[{"id":1927,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某班级组织一次环保活动，收集可回收垃圾。第一周收集了x千克废纸，第二周收集的比第一周的2倍少3千克。已知两周共收集了17千克废纸，则第一周收集了多少千克？","answer":"C","explanation":"设第一周收集废纸x千克，则第二周收集了(2x - 3)千克。根据题意，两周共收集17千克，可列方程：x + (2x - 3) = 17。化简得3x - 3 = 17，移项得3x = 20，解得x = 7。因此第一周收集了7千克废纸。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-07 13:18:07","updated_at":"2026-01-07 13:18:07","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":"6","is_correct":0},{"id":"C","content":"7","is_correct":1},{"id":"D","content":"8","is_correct":0}]},{"id":614,"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情况时，统计了每位同学每周阅读课外书的小时数，并将数据分为5组：0-2小时，2-4小时，4-6小时，6-8小时，8小时以上。已知阅读时间在4-6小时的人数最多，共12人；阅读时间在0-2小时的人数最少，只有3人；其他三组人数分别为5人、8人和7人。请问该班级共有多少名学生参与了这项统计？","answer":"C","explanation":"本题考查数据的收集与整理。根据题意，将各组人数相加即可得到总人数：0-2小时有3人，2-4小时有5人，4-6小时有12人，6-8小时有8人，8小时以上有7人。计算总和：3 + 5 + 12 + 8 + 7 = 35。因此，该班级共有35名学生参与了统计。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 21:39:31","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":"30人","is_correct":0},{"id":"B","content":"33人","is_correct":0},{"id":"C","content":"35人","is_correct":1},{"id":"D","content":"38人","is_correct":0}]},{"id":2138,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在解方程 3(x - 2) = 9 时，第一步将方程两边同时除以3，得到 x - 2 = 3。这一步骤的依据是等式的什么性质？","answer":"D","explanation":"该学生将方程两边同时除以3，这是应用了等式的基本性质：等式两边同时除以同一个不为零的数，等式仍然成立。这是七年级代数部分的重要内容，用于简化方程求解过程。","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":"等式两边同时加上同一个数，等式仍然成立","is_correct":0},{"id":"B","content":"等式两边同时减去同一个数，等式仍然成立","is_correct":0},{"id":"C","content":"等式两边同时乘同一个数，等式仍然成立","is_correct":0},{"id":"D","content":"等式两边同时除以同一个不为零的数，等式仍然成立","is_correct":1}]},{"id":259,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"一个多边形的内角和是1260°，则这个多边形从一个顶点出发可以画出___条对角线。","answer":"6","explanation":"首先根据多边形内角和公式：(n - 2) × 180° = 内角和。设边数为n，则 (n - 2) × 180 = 1260，解得 n - 2 = 7，n = 9。这是一个九边形。从一个顶点出发可以画出的对角线条数为 n - 3，即 9 - 3 = 6 条。因为不能连接自己和相邻的两个顶点，所以减去3。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"中等","points":1,"is_active":1,"created_at":"2025-12-29 14:55:08","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":2538,"subject":"数学","grade":"九年级","stage":"初中","type":"选择题","content":"某学生观察一个圆柱形水杯的正视图、俯视图和左视图，发现其正视图和左视图均为矩形，俯视图为一个圆。若该水杯的高为12 cm，底面直径为8 cm，则其正视图的矩形面积为多少？","answer":"A","explanation":"题目考查的是投影与视图中的基本几何体三视图知识。圆柱形水杯的正视图是一个矩形，其高度等于圆柱的高（12 cm），宽度等于圆柱底面的直径（8 cm）。因此，正视图的矩形面积为：12 × 8 = 96 cm²。选项A正确。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-10 16:36:43","updated_at":"2026-01-10 16:36:43","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":"96 cm²","is_correct":1},{"id":"B","content":"48 cm²","is_correct":0},{"id":"C","content":"64 cm²","is_correct":0},{"id":"D","content":"32 cm²","is_correct":0}]},{"id":700,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"某学生在绘制平面直角坐标系中的图形时，将点 A 的横坐标记为 -3，纵坐标记为 4；点 B 的横坐标记为 5，纵坐标记为 -2。