[{"id":183,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"下列各数中，最小的数是（ ）。","answer":"A","explanation":"本题考查有理数的大小比较。在数轴上，负数位于0的左侧，正数位于0的右侧，因此负数小于0，0小于正数。给出的四个数中，-3是唯一的负数，0、1、2都是非负数，所以-3最小。也可以通过数轴直观判断：越往左的数越小，-3在最左边，因此最小。故选A。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 14:01:09","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":"A","content":"-3","is_correct":1},{"id":"B","content":"0","is_correct":0},{"id":"C","content":"1","is_correct":0},{"id":"D","content":"2","is_correct":0}]},{"id":456,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"某学生调查了班级同学最喜欢的课外活动，并将结果整理成如下条形统计图（图中数据已给出）：阅读12人，运动18人，绘画10人，音乐15人。请问喜欢运动的人数比喜欢绘画的人数多百分之几？","answer":"B","explanation":"题目考查的是数据的收集、整理与描述中的百分比计算。首先确定喜欢运动的人数为18人，喜欢绘画的人数为10人。多出来的人数是18 - 10 = 8人。要求的是‘多百分之几’，即多出的部分占绘画人数的百分比，计算公式为：(多出人数 ÷ 绘画人数) × 100% = (8 ÷ 10) × 100% = 80%。因此正确答案是B。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:47:13","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":"80%","is_correct":1},{"id":"C","content":"50%","is_correct":0},{"id":"D","content":"40%","is_correct":0}]},{"id":834,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"在一次环保活动中，某班级学生共收集了120千克废纸。已知男生每人收集2.5千克，女生每人收集3千克，全班共有45人参与。设男生有x人，则女生有___人，根据题意可列出一元一次方程为___。","answer":"45 - x, 2.5x + 3(45 - x) = 120","explanation":"全班共45人，男生有x人，则女生人数为总人数减去男生人数，即45 - x。男生每人收集2.5千克，共收集2.5x千克；女生每人收集3千克，共收集3(45 - x)千克。总收集量为120千克，因此可列方程：2.5x + 3(45 - x) = 120。本题考查了一元一次方程的实际应用，涉及有理数运算和方程建模，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 00:51:02","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":134,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"下列各数中，最小的数是（ ）。","answer":"D","explanation":"在有理数中，负数小于0，0小于正数。比较负数时，绝对值越大的负数越小。-5 比 -3 更小，因此 -5 是四个选项中最小的数。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-24 09:40:59","updated_at":"2025-12-24 09:40:59","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","is_correct":0},{"id":"B","content":"0","is_correct":0},{"id":"C","content":"1","is_correct":0},{"id":"D","content":"-5","is_correct":1}]},{"id":2343,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"某公园计划修建一个等腰三角形花坛，设计要求其周长为24米，且其中一条边长为9米。已知该三角形为轴对称图形，且满足三角形三边关系。若设底边为x米，两腰各为y米，则下列哪组方程能正确描述该三角形的设计条件？","answer":"D","explanation":"本题考查等腰三角形的性质、周长计算及三角形三边关系。已知花坛为等腰三角形，周长为24米，设底边为x，两腰为y，则周长公式为 x + 2y = 24。又因三角形任意两边之和大于第三边，任意两边之差小于第三边，即 |y - y| < x < y + y 可简化为 0 < x < 2y；同时需满足 |x - y| < y < x + y。由于 y > 0 且 x > 0，最关键的约束是两边之差小于第三边：|x - y| < y，即 -y < x - y < y，化简得 0 < x < 2y，这与三角形不等式一致。选项D中的 |x - y| < y < x + y 正确表达了以y为一边时，其余两边x与y需满足的不等关系，且结合 x + 2y = 24 可完整描述设计条件。其他选项要么逻辑错误（如A中|y−y|=0，表述冗余），要么不等式方向混乱。因此正确答案为D。