2026年小升初数学重点中学入学模拟模拟试卷（含参考答案解析）

2026年小升初数学重点中学入学模拟试卷2026年小升初数学重点中学入学模拟模拟试卷（含参考答案解析）学校：班级：姓名：考号：考试时间：90分钟满分：100分适用对象：小升初考试形式：闭卷注意事项：1．请在答题区域内书写，字迹清楚，过程完整；2．可使用直尺、圆规，不得使用计算器；3．本卷含参考答案与解析，试题正文结束后另起新页；4．计算题和解决问题题须写出必要步骤，只有答案不得满分。作答提示：本卷覆盖整数与分数运算、比和比例、百分数、图形面积与体积、行程工程、统计概率和简单计数。选择题应先判断数量关系，填空题注意单位统一，计算题要写清运算顺序，解决问题要列式完整并写出答语。评分提示：主观题按步骤给分。若思路正确但计算有小误差，可保留部分步骤分；若单位换算错误、答语不完整或关键条件漏用，应按评分点相应扣分。题型选择题填空题计算题解决问题总分阅卷人分值20202040100一、选择题（本大题共10小题，每小题2分，共20分）每小题只有一个选项符合题意。请将正确选项填在题号后的括号内。1．把40支同样的笔按2:3分给甲、乙两人，甲比乙少多少支？（）A．6支B．8支C．10支D．12支2．一个数既是12的因数，又是18的因数，这样的数中最大的是（）。A．3B．4C．6D．93．算式0.75×1/3＋1/4的结果是（）。A．1/4B．1/2C．3/4D．14．一个长方体的长、宽、高分别是4厘米、3厘米、2厘米，它的表面积是（）平方厘米。A．26B．40C．52D．725．一件原价50元的商品，先涨价10%，再降价10%，现价是（）元。A．49B．49.5C．50D．50.56．甲、乙两车行驶相同的路程，速度比是3:4，则所用时间比是（）。A．3:4B．4:3C．9:16D．16:97．三位数“□52”能被3整除，方框里可填的一位数中最大的是（）。A．5B．6C．8D．98．一组数据4，7，7，9，10，12的中位数是（）。A．7B．8C．8.5D．99．下列两种量成正比例关系的是（）。A．正方形边长和面积B．圆的周长和直径C．路程一定时的速度和时间D．一个人的年龄和身高10．一个正方形的边长增加10%，它的面积增加（）。A．10%B．20%C．21%D．121%二、填空题（本大题共10小题，每小题2分，共20分）请把正确答案写在横线上。结果能化简的要化简，涉及圆周率的题目按题中要求取值。11．1.25小时:45分钟化成最简整数比是________。12．80先增加25%，再减少20%，结果是________。13．一个数除以5余3，除以6余4，除以8余6，这个数最小是________。14．一个圆的半径是5厘米，面积是________平方厘米。（π取3.14）15．在比例尺1:500000的地图上，甲、乙两地相距3.6厘米，实际距离是________千米。16．一个圆柱的底面直径是6厘米，高是10厘米，它的体积是________立方厘米。（π取3.14）17．1＋3＋5＋……＋39＝________。18．袋中有4个红球、3个蓝球、5个白球，任意摸出1个球，摸到蓝球的可能性是________。19．若x÷4＋6＝21，则x＝________。20．按规律计算：1×2＋2×3＋3×4＋……＋9×10＝________。三、计算题（本大题共4小题，每小题5分，共20分）请写出必要的计算过程。能简算的要简算；方程、比例题要写明变形依据。21．脱式计算。（1）（2）（3）（4）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________续写区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．用合适的方法计算，写出简算过程。（1）（2）（3）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________续写区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23．解方程或比例。（1）（2）（3）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________续写区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24．一个长方形的长是12厘米、宽是8厘米。从这个长方形中剪去一个半径为2厘米的半圆和一个底为4厘米、高为3厘米的三角形，两个剪去部分不重叠。求剩余图形的面积。