2026届衢州六年级数学小升初分班考试考前模拟试卷第026套强证据校准版（含答案详解与评分标准）

2026届衢州六年级数学小升初分班考试考前模拟试卷第026套强证据校准版（含答案详解与评分标准）考试时间：90分钟满分：120分适用对象：2026届小学六年级小升初分班考试备考学校：________________班级：____________姓名：____________考号：________________卷面结构选择题8题40分；填空题4题20分；解答题6题60分。能力重点数与运算、方程与比例、函数图象、平面与立体几何、统计概率、综合应用。答题要求选择题将答案填入答题框；填空题直接写结果；解答题须写出主要公式、计算过程、单位和答语。注意事项书写清楚，单位完整；需要近似时按题中要求取值；不得在密封线外书写与作答无关内容。一、选择题（本大题共8小题，每小题5分，共40分。每题只有一个正确答案）1.计算2.4×0.75+3.6÷0.45-1.25的结果是（）。A.7.55B.8.55C.9.25D.10.052.两个数分别分解质因数为甲数=2×2×3×5，乙数=2×3×3×5。它们的最大公因数与最小公倍数之和是（）。A.120B.150C.210D.2703.某地出租车计价规则为：3千米以内收费8元；超过3千米的部分每千米加收2元。设行驶路程为x千米，车费为y元。下列关于函数图象的判断正确的是（）。A.全程都满足y=2xB.0≤x≤3时，y随x按每千米2元增加C.x>3时，图象为直线y=2x+2的一段射线D.图象一定经过原点4.等腰三角形ABC中，AB=AC，∠A=40°，BD平分∠ABC并交AC于点D，则∠BDC的度数是（）。A.65°B.70°C.75°D.105°5.六位数35□42□能被45整除，方框中各填一个数字。符合条件的六位数共有（）个。A.1B.2C.3D.46.某商品先在原价基础上涨价20%，随后又按涨价后的价格降价20%。现在的价格与原价相比（）。A.不变B.降低4%C.提高4%D.降低20%7.一个圆柱形水杯的底面半径为3厘米，高为9厘米。按π取3.14计算，它的容积约是（）立方厘米。A.84.78B.169.56C.216.00D.254.348.袋中有3个红球、2个蓝球、1个黄球，除颜色外完全相同。任意不放回地取出2个球，两球都是红球的可能性是（）。A.1/10B.1/5C.2/5D.1/2选择题答题框：12345678二、填空题（本大题共4小题，每小题5分，共20分。把答案写在题中横线上）9.解方程0.75x-1.2=5.1，x=____________。10.一个长12厘米、宽8厘米的长方形纸片中剪下一个最大的圆。剩余纸片面积为____________平方厘米。（π取3.14）11.五名同学一次数学小测的平均分是82分，去掉最高分96分和最低分68分后，剩下三名同学的平均分是____________分。12.观察数列2，5，10，17，26，……，按此规律第20个数是____________。填空题作答区：9.__________10.__________11.__________12.__________三、解答题（本大题共6小题，每小题10分，共60分。写出必要的解题过程、公式和单位）13.计算与方程。（1）计算：7/12+5/8-1/6（2）解方程：2.5x-1.5=7.5________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________14.一块直角梯形花坛，上底12米，下底20米，高10米。花坛中间挖去一个半径3米的圆形喷水池，剩余部分铺草皮。（1）求需要铺草皮的面积。（π取3.14）（2）若铺草皮每平方米18元，一共需要多少元？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________15.一次衢州城市研学活动中，同学们从集合点出发，沿绿道前往目的地，全程13.5千米。前一段骑行，速度为9千米/时；后一段步行，速度为4.5千米/时；总用时2小时。求骑行路程和步行路程各是多少千米。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________16.六（1）班48名同学选择一项最想加强的数学训练，统计结果如下表。训练项目人数数学阅读12计算能力15图形几何9综合应用12（1）选择“计算能力”的同学占全班人数的百分之几？（2）若用扇形统计图表示，选择“图形几何”的扇形圆心角是多少度？（3）从全班随机抽取一名同学，抽到的同学没有选择“综合应用”的可能性是多少？（4）若年级共有240名同学，按该班比例估计，选择“图形几何”和“综合应用”的同学大约共有多少人？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________17.整理数学实验器材，甲单独完成需要10小时，乙单独完成需要15小时。甲、乙合作3小时后，乙离开，余下由甲单独完成。（1）甲还需要多少小时才能完成余下工作？（2）若甲每小时整理24件器材，这批器材一共有多少件？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.