习题练习

[{"id":1771,"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的坐标为（2a - 4, 3 - a），若点A位于第四象限，且a为整数，则a的最小值是___。","answer":"3","explanation":"第四象限要求横坐标为正，纵坐标为负。列不等式组：2a - 4 > 0 且 3 - a < 0，解得 a > 2 且 a > 3，即 a > 3。a为整数，最小值为3。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-06 15:12:36","updated_at":"2026-01-06 15:12:36","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":262,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"某学生在解方程 3(x - 4) + 2 = 5x - 10 时，第一步将括号展开后得到 3x - 12 + 2 = 5x - 10，合并同类项后得到 3x - 10 = 5x - 10。接下来，他应该将含 x 的项移到等式的一边，常数项移到另一边，于是他将 3x 移到右边，得到 -10 = 2x - 10。然后，他将 -10 移到左边，得到 ___ = 2x。","answer":"0","explanation":"从步骤 -10 = 2x - 10 开始，要将常数项移到等式左边，需在等式两边同时加上 10：-10 + 10 = 2x - 10 + 10，化简后得到 0 = 2x。因此，空白处应填 0。此题考查一元一次方程的移项与合并同类项能力，要求学生掌握等式的基本性质，属于中等难度，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 14:55:31","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":1930,"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)、点B(5, 7)和点C(x, y)共线，且点C到点A的距离是点C到点B的距离的2倍。若点C位于线段AB的延长线上，且在点B的外侧，则点C的横坐标x的值为______。","answer":"8","explanation":"由共线设C在直线AB上，利用向量比例：AC = 2CB且C在B外侧，得向量关系AC = 2CB ⇒ C分AB外分比为2:1。用外分点公式：x = (2×5 - 1×2)\/(2 - 1) = 8。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-07 14:10:07","updated_at":"2026-01-07 14:10:07","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":217,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"某学生计算一个数的相反数时，将原数 5 写成了 -5，那么他得到的结果比正确答案多了____。","answer":"10","explanation":"原数是 5，它的相反数是 -5。某学生误将原数当作 -5，计算其相反数得到 5。正确答案是 -5，而学生得到的是 5，两者之差为 5 - (-5) = 10。因此，他得到的结果比正确答案多了 10。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 14:40:14","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":2312,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"一个等腰三角形的两条边长分别为5和11，则这个三角形的周长是（ ）","answer":"B","explanation":"本题考查三角形三边关系及等腰三角形的性质。等腰三角形有两条边相等，已知两边分别为5和11，需分两种情况讨论：\n\n情况一：腰为5，底为11。此时三边为5、5、11。但5 + 5 = 10 < 11，不满足三角形两边之和大于第三边的条件，不能构成三角形。\n\n情况二：腰为11，底为5。此时三边为11、11、5。检查三边关系：11 + 11 > 5，11 + 5 > 11，均成立，可以构成三角形。\n\n因此，唯一可能的三边为11、11、5，周长为11 + 11 + 5 = 27。\n\n故正确答案为B。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-10 10:45:50","updated_at":"2026-01-10 10:45:50","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":"21","is_correct":0},{"id":"B","content":"27","is_correct":1},{"id":"C","content":"21或27","is_correct":0},{"id":"D","content":"无法确定","is_correct":0}]},{"id":721,"subject":"数学","grade":"初一","stage":"初中","type":"填空题","content":"在一次班级图书整理活动中，某学生统计了同学们捐赠的图书数量，发现捐赠数量最多的比最少的多8本，而最多的数量是最少的3倍。如果最少捐赠了___本书，那么最多捐赠了___本书。","answer":"4, 12","explanation":"设最少捐赠了x本书，则最多捐赠了3x本书。根据题意，最多比最少多8本，可列方程：3x - x = 8，解得2x = 8，x = 4。因此最少捐赠了4本，最多捐赠了3 × 4 = 12本。本题考查一元一次方程的实际应用，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":"2025-12-29 22:56:35","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":1982,"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半径为5 cm的圆，并在圆内作了一个内接等边三角形。若将该等边三角形绕其中心（即圆心）顺时针旋转120°，则旋转前后两个三角形重叠部分的面积占原三角形面积的多少？","answer":"D","explanation":"本题考查旋转与圆的综合应用，结合正多边形的对称性。等边三角形是圆的内接正三角形，其中心与圆心重合。由于等边三角形具有120°的旋转对称性，绕其中心旋转120°后，图形与原图形完全重合。因此，旋转前后两个三角形完全重叠，重叠部分的面积等于原三角形面积，即占比为1（全部）。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-07 15:02:43","updated_at":"2026-01-07 15:02:43","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":"1\/3","is_correct":0},{"id":"B","content":"1\/2","is_correct":0},{"id":"C","content":"2\/3","is_correct":0},{"id":"D","content":"全部","is_correct":1}]},{"id":399,"subject":"数学","grade":"初一","stage":"小学","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，发现一周内每天阅读时间（单位：分钟）分别为：20、25、30、35、40、45、50。若该学生想用一个统计图来直观展示这些数据的变化趋势，以下哪种统计图最合适？","answer":"B","explanation":"题目中给出的数据是按时间顺序（一周内每天）记录的阅读时间，目的是展示‘变化趋势’。折线图能够清晰地反映数据随时间变化的趋势，因此最适合用于此类情境。扇形图主要用于表示各部分占整体的比例，不适合展示趋势；条形图适合比较不同类别的数据，但不如折线图直观体现变化；频数分布直方图用于展示数据分布情况，不强调时间顺序。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 17:16:10","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":"扇形图","is_correct":0},{"id":"B","content":"折线图","is_correct":1},{"id":"C","content":"条形图","is_correct":0},{"id":"D","content":"频数分布直方图","is_correct":0}]},{"id":423,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"在一次环保知识竞赛中，某班级收集了学生家庭一周内节约用水的数据（单位：升），整理后发现：有3个家庭节约了15升，5个家庭节约了20升，2个家庭节约了25升。请问该班级学生家庭平均每周节约用水多少升？","answer":"B","explanation":"要计算平均节约用水量，需先求总节水量，再除以家庭总数。总节水量 = 3×15 + 5×20 + 2×25 = 45 + 100 + 50 = 195（升）。家庭总数 = 3 + 5 + 2 = 10（个）。平均节水量 = 195 ÷ 10 = 19（升）。因此，正确答案是B。本题考查数据的收集、整理与描述中的平均数计算，属于简单难度的基础应用。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 17:32:50","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":"18升","is_correct":0},{"id":"B","content":"19升","is_correct":1},{"id":"C","content":"20升","is_correct":0},{"id":"D","content":"21升","is_correct":0}]},{"id":799,"subject":"数学","grade":"初一","stage":"小学","type":"填空题","content":"在一次班级大扫除中，某学生负责统计各小组的打扫时间（单位：分钟）。他记录了5个小组的时间分别为：18，22，20，19，21。这些数据的平均数是____。","answer":"20","explanation":"平均数的计算方法是将所有数据相加，再除以数据的个数。计算过程为：(18 + 22 + 20 + 19 + 21) ÷ 5 = 100 ÷ 5 = 20。因此，这组数据的平均数是20。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-30 00:15:32","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":[]}]