习题练习

[{"id":2184,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在数轴上标出三个点A、B、C，分别表示有理数a、b、c。已知a < b < c，且|a| = |c|，b是a与c的中点。若c = 5，则a + b + c的值是多少？","answer":"B","explanation":"由题意知c = 5，且|a| = |c|，所以|a| = 5，即a = 5或a = -5。又因a < b < c且c = 5，若a = 5，则a = c，与a < c矛盾，故a = -5。b是a与c的中点，即b = (a + c) ÷ 2 = (-5 + 5) ÷ 2 = 0。因此a + b + c = -5 + 0 + 5 = 0。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-09 14:21:04","updated_at":"2026-01-09 14:21:04","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":"-5","is_correct":0},{"id":"B","content":"0","is_correct":1},{"id":"C","content":"5","is_correct":0},{"id":"D","content":"10","is_correct":0}]},{"id":1922,"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时间时，收集了以下数据（单位：小时）：2.5，3，1.5，4，2.5，3.5，2。若将这组数据按从小到大的顺序排列，则位于中间位置的数是：","answer":"A","explanation":"首先将数据从小到大排列：1.5，2，2.5，2.5，3，3.5，4。共有7个数据，为奇数个，因此中位数是正中间的那个数，即第4个数。第4个数是2.5，所以答案是A。本题考查数据的整理与描述中的中位数概念，属于简单难度，符合七年级学生认知水平。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-07 13:15:15","updated_at":"2026-01-07 13:15:15","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":"2.5","is_correct":1},{"id":"B","content":"3","is_correct":0},{"id":"C","content":"2.75","is_correct":0},{"id":"D","content":"3.5","is_correct":0}]},{"id":270,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"某学生在平面直角坐标系中描出四个点：A(2, 3)，B(-1, 4)，C(0, -2)，D(3, -1)。若将这些点按横坐标从小到大的顺序排列，正确的顺序是？","answer":"A","explanation":"题目要求按横坐标（即x坐标）从小到大排列四个点。首先提取各点的横坐标：A点横坐标为2，B点为-1，C点为0，D点为3。将这些横坐标排序：-1 < 0 < 2 < 3，对应点依次为B、C、A、D。因此正确顺序是B, C, A, D，对应选项A。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 15:30:01","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":"B, C, A, D","is_correct":1},{"id":"B","content":"C, B, A, D","is_correct":0},{"id":"C","content":"B, A, C, D","is_correct":0},{"id":"D","content":"D, A, C, B","is_correct":0}]},{"id":291,"subject":"数学","grade":"初一","stage":"小学","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10名同学每周课外阅读时间（单位：小时），数据如下：3，5，4，6，5，7，5，4，6，5。这组数据的众数和中位数分别是多少？","answer":"A","explanation":"首先将数据从小到大排序：3，4，4，5，5，5，5，6，6，7。众数是出现次数最多的数，其中5出现了4次，次数最多，因此众数是5。中位数是数据按顺序排列后位于中间位置的数。由于共有10个数据（偶数个），中位数为第5个和第6个数的平均数，即(5 + 5) ÷ 2 = 5。因此，众数是5，中位数是5，正确答案是A。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 15:32:36","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":"众数是5，中位数是5","is_correct":1},{"id":"B","content":"众数是4，中位数是5","is_correct":0},{"id":"C","content":"众数是5，中位数是4.5","is_correct":0},{"id":"D","content":"众数是6，中位数是5.5","is_correct":0}]},{"id":2197,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在练习本上记录了一周内每天的温度变化情况，规定比前一天升高记为正，降低记为负。已知周一到周二的温度变化为 -3℃，周三到周四的温度变化为 +5℃，周五到周六的温度变化为 -2℃。如果周一的起始温度为 10℃，那么周六的温度是多少？","answer":"B","explanation":"从周一的 10℃ 开始，周二变化 -3℃，温度为 10 - 3 = 7℃；周三到周四变化 +5℃，即温度上升 5℃，变为 7 + 5 = 12℃；周五到周六变化 -2℃，即下降 2℃，变为 12 - 2 = 10℃。