[{"id":2472,"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)、B(6, 0)，点 C 在 x 轴正半轴上，且 △ABC 是以 AB 为斜边的等腰直角三角形。点 D 是线段 AB 的中点，点 E 在 y 轴上，使得 △CDE 为等边三角形。已知一次函数 y = kx + b 的图像经过点 C 和点 E，且该函数图像与线段 AB 相交于点 F。若点 F 将线段 AB 分为 AF : FB = 1 : 2，求 k 和 b 的值，并验证 △CDE 的边长是否满足勾股定理在等边三角形中的特殊形式（即边长的平方与高的关系）。","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 14:44:14","updated_at":"2026-01-10 14:44:14","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":2265,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"在数轴上，点A表示的数是-3，点B与点A的距离为7个单位长度，且点B在原点右侧。若点C是点B关于原点的对称点，则点C表示的数是___。","answer":"B","explanation":"点A表示-3，点B与点A的距离为7个单位长度，且点B在原点右侧。因此点B可能在-3的右侧7个单位，即-3 + 7 = 4，所以点B表示4。点C是点B关于原点的对称点，即与4到原点距离相等但方向相反，因此点C表示-4。故正确答案为B。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-09 16:09:15","updated_at":"2026-01-09 16:09:15","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","is_correct":0},{"id":"B","content":"-4","is_correct":1},{"id":"C","content":"10","is_correct":0},{"id":"D","content":"-10","is_correct":0}]},{"id":202,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"某学生在计算一个数减去 15 时，误将减法当作加法，结果得到 38。那么正确的计算结果应该是 _ 。","answer":"8","explanation":"根据题意，某学生把‘减去15’算成了‘加上15’，得到错误结果38。设这个数为 x，则有 x + 15 = 38，解得 x = 38 - 15 = 23。因此，正确的计算应为 23 - 15 = 8。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 14:39:23","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":2416,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"如图，在平面直角坐标系中，点 A(1, 2)、B(4, 6)、C(7, 2) 构成三角形 ABC。若点 D 是点 A 关于直线 BC 的对称点，则点 D 的坐标最接近下列哪一项？（提示：可利用轴对称性质与一次函数求对称点）","answer":"C","explanation":"本题综合考查轴对称、一次函数、勾股定理与坐标几何知识。首先求直线 BC 的解析式：B(4,6)、C(7,2)，斜率 k = (2−6)\/(7−4) = −4\/3，得直线 BC：y − 6 = −4\/3(x − 4)，即 y = −(4\/3)x + 34\/3。点 A(1,2) 关于该直线的对称点 D 满足：AD 的中点在 BC 上，且 AD ⊥ BC。设 D(x,y)，则中点 M((1+x)\/2, (2+y)\/2) 在 BC 上，代入直线方程得 (2+y)\/2 = −(4\/3)·((1+x)\/2) + 34\/3。又因 AD 斜率为 (y−2)\/(x−1)，应与 BC 斜率 −4\/3 互为负倒数，即 (y−2)\/(x−1) = 3\/4。联立两个方程解得 x ≈ 11，y ≈ 4。因此点 D 坐标最接近 (11, 4)。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 12:27:20","updated_at":"2026-01-10 12:27:20","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, 6)","is_correct":0},{"id":"B","content":"(10, 5)","is_correct":0},{"id":"C","content":"(11, 4)","is_correct":1},{"id":"D","content":"(12, 3)","is_correct":0}]},{"id":12,"subject":"语文","grade":"初一","stage":"初中","type":"选择题","content":"《朝花夕拾》的作者是？","answer":"A","explanation":"《朝花夕拾》是鲁迅创作的回忆性散文集。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-08-29 16:33:04","updated_at":"2025-08-29 16:33:04","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":"鲁迅","is_correct":1},{"id":"B","content":"郭沫若","is_correct":0},{"id":"C","content":"茅盾","is_correct":0},{"id":"D","content":"老舍","is_correct":0}]},{"id":611,"subject":"数学","grade":"初一","stage":"小学","type":"选择题","content":"在一次班级数学测验中，某学生记录了5名同学的数学成绩（单位：分）如下：82，76，90，88，74。如果老师要求将这组数据按从小到大的顺序排列，并找出中位数，那么中位数是多少？","answer":"B","explanation":"首先将5个成绩按从小到大的顺序排列：74，76，82，88，90。由于数据个数为5（奇数个），中位数就是位于正中间的那个数，即第3个数。因此，中位数是82。本题考查的是数据的整理与描述中的中位数概念，属于简单难度，符合七年级数学课程标准要求。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 21:37:28","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":"A","content":"76","is_correct":0},{"id":"B","content":"82","is_correct":1},{"id":"C","content":"88","is_correct":0},{"id":"D","content":"90","is_correct":0}]},{"id":346,"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，记录了10名同学每周阅读的小时数分别为：3，5，4，6，3，7，5，4，5，6。这组数据的众数是多少？","answer":"C","explanation":"众数是指一组数据中出现次数最多的数。将数据从小到大排列为：3，3，4，4，5，5，5，6，6，7。其中，3出现2次，4出现2次，5出现3次，6出现2次，7出现1次。因此，出现次数最多的数是5，所以这组数据的众数是5。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 15:41:14","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":0},{"id":"B","content":"4","is_correct":0},{"id":"C","content":"5","is_correct":1},{"id":"D","content":"6","is_correct":0}]},{"id":976,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"某学生测量教室地面的长方形区域，测得长为 (2x + 3) 米，宽为 (x - 1) 米，若该区域的周长为 26 米，则 x 的值为 ___。","answer":"11\/3","explanation":"长方形的周长公式为：周长 = 2 × (长 + 宽)。根据题意，长为 (2x + 3) 米，宽为 (x - 1) 米，周长为 26 米。代入公式得：2 × [(2x + 3) + (x - 1)] = 26。先化简括号内：2x + 3 + x - 1 = 3x + 2。然后计算：2 × (3x + 2) = 6x + 4。列方程：6x + 4 = 26。解方程：6x = 22，x = 22 ÷ 6 = 11\/3。因此，x 的值为 11\/3。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 04:17:14","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":2470,"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, 6)，点B(8, 0)，点C为线段AB上的动点。以AC为边作正方形ACDE，使得点D在x轴正半轴上，点E在第一象限。连接BE，交y轴于点F。已知正方形ACDE的边长为a，且满足a² = 4x + 12，其中x为点C的横坐标。求当△BEF的面积最大时，点C的坐标及此时△BEF的面积。","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 14:39:17","updated_at":"2026-01-10 14:39:17","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":890,"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12.5千克废纸，另一名同学收集的废纸比这名学生多3.7千克，两人一共收集了___千克废纸。","answer":"28.7","explanation":"首先，第二名同学收集的废纸重量为12.5 + 3.7 = 16.2千克。然后将两人收集的废纸重量相加：12.5 + 16.2 = 28.7千克。因此，两人一共收集了28.7千克废纸。本题考查的是有理数的加法运算，属于简单难度，符合七年级有理数知识点要求。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 02:08:03","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":[]}]