习题练习

[{"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":796,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"在一次班级图书角整理活动中，某学生统计了上周同学们借阅的图书数量，发现科技类图书比文学类图书多借出8本，两类图书共借出46本。设文学类图书借出x本，则科技类图书借出___本，根据题意可列方程为___。","answer":"x + 8；x + (x + 8) = 46","explanation":"题目中明确指出科技类图书比文学类多8本，若文学类借出x本，则科技类为x + 8本。两类图书共借出46本，因此可列出方程：x + (x + 8) = 46。本题考查用字母表示数量关系及建立一元一次方程的能力，属于‘一元一次方程’知识点，符合七年级教学要求。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 00:14:51","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":983,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某班级组织了一次环保知识竞赛，共收集了30名学生的成绩。为了分析数据，老师将成绩按10分为一段进行分组，得到如下频数分布表：90～100分有5人，80～89分有12人，70～79分有8人，60～69分有4人，60分以下有1人。则这次竞赛成绩的中位数落在_______分数段内。","answer":"80～89","explanation":"中位数是将一组数据从小到大排列后，处于中间位置的数。本题共有30名学生，因此中位数是第15个和第16个数据的平均数。根据频数累计：60分以下1人，60～69分4人（累计5人），70～79分8人（累计13人），80～89分12人（累计25人）。第15和第16个数据均落在80～89分区间内，因此中位数落在80～89分数段。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 04:23:16","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":1908,"subject":"数学","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：喜欢小说的有18人，喜欢科普书的有12人，既喜欢小说又喜欢科普书的有5人。那么，只喜欢小说或只喜欢科普书的学生共有多少人？","answer":"A","explanation":"本题考查数据的收集与整理，涉及集合的简单运算。已知喜欢小说的有18人，其中包括只喜欢小说和既喜欢小说又喜欢科普书的学生；喜欢科普书的有12人，也包括只喜欢科普书和两者都喜欢的学生。两者都喜欢的人数为5人，因此只喜欢小说的人数为18 - 5 = 13人，只喜欢科普书的人数为12 - 5 = 7人。所以，只喜欢小说或只喜欢科普书的学生总人数为13 + 7 = 20人。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 13:11:09","updated_at":"2026-01-07 13:11:09","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":"20","is_correct":1},{"id":"B","content":"25","is_correct":0},{"id":"C","content":"30","is_correct":0},{"id":"D","content":"35","is_correct":0}]},{"id":2132,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在解一个一元一次方程时，将方程中的常数项2误写成了-2，结果解得x = 3。若原方程的解应为x = -1，则这个一元一次方程可能是下列哪一个？","answer":"B","explanation":"根据题意，某学生将常数项2写成-2后解得x=3，说明错误方程为x - 2 = 1（因为3 - 2 = 1成立）。而原方程应为x + 2 = 1，此时解得x = -1，符合题设条件。其他选项代入x=-1均不成立，因此正确答案是B。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-09 12:56:39","updated_at":"2026-01-09 12:56:39","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":"2x + 2 = 0","is_correct":0},{"id":"B","content":"x + 2 = 1","is_correct":1},{"id":"C","content":"3x - 2 = 1","is_correct":0},{"id":"D","content":"x - 2 = -3","is_correct":0}]},{"id":925,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"在一次班级数学测验成绩统计中，某学生将原始数据整理后绘制成频数分布直方图，发现成绩在80分到89分之间的人数占总人数的25%。如果全班共有40名学生，那么成绩在80分到89分之间的学生有___人。","answer":"10","explanation":"题目考查的是数据的收集、整理与描述中的百分比计算。已知总人数为40人，80分到89分的学生占25%，即求40的25%是多少。计算过程为：40 × 25% = 40 × 0.25 = 10。因此，该分数段的学生人数为10人。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 02:48:35","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":260,"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，第一步将方程展开为 3x - 6 + 5 = 2x + 7，第二步合并同类项得到 3x - 1 = 2x + 7，第三步将 2x 移到左边，-1 移到右边，得到 ___ = 8，最后解得 x = 8。","answer":"x","explanation":"根据题意，第三步是将 2x 从右边移到左边变为 -2x，同时将 -1 从左边移到右边变为 +1，因此左边变为 3x - 2x = x，右边变为 7 + 1 = 8，所以空格处应填 x。此题考查一元一次方程的移项与合并同类项，属于七年级代数基础内容，步骤清晰，难度适中。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"中等","points":1,"is_active":1,"created_at":"2025-12-29 14:55:11","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":2137,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在解方程时，将方程 3(x - 2) = 2x + 1 的括号展开后得到 3x - 6 = 2x + 1。接下来他应该进行的正确步骤是：","answer":"B","explanation":"在解一元一次方程时，目标是逐步将含未知数的项移到等式一边，常数项移到另一边。当前方程为 3x - 6 = 2x + 1，最合理的下一步是消去右边的 2x，因此应两边同时减去 2x，得到 x - 6 = 1，便于后续求解。选项 B 正确体现了这一化简思路，符合七年级解方程的基本步骤。","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":"两边同时加上6","is_correct":0},{"id":"B","content":"两边同时减去2x","is_correct":1},{"id":"C","content":"两边同时除以3","is_correct":0},{"id":"D","content":"两边同时乘以x","is_correct":0}]},{"id":1926,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某班级为了了解学生最喜欢的课外活动，随机抽取了40名学生进行调查，并将结果整理成如下频数分布表：\n\n| 活动类型 | 频数 |\n|----------|------|\n| 阅读 | 8 |\n| 运动 | 15 |\n| 绘画 | 6 |\n| 音乐 | 11 |\n\n若该班级共有200名学生，估计喜欢运动的学生人数最接近以下哪个数值？","answer":"C","explanation":"根据频数分布表，40名学生中有15人最喜欢运动，所占比例为 15 ÷ 40 = 0.375。用此比例估计整个班级200名学生中喜欢运动的人数：200 × 0.375 = 75。因此，估计喜欢运动的学生人数最接近75人，正确答案为C。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-07 13:16:48","updated_at":"2026-01-07 13:16:48","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":"A","content":"50","is_correct":0},{"id":"B","content":"65","is_correct":0},{"id":"C","content":"75","is_correct":1},{"id":"D","content":"85","is_correct":0}]},{"id":638,"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，收集了30名学生的成绩，并将成绩分为5个分数段进行统计。已知前四个分数段的人数分别为4、7、9、6，则第五个分数段的人数是多少？","answer":"B","explanation":"题目考查的是数据的收集与整理。总人数为30人，前四个分数段的人数分别为4、7、9、6。将这些人数相加：4 + 7 + 9 + 6 = 26。因此，第五个分数段的人数为30 - 26 = 4。所以正确答案是B。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 22:05:16","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":"3","is_correct":0},{"id":"B","content":"4","is_correct":1},{"id":"C","content":"5","is_correct":0},{"id":"D","content":"6","is_correct":0}]}]