习题练习

[{"id":2281,"subject":"数学","grade":"七年级","stage":"初中","type":"填空题","content":"在数轴上，点A表示的数是-5，点B与点A的距离为8个单位长度，且点B在原点右侧。若点C位于点A和点B之间，且AC:CB = 3:1，则点C表示的数是___。","answer":"1","explanation":"首先，点A表示-5，点B与A距离8且在原点右侧，因此点B表示-5 + 8 = 3。点C在A和B之间，且AC:CB = 3:1，说明将线段AB分成4等份，AC占3份，CB占1份。AB的长度为8，因此每份为2。从A向右移动3份，即-5 + 3×2 = -5 + 6 = 1。所以点C表示的数是1。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-09 16:27:13","updated_at":"2026-01-09 16:27:13","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":1023,"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身高数据时，将150厘米到160厘米之间的身高记录为一个区间。如果一名学生的身高是155.3厘米，那么这个数据应被归入该区间的第___个十分位段（将150到160平均分成10段，每段为1厘米）。","answer":"6","explanation":"将150厘米到160厘米的区间平均分成10段，每段为1厘米，分别对应第1段（150≤身高<151）、第2段（151≤身高<152）……第6段（155≤身高<156）。因为155.3厘米满足155 ≤ 155.3 < 156，所以它属于第6个十分位段。本题考查数据的收集与整理中对数据区间的划分与归类，属于‘数据的收集、整理与描述’知识点，符合七年级数学课程内容。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 05:40:10","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":949,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"在一次班级环保活动中，某学生收集了可回收物品的数量记录如下：塑料瓶比废纸多3个，若设废纸的数量为x个，则塑料瓶的数量可表示为___；若总共收集了15个物品，则可列出方程为___，解得x = ___。","answer":"x + 3；x + (x + 3) = 15；6","explanation":"根据题意，塑料瓶比废纸多3个，废纸为x个，则塑料瓶为x + 3个。总数量为15个，因此方程为x + (x + 3) = 15。解这个一元一次方程：2x + 3 = 15 → 2x = 12 → x = 6。因此，三个空依次填入：x + 3，x + (x + 3) = 15，6。本题综合考查了用字母表示数和列一元一次方程解决实际问题的能力，符合七年级数学课程要求。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 03:30:09","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":362,"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 P，其横坐标是 -3，纵坐标比横坐标大 5，则点 P 的坐标是（ ）","answer":"A","explanation":"根据题意，点 P 的横坐标是 -3。纵坐标比横坐标大 5，即纵坐标为 -3 + 5 = 2。因此点 P 的坐标是 (-3, 2)。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 15:45:47","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, 2)","is_correct":1},{"id":"B","content":"(3, -2)","is_correct":0},{"id":"C","content":"(-3, -8)","is_correct":0},{"id":"D","content":"(2, -3)","is_correct":0}]},{"id":2278,"subject":"数学","grade":"七年级","stage":"初中","type":"填空题","content":"在数轴上，点A表示的数是-3，点B与点A的距离为7个单位长度，且点B位于点A的右侧；点C与点B的距离为4个单位长度，且点C位于点B的左侧。那么点C表示的数是___。","answer":"0","explanation":"首先，点A表示-3，点B在点A右侧且距离为7，因此点B表示的数是-3 + 7 = 4。接着，点C在点B左侧且距离为4，因此点C表示的数是4 - 4 = 0。本题综合考查了数轴上点的位置关系与有理数加减运算，要求学生理解‘右侧’表示加法，‘左侧’表示减法，并能分步推理，属于较难题型。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-09 16:27:13","updated_at":"2026-01-09 16:27:13","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":2255,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在数轴上从点A出发，先向右移动5个单位长度到达点B，再向左移动8个单位长度到达点C。如果点A表示的数是-2，那么点C表示的数是多少？","answer":"D","explanation":"点A表示的数是-2。向右移动5个单位长度，即-2 + 5 = 3，到达点B。再从点B向左移动8个单位长度，即3 - 8 = -5，因此点C表示的数是-5。