2026年北京海淀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177套

2026年北京海淀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177套学校：________________班级：________姓名：________考号：________考试时间：90分钟满分：120分试卷用途：分班考试综合检测注意事项：1．本试卷共三大题，26小题。选择题、填空题请在指定位置作答，解答题必须写出必要的计算过程、推理过程或说明。2．考试时间90分钟，满分120分。请合理安排时间，先易后难，书写清楚，步骤完整。3．可使用直尺、三角板、量角器，不得使用具有存储、联网或拍照功能的设备。4．本卷重在考查小学阶段核心知识的综合运用、计算准确性、数学表达和升学分班所需的思维品质。题型题号每题分值合计选择题1—123分36分填空题13—183分18分解答题19—26见题号标注66分一、选择题（本大题共12小题，每小题3分，共36分）每小题只有一个选项符合题意。请把正确选项填在题后括号内。1．若a=2026，b=2025，则(a+b)÷(a-b)的值是（）。A．1B．2025C．2026D．40512．下列分数中，最接近0.618的是（）。A．3/5B．5/8C．7/12D．2/33．一只书包原价150元，先按八折出售，再使用12元优惠券，实际付款（）元。A．108B．110C．118D．1324．整数x满足-2<x÷3≤4，符合条件的x一共有（）个。A．17B．18C．19D．205．某班男生与女生人数的比是7∶5，女生有15人，这个班一共有（）人。A．21B．30C．36D．426．方程2(x-3)=3(x-5)+7的解是（）。A．x=1B．x=2C．x=3D．x=47．一个三角形两边长分别为5厘米和7厘米，第三边是整数厘米，且周长为偶数。第三边可能的取值有（）个。A．3B．4C．5D．68．把一个边长为12厘米的正方形剪成一个最大的圆，圆外剩余部分面积约为（）平方厘米。（π取3.14）A．30.96B．31.04C．113.04D．1449．小海从家到图书馆共10千米，其中前6千米骑车速度为12千米/时，后4千米步行速度为8千米/时。他全程平均速度是（）千米/时。A．9B．10C．10.5D．1110．袋中有3个红球、2个黄球、1个蓝球，除颜色外完全相同。不放回任取2个，恰好取到1个红球和1个黄球的可能性是（）。A．1/5B．1/3C．2/5D．1/211．数列2，5，11，23，47，……按同一规律排列，第7个数是（）。A．95B．143C．191D．25512．某校六年级四个班参加跳绳测试，达标人数如下表。若全年级共有160人，达标率为75%，则六（4）班达标人数是（）人。班级六（1）六（2）六（3）六（4）达标人数312930？A．24B．27C．30D．33二、填空题（本大题共6小题，每小题3分，共18分）请把结果直接写在横线上；能化简的要化简，单位要完整。13．计算：3/4-5/12+2/3=__________。14．2.6公顷=__________平方米；3时15分=__________时。15．一件商品标价480元，降价15%后仍获利20%，这件商品的进价是__________元。16．一个圆柱形水杯，底面半径3厘米，杯内水高8厘米。把一块石子完全浸入水中，水面上升到10厘米，石子的体积是__________立方厘米。（π取3.14）17．四位数35□4能被9整除，□里应填__________。18．甲、乙两人合作完成一项整理图书任务，甲单独做需要6小时，乙单独做需要9小时。两人合作2小时后，剩下的由甲单独完成，还需要__________小时。三、解答题（本大题共8小题，共66分）请写出必要的计算过程、推理过程和答语。作答区预留用于打印作答，不得只写结果。19．（8分）计算与解方程。（1）计算：4.8×1.25＋5.2÷0.4－7.5。（2）解方程：5(2x-1)-3(x+4)=2x+9。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（8分）海淀某小学六年级开展“毕业阅读月”活动。六年级共有240名学生，第一周完成阅读任务的人数占全体的45%；第二周结束时累计完成任务的人数比第一周多18人；第三周完成后，累计完成任务的人数达到全体的80%。（1）第一周完成阅读任务的学生有多少人？（2）第三周新完成阅读任务的学生有多少人？（3）还剩多少名学生未完成阅读任务？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（8分）如图形文字描述：一块校园宣传牌由一个长方形和一个等腰梯形组成。长方形长26厘米，宽12厘米；梯形上底18厘米，下底26厘米，高10厘米。现要给宣传牌正面贴保护膜，每平方厘米保护膜成本0.08元。（1）求宣传牌正面的总面积。（2）若保护膜实际购买时需多买5%作为损耗，至少应按多少平方厘米购买？（3）保护膜成本约多少元？结果保留到0.01元。