2026届山东省小升初数学分班考试模拟试卷（含答案详解与评分标准）

2026届山东省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分注意事项：1．本卷用于2026届山东省小学毕业后分班考试考前检测，重点考查数与代数、图形与几何、统计与概率、综合应用能力。2．全卷共22题，选择题10题30分，填空题6题18分，解答题6题52分，合计100分。请在规定时间内完成。3．选择题每题只有一个正确答案；填空题只填写结果；解答题必须写出必要的计算过程、推理过程或说明。4．计算结果按题目要求取值；未作特殊说明时，结果可用整数、分数或小数表示，单位必须完整。5．遇到百分数、比例尺、圆面积、行程和统计问题时，要先写清数量关系，再代入数据。6．保持卷面整洁，答题空间内作答，书写要清楚，步骤要完整。一、选择题（本大题共10小题，每小题3分，共30分。每小题只有一个正确答案）1．计算1/8×0.8＋3/8÷3/4的结果是（）。A．3/5B．1/2C．11/20D．7/102．已知a:b＝3:5，b:c＝2:7，则a:c＝（）。A．3:7B．6:35C．5:14D．15:143．一个整数既是12的倍数，又是18的倍数，且小于100。这样的整数中最大的是（）。A．36B．54C．72D．964．一支钢笔先涨价20%，再按涨价后的价格降价20%。现价与原价相比（）。A．不变B．降低4%C．提高4%D．降低20%5．一个长方体的长、宽、高分别为8厘米、5厘米、4厘米，它的表面积是（）平方厘米。A．160B．184C．200D．3206．甲单独完成一项整理试卷的任务需要12小时，乙单独完成需要18小时。两人合作3小时完成了这项任务的（）。A．1/4B．1/3C．5/12D．1/27．五名学生在一次分班模拟检测中的数学成绩分别为85分、90分、92分、88分、95分，这组数据的中位数是（）。A．88B．90C．92D．958．一个三角形三个内角的度数比是2:3:4，这个三角形最大内角是（）。A．40°B．60°C．80°D．90°9．若0.4x－3＝5，则x的值是（）。A．5B．12.5C．20D．2510．一幅山东省交通示意图的比例尺为1:6000000，图上距离3.5厘米表示实际距离（）千米。A．21B．35C．210D．350二、填空题（本大题共6小题，每小题3分，共18分）11．6.25吨＝（）千克；0.48公顷＝（）平方米。12．48和60的最大公因数是（），最小公倍数是（）。13．一件复习资料原价240元，按八五折销售后又减20元，应付（）元。14．一个圆的半径是3厘米，取π＝3.14，它的面积是（）平方厘米。15．一组数4、6、8、10、12的平均数是（）；若再加入一个数x后平均数为9，则x＝（）。16．一个正方体的表面积是96平方厘米，它的体积是（）立方厘米。三、解答题（本大题共6小题，共52分。写出必要的解题过程）17．计算与解方程。（8分）（1）4.8×25%＋5.2×1/4；（2）(3x－4)÷5＝2.8。可用关系式：25%=1/4，(3x-4)÷5=2.8。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．某校为分班考试考前检测准备A、B两种答题卡共150张。A种每张0.5元，B种每张0.8元，一共花了96元。A、B两种答题卡各买了多少张？（8分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．学校操场是一个长80米、宽45米的长方形区域。为了分班考试后的体育活动安排，准备在操场中修一条横贯长边方向、宽2米的通道，再修一条横贯宽边方向、宽2米的通道，两条通道在中央相交。其余部分铺设草坪。求通道面积和草坪面积。（8分）提示公式：长方形面积=长×宽，相交部分不要重复计算。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．某班40名学生参加小升初数学分班模拟考试，成绩按等级统计如下表。若估算时优秀按95分、良好按85分、合格按72分、待提高按60分计算，回答问题。（9分）等级优秀良好合格待提高人数121882（1）估算全班平均分；（2）求优秀率；（3）如果保持总人数不变，要使优秀率达到40%，至少还需要多少名学生由非优秀等级提升为优秀等级？