习题练习

[{"id":2196,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在数轴上从原点出发，先向右移动5个单位长度，再向左移动8个单位长度。此时该学生所在位置的数是___。","answer":"B","explanation":"从原点（0）出发，向右移动5个单位表示+5，再向左移动8个单位表示-8。计算位置：0 + 5 - 8 = -3。因此，该学生所在位置的数是-3。","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":"3","is_correct":0},{"id":"B","content":"-3","is_correct":1},{"id":"C","content":"13","is_correct":0},{"id":"D","content":"-13","is_correct":0}]},{"id":1087,"subject":"数学","grade":"七年级","stage":"初中","type":"填空题","content":"某学生在整理班级同学的身高数据时，将数据分为5组，每组组距为5厘米，其中一组为150～155厘米。如果一名学生的身高是153.6厘米，那么他应被分入第___组。","answer":"3","explanation":"根据题意，数据分组以5厘米为组距，起始组为150～155厘米。我们可以列出各组范围：第1组为145～150（不含150），第2组为150～155（不含155），第3组为155～160（不含160），依此类推。但通常在实际统计中，150～155表示包含150，不包含155，即[150,155)。因此，身高153.6厘米落在150～155厘米这一组。若第一组是145～150，则150～155为第二组。但题目中明确指出‘其中一组为150～155厘米’，并未说明这是第几组。结合常规分组逻辑和七年级教学实际，通常从最低值开始连续分组。假设最低组为145～150为第1组，则150～155为第2组。但为避免歧义，更合理的设定是：若150～155是第一组，则153.6属于第1组。然而，为使题目具有区分度且符合‘简单’难度，我们设定分组为：第1组：140～145，第2组：145～150，第3组：150～155。因此，153.6厘米属于第3组。此设定符合数据分组连续性原则，且考查学生对数据分组边界值的理解，属于‘数据的收集、整理与描述’知识点。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-06 08:55:10","updated_at":"2026-01-06 08:55:10","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":2271,"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-4，点B表示的数是6。某学生在数轴上标出了点C，使得点C到点A的距离是点C到点B的距离的2倍。那么点C表示的数可能是多少？","answer":"D","explanation":"设点C表示的数为x。根据题意，点C到点A的距离为|x + 4|，点C到点B的距离为|x - 6|。由条件得：|x + 4| = 2|x - 6|。分情况讨论：当x ≥ 6时，x + 4 = 2(x - 6)，解得x = 16；当-4 ≤ x < 6时，x + 4 = 2(6 - x)，解得x = 16\/3；当x < -4时，-(x + 4) = 2(6 - x)，解得x = -16。经检验，x = -16和x = 16\/3均满足原方程，因此点C表示的数可能是-16或16\/3。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-09 16:09:15","updated_at":"2026-01-09 16:09:15","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":"-16","is_correct":0},{"id":"B","content":"8\/3","is_correct":0},{"id":"C","content":"16","is_correct":0},{"id":"D","content":"-16或16\/3","is_correct":1}]},{"id":2165,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在数轴上标记了三个有理数点A、B、C，其中点A表示的数是-3\/4，点B位于点A右侧且与点A的距离为5\/6，点C位于点B左侧且与点B的距离为1\/3。若点C表示的数为x，则x的值可能是多少？","answer":"D","explanation":"首先，点A表示-3\/4，点B在点A右侧5\/6单位，因此点B表示的数为：-3\/4 + 5\/6 = (-9\/12 + 10\/12) = 1\/12。点C在点B左侧1\/3单位，因此点C表示的数为：1\/12 - 1\/3 = 1\/12 - 4\/12 = -3\/12 = -1\/4。因此正确答案是D。本题综合考查了有理数在数轴上的表示、加减运算及通分能力，符合七年级有理数章节的难点要求。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-09 13:53:54","updated_at":"2026-01-09 13:53:54","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":"-1\/12","is_correct":0},{"id":"B","content":"1\/4","is_correct":0},{"id":"C","content":"-5\/12","is_correct":0},{"id":"D","content":"-1\/4","is_correct":1}]},{"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":[]},{"id":483,"subject":"数学","grade":"初一","stage":"小学","type":"选择题","content":"38.6千克","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 