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（8分）下面是某校六年级80名学生一次数学分班模拟测试成绩分布情况。90分及以上：18人；80—89分：26人；70—79分：21人；60—69分：10人；60分以下：5人。（1）这次测试的及格率是多少？（2）如果把80分及以上记为“优秀”，优秀率是多少？（3）若学校计划从80分以下学生中选出12人参加基础巩固小组，已知70—79分段选8人，则60分以下与60—69分段一共应选多少人？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23．（8分）一个三位数的十位数字是4，个位数字比百位数字大2。这个三位数能被6整除。求所有满足条件的三位数，并说明理由。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24．（8分）甲、乙两地相距72千米。小明从甲地骑行去乙地，前1.5小时速度为16千米/时，之后因逆风速度降为12千米/时。小华同时从乙地出发骑行去甲地，速度保持14千米/时。（1）小明出发1.5小时后离甲地多少千米？（2）两人出发后多少小时相遇？（3）相遇地点离甲地多少千米？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25．（9分）某校购买A、B两种跳绳共120根，其中A型每根18元，B型每根25元。已知购买B型的根数比A型的2倍少15根。（1）A型、B型各购买多少根？（2）这批跳绳共花费多少元？（3）若商家满2500元减150元，学校实际支付多少元？实际平均每根跳绳多少元？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________26．（9分）综合探究。将若干个边长为1厘米的小正方形按规律拼成“阶梯形”。第1个图形有1个小正方形；第2个图形第一层2个、第二层1个，共3个；第3个图形三层分别有3、2、1个，共6个；依此类推。（1）第6个图形有多少个小正方形？（2）第n个图形有多少个小正方形？用含n的式子表示。（3）如果某个阶梯形一共有136个小正方形，它是第几个图形？（4）第8个图形的周长是多少厘米？请写出推理过程。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与解析及评分标准评分标准总表大题题号范围分值设置得分说明一、选择题1—12每题3分，共36分选对得3分，错选、多选或不选得0分。二、填空题13—18每题3分，共18分结果正确、单位正确得3分；结果正确但单位缺失或不规范酌情扣1分。三、解答题19—24每题8分，共48分按步骤给分，关键式、计算、结论分别评分。三、解答题25—26每题9分，共18分按建模、运算、推理、答语给分，过程合理可酌情给分。一、选择题答案与解析1．D。a-b=1，a+b=4051，所以(a+b)÷(a-b)=4051。2．B。3/5=0.6，5/8=0.625，7/12约0.583，2/3约0.667。0.625与0.618相差0.007，最接近。3．A。八折后为150×0.8=120元，再减12元，实际付款108元。4．B。由-2<x÷3≤4，三边同乘3得-6<x≤12，整数为-5到12，共18个。5．C。女生5份对应15人，1份为3人，全班12份，共36人。6．B。2x-6=3x-15+7=3x-8，移项得x=2。7．B。三角形第三边x满足2<x<12，整数x为3至11；周长12+x为偶数，所以x为偶数，取4、6、8、10，共4个。8．A。最大圆半径为6厘米，圆面积为3.14×6×6=113.04平方厘米，正方形面积144平方厘米，剩余30.96平方厘米。9．B。前6千米用时6÷12=0.5小时，后4千米用时4÷8=0.5小时，总路程10千米，总时间1小时，平均速度10千米/时。10．C。两次取球不放回，恰好1红1黄的取法有3×2=6种，总取法C(6,2)=15种，可能性为6/15=2/5。11．C。每一项等于前一项乘2再加1：2，5，11，23，47，95，191，所以第7个数是191。12．C。全年级达标人数160×75%=120人，前三班达标31+29+30=90人，六（4）班达标120-90=30人。二、填空题答案与解析13．1。3/4=9/12，2/3=8/12，9/12-5/12+8/12=12/12=1。14．26000；3.25。1公顷=10000平方米，2.6公顷=26000平方米；15分=0.25时，所以3时15分=3.25时。15．340。降价后售价为480×(1-15%)=408元，售价是进价的120%，进价408÷1.2=340元。16．56.52。石子完全浸入后排开水的体积等于水面上升部分体积：3.14×3×3×(10-8)=56.52立方厘米。17．6。能被9整除的数各位数字和是9的倍数。3+5+□+4=12+□，只有□=6时为18。18．8/3。甲每小时完成1/6，乙每小时完成1/9，合作2小时完成2×(1/6+1/9)=5/9，剩下4/9；由甲单独完成需(4/9)÷(1/6)=8/3小时。三、解答题答案详解与评分标准19．答案：（1）4.8×