[{"id":2446,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"某校八年级开展‘数学建模’活动，研究校园内一座直角三角形花坛的围栏长度。已知花坛的两条直角边分别为√12米和√27米，现需在斜边上安装装饰灯带。若每米灯带成本为8元，则安装整条斜边灯带的总费用最接近以下哪个数值？","answer":"B","explanation":"首先化简两条直角边：√12 = 2√3，√27 = 3√3。根据勾股定理，斜边c = √[(2√3)² + (3√3)²] = √[12 + 27] = √39 ≈ 6.245米。每米灯带8元，总费用为6.245 × 8 ≈ 49.96元，最接近48元。因此选B。本题综合考查二次根式化简与勾股定理的实际应用，难度适中。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 13:42:55","updated_at":"2026-01-10 13:42:55","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":"A","content":"40元","is_correct":0},{"id":"B","content":"48元","is_correct":1},{"id":"C","content":"56元","is_correct":0},{"id":"D","content":"64元","is_correct":0}]},{"id":1098,"subject":"数学","grade":"七年级","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垃圾共12.5千克，其中废纸占8.3千克，塑料瓶占2.7千克，其余为金属。若金属的重量用代数式表示为 12.5 - 8.3 - 2.7，则金属的重量是___千克。","answer":"1.5","explanation":"根据题意，金属的重量等于总重量减去废纸和塑料瓶的重量，即 12.5 - 8.3 - 2.7。先计算 12.5 - 8.3 = 4.2，再计算 4.2 - 2.7 = 1.5。因此，金属的重量是1.5千克。本题考查有理数的加减运算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":"2026-01-06 08:57:01","updated_at":"2026-01-06 08:57:01","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":837,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某班级组织植树活动，计划种植一批树苗。如果每行种8棵，则最后多出5棵；如果每行种10棵，则最后缺少3棵。设共有x棵树苗，根据题意可列出一元一次方程：________。","answer":"8y + 5 = 10y - 3（或等价形式，如：x = 8y + 5 且 x = 10y - 3，最终化简为 8y + 5 = 10y - 3）","explanation":"设共种了y行，则根据第一种种植方式，树苗总数为8y + 5；根据第二种方式，树苗总数为10y - 3。由于树苗总数不变，因此可列方程8y + 5 = 10y - 3。此题考查一元一次方程的实际建模能力，属于简单难度，符合七年级学生认知水平。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 00:53:42","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":469,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"在一次环保知识问卷调查中，某班级共发放了60份问卷，回收有效问卷54份。请问该问卷的有效回收率是多少？","answer":"B","explanation":"有效回收率的计算公式为：有效回收率 = (有效问卷数量 ÷ 发放问卷总数) × 100%。根据题意，有效问卷为54份，发放总数为60份，因此有效回收率为 (54 ÷ 60) × 100% = 0.9 × 100% = 90%。故正确答案为B。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:53:49","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":"85%","is_correct":0},{"id":"B","content":"90%","is_correct":1},{"id":"C","content":"95%","is_correct":0},{"id":"D","content":"100%","is_correct":0}]},{"id":2770,"subject":"历史","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在参观博物馆时看到一件唐代的陶俑，其服饰风格融合了中亚地区的特点，面部轮廓立体，手持胡琴。这件文物最能反映唐代哪一方面的历史特征？","answer":"C","explanation":"题目中的陶俑具有中亚服饰特征和胡琴等外来文化元素，说明唐代社会受到外来文化的影响。唐朝国力强盛，对外交通发达，通过丝绸之路与中亚、西亚等地频繁交流，吸收了大量外来艺术、音乐和服饰文化。因此，这件文物最能体现唐代中外文化交流频繁的特点。选项A与题干无关；选项B错误，唐代是开放的朝代；选项D不符合史实，佛教虽盛行但并未取代本土信仰。故正确答案为C。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-12 10:41:04","updated_at":"2026-01-12 10:41:04","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":"A","content":"唐代农业技术高度发达","is_correct":0},{"id":"B","content":"唐代实行严格的闭关锁国政策","is_correct":0},{"id":"C","content":"唐代中外文化交流频繁","is_correct":1},{"id":"D","content":"唐代佛教完全取代了本土信仰","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":2360,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"在一次校园绿化设计中，某学生需要计算一个由两个全等直角三角形拼接而成的菱形花坛的对角线长度。已知每个直角三角形的两条直角边分别为√12米和√27米，且这两个直角边分别作为菱形的两条对角线的一半。求该菱形花坛的面积。","answer":"C","explanation":"首先化简已知的直角边：√12 = 2√3，√27 = 3√3。根据题意，这两个直角边分别是一条对角线的一半，因此菱形的两条对角线长度分别为2 × 2√3 = 4√3（米）和2 × 3√3 = 6√3（米）。菱形的面积公式为：面积 = (对角线1 × 对角线2) ÷ 2。代入得：面积 = (4√3 × 6√3) ÷ 2 = (24 × 3) ÷ 2 = 72 ÷ 2 = 36（平方米）。因此正确答案为C。本题综合考查了二次根式的化简、勾股定理背景下的几何理解以及菱形面积公式的应用，难度适中。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 11:12:45","updated_at":"2026-01-10 11:12:45","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":"18平方米","is_correct":0},{"id":"B","content":"27平方米","is_correct":0},{"id":"C","content":"36平方米","is_correct":1},{"id":"D","content":"54平方米","is_correct":0}]},{"id":1820,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"某班级在一次数学测验中，五名学生的成绩分别为：82分、76分、90分、88分和84分。这组成绩的平均数是多少？","answer":"B","explanation":"平均数的计算公式是：所有数据之和除以数据的个数。首先将五名学生的成绩相加：82 + 76 + 90 + 88 + 84 = 420。然后将总和除以人数5：420 ÷ 5 = 84。因此，这组成绩的平均数是84分，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":"2026-01-06 16:21:55","updated_at":"2026-01-06 16:21:55","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":"A","content":"82分","is_correct":0},{"id":"B","content":"84分","is_correct":1},{"id":"C","content":"86分","is_correct":0},{"id":"D","content":"88分","is_correct":0}]},{"id":2477,"subject":"数学","grade":"八年级","stage":"初中","type":"解答题","content":"如图，在平面直角坐标系中，点 A(0, 4)，点 B(6, 0)，点 C 在 x 轴正半轴上，且 △ABC 是等腰三角形，AB = AC。过点 A 作直线 l 垂直于 BC，垂足为点 D。点 E 是线段 AD 上一点（不与 A、D 重合），连接 BE 并延长交 y 轴于点 F。已知直线 BE 的解析式为 y = kx + b，且满足 k = -\\\\frac{1}{2}。若四边形 AOFC 的面积为 15，其中 O 为坐标原点，求点 C 的横坐标。","answer":"待完善","explanation":"解析待完善","solution_steps":"待完善","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 15:05:28","updated_at":"2026-01-10 15:05:28","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":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":[]}]