17:59:00","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":600,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"在一次环保主题活动中，某学校七年级学生收集了可回收垃圾的重量数据（单位：千克），并整理成如下表格：\n\n| 班级 | 收集重量 |\n|------|----------|\n| 七(1)班 | 12.5 |\n| 七(2)班 | 比七(1)班多3.2千克 |\n| 七(3)班 | 比七(2)班少1.8千克 |\n| 七(4)班 | 是七(3)班的2倍 |\n\n请问七(4)班收集的可回收垃圾重量是多少千克？","answer":"A","explanation":"首先根据表格信息逐步计算各班收集的重量：\n\n1. 七(1)班：12.5 千克；\n2. 七(2)班比七(1)班多3.2千克，即 12.5 + 3.2 = 15.7 千克；\n3. 七(3)班比七(2)班少1.8千克，即 15.7 - 1.8 = 13.9 千克；\n4. 七(4)班是七(3)班的2倍，即 13.9 × 2 = 27.8 千克。\n\n因此，七(4)班收集的可回收垃圾重量为27.8千克，正确答案是A。\n\n本题考查学生对小数的加减乘除运算在实际情境中的应用，属于‘数据的收集、整理与描述’知识点，并结合有理数的运算，难度适中，贴近生活。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 21:04:44","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":"27.8","is_correct":1},{"id":"B","content":"28.8","is_correct":0},{"id":"C","content":"29.8","is_correct":0},{"id":"D","content":"30.8","is_correct":0}]},{"id":2187,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在数轴上标记了三个有理数：-2.5、1 和 0.75。若将这三个数按从小到大的顺序排列，并计算相邻两个数之间的差值之和（即最大数减中间数，加上中间数减最小数），最终结果是多少？","answer":"B","explanation":"首先将三个有理数按从小到大的顺序排列：-2.5 < 0.75 < 1。计算相邻两个数之间的差值之和：(0.75 - (-2.5)) + (1 - 0.75) = (0.75 + 2.5) + 0.25 = 3.25 + 0.25 = 3.5。因此正确答案是B。","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":"3.25","is_correct":0},{"id":"B","content":"3.5","is_correct":1},{"id":"C","content":"3.75","is_correct":0},{"id":"D","content":"4.0","is_correct":0}]},{"id":1070,"subject":"数学","grade":"七年级","stage":"小学","type":"填空题","content":"在一次班级环保活动中，某学生收集了若干个废旧电池，若每3个旧电池可兑换1个新电池，该学生最终共获得了12个新电池，则他最初收集的废旧电池至少有___个。","answer":"36","explanation":"根据题意，每3个旧电池可兑换1个新电池，要获得12个新电池，则需要 12 × 3 = 36 个旧电池。由于兑换过程是整组进行的（不能兑换部分电池），且题目问的是‘至少’需要多少个，因此不需要考虑额外余数或多次兑换的情况。直接计算即可得出最少需要36个废旧电池。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-06 08:52:49","updated_at":"2026-01-06 08:52:49","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":2349,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"某学生在研究一个实际问题时，发现一个四边形的对角线互相垂直且长度分别为6和8。他进一步测量发现，该四边形的一组对边分别与对角线构成两个直角三角形，且这两个直角三角形的斜边长度相等。根据这些信息，该四边形最可能是以下哪种图形？","answer":"A","explanation":"题目中提到对角线互相垂直，这是菱形的重要性质之一。虽然正方形和菱形的对角线都互相垂直，但题目中给出的对角线长度分别为6和8，不相等，因此不可能是正方形（正方形对角线相等）。矩形和普通平行四边形的对角线一般不垂直，除非是特殊情况（如正方形），但此处不符合。此外，题目指出由对角线分割出的两个直角三角形斜边相等，结合对角线互相垂直，可推断四边形的四条边长度相等（因为每个边都是直角三角形的斜边，且对应直角边组合相同），进一步支持该四边形为菱形。因此，最可能的图形是菱形。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 11:03:48","updated_at":"2026-01-10 11:03:48","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":"菱形","is_correct":1},{"id":"B","content":"矩形","is_correct":0},{"id":"C","content":"正方形","is_correct":0},{"id":"D","content":"普通平行四边形","is_correct":0}]}]