[{"id":190,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"下列运算中，正确的是（ ）。","answer":"D","explanation":"本题考查的是七年级整式加减中的同类项合并。同类项是指所含字母相同，并且相同字母的指数也相同的项，只有同类项才能合并。选项A中，3a和2b不是同类项，不能合并，错误；选项B中，5y² - 2y² = 3y²，而不是3，漏掉了字母部分，错误；选项C中，4x²y和5xy²所含字母的指数不同（x和y的次数不对应），不是同类项，不能合并，错误；选项D中，7mn和3nm是同类项（因为mn = nm），可以合并，7mn - 3nm = 7mn - 3mn = 4mn，正确。因此，正确答案是D。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 14:02:14","updated_at":"2025-12-30 11:11:27","sort_order":0,"source":null,"tags":null,"analysis":null,"knowledge_point":null,"difficulty_coefficient":null,"suggested_time":null,"accuracy_rate":null,"usage_count":0,"last_used":null,"view_count":0,"favorite_count":0,"options":[{"id":"A","content":"3a + 2b = 5ab","is_correct":0},{"id":"B","content":"5y² - 2y² = 3","is_correct":0},{"id":"C","content":"4x²y - 5xy² = -x²y","is_correct":0},{"id":"D","content":"7mn - 3nm = 4mn","is_correct":1}]},{"id":1065,"subject":"数学","grade":"七年级","stage":"初中","type":"填空题","content":"在一次班级环保活动中，某学生收集了可回收垃圾的重量为 (3x - 2) 千克，其他同学共收集了 (x + 5) 千克。若全班总共收集了 20 千克可回收垃圾，则 x 的值是___。","answer":"17\/4","explanation":"根据题意，某学生收集的垃圾重量为 (3x - 2) 千克，其他同学收集了 (x + 5) 千克，全班总重量为 20 千克。可列方程：(3x - 2) + (x + 5) = 20。合并同类项得：4x + 3 = 20。移项得：4x = 17，解得 x = 17\/4。该题考查整式的加减与一元一次方程的综合应用，符合七年级数学知识范围。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-06 08:52:17","updated_at":"2026-01-06 08:52:17","sort_order":0,"source":null,"tags":null,"analysis":null,"knowledge_point":null,"difficulty_coefficient":null,"suggested_time":null,"accuracy_rate":null,"usage_count":0,"last_used":null,"view_count":0,"favorite_count":0,"options":[]},{"id":2257,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"在数轴上，点A表示的数是-3，点B表示的数是5。若点C是线段AB的中点，则点C表示的数是___。","answer":"A","explanation":"点C是线段AB的中点，其表示的数为点A和点B所表示数的平均数。计算过程为：(-3 + 5) ÷ 2 = 2 ÷ 2 = 1。因此，点C表示的数是1，对应选项A。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-09 16:03:06","updated_at":"2026-01-09 16:03:06","sort_order":0,"source":null,"tags":null,"analysis":null,"knowledge_point":null,"difficulty_coefficient":null,"suggested_time":null,"accuracy_rate":null,"usage_count":0,"last_used":null,"view_count":0,"favorite_count":0,"options":[{"id":"A","content":"1","is_correct":1},{"id":"B","content":"2","is_correct":0},{"id":"C","content":"-1","is_correct":0},{"id":"D","content":"4","is_correct":0}]},{"id":1986,"subject":"数学","grade":"九年级","stage":"初中","type":"选择题","content":"某学生在纸上画了一个边长为8 cm的正方形，并在正方形内部以其中一条对角线为对称轴，画了一个与该对角线重合的等腰直角三角形。若将该三角形绕正方形的中心顺时针旋转90°，则旋转前后两个三角形重叠部分的面积是多少？（π取3.14）","answer":"A","explanation":"本题考查旋转与几何图形的综合应用，重点在于理解旋转对称性和图形重叠关系。正方形边长为8 cm，其对角线长度为√(8² + 8²) = √128 = 8√2 cm。以其中一条对角线为对称轴画的等腰直角三角形，其两条直角边均为8 cm，面积为(1\/2) × 8 × 8 = 32 cm²。