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．甲、乙两车分别从相距160千米的两地同时相向而行，甲车每小时行48千米，乙车每小时行32千米。（9分）（1）两车同时出发，几小时后相遇？（2）若乙车先出发0.5小时，甲车再出发，甲车出发后几小时两车相遇？可用关系式：路程=速度×时间。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．学校为小升初分班考试后的分层辅导采购A、B两类复习资料共90套。A类每套原价18元，实际购买时优惠10%；B类每套12元且不优惠。实际共付款1290元。（10分）（1）A、B两类资料各购买多少套？（2）A类资料发给数学重点提高组学生，每人1套后剩2套；后来又有3名学生加入提高组，最终还需要补买多少套A类资料？可用数量关系：总价=单价×数量。______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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备用作答区（不计分）本区可用于解答题补充步骤、检查计算和草稿整理，阅卷时以题目对应作答内容为准。

参考答案与解析一、选择题答案与解析（每题3分，共30分）题号12345678910答案ABCBBCBCCC1．选A。1/8×0.8＝0.1，3/8÷3/4＝3/8×4/3＝1/2＝0.5，和为0.6＝3/5。本题考查分数、小数互化和分数除法，容易把3/8÷3/4误算成3/8×3/4。审题时要先确定运算顺序，乘除运算从左到右进行；把除法转化成乘法时，必须乘除数的倒数。2．选B。由a:b＝3:5可知a和b可看作3份、5份；由b:c＝2:7可知b和c可看作2份、7份。统一b的份数，取5和2的最小公倍数10，得到a:b＝6:10，b:c＝10:35，所以a:c＝6:35。本题考查连比转化，不能直接把3和7组成3:7。3．选C。既是12的倍数又是18的倍数，说明该整数是12和18的公倍数。12＝2^2×3，18＝2×3^2，最小公倍数是2^2×3^2＝36。小于100的36的倍数有36和72，下一项108已经超过100，因此最大为72。4．选B。设原价为1，涨价20%后为1×（1＋20%）＝1.2；再降价20%是按1.2降价，现价为1.2×（1－20%）＝0.96。现价比原价少1－0.96＝0.04，即降低4%。本题说明连续涨跌的基准不同，不能简单认为涨20%再降20%就不变。5．选B。长方体表面积＝2×（长×宽＋长×高＋宽×高）＝2×（8×5＋8×4＋5×4）＝2×92＝184平方厘米。计算时要把三组相对面的面积全部包括，不能只算底面积或侧面积。6．选C。甲每小时完成1/12，乙每小时完成1/18，两人合做每小时完成1/12＋1/18＝3/36＋2/36＝5/36。合作3小时完成3×5/36＝15/36＝5/12。本题考查工程问题中的工作效率、工作时间和工作总量关系。7．选B。求中位数必须先排序：85、88、90、92、95。五个数据中处于正中间的第三个数是90，因此中位数是90。中位数反映数据的中间位置，与平均数不同，不需要把所有数据相加再除以个数。8．选C。三角形内角和是180°，三个角的份数总和为2＋3＋4＝9，每份是180°÷9＝20°。最大角占4份，所以最大角为4×20°＝80°。三角形最大角小于90°，也可判断它是锐角三角形。9．选C。0.4x－3＝5，两边同时加3得0.4x＝8，再用8÷0.4求得x＝20。也可以把0.4看作2/5，方程为2/5x＝8，x＝8÷2/5＝20。解方程时每一步都要保持等式两边同时进行同一种运算。10．选C。比例尺1:6000000表示图上1厘米代表实际6000000厘米。图上3.5厘米代表3.5×6000000＝21000000厘米。因为100000厘米＝1千米，所以21000000厘米＝210千米。单位换算是本题的主要失分点。选择题评分标准：每题3分；选项正确得3分，未选、错选或多选不得分。若答题卡涂写不清、一个题号出现两个及以上选项，按不得分处理。