因此周六的温度是 10℃，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 14:25:31","updated_at":"2026-01-09 14:25:31","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":"8℃","is_correct":0},{"id":"B","content":"10℃","is_correct":1},{"id":"C","content":"12℃","is_correct":0},{"id":"D","content":"14℃","is_correct":0}]},{"id":663,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某学生调查了班级同学每天使用手机的时间（单位：分钟），将数据整理后发现，使用时间在30分钟以下的有8人，30到60分钟的有12人，60到90分钟的有15人，90分钟以上的有5人。则使用手机时间在60分钟及以上的学生占总人数的百分比是____%。","answer":"50","explanation":"首先计算总人数：8 + 12 + 15 + 5 = 40人。使用手机时间在60分钟及以上的包括“60到90分钟”和“90分钟以上”两组，共15 + 5 = 20人。因此所占百分比为(20 ÷ 40) × 100% = 50%。本题考查数据的收集、整理与描述中的频数统计与百分比计算，属于简单难度。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 22:16:54","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":2469,"subject":"数学","grade":"八年级","stage":"初中","type":"解答题","content":"如图，在平面直角坐标系中，点A(0, 0)，点B(6, 0)，点C(6, 8)，点D(0, 8)构成矩形ABCD。将矩形沿对角线AC折叠，使得点D落在点D′的位置，且D′落在矩形内部。连接BD′，交AC于点E。已知折叠后△AD′C ≌ △ADC，且D′E = √k。求k的值。","answer":"待完善","explanation":"解析待完善","solution_steps":"待完善","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 14:34:25","updated_at":"2026-01-10 14:34:25","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":602,"subject":"数学","grade":"初一","stage":"小学","type":"选择题","content":"2小时","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 21:13:00","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":630,"subject":"数学","grade":"初一","stage":"小学","type":"选择题","content":"某学校组织七年级学生参加环保知识竞赛，参赛学生的成绩被分为五个等级：优秀、良好、中等、及格、不及格。为了统计各等级人数，老师将数据整理成如下表格：\n\n| 等级 | 人数 |\n|--------|------|\n| 优秀 | 12 |\n| 良好 | 18 |\n| 中等 | 15 |\n| 及格 | 10 |\n| 不及格 | 5 |\n\n如果老师想用扇形统计图表示各等级人数所占百分比，那么表示“良好”等级的扇形圆心角的度数是多少？","answer":"B","explanation":"首先计算总人数：12 + 18 + 15 + 10 + 5 = 60人。\n“良好”等级人数为18人，占总人数的比例为18 ÷ 60 = 0.3，即30%。\n扇形统计图中，整个圆为360度，因此“良好”等级对应的圆心角为：360 × 0.3 = 108度。\n所以正确答案是B选项。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 21:55:35","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":"A","content":"90度","is_correct":0},{"id":"B","content":"108度","is_correct":1},{"id":"C","content":"120度","is_correct":0},{"id":"D","content":"144度","is_correct":0}]},{"id":2209,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在记录一周内每天的温度变化时，以20℃为标准，高于20℃的部分记为正数，低于20℃的部分记为负数。已知周三的温度变化记为-3℃，周五的温度变化记为+5℃。那么周三和周五的实际温度相差多少摄氏度？","answer":"D","explanation":"周三的温度变化为-3℃，表示实际温度是20 - 3 = 17℃；周五的温度变化为+5℃，表示实际温度是20 + 5 = 25℃。两者相差25 - 17 = 8℃。因此正确答案是D。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-09 14:25:31","updated_at":"2026-01-09 14:25:31","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":"2℃","is_correct":0},{"id":"B","content":"3℃","is_correct":0},{"id":"C","content":"5℃","is_correct":0},{"id":"D","content":"8℃","is_correct":1}]}]