[{"id":2518,"subject":"数学","grade":"九年级","stage":"初中","type":"选择题","content":"某学生设计了一个圆形花坛，其边缘由一段抛物线形状的装饰带和一段圆弧拼接而成。已知抛物线的顶点在原点，且经过点 (2, -4)，而圆弧所在的圆以原点为圆心，半径为 2。若装饰带与圆弧在点 (2, -4) 处平滑连接，则该抛物线的解析式为（ ）。","answer":"A","explanation":"题目中说明抛物线的顶点在原点，因此可设其解析式为 y = ax²。又已知该抛物线经过点 (2, -4)，代入得：-4 = a × 2² → -4 = 4a → a = -1。因此抛物线的解析式为 y = -x²。虽然题目提到与圆弧连接，但问题仅要求求出抛物线解析式，且点 (2, -4) 确实在 y = -x² 上，而半径为 2 的圆上点 (2, -4) 并不在圆上（因为 2² + (-4)² = 20 ≠ 4），这说明‘平滑连接’在此题中仅为情境设定，不影响抛物线解析式的求解。关键信息是顶点在原点且过 (2, -4)，由此唯一确定解析式为 y = -x²。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-10 15:49:55","updated_at":"2026-01-10 15:49:55","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":"y = -x²","is_correct":1},{"id":"B","content":"y = -2x²","is_correct":0},{"id":"C","content":"y = -x² + 4","is_correct":0},{"id":"D","content":"y = -2x² + 4","is_correct":0}]},{"id":361,"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，发现一组数据的最小值是148厘米，最大值是172厘米。若将这组数据分为5组，则每组的组距最接近多少厘米？","answer":"B","explanation":"首先计算极差：最大值减去最小值，即172 - 148 = 24厘米。要将数据分为5组，则组距 = 极差 ÷ 组数 = 24 ÷ 5 = 4.8厘米。由于组距通常取整数，且要覆盖整个数据范围，因此应向上取整为5厘米。若取4厘米，则5组只能覆盖20厘米（5×4），不足以包含24厘米的极差；而5厘米可以覆盖25厘米，满足要求。因此最接近且合理的组距是5厘米。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 15:45:34","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":"4厘米","is_correct":0},{"id":"B","content":"5厘米","is_correct":1},{"id":"C","content":"6厘米","is_correct":0},{"id":"D","content":"7厘米","is_correct":0}]},{"id":2399,"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，设计图纸显示其底边长为8米，两腰相等且与底边的夹角均为60°。施工前需计算花坛的周长和面积，以便准备材料。已知该三角形可被分割为两个全等的直角三角形，且其中一个直角三角形的两条直角边分别为4米和4√3米。根据这些信息，以下关于该花坛的说法正确的是：","answer":"A","explanation":"由题意知，该三角形为等腰三角形，底边为8米，底角为60°。由于底角为60°，顶角也为60°，因此这是一个等边三角形，三边均为8米。故周长为 8 + 8 + 8 = 24 米。将等边三角形沿高线分割，得到两个全等的直角三角形，底边一半为4米，高为 √(8² - 4²) = √(64 - 16) = √48 = 4√3 米，与题目描述一致。面积为 (底 × 高) \/ 2 = (8 × 4√3) \/ 2 = 16√3 平方米。因此选项A正确。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 12:06:48","updated_at":"2026-01-10 12:06:48","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":"该三角形的周长为24米，面积为16√3平方米","is_correct":1},{"id":"B","content":"该三角形的周长为16米，面积为8√3平方米","is_correct":0},{"id":"C","content":"该三角形的周长为24米，面积为8√3平方米","is_correct":0},{"id":"D","content":"该三角形的周长为16米，面积为16√3平方米","is_correct":0}]},{"id":1988,"subject":"数学","grade":"九年级","stage":"初中","type":"选择题","content":"某学生在纸上画了一个边长为6 cm的正方形ABCD，以顶点A为原点建立平面直角坐标系，AB边在x轴正方向，AD边在y轴正方向。若将正方形绕原点A逆时针旋转30°，则旋转后点B的坐标最接近以下哪一项？（结果保留两位小数，cos30°≈0.87，sin30°=0.5）","answer":"A","explanation":"本题考查旋转与坐标变换的综合应用，结合锐角三角函数知识。初始时点B坐标为(6, 0)。将点B绕原点A逆时针旋转30°，其新坐标可通过旋转公式计算：x' = x·cosθ - y·sinθ，y' = x·sinθ + y·cosθ。代入x=6，y=0，θ=30°，得x' = 6×0.87 - 0×0.5 = 5.22，y' = 6×0.5 + 0×0.87 = 3.00。因此旋转后点B的坐标约为(5.22, 3.00)，对应选项A。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-07 15:06:54","updated_at":"2026-01-07 15:06:54","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":"(5.22, 3.00)","is_correct":1},{"id":"B","content":"(3.00, 5.22)","is_correct":0},{"id":"C","content":"(4.24, 4.24)","is_correct":0},{"id":"D","content":"(6.00, 0.00)","is_correct":0}]},{"id":2773,"subject":"历史","grade":"七年级","stage":"初中","type":"选择题","content":"唐朝时期，长安城作为当时世界上最大的城市之一，吸引了来自世界各地的商人、使节和留学生。其中，日本曾多次派遣使团来到中国学习政治制度、文化艺术和佛教思想，这些使团在历史上被称为：","answer":"B","explanation":"本题考查的是唐朝中外交流的重要史实。日本在隋唐时期多次派遣使节来华学习，其中在隋朝时期称为‘遣隋使’，而在唐朝时期则称为‘遣唐使’。题目明确指出是‘唐朝时期’，因此正确答案应为‘遣唐使’。选项A虽然与日本派遣使节有关，但时间不符；选项C和D虽描述了部分事实，但不是历史专有名词，不符合史实表述。因此，B选项准确、科学，符合七年级学生对中外交流知识点的掌握要求。