压轴题：把一张长24厘米、宽18厘米的长方形硬纸板，在四个角分别剪去边长为x厘米的小正方形，再折成一个无盖长方体纸盒。若纸盒底面积为216平方厘米，求：（1）剪去的小正方形边长x是多少厘米；（2）这个无盖纸盒的容积是多少立方厘米；（3）这个无盖纸盒的表面积是多少平方厘米。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________四、草稿与检查区（可用于计算、画图、列式和验算）本区域不单独计分，建议用于整理草稿、标注单位、检查结果是否符合题意。交卷前可按题号核对：选择题8题、填空题4题、解答题6题，合计120分。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析本答案区按题号1—18逐题给出结果、依据、关键步骤与采分点。解答题评分以思路正确、公式合理、计算准确、单位完整为基本原则；不同方法只要逻辑严密、结论正确，可按相应采分点给分。一、选择题答案12345678BCCCBBDB二、填空题答案91011128.445.7682401详细解析与评分标准知识点与采分核对表题号核心知识关键证据常见失分点1小数四则混合运算先乘除后加减，逐步求中间值把0.45错看成4.5，或运算顺序混乱2质因数分解、公因数与公倍数公共质因数取小指数，公倍数取大指数只求其中一个量，忘记题目要求求和3分段函数与图象起步价是固定值，超过部分才按单价增加误认为图象经过原点或全程正比例4等腰三角形与角平分线底角相等，角平分后用三角形内角和把相邻补角误当成同一角5整除特征能被45整除即同时能被5和9整除只检查个位，不检查数字和6百分数连续变化第二次变化的基数是涨价后的价格把涨20%和降20%直接抵消7圆柱体积底面积乘高，半径与直径区分清楚把半径当直径或漏乘高8不放回概率总取法数与红红取法数对应比较第二次仍按原总数计算9一元一次方程移项、除以系数，小数除法准确移项符号错误或商的小数点错位10长方形内最大圆最大圆直径等于短边，剩余面积作差把短边当半径11平均数先求总分，再扣除最高最低分用82直接作为三人总分计算12数列规律相邻差是连续奇数，通项为n²+1只继续写几项，未推广到第20项13分数运算与方程通分、移项、解方程每步清楚通分分母不统一，或移项方向错误14梯形面积、圆面积、单价应用先求整体，再扣除圆形水池面积，再乘单价用直径代替半径或用整体面积算费用15行程问题方程路程÷速度=时间，总时间为2小时把两段路程或两段时间混淆16统计与可能性百分数、圆心角、概率、按比例估计把圆心角误乘100%，估计人数未合并项目17工程问题工作效率相加后乘合作时间，余量除以甲效率把工作时间相加当作效率相加18立体展开与方程底面长宽为24-2x、18-2x，舍去不合题意根忘记纸盒无盖，或不说明舍根理由使用本表时，应把“结果正确”与“过程证据”同时核对。选择题重在判断依据，填空题重在唯一结果，解答题重在列式、计算、单位和答语。评分时不因采用不同解法而扣分，只要推理链条完整、数值和单位正确，即可按同等采分点给分。1.（5分）答案：B。依据：先按乘除法，再按加减法。计算过程：2.4×0.75=1.8，3.6÷0.45=8，1.8+8-1.25=8.55评分标准：选B得5分；只计算出前两个中间结果但未完成选择，可按教师讲评时作为过程性订正，不计本题卷面分。易错点是把0.45看成4.5，或将1.25提前与0.75相加。2.（5分）答案：C。甲数=60，乙数=90。最大公因数取公共质因数的较小指数，最小公倍数取各质因数的较大指数。关键计算：最大公因数=2×3×5=30；最小公倍数=2^2×3^2×5=180；30+180=210评分标准：选C得5分。易错点是只求最大公因数或只求最小公倍数，没有按题意求两者之和。3.（5分）答案：C。3千米以内车费固定为8元，图象不是经过原点的正比例图象；超过3千米后，每增加1千米车费增加2元，因此后半段是斜率为2的射线。当x>3时：y=8+2(x-3)=2x+2评分标准：选C得5分。易错点是把“起步价含3千米”理解为从0千米开始按每千米2元收费，导致误选A或D。4.（5分）答案：C。因为AB=AC，底角相等。计算：∠ABC=∠ACB=(180°-40°)÷2=70°BD平分∠ABC，所以：∠ABD=35°在三角形ABD中：∠ADB=180°-40°-35°=105°D在直线AC上，因此：∠BDC=180°-105°=75°评分标准：选C得5分。易错点是把∠ADB与∠BDC混为同一个角，或忘记相邻补角关系。5.（5分）答案：B。能被45整除，必须同时能被5和9整除。个位数字只能是0或5；各位数字和必须是9的倍数。设百位为a、个位为b，则各位数字和为：3+5+a+4+2+b=14+a+b若b=0，则14+a为9的倍数，a=4；若b=5，则19+a为9的倍数，a=8。因此有354420和358425两个数。评分标准：选B得5分。易错点是只检查能被5整除，没有再检查能被9整除。6.（5分）答案：B。设原价为a元，先涨价20%后价格为1.2a，再降价20%是按1.2a为基数下降。现价为：1.2a×(1-20%)=1.2a×0.8=0.96a现价是原价的96%，比原价