（π取3.14）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________续写区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________四、解决问题（本大题共5小题，每小题8分，共40分）请认真审题，列式或列方程解答，并写出答语。过程完整、单位正确、结论清楚。25．文具店有一批同款笔记本。前120本按原价的九折售出，剩下80本按原价的七五折售出，这批笔记本一共收入3360元。每本笔记本的原价是多少元？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________解题过程续写区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________26．一项工程，甲队单独做12天完成，乙队单独做18天完成。两队合作3天后，甲队因故离开，剩下的工程由乙队单独完成。乙队还需要多少天完成？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________解题过程续写区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________27．甲、乙两地相距210千米。客车从甲地出发，货车从乙地出发，两车同时相向而行，1.5小时后相遇。已知客车每小时比货车多行10千米，求客车和货车的速度。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________解题过程续写区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________28．一个圆柱形水桶，内底面半径为10厘米，原来水深12厘米。把一块长12厘米、宽8厘米、高10厘米的长方体铁块完全浸没在水中，水没有溢出。水面上升了多少厘米？（π取3.14，结果保留两位小数）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________解题过程续写区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________29．在1到200的整数中，能被3或5整除，但不能被15整除的数有多少个？请说明你的统计方法。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________解题过程续写区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与解析说明：以下答案按题号逐题给出。客观题列出关键依据，计算题列出主要过程，解决问题给出评分点。阅卷时可根据学生实际步骤酌情给分，但不得改变题号、分值和总分结构。一、选择题1．【答案】B。总数40支按2:3分配，甲占总数的2/(2＋3)，乙占总数的3/(2＋3)。甲得16支，乙得24支，甲比乙少8支。关键是先求总份数，再按份数分配。【考查点】考查按比例分配和差量理解。先求每份数量，比直接比较百分数更稳妥。2．【答案】C。既是12的因数又是18的因数，就是12和18的公因数。12的因数有1、2、3、4、6、12，18的因数有1、2、3、6、9、18，最大公因数是6。【考查点】考查公因数。列因数时要完整，不能把最大公因数误认为最小公倍数。3．【答案】B。0.75等于3/4，3/4×1/3＝1/4，再加1/4等于1/2。计算小数和分数混合题时，通常先把小数转化成分数，便于约分。【考查点】考查分数、小数互化和四则混合运算。乘法先算，最后再合并同类分数。4．【答案】C。长方体表面积等于2×(长×宽＋长×高＋宽×高)。代入4、3、2得2×(12＋8＋6)＝52平方厘米。【考查点】考查长方体表面积公式。三个不同面的面积都要计入，并且每种面有两个。5．【答案】B。先涨价10%后价格为50×1.1＝55元，再降价10%后为55×0.9＝49.5元。涨价和降价的基数不同，不能直接抵消。【考查点】考查百分数连续变化。两次变化的单位“1”不同，不能用10%－10%直接判断。6．【答案】B。路程相同时，时间和速度成反比例。速度比是3:4，所用时间比应是4:3。【考查点】考查反比例关系。相同路程下速度越快时间越短，时间比要把速度比倒过来。7．【答案】C。一个数能被3整除，数字和必须是3的倍数。□52的数字和是□＋7，方框可填2、5、8，其中最大是8。【考查点】考查整除特征。被3整除只看数字和，方框可以逐个试验后取最大值。8．【答案】B。这组数据已经从小到大排列，共6个数，中位数是第3个和第4个数的平均数，即(7＋9)÷2＝8。