正方形中心是对角线的交点，也是旋转中心。当该三角形绕正方形中心顺时针旋转90°时，由于正方形具有90°旋转对称性，且原三角形关于中心对称，旋转后的三角形将与原三角形关于中心成轴对称。两个三角形重叠的部分是一个较小的等腰直角三角形，其直角边为原三角形直角边的一半，即4 cm。因此，重叠部分面积为(1\/2) × 4 × 4 = 8 cm²。但进一步分析发现，实际重叠区域是由两个45°-45°-90°三角形组成，每个面积为8 cm²，总重叠面积为16 cm²。故正确答案为A。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-07 15:05:54","updated_at":"2026-01-07 15:05:54","sort_order":0,"source":null,"tags":null,"analysis":null,"knowledge_point":null,"difficulty_coefficient":null,"suggested_time":null,"accuracy_rate":null,"usage_count":0,"last_used":null,"view_count":0,"favorite_count":0,"options":[{"id":"A","content":"16 cm²","is_correct":1},{"id":"B","content":"24 cm²","is_correct":0},{"id":"C","content":"32 cm²","is_correct":0},{"id":"D","content":"8 cm²","is_correct":0}]},{"id":472,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"某学生记录了连续5天每天完成的数学练习题数量，分别为：8道、10道、x道、12道、9道。已知这5天平均每天完成10道题，那么第3天完成的题数x是多少？","answer":"C","explanation":"根据题意，5天平均每天完成10道题，因此总题数为 5 × 10 = 50 道。已知其他四天完成的题数分别为8、10、12、9，将它们相加：8 + 10 + 12 + 9 = 39。设第3天完成的题数为x，则有 39 + x = 50，解得 x = 11。因此，第3天完成了11道题。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:54:38","updated_at":"2025-12-30 11:11:27","sort_order":0,"source":null,"tags":null,"analysis":null,"knowledge_point":null,"difficulty_coefficient":null,"suggested_time":null,"accuracy_rate":null,"usage_count":0,"last_used":null,"view_count":0,"favorite_count":0,"options":[{"id":"A","content":"9","is_correct":0},{"id":"B","content":"10","is_correct":0},{"id":"C","content":"11","is_correct":1},{"id":"D","content":"12","is_correct":0}]},{"id":1064,"subject":"数学","grade":"七年级","stage":"初中","type":"填空题","content":"在一次环保活动中，某学生记录了连续5天每天回收的废纸重量（单位：千克）分别为：2.5、3、2.8、3.2、2.7。为了估算一个月（按30天计算）大约能回收多少千克废纸，他先计算了这5天的平均每天回收量，再用这个平均数乘以30。请问他计算出的月回收量估计值是___千克。","answer":"86.4","explanation":"首先计算5天回收废纸的总重量：2.5 + 3 + 2.8 + 3.2 + 2.7 = 14.2（千克）。然后求平均每天回收量：14.2 ÷ 5 = 2.84（千克\/天）。最后估算一个月（30天）的回收量：2.84 × 30 = 86.4（千克）。本题考查数据的收集、整理与描述中的平均数计算及其应用，属于简单难度，符合七年级数学课程内容。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-06 08:52:13","updated_at":"2026-01-06 08:52:13","sort_order":0,"source":null,"tags":null,"analysis":null,"knowledge_point":null,"difficulty_coefficient":null,"suggested_time":null,"accuracy_rate":null,"usage_count":0,"last_used":null,"view_count":0,"favorite_count":0,"options":[]},{"id":1766,"subject":"数学","grade":"七年级","stage":"初中","type":"填空题","content":"在平面直角坐标系中，点A的坐标为（2，5），点B在x轴上，且线段AB的长度为13。若点B位于原点右侧，则点B的横坐标为____。","answer":"14","explanation":"根据题意，点A(2, 5)，点B在x轴上，设其坐标为(x, 0)，且AB = 13。利用两点间距离公式：√[(x - 2)² + (0 - 5)²] = 13。两边平方得：(x - 2)² + 25 = 169，即(x - 2)² = 144。解得x - 2 = ±12，所以x = 14 或 x = -10。由于点B位于原点右侧，x > 0，因此x = 14。故点B的横坐标为14。