[{"id":255,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"某学生在解方程时，将方程 3(x - 2) = 2x + 5 的括号展开后得到 3x - 6 = 2x + 5，然后移项合并同类项，最终解得 x = ___。","answer":"11","explanation":"首先将方程 3(x - 2) = 2x + 5 展开，得到 3x - 6 = 2x + 5。接着将含 x 的项移到等式左边，常数项移到右边：3x - 2x = 5 + 6，即 x = 11。因此，方程的解为 x = 11。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"中等","points":1,"is_active":1,"created_at":"2025-12-29 14:54:30","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":1025,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某学生调查了班级同学最喜欢的运动项目，收集数据后发现：喜欢篮球的人数是喜欢跳绳人数的2倍，喜欢跳绳的人数比喜欢踢毽子的人数多3人，而喜欢踢毽子的人数是4人。那么，喜欢篮球的人数是____人。","answer":"14","explanation":"根据题意，喜欢踢毽子的人数是4人。喜欢跳绳的人数比踢毽子多3人，因此跳绳人数为 4 + 3 = 7 人。喜欢篮球的人数是跳绳人数的2倍，所以篮球人数为 7 × 2 = 14 人。本题考查数据的收集与整理，结合有理数运算，通过逐步推理得出结果。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 05:42:40","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":805,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"某学生在整理班级同学的课外阅读情况时，收集了每位同学每月阅读的书籍数量，并将数据按从小到大的顺序排列。已知这组数据的中位数是4，且数据个数为奇数。如果去掉最大的一个数据后，新的中位数变为3.5，那么原数据中最少有多少个数据？____","answer":"7","explanation":"设原数据有n个，且n为奇数。中位数为第(n+1)\/2个数，已知为4。去掉最大的一个数据后，剩下n-1个数据（偶数个），中位数为中间两个数的平均数，即第(n-1)\/2个和第(n+1)\/2个数据的平均值为3.5。由于原数据有序，去掉最大值后，中间两个数应分别为3和4（因为(3+4)\/2=3.5）。为了使这种情况成立，原数据中第(n+1)\/2个数必须是4，且其前一个数为3。当n=7时，原数据第4个数为4，去掉最大值后剩下6个数，第3和第4个数分别为3和4，满足新中位数为3.5。若n<7（如n=5），则无法满足去掉最大值后中间两数为3和4的条件。因此原数据最少有7个。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 00:22:41","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":430,"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，老师将成绩分为四个等级：优秀、良好、及格、不及格。统计后发现，优秀人数占总人数的25%，良好人数是优秀人数的2倍，及格人数比良好人数少10人，不及格人数为5人。若该班总人数为x，则可列出一元一次方程为：","answer":"A","explanation":"设总人数为x。根据题意：优秀人数为25%即0.25x；良好人数是优秀的2倍，即2 × 0.25x = 0.5x；及格人数比良好人数少10人，即0.5x - 10；不及格人数为5人。总人数等于各部分人数之和，因此方程为：x = 0.25x + 0.5x + (0.5x - 10) + 5。选项A正确。其他选项在良好人数或及格人数的计算上存在错误。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:35:07","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":"x = 0.25x + 0.5x + (0.5x - 10) + 5","is_correct":1},{"id":"B","content":"x = 0.25x + 0.25x + (0.25x - 10) + 5","is_correct":0},{"id":"C","content":"x = 0.25x + 0.5x + (0.25x - 10) + 5","is_correct":0},{"id":"D","content":"x = 0.25x + 0.5x + (0.5x + 10) + 5","is_correct":0}]},{"id":2461,"subject":"数学","grade":"八年级","stage":"初中","type":"填空题","content":"某校八年级学生参加数学竞赛，成绩分布如下表所示。若将成绩按从小到大的顺序排列，则第15个数据是85分，第16个数据是88分，那么这次竞赛成绩的中位数是____分。","answer":"86.5","explanation":"中位数是数据排序后中间两个数的平均数。第15和第16个数据分别为85和88，中位数为(85 + 88) ÷ 2 = 86.5。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 14:14:55","updated_at":"2026-01-10 14:14:55","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":438,"subject":"数学","grade":"初一","stage":"小学","type":"选择题","content":"某班级在一次数学测验中，收集了20名学生的成绩（单位：分），数据如下：68, 72, 75, 76, 78, 79, 80, 82, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 94, 98。