[{"id":250,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"一个长方形的长比宽多5厘米，若其周长为38厘米，则这个长方形的宽是___厘米。","answer":"7","explanation":"设长方形的宽为x厘米，则长为(x + 5)厘米。根据长方形周长公式：周长 = 2 × (长 + 宽)，代入已知条件得：2 × (x + x + 5) = 38。化简得：2 × (2x + 5) = 38，即4x + 10 = 38。解得4x = 28，x = 7。因此，长方形的宽是7厘米。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"中等","points":1,"is_active":1,"created_at":"2025-12-29 14:54:08","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":467,"subject":"数学","grade":"初一","stage":"小学","type":"选择题","content":"42","answer":"待完善","explanation":"解析待完善","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:52:39","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":805,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"某学生在整理班级同学的课外阅读情况时，收集了每位同学每月阅读的书籍数量，并将数据按从小到大的顺序排列。已知这组数据的中位数是4，且数据个数为奇数。如果去掉最大的一个数据后，新的中位数变为3.5，那么原数据中最少有多少个数据？____","answer":"7","explanation":"设原数据有n个，且n为奇数。中位数为第(n+1)\/2个数，已知为4。去掉最大的一个数据后，剩下n-1个数据（偶数个），中位数为中间两个数的平均数，即第(n-1)\/2个和第(n+1)\/2个数据的平均值为3.5。由于原数据有序，去掉最大值后，中间两个数应分别为3和4（因为(3+4)\/2=3.5）。为了使这种情况成立，原数据中第(n+1)\/2个数必须是4，且其前一个数为3。当n=7时，原数据第4个数为4，去掉最大值后剩下6个数，第3和第4个数分别为3和4，满足新中位数为3.5。若n<7（如n=5），则无法满足去掉最大值后中间两数为3和4的条件。因此原数据最少有7个。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 00:22:41","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":1875,"subject":"语文","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在整理班级同学的课外阅读情况时，收集了以下数据：全班40人，每人每周阅读时间（单位：小时）分布在区间[1, 10]内，且均为整数。他将数据分为5组，每组8人，并计算出每组的平均阅读时间分别为：3.5、4.25、5.0、6.75、8.0。若该学生想用这些数据绘制一个频数分布直方图，并发现其中某一组的实际总阅读时间比按平均数估算的总时间多出2小时，则该组最可能是哪一组？","answer":"C","explanation":"本题考查数据的收集、整理与描述，以及对平均数与总和关系的理解。每组有8人，因此按平均数估算的总阅读时间 = 平均数 × 8。实际总时间比估算多出2小时，说明该组的实际总和 = 平均数 × 8 + 2。由于每人阅读时间为整数，总时间也必为整数。我们逐项分析：A组：3.5 × 8 = 28，+2 = 30（整数，可能）；B组：4.25 × 8 = 34，+2 = 36（整数，可能）；C组：6.75 × 8 = 54，+2 = 56（整数，可能）；D组：8.0 × 8 = 64，+2 = 66（整数，可能）。但关键在于“平均数为6.75”意味着总和为54，而54 ÷ 8 = 6.75，说明原始数据总和为54。若实际多出2小时，则总和为56，平均为7.0。但题目说“按平均数估算”是基于报告的6.75，而实际更高，说明原始分组数据可能被低估。然而，6.75 = 27\/4，说明总和54是3的倍数，而56不是8的倍数导致平均变为7，这在整数数据中是可能的。但更关键的是，6.75是唯一一个非半整数的平均数（3.5、4.25、5.0、8.0均为0.25的倍数，但6.75也符合），但结合“多出2小时”这一异常，最可能出现在中间偏高组，因为极端组（如3.5或8.0）数据分布受限，而6.75组处于中间偏上，数据波动空间大，更容易出现统计偏差。综合分析，C组最可能因数据分布不均导致估算偏差，故选C。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-07 09:54:14","updated_at":"2026-01-07 09:54:14","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":"平均阅读时间为3.5小时的一组","is_correct":0},{"id":"B","content":"平均阅读时间为4.25小时的一组","is_correct":0},{"id":"C","content":"平均阅读时间为6.75小时的一组","is_correct":1},{"id":"D","content":"平均阅读时间为8.0小时的一组","is_correct":0}]},{"id":2141,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在解方程 3(x - 2) = 2x + 1 时，第一步去括号得到 3x - 6 = 2x + 1，第二步移项得到 3x - 2x = 1 + 6，第三步合并同类项得到 x = 7。该学生解题过程中哪一步开始出现错误？","answer":"D","explanation":"该学生解题过程完全正确：第一步去括号符合乘法分配律，3(x - 2) = 3x - 6；第二步移项将含x项移到左边，常数项移到右边，符号变换正确；第三步合并同类项得到 x = 7，代入原方程验证成立。因此整个解答过程无误。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-09 13:00:46","updated_at":"2026-01-09 13:00:46","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":"第一步","is_correct":0},{"id":"B","content":"第二步","is_correct":0},{"id":"C","content":"第三步","is_correct":0},{"id":"D","content":"没有错误，解答正确","is_correct":1}]},{"id":889,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"在某次班级大扫除中，一组学生负责擦窗户。