习题练习

[{"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":2758,"subject":"历史","grade":"七年级","stage":"初中","type":"选择题","content":"考古学家在河南安阳发现了一处大型商代遗址，出土了大量刻有文字的龟甲和兽骨。这些文字主要用于记录商王占卜的内容，对研究商朝历史具有重要价值。这种文字被称为：","answer":"A","explanation":"题干中提到‘刻有文字的龟甲和兽骨’以及‘用于记录商王占卜的内容’，这是甲骨文的典型特征。甲骨文是商朝时期刻在龟甲和兽骨上的文字，主要用于占卜记事，是中国已发现的古代文字中时代最早、体系较为完整的文字。金文主要铸刻在青铜器上，盛行于西周；小篆是秦朝统一后的标准字体；隶书则流行于汉代。因此，根据出土文物的材质和用途，正确答案为A。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-12 10:39:39","updated_at":"2026-01-12 10:39:39","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":"甲骨文","is_correct":1},{"id":"B","content":"金文","is_correct":0},{"id":"C","content":"小篆","is_correct":0},{"id":"D","content":"隶书","is_correct":0}]},{"id":2413,"subject":"数学","grade":"八年级","stage":"初中","type":"选择题","content":"在一次数学实践活动中，某学生测量了一个等腰三角形的底边和腰长，发现底边长为8 cm，腰长为5 cm。随后，该学生将这个三角形沿其对称轴折叠，使两个腰完全重合。若将折叠后的图形展开，并在三角形内部作一条平行于底边的线段，使得这条线段将三角形的面积分为相等的两部分，则这条线段的长度是多少？","answer":"A","explanation":"首先，已知等腰三角形底边为8 cm，腰长为5 cm。利用勾股定理可求出高：从顶点向底边作高，将底边平分，得到两个直角三角形，直角边分别为4 cm和h，斜边为5 cm。由勾股定理得 h² + 4² = 5²，解得 h = 3 cm，因此三角形面积为 (1\/2)×8×3 = 12 cm²。要求作一条平行于底边的线段，将面积分为相等的两部分，即上方小三角形面积为6 cm²。由于小三角形与原三角形相似，面积比为1:2，因此边长比为 √(1\/2) = 1\/√2。原底边为8 cm，故所求线段长度为 8 × (1\/√2) = 8\/√2 = 4√2 cm。因此正确答案为A。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"中等","points":1,"is_active":1,"created_at":"2026-01-10 12:26:35","updated_at":"2026-01-10 12:26:35","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√2 cm","is_correct":1},{"id":"B","content":"4 cm","is_correct":0},{"id":"C","content":"2√6 cm","is_correct":0},{"id":"D","content":"3√3 cm","is_correct":0}]},{"id":1949,"subject":"数学","grade":"七年级","stage":"初中","type":"填空题","content":"某学生在平面直角坐标系中绘制了一个四边形ABCD，其顶点坐标分别为A(1, 2)、B(5, 2)、C(7, -1)、D(3, -1)。若将该四边形沿x轴正方向平移3个单位，再沿y轴负方向平移4个单位，则平移后点C的坐标为____。","answer":"(10, -5)","explanation":"平移规则：横坐标加3，纵坐标减4。原C(7, -1) → 7+3=10，-1-4=-5。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-07 14:14:25","updated_at":"2026-01-07 14:14:25","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":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":576,"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，将数据按从小到大的顺序排列，并制作了频数分布表。已知身高在150cm到155cm（含150cm，不含155cm）这一组的人数为8人，占总人数的20%。那么，该班级参加统计的学生总人数是多少？","answer":"B","explanation":"题目中给出身高在150cm到155cm这一组的人数为8人，占总人数的20%。设总人数为x，则可列出一元一次方程：8 = 20% × x，即8 = 0.2x。解这个方程，两边同时除以0.2，得到x = 8 ÷ 0.2 = 40。因此，该班级参加统计的学生总人数是40人。此题考查了数据的收集与整理中频数与百分比的关系，以及一元一次方程的简单应用，符合七年级数学课程内容。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 19:58:46","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":"32人","is_correct":0},{"id":"B","content":"40人","is_correct":1},{"id":"C","content":"45人","is_correct":0},{"id":"D","content":"50人","is_correct":0}]},{"id":1695,"subject":"数学","grade":"七年级","stage":"初中","type":"解答题","content":"某城市为改善交通状况，计划在一条主干道上设置若干个智能公交站。已知该道路在平面直角坐标系中沿x轴方向延伸，起点坐标为(0, 0)，终点坐标为(12, 0)。规划部门决定在这些站点中设置A、B、C三类站点，其中A类站点每2千米设一个，B类站点每3千米设一个，C类站点每4千米设一个，均从起点开始设置（即起点处同时设有A、B、C三类站点）。若某学生从起点出发，沿道路步行，每经过一个站点就记录一次，问：该学生在到达终点前，共会经过多少个不同的站点？（注：若某位置同时设有多个类型的站点，只算作一个站点）","answer":"1. 确定各类站点的位置：\n - A类站点：每2千米一个，位置为 x = 0, 2, 4, 6, 8, 10, 12\n 共 7 个位置\n - B类站点：每3千米一个，位置为 x = 0, 3, 6, 9, 12\n 共 5 个位置\n - C类站点：每4千米一个，位置为 x = 0, 4, 8, 12\n 共 4 个位置\n\n2. 列出所有站点坐标并去重：\n 合并三类站点的所有x坐标：\n {0, 2, 3, 4, 6, 8, 9, 10, 12}\n 注意：6出现在A和B类，4和12出现在A和C类，0出现在三类中，但每个坐标只算一次\n\n3. 统计不同站点的总数：\n 上述集合中共有 9 个不同的x坐标值\n\n4. 因此，该学生从起点到终点（含起点和终点），共经过 9 个不同的站点\n\n答：该学生共会经过 9 个不同的站点。","explanation":"本题综合考查了平面直角坐标系、有理数（坐标值）、数据的收集与整理（分类统计、去重）以及实际应用建模能力。解题关键在于理解‘不同站点’的含义——即使多个类型站点位于同一位置，也只计为一个物理站点。因此需要分别列出A、B、C三类站点的所有位置，然后合并并去除重复的坐标点。这涉及集合思想的应用，虽然七年级尚未系统学习集合，但通过列表和观察可以实现去重操作。题目背景新颖，结合了城市规划与数学建模，避免了传统行程问题的套路，强调对‘位置唯一性’的理解和数据处理能力，符合困难难度要求。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-06 13:39:12","updated_at":"2026-01-06 13:39:12","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":323,"subject":"数学","grade":"初一","stage":"小学","type":"选择题","content":"中位数是152，众数是148","answer":"答案待完善","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 15:38:18","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":293,"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时，随机抽取了10名同学，记录他们每周课外阅读的小时数分别为：3, 5, 4, 6, 3, 7, 5, 4, 5, 6。请问这组数据的众数是多少？","answer":"C","explanation":"众数是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，出现次数最多的是5，共出现3次，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 15:33:01","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":"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":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}]}]