二、填空题答案与解析（每题3分，共18分）题号答案关键解析116250；48001吨＝1000千克，1公顷＝10000平方米。1212；24048＝2^4×3，60＝2^2×3×5。13184240×85%＝204，204－20＝184。1428.26圆面积＝πr^2＝3.14×3×3＝28.26。158；14前5个数和40；加入x后总和为54。16646a^2＝96，a＝4，体积4^3＝64。11．单位换算要看进率方向。吨换千克是高级单位化低级单位，要乘1000，6.25×1000＝6250；公顷换平方米也要乘进率10000，0.48×10000＝4800。12．最大公因数取两个数共有因数中最大的一个，可用短除法或分解质因数；最小公倍数是同时包含两个数全部质因数的最小整数。48和60的最大公因数为12，最小公倍数为240。13．八五折表示按原价的85%付款，先算折后价格240×0.85＝204，再减20元，最终应付184元。折扣题要分清“打折”和“再减”的先后顺序。14．圆面积公式是S＝πr^2，半径为3厘米，不是直径。代入得3.14×3^2＝28.26平方厘米。若把3当成直径，会得到错误结果。15．4、6、8、10、12的和为40，平均数是40÷5＝8。加入一个数后共有6个数，平均数9对应总和54，因此新增数x＝54－40＝14。16．正方体6个面完全相同，表面积96平方厘米表示每个面的面积是96÷6＝16平方厘米，棱长为4厘米，体积为4×4×4＝64立方厘米。填空题评分标准：每题3分；有两个空的题目，每空1.5分。结果等值但写法不同可得分；单位题中单位与数值共同构成答案，若数值正确但单位换算方向错误，该空不得分。三、解答题答案详解与评分标准（共52分）17．计算与解方程。（8分）（1）4.8×25%＋5.2×1/4＝4.8×1/4＋5.2×1/4＝（4.8＋5.2）×1/4＝10×1/4＝2.5。这里把25%转化为1/4后，可以发现两个乘法算式含有相同因数1/4，因此用乘法分配律逆用会更简便。（2）(3x－4)÷5＝2.8，两边同时乘5，得3x－4＝14；两边同时加4，得3x＝18；两边同时除以3，得x＝6。把x＝6代入原方程，左边为(18－4)÷5＝14÷5＝2.8，与右边相等，结果正确。评分标准：第（1）小题4分，化25%为1/4或正确处理百分数得1分，正确使用乘法分配律或按顺序计算得2分，结果2.5得1分；第（2）小题4分，去分母得1分，移项得1分，求出x得1分，检验或书写完整得1分。若计算过程正确但结果书写为等值分数，也可得结果分。18．答题卡采购问题。（8分）方法一：设A种答题卡买x张，则B种答题卡买（150－x）张。根据总价列方程：0.5x＋0.8（150－x）＝96。化简得0.5x＋120－0.8x＝96，－0.3x＝－24，x＝80。B种答题卡为150－80＝70张。方法二：假设150张全买A种，应花150×0.5＝75元，比实际少96－75＝21元。每把1张A种换成B种，费用增加0.8－0.5＝0.3元，需要换21÷0.3＝70张，所以B种70张，A种80张。答：A种答题卡买80张，B种答题卡买70张。检验：80＋70＝150，80×0.5＋70×0.8＝40＋56＝96，符合题意。评分标准：设未知数或用假设法整理数量关系得2分；列出正确等量关系或差额关系得3分；求出A种80张得2分；求出B种70张并作答得1分。若只写结果无过程，最多得3分；若过程能体现总数和总价两个条件，即使计算小错，可按步骤给分。19．通道与草坪面积问题。（8分）横贯长边方向的通道可以看成一个长80米、宽2米的长方形，面积为80×2＝160平方米；横贯宽边方向的通道可以看成一个长45米、宽2米的长方形，面积为45×2＝90平方米。两条通道在中央相交，相交部分是2米×2米的正方形。如果直接把160和90相加，中央正方形被算了两次，因此要减去一次：2×2＝4平方米。通道总面积＝160＋90－4＝246平方米。操场总面积＝80×45＝3600平方米。其余部分铺设草坪，所以草坪面积＝3600－246＝3354平方米。答：通道面积为246平方米，草坪面积为3354平方米。评分标准：算出两条通道面积各得1.5分，共3分；能判断相交部分重复并减去4平方米得2分；算出操场总面积得1分；算出草坪面积得1.5分；答句和单位完