如果每扇窗户需要2分钟擦干净，他们一共用了24分钟完成任务，那么这组学生一共擦了____扇窗户。","answer":"12","explanation":"题目中给出每扇窗户需要2分钟，总用时24分钟。要求擦了多少扇窗户，可以用总时间除以每扇窗户所需时间：24 ÷ 2 = 12。这是一道简单的一元一次方程应用题，设擦了x扇窗户，则2x = 24，解得x = 12。考查学生将实际问题转化为方程并求解的能力，属于一元一次方程知识点，难度简单。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 02:01:51","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":251,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"某学生在解方程 3(x - 2) + 5 = 2x + 7 时，第一步将等式左边展开得到 3x - 6 + 5，合并同类项后为 3x - 1；第二步将方程写成 3x - 1 = 2x + 7；第三步将 2x 移到左边，-1 移到右边，得到 3x - 2x = 7 + 1；第四步解得 x = ___。","answer":"8","explanation":"根据题目描述的解方程步骤：第一步展开括号正确，3(x - 2) = 3x - 6，再加5得 3x - 1；第二步方程为 3x - 1 = 2x + 7；第三步移项，将含x的项移到左边，常数项移到右边，即 3x - 2x = 7 + 1；第四步计算得 x = 8。此过程符合解一元一次方程的基本步骤，移项变号规则应用正确，最终结果为8。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"中等","points":1,"is_active":1,"created_at":"2025-12-29 14:54:13","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":466,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"某班级在一次数学测验中，男生有15人，平均成绩为78分；女生有20人，平均成绩为82分。全班学生的平均成绩是多少分？","answer":"C","explanation":"要计算全班的平均成绩，需要先求出全班的总分，再除以全班总人数。男生总分 = 15 × 78 = 1170（分），女生总分 = 20 × 82 = 1640（分），全班总分 = 1170 + 1640 = 2810（分）。全班总人数 = 15 + 20 = 35（人）。因此，全班平均成绩 = 2810 ÷ 35 = 80.2857…，四舍五入保留一位小数约为80.3分。故正确答案为C。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:52:08","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":"79.5分","is_correct":0},{"id":"B","content":"80分","is_correct":0},{"id":"C","content":"80.3分","is_correct":1},{"id":"D","content":"81分","is_correct":0}]},{"id":265,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某学生在解方程 3(x - 2) + 5 = 2x + 7 时，第一步去括号后得到 3x - 6 + 5 = 2x + 7，合并同类项后得到 3x - 1 = 2x + 7。该学生接下来将含 x 的项移到等式左边，常数项移到右边，得到 3x - 2x = 7 + ___，空格处应填入的数是___。","answer":"1","explanation":"根据等式的基本性质，移项时要变号。原式 3x - 1 = 2x + 7 中，将 2x 移到左边变为 -2x，将 -1 移到右边变为 +1，因此右边应为 7 + 1。所以空格处应填入 1。这一过程考查了学生对解一元一次方程中移项法则的理解与应用，属于七年级代数运算中的核心知识点。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"中等","points":1,"is_active":1,"created_at":"2025-12-29 14:56:37","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":1683,"subject":"数学","grade":"七年级","stage":"初中","type":"解答题","content":"某市举办青少年科技创新大赛，参赛学生需提交项目并完成现场展示。评委会根据创新性、实用性和展示效果三项指标打分，每项满分均为100分。最终成绩按加权平均计算：创新性占40%，实用性占35%，展示效果占25%。已知一名学生的创新性得分比实用性得分高10分，展示效果得分是实用性得分的1.2倍。若该学生最终加权成绩不低于88分，求其实用性得分至少为多少分？（结果保留整数）","answer":"设该学生实用性得分为 x 分。\n\n根据题意：\n- 创新性得分为 x + 10 分；\n- 展示效果得分为 1.2x 分；\n- 加权成绩 = 创新性 × 40% + 实用性 × 35% + 展示效果 × 25%；\n- 要求加权成绩 ≥ 88 分。\n\n代入得不等式：\n0.4(x + 10) + 0.35x + 0.25(1.2x) ≥ 88\n\n展开计算：\n0.4x + 4 + 0.35x + 0.3x ≥ 88\n\n合并同类项：\n(0.4x + 0.35x + 0.3x) + 4 ≥ 88\n1.05x + 4 ≥ 88\n\n移项：\n1.05x ≥ 84\n\n两边同除以 1.05：\nx ≥ 84 ÷ 1.05\nx ≥ 80\n\n因此，实用性得分至少为 80 分。\n\n答：该学生实用性得分至少为 80 分。","explanation":"本题综合考查了一元一次不等式的建立与求解，同时融合了加权平均数的概念，属于实际应用类问题。解题关键在于正确设定未知数，并根据文字描述准确表达各项得分之间的关系。特别需要注意的是展示效果是实用性得分的1.2倍，即1.2x，以及各项权重之和为100%。在列不等式时，要将百分数转化为小数进行计算，最后通过解不等式得到最小整数值。题目情境新颖，贴近现实，考查学生将实际问题转化为数学模型的能力，符合七年级数学课程标准中对不等式与数据处理的综合应用要求。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-06 13:32:43","updated_at":"2026-01-06 13:32:43","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":[]}]