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-06 15:00:48","updated_at":"2026-01-06 15:00:48","sort_order":0,"source":null,"tags":null,"analysis":null,"knowledge_point":null,"difficulty_coefficient":null,"suggested_time":null,"accuracy_rate":null,"usage_count":0,"last_used":null,"view_count":0,"favorite_count":0,"options":[]},{"id":733,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"在一次班级图书角统计中，某学生记录了五种图书的数量，分别是故事书12本，科普书8本，漫画书15本，历史书6本，文学书9本。若用条形统计图表示这些数据，则纵轴上表示图书数量的单位长度应能整除所有数据，且单位长度尽可能大，那么纵轴的单位长度应为___本。","answer":"1","explanation":"为了使条形统计图的纵轴单位长度能整除所有图书数量（12、8、15、6、9），且单位长度尽可能大，需要求这些数的最大公约数。分解各数：12=2×2×3，8=2×2×2，15=3×5，6=2×3，9=3×3。这些数没有共同的质因数（除了1），因此它们的最大公约数是1。所以纵轴的单位长度最大只能是1本。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 23:04:46","updated_at":"2025-12-30 11:11:27","sort_order":0,"source":null,"tags":null,"analysis":null,"knowledge_point":null,"difficulty_coefficient":null,"suggested_time":null,"accuracy_rate":null,"usage_count":0,"last_used":null,"view_count":0,"favorite_count":0,"options":[]},{"id":1890,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某校七年级开展‘节约用水’主题调查活动，随机抽取了50名学生记录一周内每天的用水量（单位：升），并将数据整理成频数分布表。已知用水量在10～15升（含10升，不含15升）的学生人数占总人数的24%，用水量在15～20升的学生比用水量在5～10升的学生多6人，而用水量在20～25升的人数是用水量在5～10升人数的2倍。若用水量在5～10升的学生有x人，则根据以上信息可列方程为：","answer":"A","explanation":"根据题意，总人数为50人。用水量在10～15升的学生占24%，即0.24×50=12人。设用水量在5～10升的学生有x人，则用水量在15～20升的学生为(x+6)人，用水量在20～25升的学生为2x人。四个区间人数之和应等于总人数50，因此方程为：x（5～10升）+ (x+6)（15～20升）+ 2x（20～25升）+ 12（10～15升）= 50。整理得：x + x + 6 + 2x + 12 = 50，即4x + 18 = 50。选项A正确表达了这一关系。其他选项中，B错误地将百分比直接代入而未计算具体人数，C符号错误，D遗漏了10～15升区间的人数。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-07 10:13:21","updated_at":"2026-01-07 10:13:21","sort_order":0,"source":null,"tags":null,"analysis":null,"knowledge_point":null,"difficulty_coefficient":null,"suggested_time":null,"accuracy_rate":null,"usage_count":0,"last_used":null,"view_count":0,"favorite_count":0,"options":[{"id":"A","content":"x + (x + 6) + 2x + 12 = 50","is_correct":1},{"id":"B","content":"x + (x + 6) + 2x + 0.24×50 = 50","is_correct":0},{"id":"C","content":"x + (x - 6) + 2x + 12 = 50","is_correct":0},{"id":"D","content":"x + (x + 6) + 2x = 50 - 0.24×50","is_correct":0}]},{"id":203,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"一个长方形的长是8厘米，宽是5厘米，它的面积是_空白处_平方厘米。","answer":"40","explanation":"长方形的面积计算公式是：面积 = 长 × 宽。题目中给出的长是8厘米，宽是5厘米，因此面积为 8 × 5 = 40 平方厘米。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 14:39:26","updated_at":"2025-12-30 11:11:27","sort_order":0,"source":null,"tags":null,"analysis":null,"knowledge_point":null,"difficulty_coefficient":null,"suggested_time":null,"accuracy_rate":null,"usage_count":0,"last_used":null,"view_count":0,"favorite_count":0,"options":[]}]