习题练习

[{"id":887,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某班级组织了一次环保知识竞赛，参赛学生需要回答关于垃圾分类的问题。比赛结束后，统计发现答对第一题的学生有18人，答对第二题的学生有24人，两题都答对的学生有10人。那么，至少答对一题的学生共有___人。","answer":"32","explanation":"本题考查数据的收集、整理与描述中的集合思想。根据容斥原理，至少答对一题的学生人数 = 答对第一题的人数 + 答对第二题的人数 - 两题都答对的人数。即：18 + 24 - 10 = 32。因此，至少答对一题的学生共有32人。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 01:58:39","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":1942,"subject":"数学","grade":"七年级","stage":"初中","type":"填空题","content":"某学生调查了所在班级同学每天使用手机的时间（单位：小时），将数据分为5组并绘制频数分布直方图。已知前四组的频数分别为4、7、9、5，第五组的频率为0.2，则该班级共有___名学生。","answer":"30","explanation":"设总人数为x，第五组频数为0.2x。前四组频数和为4+7+9+5=25，故25+0.2x=x，解得x=30。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-07 14:12:04","updated_at":"2026-01-07 14:12:04","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":832,"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，其中塑料瓶占总数的3\/8，废纸占总数的1\/4，其余为金属罐。若金属罐的数量比废纸多12个，则该学生一共收集了___个可回收物品。","answer":"96","explanation":"设该学生一共收集了x个可回收物品。根据题意，塑料瓶占3\/8，即(3\/8)x；废纸占1\/4，即(1\/4)x；金属罐占剩余部分，即x - (3\/8)x - (1\/4)x = (3\/8)x。题目说明金属罐比废纸多12个，因此列出方程：(3\/8)x - (1\/4)x = 12。将1\/4化为2\/8，得(3\/8 - 2\/8)x = 12，即(1\/8)x = 12，解得x = 96。所以该学生一共收集了96个可回收物品。本题考查一元一次方程的实际应用，结合分数运算，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 00:49:22","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":422,"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：25，30，28，35，32，27，33。为了分析阅读时间的分布情况，该学生计算了这组数据的平均数。请问这组数据的平均数是多少？","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。具体步骤如下：首先，将每天的阅读时间相加：25 + 30 + 28 + 35 + 32 + 27 + 33 = 210（分钟）。然后，用总和除以天数（7天）：210 ÷ 7 = 30（分钟）。因此，这组数据的平均数是30分钟，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 17:32:46","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":"28分钟","is_correct":0},{"id":"B","content":"29分钟","is_correct":0},{"id":"C","content":"30分钟","is_correct":1},{"id":"D","content":"31分钟","is_correct":0}]},{"id":472,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"某学生记录了连续5天每天完成的数学练习题数量，分别为：8道、10道、x道、12道、9道。已知这5天平均每天完成10道题，那么第3天完成的题数x是多少？","answer":"C","explanation":"根据题意，5天平均每天完成10道题，因此总题数为 5 × 10 = 50 道。已知其他四天完成的题数分别为8、10、12、9，将它们相加：8 + 10 + 12 + 9 = 39。设第3天完成的题数为x，则有 39 + x = 50，解得 x = 11。因此，第3天完成了11道题。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:54:38","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":"A","content":"9","is_correct":0},{"id":"B","content":"10","is_correct":0},{"id":"C","content":"11","is_correct":1},{"id":"D","content":"12","is_correct":0}]},{"id":144,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"小明在解一个一元一次方程时，将方程 3x + 5 = 20 的解法写成了以下步骤：第一步，3x = 20 - 5；第二步，3x = 15；第三步，x = 5。小红说小明的解法完全正确，小刚说小明漏掉了检验步骤。根据初一数学的学习要求，以下说法正确的是：","answer":"B","explanation":"根据初一数学课程标准，解一元一次方程的核心是运用等式的基本性质进行变形。小明的解法中，第一步利用等式两边同时减去5，第二步化简，第三步两边同时除以3，每一步都正确。虽然在实际教学中常建议检验，但题目问的是‘解法是否正确’，而非‘是否完整’。只要变形过程正确且结果无误，解法就是正确的。因此选项B正确。选项D强调‘必须检验’，但课程标准并未强制要求每一步解答都必须写出检验，故不选。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-24 11:30:06","updated_at":"2025-12-24 11:30:06","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":"小明的解法错误，因为第一步不应该移项","is_correct":0},{"id":"B","content":"小明的解法正确，因为每一步都符合等式性质，且结果正确","is_correct":1},{"id":"C","content":"小明的解法错误，因为第三步应该写成 x = 15 ÷ 3","is_correct":0},{"id":"D","content":"小明的解法不完整，必须写出检验过程才算完整解答","is_correct":0}]},{"id":538,"subject":"数学","grade":"初一","stage":"小学","type":"选择题","content":"某学生在整理班级同学的课外阅读时间时，收集了以下数据（单位：小时）：2，3，5，4，3，6，4，3。为了分析数据，他制作了频数分布表。请问阅读时间为3小时的人数占总人数的几分之几？","answer":"A","explanation":"首先统计总人数：数据共有8个，即总人数为8。接着统计阅读时间为3小时的人数：在数据2，3，5，4，3，6，4，3中，数字3出现了3次。因此，阅读时间为3小时的人数占总人数的比例为3\/8，即八分之三。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 18:50:01","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":"八分之三","is_correct":1},{"id":"B","content":"四分之一","is_correct":0},{"id":"C","content":"二分之一","is_correct":0},{"id":"D","content":"八分之五","is_correct":0}]},{"id":1928,"subject":"数学","grade":"七年级","stage":"初中","type":"填空题","content":"在平面直角坐标系中，点A(2, 3)绕原点逆时针旋转90°后得到点B，再将点B向右平移4个单位，得到点C。若点C的坐标为(a, b)，则a + b的值为____。","answer":"5","explanation":"点A(2,3)绕原点逆时针旋转90°得B(-3,2)，再向右平移4个单位得C(1,2)，故a=1, b=2，a+b=3。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-07 14:09:57","updated_at":"2026-01-07 14:09:57","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":820,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"在一次班级环保活动中，某学生收集了可回收垃圾和不可回收垃圾共30袋。已知可回收垃圾每袋重2千克，不可回收垃圾每袋重1.5千克，这些垃圾总重量为54千克。设可回收垃圾有x袋，则根据题意可列出一元一次方程：2x + 1.5(______) = 54。","answer":"30 - x","explanation":"题目中已知垃圾总袋数为30袋，可回收垃圾有x袋，则不可回收垃圾的袋数就是总袋数减去可回收袋数，即30 - x袋。因此，在列方程时，不可回收垃圾的总重量应为1.5乘以(30 - x)。所以空白处应填30 - x。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 00:37:52","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":504,"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，老师将成绩整理后绘制成频数分布直方图，发现成绩在80分到90分之间的学生人数最多。这说明该分数段的什么统计量最大？","answer":"C","explanation":"题目中提到“成绩在80分到90分之间的学生人数最多”，这表示该分数段出现的次数最多。在统计学中，一组数据中出现次数最多的数值称为众数。因此，80分到90分这个区间对应的众数最大。平均数是所有数据的总和除以个数，中位数是数据排序后位于中间的数，极差是最大值与最小值之差，它们都不能直接由‘人数最多’得出。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 18:10:48","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":"平均数","is_correct":0},{"id":"B","content":"中位数","is_correct":0},{"id":"C","content":"众数","is_correct":1},{"id":"D","content":"极差","is_correct":0}]}]