若他将这两个点关于 y 轴对称后得到新点 A' 和 B'，则点 A' 的坐标是 _ ，点 B' 的坐标是 _ 。","answer":"A' 的坐标是 (3, 4)，B' 的坐标是 (-5, -2)","explanation":"在平面直角坐标系中，一个点关于 y 轴对称时，其横坐标变为相反数，纵坐标保持不变。点 A 的坐标为 (-3, 4)，关于 y 轴对称后，横坐标 -3 变为 3，纵坐标 4 不变，因此 A' 的坐标为 (3, 4)。点 B 的坐标为 (5, -2)，关于 y 轴对称后，横坐标 5 变为 -5，纵坐标 -2 不变，因此 B' 的坐标为 (-5, -2)。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 22:42:05","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":238,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"某学生在计算一个数的相反数时，误将该数加上了3，结果得到5。那么这个数的正确相反数应该是____。","answer":"-2","explanation":"设这个数为x。根据题意，某学生误将x加上3得到5，即x + 3 = 5，解得x = 2。这个数的相反数是-2。因此，正确答案是-2。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 14:41:33","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":756,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某学生测量教室中一个长方形黑板的周长为360厘米，已知它的长是宽的2倍，那么这个黑板的宽是___厘米。","answer":"60","explanation":"设黑板的宽为x厘米，则长为2x厘米。根据长方形周长公式：周长 = 2 × (长 + 宽)，代入得：2 × (2x + x) = 360。化简得：2 × 3x = 360，即6x = 360。解得x = 60。因此，黑板的宽是60厘米。本题考查一元一次方程在实际问题中的应用，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 23:26:55","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":2435,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"在一次校园绿化项目中，工人师傅用四块相同的等腰直角三角形地砖拼接成一个轴对称图形，拼接方式如图所示（每块地砖的直角边长为√2米）。若拼接后的大图形是一个正方形，且内部形成一个较小的空白正方形区域，则该空白正方形的面积是多少？","answer":"B","explanation":"每块等腰直角三角形地砖的直角边长为√2米，因此每条直角边对应的斜边（即等腰直角三角形的斜边）长度为：√[(√2)² + (√2)²] = √(2 + 2) = √4 = 2（米）。四块这样的三角形地砖以斜边朝外、直角顶点朝内拼接，可形成一个大正方形，其边长等于原三角形斜边的长度，即2米，故大正方形面积为 2 × 2 = 4 平方米。每块三角形面积为 (1\/2) × √2 × √2 = (1\/2) × 2 = 1 平方米，四块总面积为 4 × 1 = 4 平方米。由于大正方形总面积也为4平方米，说明拼接紧密，但中间空白区域实际由四个直角顶点围成。观察可知，四个直角顶点位于大正方形的中心区域，彼此间距构成一个小正方形，其边长等于两个直角边在水平和垂直方向上的投影差。通过坐标法或几何分析可得，空白正方形边长为√2米，因此面积为 (√2)² = 2 平方米。故正确答案为 B。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 13:07:22","updated_at":"2026-01-10 13:07:22","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 平方米","is_correct":0},{"id":"B","content":"2 平方米","is_correct":1},{"id":"C","content":"√2 平方米","is_correct":0},{"id":"D","content":"4 平方米","is_correct":0}]},{"id":413,"subject":"数学","grade":"初一","stage":"小学","type":"选择题","content":"某学生调查了班级同学每天使用手机的时间（单位：分钟），并将数据整理成如下频数分布表：\n\n| 使用时间区间 | 频数（人数） |\n|---------------|--------------|\n| 0–30 | 8 |\n| 31–60 | 12 |\n| 61–90 | 15 |\n| 91–120 | 10 |\n| 121以上 | 5 |\n\n请问这组数据的中位数最可能落在哪个区间？","answer":"C","explanation":"首先计算总人数：8 + 12 + 15 + 10 + 5 = 50人。中位数是第25和第26个数据的平均值。累计频数：0–30分钟有8人，31–60分钟累计为8+12=20人，61–90分钟累计为20+15=35人。由于第25和第26个数据都落在累计频数超过25的区间，即61–90分钟区间内，因此中位数最可能落在61–90分钟。故正确答案为C。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:30:07","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":"0–30分钟","is_correct":0},{"id":"B","content":"31–60分钟","is_correct":0},{"id":"C","content":"61–90分钟","is_correct":1},{"id":"D","content":"91–120分钟","is_correct":0}]}]