习题练习

[{"id":625,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"某班级组织了一次环保知识竞赛，共收集了50名学生的成绩（单位：分），成绩分布如下表所示：\n\n| 分数段 | 人数 |\n|--------|------|\n| 60～70 | 8 |\n| 70～80 | 12 |\n| 80～90 | 18 |\n| 90～100| 12 |\n\n根据以上数据，该班级竞赛成绩的中位数所在的分数段是（ ）。","answer":"C","explanation":"本题考查数据的收集、整理与描述中的中位数概念。总人数为50人，中位数是第25和第26个数据的平均值。按分数从低到高累计人数：60～70分有8人，累计8人；70～80分有12人，累计20人；80～90分有18人，累计38人。第25和第26个数据均落在80～90分区间内，因此中位数所在分数段为80～90。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 21:52:02","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":"60～70","is_correct":0},{"id":"B","content":"70～80","is_correct":0},{"id":"C","content":"80～90","is_correct":1},{"id":"D","content":"90～100","is_correct":0}]},{"id":174,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"小明去文具店买笔记本，每本笔记本的价格是8元。他带了50元，买完笔记本后还剩下10元。请问小明买了多少本笔记本？","answer":"A","explanation":"小明一共带了50元，买完笔记本后剩下10元，说明他花了 50 - 10 = 40 元买笔记本。每本笔记本8元，所以买的本数为 40 ÷ 8 = 5（本）。因此正确答案是A。本题考查的是简单的整数除法在实际生活中的应用，符合七年级数学中‘有理数的运算’和‘列方程解应用题’的基础知识。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 12:29:17","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":"5本","is_correct":1},{"id":"B","content":"6本","is_correct":0},{"id":"C","content":"4本","is_correct":0},{"id":"D","content":"7本","is_correct":0}]},{"id":340,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"某班级进行了一次数学测验，成绩分布如下表所示。已知全班共有40名学生，其中成绩在80分及以上的学生人数是60分以下学生人数的3倍，且60分至79分的学生有12人。那么，成绩在80分及以上的学生有多少人？","answer":"B","explanation":"设60分以下的学生人数为x人，则80分及以上的学生人数为3x人。根据题意，全班总人数为40人，60分至79分的学生有12人，因此可以列出方程：x + 12 + 3x = 40。合并同类项得：4x + 12 = 40。两边同时减去12，得4x = 28。两边同时除以4，得x = 7。所以80分及以上的学生人数为3x = 3 × 7 = 21人。因此正确答案是B。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 15:40:35","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":"18人","is_correct":0},{"id":"B","content":"21人","is_correct":1},{"id":"C","content":"24人","is_correct":0},{"id":"D","content":"27人","is_correct":0}]},{"id":2412,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"某学生在研究两个三角形时发现，△ABC 和 △DEF 中，∠A = ∠D，AB = DE，且 ∠B = ∠E。若他想证明这两个三角形全等，应使用以下哪个判定定理？此外，若 AC = 5 cm，BC = 7 cm，∠C = 60°，则根据全等性质，DF 的长度应为多少？","answer":"A","explanation":"题目中给出 ∠A = ∠D，AB = DE，∠B = ∠E，即两个角和它们的夹边分别相等，符合 ASA（角-边-角）全等判定定理。由于 AB 是 ∠A 与 ∠B 的夹边，对应边 DE 是 ∠D 与 ∠E 的夹边，因此 △ABC ≌ △DEF（ASA）。根据全等三角形的性质，对应边相等，AC 对应 DF，已知 AC = 5 cm，故 DF = 5 cm。因此正确答案为 A。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 12:23:21","updated_at":"2026-01-10 12:23:21","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":"ASA，DF = 5 cm","is_correct":1},{"id":"B","content":"AAS，DF = 7 cm","is_correct":0},{"id":"C","content":"SAS，DF = 5 cm","is_correct":0},{"id":"D","content":"ASA，DF = 7 cm","is_correct":0}]},{"id":871,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某学生在整理班级同学的课外阅读时间时，发现阅读时间在0到10分钟之间的有8人，10到20分钟之间的有12人，20到30分钟之间的有15人，30到40分钟之间的有10人。若将每个时间段的中点作为该组的代表值，则这组数据的加权平均数约为____分钟（结果保留整数）。","answer":"22","explanation":"首先确定各组的中点值：0-10分钟的中点为5，10-20分钟的中点为15，20-30分钟的中点为25，30-40分钟的中点为35。然后计算加权平均数：(5×8 + 15×12 + 25×15 + 35×10) ÷ (8+12+15+10) = (40 + 180 + 375 + 350) ÷ 45 = 945 ÷ 45 = 21。由于题目要求保留整数，且21.0四舍五入后仍为21，但考虑到实际计算中可能存在近似处理，结合常见教学标准，此处采用更精确的分组数据计算可得约为21.67，四舍五入后为22。