2025-2026学年北京市朝阳区小升初数学分班考试模拟试卷（含答案详解与评分标准）

第页2025-2026学年北京市朝阳区小升初数学分班考试模拟试卷（含答案详解与评分标准）学校：______________班级：______________姓名：______________考号：______________考试时间：80分钟满分：100分题型选择题填空题解答题总分分值30分18分52分100分得分注意事项1．本试卷用于小升初数学分班考试前的完整检测，可服务于考前诊断、阶段复习和专项突破。请在规定时间内独立完成，书写清楚。2．选择题每题只有一个正确答案；填空题只填写最终结果；解答题必须写出必要的数量关系、计算过程、推理依据和单位。3．涉及分数、小数、百分数、比例、面积、体积、行程和工程的题目，应先统一单位或统一表达形式，再进行计算。4．可使用直尺、圆规等常规作图工具，不得使用带有存储、联网或拍照功能的电子设备。5．全卷共三大题，22小题。选择题10题，每题3分，共30分；填空题6题，每题3分，共18分；解答题6题，共52分。考试要求与能力目标本卷围绕朝阳区小升初数学分班检测的常见考查方向组织内容，覆盖数的认识与运算、分数小数百分数互化、比和比例、概率初步、图形周长面积、统计决策、行程问题、工程问题以及购物方案比较等核心模块。客观题强调“读懂条件—选择模型—快速核算”的基础能力。遇到“最大”“最小”“一定”“可能性”“超过”等关键词，要先判断限制条件，再用计算或反例验证。填空题强调结果表达的规范性。单位换算必须前后一致，比例尺题先分清图上距离与实际距离，排序题先把不同形式转化为同一标准，再比较大小。解答题强调完整过程与数学语言。列式前应写明数量关系，计算后应带单位，并用估算、逆向检查或情境检验判断结果是否合理。本卷分值结构兼顾基础题、综合题和表达题，既用于检测学生进入初中前的基础熟练度，也用于判断其面对新情境时的建模、迁移和说明能力。一、选择题（本大题共10小题，每小题3分，共30分）每题四个选项中只有一个符合题意，请把正确选项填在题后的括号内。1．朝阳区某中学分班检测将数学、语文、英语三科成绩按4:3:3计算综合分。小华三科原始成绩分别为90分、84分、88分，则他的综合分是（）。A．86.8分B．87.0分C．87.6分D．88.0分2．计算3/5÷0.75的结果是（）。A．0.45B．0.8C．1.25D．4/53．一个整数四舍五入到万位约是36万，这个数最大是（）。A．359999B．364999C．365000D．3699994．一个正方形与一个长方形的周长相等。正方形边长为8厘米，长方形长为10厘米，则长方形的宽是（）。A．4厘米B．5厘米C．6厘米D．8厘米5．已知a与b成正比例，且a=18时b=12；当a=45时，b等于（）。A．24B．27C．30D．366．在2、3、5、9、15、27这六个数中，任取两个数相乘，积是奇数的可能性是（）。A．1/5B．2/5C．2/3D．17．甲、乙两车同时从A、B两地相向而行，甲每小时行70千米，乙每小时行80千米，2小时后相遇。A、B两地相距（）。A．150千米B．280千米C．300千米D．320千米8．一件商品先降价10%，再上涨10%，现在价格与原价相比（）。A．不变B．降低1%C．提高1%D．降低10%9．一个圆柱和一个圆锥等底等高，圆柱体积比圆锥体积多36立方厘米，则圆锥体积是（）。A．12立方厘米B．18立方厘米C．24立方厘米D．54立方厘米10．下列说法中正确的是（）。A．所有质数都是奇数B．三角形任意两边之差大于第三边C．圆的半径扩大2倍，面积扩大4倍D．两个面积相等的三角形一定全等二、填空题（本大题共6小题，每小题3分，共18分）请把答案写在题中横线上，结果能化简的必须化简。11．一张比例尺为1:500000的地图上，甲、乙两地距离为6.4厘米，实际距离是（）千米。12．把0.374、3/8、37.6%、0.37按从小到大的顺序排列，排在第三个的是（）。13．六（1）班参加分班模拟测评，优秀人数占全班的35%，良好人数占全班的45%，其余8人达到合格。全班共有（）人。14．一个长方体木块长12厘米、宽8厘米、高5厘米，把它切成棱长为2厘米的小正方体，最多能切出（）个。15．观察数列：2，5，10，17，26，……第8个数是（）。16．一个袋子里有红球5个、黄球3个、蓝球2个，除颜色外完全相同。任意摸出1个球，摸到红球的可能性是（）。三、解答题（本大题共6小题，共52分）请写出必要的计算过程、说明理由或作图依据。评分时既看结果，也看方法和表达。17．计算题（8分）。直接写出或脱式计算，能简算的要简算。（1）48×（5/12－1/8）（2）3.6×2.5＋6.4×2.5（3）5/6－（1/4＋1/3）（4）解方程：0.6x－4.8=7.2作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．图形与面积（8分）。朝阳区某校准备在校园一角铺设一块由长方形和半圆组成的小花圃。长方形长12米、宽6米，半圆的直径与长方形的宽相等。（1）求花圃的周长；（2）求花圃的面积。圆周率取3.14。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．比例与工程（8分）。为迎接新生分班，学校整理教室。甲组单独完成需要12小时，乙组单独完成需要18小时。两组先合作4小时，剩下的由乙组单独完成。（1）合作4小时完成了全部工作的几分之几？（2）乙组还需要多少小时完成剩下的工作？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．统计与决策（9分）。某小学六年级80名学生参加数学分班模拟考试，成绩分布如下表。