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-12 10:42:32","updated_at":"2026-01-12 10:42:32","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":"遣隋使","is_correct":0},{"id":"B","content":"遣唐使","is_correct":1},{"id":"C","content":"留学生团","is_correct":0},{"id":"D","content":"文化交流使","is_correct":0}]},{"id":2192,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在记录一周内每天气温变化时，发现某天的气温比前一天上升了5℃，记作+5℃。如果第二天的气温又比当天下降了8℃，那么第二天的气温变化应记作多少？","answer":"B","explanation":"气温下降应使用负数表示。题目中明确指出‘下降了8℃’，因此变化量应记为-8℃。选项B正确。其他选项中，A表示上升，C和D是数值计算错误或符号错误，不符合题意。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-09 14:25:31","updated_at":"2026-01-09 14:25:31","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":"A","content":"+8℃","is_correct":0},{"id":"B","content":"-8℃","is_correct":1},{"id":"C","content":"+3℃","is_correct":0},{"id":"D","content":"-3℃","is_correct":0}]},{"id":2502,"subject":"数学","grade":"九年级","stage":"初中","type":"选择题","content":"如图，一个圆形花坛被两条互相垂直的直径分成四个相等的扇形区域。现要在其中一个扇形区域内修建一个矩形观景台，要求矩形的两个顶点在圆弧上，另外两个顶点分别在两条半径上，且矩形的一边与其中一条半径重合。若花坛的半径为4米，则该矩形观景台的最大可能面积为多少平方米？","answer":"A","explanation":"设矩形在半径上的边长为x（0 < x < 4），由于矩形的一个角位于圆心，且两边分别沿两条垂直半径方向，则其对角顶点位于圆弧上，满足圆的方程x² + y² = 4² = 16。因为矩形两边分别平行于两条半径，所以另一边的长度为y = √(16 - x²)。但注意：此处矩形实际是以圆心为一个顶点，两边沿半径方向延伸长度x和y，但由于题目要求矩形两个顶点在圆弧上，另两个在半径上，且一边与半径重合，因此更合理的建模是：设矩形与半径重合的一边长度为x，则其对边也在圆弧上，由对称性和几何关系可得另一边长为x（因角度为90°，形成等腰直角结构）。进一步分析可知，当矩形为正方形时面积最大。利用坐标法：设矩形顶点为(0,0)、(x,0)、(x,x)、(0,x)，则点(x,x)必须在圆内或圆上，即x² + x² ≤ 16 → 2x² ≤ 16 → x² ≤ 8 → x ≤ 2√2。此时面积S = x² ≤ 8。当x = 2√2时，点(2√2, 2√2)恰好在圆上（因(2√2)² + (2√2)² = 8 + 8 = 16），满足条件。故最大面积为8平方米。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-10 15:25:56","updated_at":"2026-01-10 15:25:56","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":"8","is_correct":1},{"id":"B","content":"4√2","is_correct":0},{"id":"C","content":"6","is_correct":0},{"id":"D","content":"4","is_correct":0}]},{"id":444,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"在一次班级大扫除中，某学生负责统计同学们带来的清洁工具数量。他记录了抹布、扫帚和拖把的总数为28件。已知抹布比扫帚多4件，拖把比扫帚少2件。问扫帚有多少件？","answer":"B","explanation":"设扫帚有x件，则抹布有(x + 4)件，拖把有(x - 2)件。根据题意，三种工具的总数为28件，可列方程：x + (x + 4) + (x - 2) = 28。化简得：3x + 2 = 28，解得3x = 26，x = 10。因此，扫帚有10件。此题考查一元一次方程的实际应用，通过设未知数、列方程、解方程的过程，帮助学生理解如何将生活问题转化为数学问题并求解。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:43:25","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":"8件","is_correct":0},{"id":"B","content":"10件","is_correct":1},{"id":"C","content":"12件","is_correct":0},{"id":"D","content":"14件","is_correct":0}]},{"id":258,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某学生在解方程 3(x - 2) + 5 = 2x + 7 时，第一步将等式左边展开得到 3x - 6 + 5，合并后变为 3x - 1。接着他将等式右边的 2x 移到左边，常数项 7 移到右边，得到 3x - 2x = 7 + 1。按照这个步骤继续解下去，最终 x 的值是___","answer":"8","explanation":"根据题目描述的解题步骤：原方程为 3(x - 2) + 5 = 2x + 7。第一步展开括号得 3x - 6 + 5，合并常数项后为 3x - 1。此时方程变为 3x - 1 = 2x + 7。将 2x 移到左边变为 -2x，将 -1 移到右边变为 +1，得到 3x - 2x = 7 + 1，即 x = 8。因此，最终解为 x = 8。该题考查一元一次方程的解法，包括去括号、移项和合并同类项，符合七年级数学课程内容。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"中等","points":1,"is_active":1,"created_at":"2025-12-29 14:55:01","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":2451,"subject":"数学","grade":"八年级","stage":"初中","type":"填空题","content":"某学生在研究一个轴对称图形时，发现其对称轴是直线x=3，且图形上一点A的坐标为(5, 4)。若点A关于该对称轴的对称点为B，则点B的横坐标为___。","answer":"1","explanation":"对称轴为x=3，点A(5,4)到对称轴的距离为5−3=2，对称点B在对称轴另一侧相同距离处，故横坐标为3−2=1。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 13:54:59","updated_at":"2026-01-10 13:54:59","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":[]}]