如果将这些成绩按从小到大的顺序排列，那么中位数是多少？","answer":"B","explanation":"中位数是指将一组数据按从小到大（或从大到小）的顺序排列后，处于中间位置的数。如果数据个数为偶数，则中位数是中间两个数的平均数。本题共有20个数据，是偶数个，因此中位数是第10个和第11个数据的平均数。将数据排序后，第10个数是83，第11个数是85。计算中位数：(83 + 85) ÷ 2 = 168 ÷ 2 = 84。因此，中位数是84分。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:40:10","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":"A","content":"83分","is_correct":0},{"id":"B","content":"84分","is_correct":1},{"id":"C","content":"85分","is_correct":0},{"id":"D","content":"86分","is_correct":0}]},{"id":512,"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身高数据时，制作了如下频数分布表：\n\n身高区间（cm） | 频数\n--------------|------\n140～145 | 3\n145～150 | 5\n150～155 | 8\n155～160 | 10\n160～165 | 4\n\n若该班共有30名学生，则身高在150cm及以上的学生人数占全班人数的百分比是多少？","answer":"C","explanation":"首先确定身高在150cm及以上的学生人数。根据表格，150～155cm有8人，155～160cm有10人，160～165cm有4人。将这些频数相加：8 + 10 + 4 = 22人。全班共有30名学生，因此所占百分比为 (22 ÷ 30) × 100% ≈ 73.3%。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 18:16:35","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":"60%","is_correct":0},{"id":"B","content":"66.7%","is_correct":0},{"id":"C","content":"73.3%","is_correct":1},{"id":"D","content":"80%","is_correct":0}]},{"id":642,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"在一次校园植物观察活动中，某学生记录了5种植物的高度（单位：厘米），分别为12、15、18、15、20。这组数据的中位数是____。","answer":"15","explanation":"首先将这组数据按从小到大的顺序排列：12、15、15、18、20。由于数据个数为5（奇数个），中位数就是位于中间位置的数，即第3个数。第3个数是15，因此这组数据的中位数是15。本题考查的是数据的收集、整理与描述中的中位数概念，属于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":"2025-12-29 22:08:56","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":2376,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"某学生用一张矩形纸片制作一个无盖长方体盒子，纸片的长为 24 cm，宽为 18 cm。从四个角各剪去一个边长为 x cm 的正方形，然后将四边折起形成盒子。若要求盒子的容积为 400 cm³，则 x 的值应满足的方程是：","answer":"A","explanation":"制作无盖长方体盒子时，从矩形纸片的四个角各剪去一个边长为 x 的正方形后，折起四边形成盒子。此时，盒子的高为 x cm，底面的长为 (24 - 2x) cm，宽为 (18 - 2x) cm。容积 = 长 × 宽 × 高，即 V = x(24 - 2x)(18 - 2x)。题目给出容积为 400 cm³，因此方程为 x(24 - 2x)(18 - 2x) = 400。选项 A 正确。选项 B 错误，因为未考虑两边都剪去 x；选项 C 缺少高度项 x；选项 D 错误地将 x 平方，不符合实际几何意义。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 11:27:47","updated_at":"2026-01-10 11:27:47","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":"x(24 - 2x)(18 - 2x) = 400","is_correct":1},{"id":"B","content":"x(24 - x)(18 - x) = 400","is_correct":0},{"id":"C","content":"(24 - x)(18 - x) = 400","is_correct":0},{"id":"D","content":"x²(24 - 2x)(18 - 2x) = 400","is_correct":0}]},{"id":908,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某班级组织学生参加植树活动，原计划每天植树50棵，实际每天比原计划多种树10棵，结果提前2天完成了植树任务。那么原计划需要___天完成植树任务。","answer":"12","explanation":"设原计划需要 x 天完成任务，则总植树量为 50x 棵。实际每天植树 50 + 10 = 60 棵，用了 (x - 2) 天完成，因此有方程：60(x - 2) = 50x。解这个一元一次方程：60x - 120 = 50x → 10x = 120 → x = 12。所以原计划需要12天完成任务。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 02:28:11","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":[]}]