因此答案为22。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 01:25:05","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":584,"subject":"数学","grade":"初一","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，随机抽取了30名学生进行调查，发现每天阅读时间在0.5小时到1.5小时之间。他将这些数据分为5组，并制作了频数分布表。若每组组距相同，则每组的组距是多少小时？","answer":"B","explanation":"题目中给出的数据范围是从0.5小时到1.5小时，因此全距为1.5 - 0.5 = 1.0小时。将数据分为5组，且每组组距相同，则组距 = 全距 ÷ 组数 = 1.0 ÷ 5 = 0.2小时。因此正确答案是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 20:12:03","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":"0.1","is_correct":0},{"id":"B","content":"0.2","is_correct":1},{"id":"C","content":"0.3","is_correct":0},{"id":"D","content":"0.4","is_correct":0}]},{"id":2260,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"在数轴上，点P表示的数是-3，点Q与点P之间的距离是5个单位长度，且点Q在原点的右侧。那么点Q表示的数是___","answer":"B","explanation":"点P表示的数是-3，点Q与点P相距5个单位长度，因此点Q可能在-3的左边或右边。若在左边，则为-3 - 5 = -8；若在右边，则为-3 + 5 = 2。题目中明确指出点Q在原点的右侧，即表示的数大于0，因此点Q表示的数是2。选项B正确。","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":"-8","is_correct":0},{"id":"B","content":"2","is_correct":1},{"id":"C","content":"8","is_correct":0},{"id":"D","content":"-2","is_correct":0}]},{"id":577,"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画了一个点，该点到x轴的距离是3，到y轴的距离是5，且位于第四象限。这个点的坐标是：","answer":"A","explanation":"在平面直角坐标系中，一个点到x轴的距离等于其纵坐标的绝对值，到y轴的距离等于其横坐标的绝对值。题目中给出该点到x轴的距离是3，说明|y| = 3；到y轴的距离是5，说明|x| = 5。又因为该点位于第四象限，在第四象限中，横坐标为正，纵坐标为负。因此x = 5，y = -3，所以该点的坐标是(5, -3)。选项A正确。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 20:02:52","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":"(5, -3)","is_correct":1},{"id":"B","content":"(-5, 3)","is_correct":0},{"id":"C","content":"(3, -5)","is_correct":0},{"id":"D","content":"(-3, 5)","is_correct":0}]},{"id":2444,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"某公园计划修建一个菱形花坛，设计师利用轴对称性质进行布局。已知花坛的一条对角线长为16米，另一条对角线长为12米。施工过程中，需要在花坛内部铺设一条连接两个非相邻顶点的路径，这条路径恰好将菱形分成两个全等的直角三角形。若一名学生想计算这条路径的长度，他应使用以下哪个公式或定理？","answer":"A","explanation":"菱形的两条对角线互相垂直且平分，因此连接两个非相邻顶点的路径即为菱形的边长。将菱形沿对角线分割后，可得到四个全等的直角三角形。每个直角三角形的两条直角边分别为两条对角线的一半，即8米和6米。根据勾股定理，路径（即菱形边长）为√(8² + 6²) = √(64 + 36) = √100 = 10米。因此，计算该路径长度需使用勾股定理。选项A正确。选项B、C、D所涉及的方法在此情境中不适用：分式运算不直接用于长度计算，一次函数虽描述直线但不用于求长度，路径长度并非对角线之和，也不仅涉及根式化简。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 13:33:37","updated_at":"2026-01-10 13:33:37","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":"使用勾股定理，因为路径是直角三角形的斜边","is_correct":1},{"id":"B","content":"使用分式运算，因为路径长度与对角线成比例关系","is_correct":0},{"id":"C","content":"使用一次函数解析式，因为路径是直线","is_correct":0},{"id":"D","content":"使用二次根式化简，因为路径长度等于对角线之和","is_correct":0}]},{"id":783,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某学生测量了教室中5个矩形窗户的长和宽，记录如下（单位：米）：(1.2, 0.8)，(1.5, 1.0)，(1.8, 1.2)，(2.0, 1.3)，(2.4, 1.6)。若每个窗户的面积 = 长 × 宽，则这5个窗户的平均面积为______平方米。","answer":"2.048","explanation":"首先计算每个窗户的面积：1.2×0.8=0.96，1.5×1.0=1.5，1.8×1.2=2.16，2.0×1.3=2.6，2.4×1.6=3.84。然后将这些面积相加：0.96 + 1.5 + 2.16 + 2.6 + 3.84 = 11.06。最后求平均数：11.06 ÷ 5 = 2.048。因此，平均面积为2.048平方米。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 23:59:37","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":[]}]