王林的最终成绩为( ) A. 8分 B. 8.1分 C. 8.2分 D. 8.3分","options":[{"label":"A","text":"8分"},{"label":"B","text":"8.1分"},{"label":"C","text":"8.2分"},{"label":"D","text":"8.3分"}],"answer":"","solution":"","stem_html":"王林参加＂优秀社区干部＂评选, 责任心、组织能力、群众基础三项得分(十分制) 分别为8分，9分，7分, 若将三项得分依次按3: 5: 2的比例确定最终成绩, 则王林的最终成绩为( )
A. 8分
B. 8.1分
C. 8.2分
D. 8.3分
","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T09:54:21"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T09:54:21"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T09:54:21"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-11-10T09:55:27"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T09:55:27"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-11-10T09:55:38"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-11-10T09:55:38"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-11-10T09:56:25"},{"type":"QUALITY_GATE","status":"FAIL","score":0.975,"created_at":"2026-11-10T09:56:25"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-11-10T09:58:10"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-11-10T09:58:10"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T09:59:53"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-11-10T09:59:53"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-11-10T09:59:53"}],"detail_url":"/questions/181777","edit_url":"/questions/181777/edit","json_url":"/api/questions/181777","recheck_url":"/api/questions/181777/recheck"},{"id":181750,"job_id":11,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.913,"source_file":"青岛版/七上/杜辉Q_18951362233_215_检测.pdf","job_source":"数学-青岛版.zip","pages":[3,3],"stem":"已知有理数a,b,其中数a在如图所示的数轴上对应点M,b 是负数,且 b在数轴上对应的点与原点的距离为\\(3. \\frac{(1)}{(2)}\\)a =______, b =______.\\(\\frac{1}{2}\\)−\\(1 \\frac{1}{2}\\)| −4|, −(−2.5).并用\"<\"把这些数连接起来. 在数轴上表示下列各数: +(−5), −3.5,","options":[],"answer":"∵ 数a在数轴上对应点M,b是负数，且b在数轴上对应的点与原点的距离为3， ∴ a= 2,b= −3；","solution":"\\(\\frac{(1)}{(2)} +(−5) =\\)−5, | −4| = 4, −(−2.5) = 2.5，在数轴上表示各数，如下图：用 ＂ <＂连接各数为： + (−5) < −3.5 < −\\(1 \\frac{1}{2}\\)<\\(\\frac{1}{2}\\)< −(−2.5) < | −4|．","stem_html":"已知有理数a,b,其中数a在如图所示的数轴上对应点M,b 是负数,且 b在数轴上对应的点与原点的距离为\\(3. \\frac{(1)}{(2)}\\)a =______, b =______.\\(\\frac{1}{2}\\)−\\(1 \\frac{1}{2}\\)| −4|, −(−2.5).并用\"<\"把这些数连接起来. 在数轴上表示下列各数: +(−5), −3.5,
","answer_html":"∵ 数a在数轴上对应点M,b是负数，且b在数轴上对应的点与原点的距离为3， ∴ a= 2,b= −3；","solution_html":"\\(\\frac{(1)}{(2)} +(−5) =\\)−5, | −4| = 4, −(−2.5) = 2.5，在数轴上表示各数，如下图：用 ＂ <＂连接各数为： + (−5) < −3.5 < −\\(1 \\frac{1}{2}\\)<\\(\\frac{1}{2}\\)< −(−2.5) < | −4|．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-11-10T09:40:11"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-11-10T09:40:11"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-11-10T09:40:11"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-11-10T09:41:59"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-11-10T09:43:40"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-11-10T09:43:40"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T09:43:40"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-11-10T09:47:30"},{"type":"QUALITY_GATE","status":"FAIL","score":0.913,"created_at":"2026-11-10T09:47:30"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-11-10T09:50:52"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-11-10T09:50:52"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-11-10T09:54:26"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-11-10T09:54:26"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-11-10T09:54:26"}],"detail_url":"/questions/181750","edit_url":"/questions/181750/edit","json_url":"/api/questions/181750","recheck_url":"/api/questions/181750/recheck"},{"id":181773,"job_id":9,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"沪教版/八下/周琼玟Q_18978751881_920.pdf","job_source":"数学-沪教版.zip","pages":[4,4],"stem":"某学校在＂爱护地球，绿化祖国＂的活动中，组织学生开展植树活 动，为了解全校学生的植树情况，学校随机抽查了100名学生的植 树情况，将调查数据绘制成如图所示的条形图，则平均每人植树____棵．","options":[],"answer":"","solution":"","stem_html":"某学校在＂爱护地球，绿化祖国＂的活动中，组织学生开展植树活 动，为了解全校学生的植树情况，学校随机抽查了100名学生的植 树情况，将调查数据绘制成如图所示的条形图，则平均每人植树____棵．
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/05193cba-e677-4c3c-96b6-95e5bb24a870/20c604c33376.png\" "\\"点击查看原图\\"")
如图，某学校抽查了10名八年级学生的数学期中成绩，则这10名学生的数学平均成绩为( )\\(\\frac{(A)88}{(B)87}\\frac{(C)86}{(D)85}\\)
![\"\"](\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/11/fa6762c7-a95b-46b0-8a9d-477bfc6d7525/3491181f-c988-4851-95cf-213f1861c87a/bd1242fdac44.png\" "\\"点击查看原图\\"")