习题练习

[{"id":284,"subject":"数学","grade":"初一","stage":"小学","type":"选择题","content":"8","answer":"答案待完善","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 15:31:38","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":420,"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，随机抽取了30名同学进行调查，记录了他们每周课外阅读的时间（单位：小时），并将数据整理成如下频数分布表：\n\n| 阅读时间（小时） | 频数 |\n|------------------|------|\n| 0 ≤ x < 2 | 6 |\n| 2 ≤ x < 4 | 10 |\n| 4 ≤ x < 6 | 8 |\n| 6 ≤ x < 8 | 4 |\n| 8 ≤ x < 10 | 2 |\n\n根据以上数据，这组数据的众数所在的组别是：","answer":"B","explanation":"众数是指一组数据中出现次数最多的数据。在本题中，频数分布表显示了不同阅读时间区间内的人数。观察频数列：0 ≤ x < 2 有6人，2 ≤ x < 4 有10人，4 ≤ x < 6 有8人，6 ≤ x < 8 有4人，8 ≤ x < 10 有2人。其中频数最大的是10，对应的是“2 ≤ x < 4”这一组。因此，众数所在的组别是“2 ≤ x < 4”。注意：这里问的是众数所在的‘组别’，而不是具体数值，所以只需找出频数最大的组即可。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:32:29","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 ≤ x < 2","is_correct":0},{"id":"B","content":"2 ≤ x < 4","is_correct":1},{"id":"C","content":"4 ≤ x < 6","is_correct":0},{"id":"D","content":"6 ≤ x < 8","is_correct":0}]},{"id":1770,"subject":"数学","grade":"七年级","stage":"初中","type":"填空题","content":"某学生在平面直角坐标系中画出一个三角形，三个顶点的坐标分别为 A(2, 3)、B(6, 7)、C(4, -1)。若将该三角形先向右平移 3 个单位，再向下平移 2 个单位，得到新三角形 A'B'C'，则点 B' 的坐标为____。","answer":"(9, 5)","explanation":"点 B(6, 7) 向右平移 3 个单位，横坐标加 3 得 9；向下平移 2 个单位，纵坐标减 2 得 5。因此 B' 坐标为 (9, 5)。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-06 15:12:31","updated_at":"2026-01-06 15:12:31","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":1835,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"如图，在平面直角坐标系中，点 A(0, 4)、B(3, 0)、C(0, 0) 构成直角三角形 ABC，∠C 为直角。将 △ABC 沿直线 y = x 翻折得到 △A'B'C'，则点 B' 的坐标是（ ）。","answer":"A","explanation":"本题综合考查轴对称与坐标变换、勾股定理及一次函数图像的理解。已知直线 y = x 是翻折对称轴，翻折即关于直线 y = x 作轴对称变换。在平面直角坐标系中，一个点 (a, b) 关于直线 y = x 的对称点为 (b, a)。因此，点 B(3, 0) 关于直线 y = x 的对称点 B' 的坐标为 (0, 3)。验证：点 A(0, 4) 对称后为 A'(4, 0)，点 C(0, 0) 对称后仍为 (0, 0)，符合翻折性质。故正确答案为 A。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-06 16:49:35","updated_at":"2026-01-06 16:49:35","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, 3)","is_correct":1},{"id":"B","content":"(3, 0)","is_correct":0},{"id":"C","content":"(4, 0)","is_correct":0},{"id":"D","content":"(0, 4)","is_correct":0}]},{"id":495,"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数据时，发现一周内每天阅读时间（单位：分钟）分别为：30、45、0、60、35、50、40。如果去掉一个最低值和一个最高值后，剩余数据的平均数是多少？","answer":"C","explanation":"首先将数据按从小到大排列：0、30、35、40、45、50、60。最低值是0，最高值是60，去掉这两个值后，剩余数据为：30、35、40、45、50。计算这五个数的平均数：(30 + 35 + 40 + 45 + 50) ÷ 5 = 200 ÷ 5 = 42。因此，正确答案是C。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 18:06:51","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":"A","content":"40","is_correct":0},{"id":"B","content":"41","is_correct":0},{"id":"C","content":"42","is_correct":1},{"id":"D","content":"43","is_correct":0}]},{"id":2313,"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，工人师傅需要在一块矩形空地的对角线上铺设一条石板路。已知这块空地的长为8米，宽为6米。为了估算石板数量，需要先计算对角线的长度。根据勾股定理，这条对角线的长度最接近以下哪个值？","answer":"B","explanation":"本题考查勾股定理在矩形对角线计算中的应用。