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 11:00:01","updated_at":"2026-01-10 11:00:01","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 + 2y = 24 且 |y - y| < x < y + y","is_correct":0},{"id":"B","content":"x + 2y = 24 且 |y - x| < y < y + x","is_correct":0},{"id":"C","content":"x + 2y = 24 且 |y - y| < x < 2y","is_correct":0},{"id":"D","content":"x + 2y = 24 且 |x - y| < y < x + y","is_correct":1}]},{"id":2443,"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，工人师傅需要用钢筋焊接一个等腰三角形的支架。已知该支架的底边长为8米，两腰相等，且其周长不超过26米。为了确保结构稳定，要求支架的高（从顶点到底边的垂直距离）必须大于5米。若设腰长为x米，则x的取值范围是（ ）。","answer":"A","explanation":"本题综合考查等腰三角形性质、勾股定理、不等式组的应用。首先，由题意知底边为8米，腰长为x米，周长为2x + 8 ≤ 26，解得x ≤ 9。其次，作等腰三角形的高，将底边平分，得到两个直角三角形，每个直角三角形的底边为4米，斜边为x，高h满足勾股定理：h = √(x² - 4²) = √(x² - 16)。根据题意h > 5，即√(x² - 16) > 5，两边平方得x² - 16 > 25，即x² > 41，解得x > √41 ≈ 6.4。结合x ≤ 9且x > √41，而√41 > 6，因此x必须大于6（因为x为长度，且需满足严格大于√41），同时不超过9。综上，x的取值范围是6 < x ≤ 9。选项A正确。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 13:31:21","updated_at":"2026-01-10 13:31:21","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":"6 < x ≤ 9","is_correct":1},{"id":"B","content":"x > 6","is_correct":0},{"id":"C","content":"5 < x ≤ 9","is_correct":0},{"id":"D","content":"6 ≤ x < 9","is_correct":0}]},{"id":579,"subject":"数学","grade":"初一","stage":"小学","type":"选择题","content":"平均数","answer":"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 20:05:28","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":954,"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，将数据分为150～155cm、155～160cm、160～165cm、165～170cm四个组，并制作了频数分布表。如果160～165cm这一组的频数是12，所占百分比为30%，那么参加统计的学生总人数是____人。","answer":"40","explanation":"已知160～165cm组的频数为12，占总人数的30%。设总人数为x，则有方程：12 = 30% × x，即12 = 0.3x。解这个一元一次方程，得x = 12 ÷ 0.3 = 40。因此，参加统计的学生总人数是40人。本题考查数据的收集、整理与描述中频数与百分比的关系，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":"2025-12-30 03:39:08","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":335,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"某学生在整理班级同学最喜欢的运动项目数据时，制作了如下频数分布表。已知喜欢篮球的人数占总人数的30%，总人数为40人，则喜欢篮球的人数是多少？","answer":"B","explanation":"题目要求计算喜欢篮球的人数。已知总人数为40人，喜欢篮球的人数占总人数的30%。计算方法是：40 × 30% = 40 × 0.3 = 12。因此，喜欢篮球的人数是12人。本题考查的是数据的收集、整理与描述中的百分比计算，属于七年级数学中数据处理的基础知识，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 15:39:57","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":"10","is_correct":0},{"id":"B","content":"12","is_correct":1},{"id":"C","content":"15","is_correct":0},{"id":"D","content":"18","is_correct":0}]},{"id":697,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"某学生测量了一个长方形花坛的周长和一条边的长度，发现周长是18米，其中一条边长是5米，那么与这条边相邻的另一条边的长度是____米。","answer":"4","explanation":"长方形的周长公式是：周长 = 2 × (长 + 宽)。已知周长为18米，一条边为5米，设另一条边为x米，则有方程：2 × (5 + x) = 18。两边同时除以2，得5 + x = 9，解得x = 4。因此，另一条边的长度是4米。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 22:39:15","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":[]}]