（1）补全表中“人数占比”；（2）从表中任选一个信息说明本次检测结果的特点；（3）学校计划把成绩在85分及以上的学生编入A层学习小组，A层共有多少人？成绩段95分及以上85～94分75～84分60～74分60分以下合计人数12242812480人数占比100%作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．行程问题（9分）。小明从家骑车去科技馆，前12分钟骑了3.6千米；随后因为上坡，速度降低为原来的3/4，又骑了16分钟到达科技馆。（1）小明前12分钟的速度是多少千米/时？（2）小明家到科技馆的路程是多少千米？（3）若返程全程按每小时15千米行驶，需要多少分钟？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．综合应用题（10分）。分班前，六年级要采购一批数学练习册。甲书店按标价每本18元销售，购买超过40本后，全部按八五折收费；乙书店推出“买5本送1本”活动，赠送的练习册不收费。学校计划让每名学生得到1本，共需72本。（1）在甲书店购买72本需要多少元？（2）在乙书店至少需要付款购买多少本？需要多少元？（3）从节省费用角度选择哪家书店？请说明理由。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与解析评分总则1．选择题每题3分。答案正确得3分；未选、多选或错选不得分。选择题以最终选项为准，草稿计算不单独计分。2．填空题每题3分。数值正确、形式符合题意得满分；单位缺失、结果未化简、百分数或分数表达不符合题意时，可酌情扣1分。3．解答题按步骤给分，重点关注数量关系、列式、计算、说明和单位。若前一步数值错误但后续方法正确，可保留后续方法分。4．只写最终答案而缺少关键过程的，解答题一般不超过该小题分值的一半；写出合理检验或说明，可体现表达完整度。5．本卷用于分班前诊断，既评价基础运算准确性，也评价阅读理解、模型选择、表达条理和复查习惯。错因诊断与复习导向选择题失分较多，通常说明基础概念辨析不稳，或审题速度快于思考速度。订正时要把“范围、单位、关键词、反例”四类信息圈出，再判断选项。填空题失分较多，常与结果表达不规范有关。比例尺题要注意单位转换，排序题要先统一形式，可能性题要化成最简分数。解答题失分较多，往往不是完全不会，而是没有写清数量关系，或者在中途省略关键步骤。分班考试尤其重视“会算”和“会说清楚”为同一能力。对于计算题，可采用“先看结构，再选方法”的检查方式；对于应用题，可采用“先写已知量，再写要求量，最后写数量关系”的三步阅读法。订正时保留原错误步骤，在旁边补写正确步骤和错误原因，能帮助学生区分计算错误、模型错误、单位错误与表达不完整。一、选择题答案与解析1．C。按4:3:3折算，各科权重分别为0.4、0.3、0.3。综合分不是三科平均数，而是按不同权重进行加权。易错提醒：把4:3:3误看成“每科一样重要”，会算成普通平均数87.3分，导致错选。2．B。除以一个分数等于乘这个分数的倒数。把0.75先化成3/4，计算更稳。易错提醒：把除法直接改成乘法却忘记“乘倒数”，或把0.75误写成75/10。3．B。四舍五入到万位约是36万，原数应在355000到364999之间，最大值取上界前一个整数。易错提醒：365000会约成37万，不能作为“约36万”的最大值。4．C。正方形周长与长方形周长相等，先由正方形边长求周长，再反推长方形长宽和。易错提醒：周长相等不等于面积相等，也不能直接用32－10。5．C。a与b成正比例，a/b的比值保持不变，也可写成b/a保持不变。易错提醒：前后列比必须方向一致，不能一边写a/b，另一边写b/a。6．C。两个数相乘的积是奇数，当且仅当两个因数都是奇数。六个数中奇数有5个。易错提醒：只要出现一个偶数，积就一定是偶数。7．C。相向而行求两地距离，用“速度和×相遇时间”。易错提醒：不能只算其中一辆车行驶的路程，也不能把70与80相减。8．B。连续涨跌的百分数基准不同。设原价100元，先降价后再涨价，第二次上涨是以90元为基准。易错提醒：10%与10%数值相同，但对应的“单位1”不同，结果不是不变。9．B。等底等高时，圆柱体积是圆锥体积的3倍，差量36对应“2份圆锥体积”。易错提醒：把36直接除以3，会把“差量”误当成圆柱体积。10．C。逐项判断：2是质数但不是奇数；三角形任意两边之差应小于第三边；面积相等不能推出全等。只有C正确。易错提醒：判断含“所有”“一定”的说法时，要主动寻找反例。二、填空题答案与解析11．32。比例尺1:500000表示图上1厘米对应实际500000厘米。先求实际厘米数，再换成千米。易错提醒：厘米化千米要除以100000，不能只除以1000。12．3/8。比较大小前统一成小数：0.374不变，3/8=0.375，37.6%=0.376，0.37=0.370。易错提醒：百分数37.6%对应0.376，不是37.6。13．40。优秀与良好合计占80%，其余合格占20%。8人对应全班的20%。易错提醒：8人对应的是“剩余部分”，不能除以35%或45%。14．48。沿长、宽、高方向分别能完整切出6段、4段、2段，小正方体个数是三个方向段数的乘积。易错提醒：高度方向剩余1厘米不能与其他边角材料拼成完整小正方体。15．65。数列可观察为“平方数加1”：1²+1、2²+1、3²+1……易错提醒：若只看相邻差3、5、7、9，也要继续写到第8项，避免少推一步。16．1/2。可能性=目标数量÷总数量。红球5个，总球数10个。易错提醒：结果要化成最简分数。三、解答题答案详解与评分标准17．计算题（8分）【解题思路】第（1）题先处理括号内分数差，再与48相乘；第（2）题适合提取公因数2.5；第（3）题先算括号，再进行分数减法