【考查点】考查中位数。偶数个数据取中间两个数的平均数，不是简单取第3个数。9．【答案】B。圆的周长C＝πd，π是固定的比值，所以圆的周长和直径成正比例。正方形面积与边长不是一次关系，路程一定时速度与时间成反比例。【考查点】考查正比例的判定。两个相关量的比值一定时才成正比例。10．【答案】C。设原边长为1，原面积为1。边长增加10%后为1.1，面积为1.1×1.1＝1.21，比原来增加0.21，也就是21%。【考查点】考查面积随边长变化的平方关系。边长增加10%不等于面积增加10%。二、填空题11．【答案】5:3。1.25小时＝75分钟，75:45同时除以15，得到5:3。化比时必须先统一单位。【考查点】本题先统一时间单位，再把比的前项和后项同时除以最大公因数。12．【答案】80。80增加25%得80×1.25＝100，再减少20%得100×0.8＝80。【考查点】连续百分数问题应逐步计算，每一步的单位“1”都随结果改变。13．【答案】118。题意可转化为这个数加2后能同时被5、6、8整除。5、6、8的最小公倍数是120，所以最小的数是120－2＝118。【考查点】余数分别比除数小2，说明加2后是公倍数，这是转化思想的典型应用。14．【答案】78.5。圆面积S＝πr²＝3.14×5²＝78.5平方厘米。【考查点】半径平方后再乘圆周率，不能把周长公式和面积公式混用。15．【答案】18。实际距离＝图上距离÷比例尺＝3.6×500000厘米＝1800000厘米＝18千米。【考查点】比例尺题注意厘米、米、千米的进率，结果应按题目要求用千米表示。16．【答案】282.6。圆柱体积＝底面积×高＝3.14×(6÷2)²×10＝3.14×9×10＝282.6立方厘米。【考查点】圆柱底面半径是直径的一半，先求半径再求底面积。17．【答案】400。1到39的连续奇数共有20个，前20个奇数的和是20²＝400；也可首尾配对求和。【考查点】连续奇数和可用平方数规律，也可用等差数列配对思想。18．【答案】1/4。球的总数是4＋3＋5＝12个，蓝球3个，所以摸到蓝球的可能性是3/12＝1/4。【考查点】可能性等于有利结果数除以总结果数，最后要约成最简分数。19．【答案】60。x÷4＋6＝21，先两边同时减6得x÷4＝15，再两边同时乘4，x＝60。【考查点】解方程时遵循逆运算顺序，先处理加减，再处理乘除。20．【答案】330。1×2＋2×3＋……＋9×10，可以分别计算后相加，也可利用n(n＋1)的求和规律，结果为330。【考查点】此类乘积求和可直接列表计算，也可把相邻自然数乘积按规律累加。三、计算题21．【答案】（1）1.1；（2）9；（3）5.6；（4）6/5。解析：（1）（2）（3）（4）评分建议：每小题过程和结果各占主要分值；能正确通分、约分或处理运算顺序即可得相应步骤分，结果写成1.2或6/5均可按等值处理。关键步骤补充：第（1）小题可把0.75化成3/4，也可统一成小数，重点是先乘除后加减；第（2）小题先算5/6－7/12＝3/12，再与36相乘；第（3）小题先算括号内0.8×3/4＝0.6，再完成除法；第（4）小题括号内先算7/9×3/14＝1/6，再与5/6相加后除以5/6。易错提醒：分数除法要乘倒数，不能把除以5/6写成乘5/6；小数与分数混合运算时，若直接用小数计算，应保留足够精度。评分点补充：每个小题都应给出关键中间量，能体现运算顺序、通分或约分过程；若结果正确但过程缺少括号处理，按步骤完整性扣分。22．【答案】（1）100；（2）15；（3）4050。解析：本题主要考查运算定律和提取公因数。（1）（2）（3）评分建议：能发现32＝8×4、能提取15或2025作公因数，是本题的关键。若直接竖式计算正确，也可得结果分，但简算过程不充分时酌情扣步骤分。关键步骤补充：第（1）小题把32拆成8×4后，可利用12.5×8和4×0.25两个凑整组合；第（2）小题提取公因数15后，7/11＋4/11＝1；第（3）小题把2025看作共同因数，转化为2025×(2026－2024)。易错提醒：简算题不能只写最终结果，应写出使用运算定律的关键一行；第（3）小题若直接逐个大数相乘，容易出现位数错误。评分点补充：能正确识别并使用乘法交换律、结合律或分配律给主要过程分；若不用简算但计算正确，可给结果分和部分过程分。23．【答案】（1）x＝2；（2）x＝6；（3）x＝18。（1）（2）（3）评分建议：每小题应写出等式两边同加、同减、同乘或同除后的关键过程。只有答案而无过程，最多给结果分。关键步骤补充：第（1）小题先移项得到5x＝10；第（2）小题可先交叉相乘或先把3.5/7化成1/2；第（3）小题先两边减5，再把2/3x＝12转化为x＝12÷2/3。易错提醒