选项D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":"-5","is_correct":0},{"id":"B","content":"-10","is_correct":0},{"id":"C","content":"1","is_correct":0},{"id":"D","content":"-5","is_correct":1}]},{"id":2016,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"在一次校园绿化活动中，某学生设计了一块等腰三角形花坛，已知其底边长为6米，两腰相等且长度为5米。若要在花坛内部铺设一条从顶点到底边中点的路径，则这条路径的长度为多少？","answer":"B","explanation":"本题考查勾股定理在等腰三角形中的应用。等腰三角形中，从顶点到底边中点的线段既是高，也是中线。因此，可将原三角形分为两个全等的直角三角形，每个直角三角形的斜边为腰长5米，底边为3米（因为底边6米被中点平分）。设路径（即高）为h，根据勾股定理：h² + 3² = 5²，即h² + 9 = 25，解得h² = 16，所以h = 4米。因此，这条路径的长度为4米，正确答案为B。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-09 10:30:30","updated_at":"2026-01-09 10:30:30","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米","is_correct":0},{"id":"B","content":"4米","is_correct":1},{"id":"C","content":"5米","is_correct":0},{"id":"D","content":"√34米","is_correct":0}]},{"id":680,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"在一次班级图书角统计中，某学生发现科普类书籍比文学类书籍多8本，两类书籍共有32本。设文学类书籍有x本，则根据题意可列出一元一次方程：_x + (x + 8) = 32_，解得x = _12_，因此科普类书籍有_20_本。","answer":"x + (x + 8) = 32；12；20","explanation":"根据题意，文学类书籍为x本，科普类比文学类多8本，即为(x + 8)本。两类书总数为32本，因此可列方程：x + (x + 8) = 32。解这个方程：2x + 8 = 32 → 2x = 24 → x = 12。所以文学类有12本，科普类有12 + 8 = 20本。本题考查一元一次方程的建立与求解，属于七年级上册重点内容。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 22:28:51","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":1982,"subject":"数学","grade":"九年级","stage":"初中","type":"选择题","content":"某学生在纸上画了一个半径为5 cm的圆，并在圆内作了一个内接等边三角形。若将该等边三角形绕其中心（即圆心）顺时针旋转120°，则旋转前后两个三角形重叠部分的面积占原三角形面积的多少？","answer":"D","explanation":"本题考查旋转与圆的综合应用，结合正多边形的对称性。等边三角形是圆的内接正三角形，其中心与圆心重合。由于等边三角形具有120°的旋转对称性，绕其中心旋转120°后，图形与原图形完全重合。因此，旋转前后两个三角形完全重叠，重叠部分的面积等于原三角形面积，即占比为1（全部）。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-07 15:02:43","updated_at":"2026-01-07 15:02:43","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":"A","content":"1\/3","is_correct":0},{"id":"B","content":"1\/2","is_correct":0},{"id":"C","content":"2\/3","is_correct":0},{"id":"D","content":"全部","is_correct":1}]},{"id":165,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"已知一个等腰三角形的两边长分别为5 cm和8 cm，则这个三角形的周长可能是多少？","answer":"D","explanation":"等腰三角形有两条边相等。题目中给出的两边分别为5 cm和8 cm，因此有两种可能：① 两条相等的边为5 cm，底边为8 cm，此时三边为5 cm、5 cm、8 cm，满足三角形两边之和大于第三边（5+5>8），周长为5+5+8=18 cm；② 两条相等的边为8 cm，底边为5 cm，此时三边为8 cm、8 cm、5 cm，也满足三角形三边关系（8+5>8），周长为8+8+5=21 cm。因此周长可能是18 cm或21 cm，正确答案为D。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2025-12-24 12:00:27","updated_at":"2025-12-24 12:00:27","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":"13 cm","is_correct":0},{"id":"B","content":"18 cm","is_correct":0},{"id":"C","content":"21 cm","is_correct":0},{"id":"D","content":"18 cm 或 21 cm","is_correct":1}]}]