[{"id":2169,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在数轴上标记了三个有理数点A、B、C，其中点A表示的数是-3.5，点B位于点A右侧4.2个单位长度处，点C位于点B左侧2.8个单位长度处。若将这三个点所表示的数按从小到大的顺序排列，正确的顺序是？","answer":"B","explanation":"首先确定各点表示的有理数：点A为-3.5；点B在A右侧4.2个单位，即-3.5 + 4.2 = 0.7；点C在B左侧2.8个单位，即0.7 - 2.8 = -2.1。因此三个数分别为：A=-3.5，B=0.7，C=-2.1。比较大小：-3.5 < -2.1 < 0.7，即A < C < B。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-09 13:53:54","updated_at":"2026-01-09 13:53:54","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":"A < B < C","is_correct":0},{"id":"B","content":"A < C < B","is_correct":1},{"id":"C","content":"C < A < B","is_correct":0},{"id":"D","content":"B < C < A","is_correct":0}]},{"id":372,"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，发现将数据按从小到大的顺序排列后，位于正中间的两个数分别是158和160，则这组数据的中位数是：","answer":"B","explanation":"中位数是将一组数据按大小顺序排列后，处于中间位置的数。当数据个数为偶数时，中位数是中间两个数的平均数。题目中给出中间两个数是158和160，因此中位数为(158 + 160) ÷ 2 = 318 ÷ 2 = 159。所以正确答案是B。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 15:49:21","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":"158","is_correct":0},{"id":"B","content":"159","is_correct":1},{"id":"C","content":"160","is_correct":0},{"id":"D","content":"162","is_correct":0}]},{"id":2158,"subject":"数学","grade":"七年级","stage":"初中","type":"选择题","content":"某学生在数轴上从原点出发，先向右移动3.5个单位长度，再向左移动5.2个单位长度，最后又向右移动1.8个单位长度。此时该学生所在位置的点表示的有理数是多少？","answer":"D","explanation":"根据题意，从原点出发，向右为正方向，向左为负方向。第一次移动+3.5，第二次移动-5.2，第三次移动+1.8。计算总位移：3.5 - 5.2 + 1.8 = (3.5 + 1.8) - 5.2 = 5.3 - 5.2 = 0.1。因此，最终位置表示的有理数是0.1。","solution_steps":"","common_mistakes":"","learning_suggestions":"","difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-09 13:07:43","updated_at":"2026-01-09 13:07:43","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":"0.1","is_correct":0},{"id":"B","content":"-0.1","is_correct":0},{"id":"C","content":"0.5","is_correct":0},{"id":"D","content":"0.1","is_correct":1}]},{"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":194,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"小明买了3支铅笔和2本笔记本，共花费18元。已知每本笔记本比每支铅笔贵3元。设每支铅笔的价格为x元，则下列方程正确的是（ ）","answer":"A","explanation":"题目中设每支铅笔的价格为x元，因为每本笔记本比每支铅笔贵3元，所以每本笔记本的价格为(x + 3)元。小明买了3支铅笔，总价为3x元；买了2本笔记本，总价为2(x + 3)元。根据总花费为18元，可列出方程：3x + 2(x + 3) = 18。因此，正确选项是A。其他选项错误地将笔记本价格设为比铅笔便宜，或混淆了数量与单价的关系。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 14:03:39","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":"3x + 2(x + 3) = 18","is_correct":1},{"id":"B","content":"3x + 2(x - 3) = 18","is_correct":0},{"id":"C","content":"3(x + 3) + 2x = 18","is_correct":0},{"id":"D","content":"3(x - 3) + 2x = 18","is_correct":0}]},{"id":1097,"subject":"数学","grade":"七年级","stage":"小学","type":"填空题","content":"某学生在整理班级同学的身高数据时，发现将每个人的身高（单位：厘米）减去150后，得到的新数据中，最小值为-8，最大值为12。那么原始身高数据中，最矮的同学身高是____厘米。","answer":"142","explanation":"题目中给出的是每个身高减去150后的结果，最小值为-8。这意味着最矮的同学的身高比150厘米少8厘米。因此，原始身高为150 - 8 = 142厘米。这是基于有理数中的减法运算和数据的简单变换，符合七年级‘数据的收集、整理与描述’以及‘有理数’的知识点。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2026-01-06 08:56:53","updated_at":"2026-01-06 08:56:53","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":1638,"subject":"数学","grade":"七年级","stage":"初中","type":"解答题","content":"某城市为了解七年级学生每日完成数学作业所用时间，随机抽取了100名学生进行调查，并将数据整理如下：作业时间在30分钟以下的有15人，30～60分钟的有40人，60～90分钟的有30人，90分钟以上的有15人。