矩形对角线将矩形分成两个直角三角形，其中两条直角边分别为矩形的长和宽。根据勾股定理：对角线² = 长² + 宽² = 8² + 6² = 64 + 36 = 100。因此，对角线 = √100 = 10（米）。故正确答案为B。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-10 10:46:09","updated_at":"2026-01-10 10:46:09","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":"9米","is_correct":0},{"id":"B","content":"10米","is_correct":1},{"id":"C","content":"11米","is_correct":0},{"id":"D","content":"12米","is_correct":0}]},{"id":2305,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"某学生在研究轴对称图形时，将一张矩形纸片沿一条直线对折，使得折痕两侧的部分完全重合。已知矩形的长为8 cm，宽为6 cm，若折痕恰好经过矩形的一个顶点和对边上的一点，且该折痕是矩形的对称轴，则这条折痕的长度为多少？","answer":"C","explanation":"本题考查轴对称与勾股定理的综合应用。矩形沿折痕对折后完全重合，说明折痕是图形的对称轴。题目中折痕经过一个顶点和对边上的一点，且为对称轴，意味着折痕是该顶点到对边中点的连线（因为只有这样才能保证对称）。假设矩形ABCD中，A为顶点，对边为CD，则折痕为A到CD中点M的线段AM。在矩形中，AD = 6 cm，DM = 4 cm（因为CD = 8 cm，中点到端点为一半）。在直角三角形ADM中，由勾股定理得：AM² = AD² + DM² = 6² + 4² = 36 + 16 = 52，但此计算错误。正确分析应为：若折痕经过顶点A和对边BC上的点P，且为对称轴，则P应为BC中点。此时AP为折痕。在矩形中，AB = 8 cm，BP = 3 cm（宽的一半），则AP² = AB² + BP² = 8² + 3² = 64 + 9 = 73，故AP = √73 cm。因此正确答案为C。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-10 10:44:46","updated_at":"2026-01-10 10:44:46","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":"5 cm","is_correct":0},{"id":"B","content":"√39 cm","is_correct":0},{"id":"C","content":"√73 cm","is_correct":1},{"id":"D","content":"10 cm","is_correct":0}]},{"id":1006,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某班级组织植树活动，若每名学生种3棵树，则还剩10棵树没人种；若每名学生种4棵树，则最后一名学生只需种2棵树。这个班级共有___名学生。","answer":"12","explanation":"设这个班级共有x名学生。根据题意，树的总数不变。第一种情况：每名学生种3棵，还剩10棵，所以总树数为3x + 10。第二种情况：前(x - 1)名学生每人种4棵，最后一名学生种2棵，总树数为4(x - 1) + 2 = 4x - 4 + 2 = 4x - 2。因为树的数量相同，列方程：3x + 10 = 4x - 2。解这个一元一次方程：移项得10 + 2 = 4x - 3x，即12 = x。所以这个班级共有12名学生。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 05:03:53","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":1939,"subject":"数学","grade":"七年级","stage":"初中","type":"填空题","content":"某学生调查了班级同学每周用于体育锻炼的时间（单位：小时），将数据整理后发现，锻炼时间在4小时及以下的有12人，5小时的有8人，6小时的有x人，7小时的有y人。已知这组数据的平均数为5.5小时，且众数为6小时，则x + y的值为____。","answer":"15","explanation":"由众数为6知x最大；设总人数为30+x+y，列平均数方程：(12×4+8×5+6x+7y)\/(30+x+y)=5.5，化简得x+1.5y=15。因x>8且为整数，试值得x=9,y=4不满足，x=6,y=6不满足，x=3,y=8时x非最大，最终x=12,y=2满足条件，x+y=14？重新计算：正确解为x=12,y=2不满足众数，实际x=9,y=4时x=9>8成立，x+y=13？更正：正确解为x...","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-07 14:11:19","updated_at":"2026-01-07 14:11:19","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":395,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"某学生记录了一周内每天完成数学作业所用的时间（单位：分钟），数据如下：45，50，48，52，47，49，51。为了分析这些数据，该学生计算了这组数据的平均数。请问这组数据的平均数最接近以下哪个值？","answer":"C","explanation":"要计算这组数据的平均数，需要将所有数据相加，然后除以数据的个数。数据为：45，50，48，52，47，49，51，共7个数据。求和：45 + 50 + 48 + 52 + 47 + 49 + 51 = 342。平均数为 342 ÷ 7 ≈ 48.857。这个值最接近50，因此正确答案是C。本题考查的是数据的收集、整理与描述中的平均数计算，属于七年级数学课程内容，难度为简单。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:14:48","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":"46","is_correct":0},{"id":"B","content":"48","is_correct":0},{"id":"C","content":"50","is_correct":1},{"id":"D","content":"52","is_correct":0}]}]