现计划从这100名学生中按比例抽取20人进行深入访谈。已知被抽中的学生中，作业时间在60分钟以上的学生人数为m，且该城市共有5000名七年级学生。若用样本中作业时间在90分钟以上的学生频率估计总体，求该城市七年级学生中作业时间在90分钟以上的人数；并求m的值。","answer":"第一步：根据样本数据，作业时间在90分钟以上的学生有15人，总样本为100人，因此频率为15 ÷ 100 = 0.15。\n\n第二步：用样本频率估计总体，该城市共有5000名七年级学生，因此作业时间在90分钟以上的人数约为：\n5000 × 0.15 = 750（人）。\n\n第三步：从100名学生中按比例抽取20人，抽样比例为20 ÷ 100 = 1\/5。\n\n第四步：原样本中作业时间在60分钟以上的学生包括60～90分钟和90分钟以上两部分，共30 + 15 = 45人。\n\n第五步：按比例抽取，则被抽中的学生中作业时间在60分钟以上的人数为：\n45 × (1\/5) = 9（人），即m = 9。\n\n最终答案：该城市七年级学生中作业时间在90分钟以上的人数约为750人，m的值为9。","explanation":"本题综合考查了数据的收集、整理与描述中的频数、频率、样本估计总体以及按比例抽样等核心概念。解题关键在于理解频率的定义（频数 ÷ 总数），并能将其应用于总体估计；同时掌握按比例抽样的方法，即各组抽取人数 = 原组人数 × 抽样比例。题目设置了真实情境，要求学生从多个数据组中提取信息并进行两步计算，体现了数据分析在实际问题中的应用，难度较高，适合考查学生的综合数据处理能力。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-06 13:08:48","updated_at":"2026-01-06 13:08:48","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":1776,"subject":"数学","grade":"七年级","stage":"初中","type":"解答题","content":"某校七年级组织学生参加数学实践活动，调查校园内不同区域的植物种类数量。调查结果显示，A区域有x种植物，B区域有y种植物，其中A区域植物种类数比B区域的2倍少3种，且两个区域共有植物种类27种。活动结束后，学校计划在平面直角坐标系中标出这两个区域的相对位置：将A区域的位置设为点A(2, 3)，B区域的位置设为点B(a, b)，且线段AB的中点为M(5, -1)。已知点B在第四象限，求a和b的值，并计算点B到x轴的距离。","answer":"根据题意，列出方程组：\n\n1. A区域植物种类比B区域的2倍少3种：\nx = 2y - 3\n\n2. 两个区域共有27种植物：\nx + y = 27\n\n将第一个方程代入第二个方程：\n(2y - 3) + y = 27\n3y - 3 = 27\n3y = 30\ny = 10\n\n代入x = 2y - 3得：\nx = 2×10 - 3 = 17\n\n所以A区域有17种植物，B区域有10种植物。\n\n接下来求点B的坐标。\n已知A(2, 3)，B(a, b)，中点M(5, -1)。\n根据中点坐标公式：\n中点横坐标：(2 + a)\/2 = 5\n解得：2 + a = 10 → a = 8\n\n中点纵坐标：(3 + b)\/2 = -1\n解得：3 + b = -2 → b = -5\n\n所以点B的坐标为(8, -5)。\n\n点B在第四象限（横坐标为正，纵坐标为负），符合条件。\n\n点B到x轴的距离为其纵坐标的绝对值：|b| = |-5| = 5。\n\n答：a = 8，b = -5，点B到x轴的距离为5。","explanation":"本题综合考查二元一次方程组和平面直角坐标系中的中点坐标公式。首先根据文字条件建立关于x和y的二元一次方程组，解出两个区域的植物种类数；然后利用中点坐标公式，结合已知点A和中点M的坐标，求出点B的坐标(a, b)；最后根据点B在第四象限验证合理性，并计算其到x轴的距离。关键步骤是正确列出方程组并准确应用中点公式。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-06 15:14:32","updated_at":"2026-01-06 15:14:32","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":1772,"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画出一个三角形ABC，其中点A的坐标为(2, 3)，点B在x轴上，点C在y轴上，且三角形ABC的面积为6。若点B的横坐标为正，点C的纵坐标为正，则点B的坐标为____，点C的坐标为____。","answer":"(4, 0), (0, 3)","explanation":"设B(b, 0)，C(0, c)，利用三角形面积公式S = 1\/2 × |b| × |c| = 6，结合A(2,3)共面关系，解得b=4，c=3，故B(4,0)，C(0,3)。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"困难","points":1,"is_active":1,"created_at":"2026-01-06 15:12:45","updated_at":"2026-01-06 15:12:45","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":283,"subject":"数学","grade":"初一","stage":"初中","type":"选择题","content":"某学生在平面直角坐标系中描出三个点 A(1, 2)、B(3, 2) 和 C(3, 5)，然后连接这三个点形成一个三角形。这个三角形最可能的形状是：","answer":"B","explanation":"首先，根据坐标描点：点 A(1, 2) 和点 B(3, 2) 的 y 坐标相同，说明 AB 是一条水平线段，长度为 |3 - 1| = 2。点 B(3, 2) 和点 C(3, 5) 的 x 坐标相同，说明 BC 是一条竖直线段，长度为 |5 - 2| = 3。因此，AB 与 BC 互相垂直，在点 B 处形成直角。根据定义，有一个角是直角的三角形是直角三角形。所以这个三角形最可能是直角三角形。","solution_steps":null,"common_mistakes":null,"learning_suggestions":null,"difficulty":"简单","points":1,"is_active":1,"created_at":"2025-12-29 15:31:27","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":"等边三角形","is_correct":0},{"id":"B","content":"直角三角形","is_correct":1},{"id":"C","content":"钝角三角形","is_correct":0},{"id":"D","content":"锐角三角形","is_correct":0}]}]