2026学年北师大版六年级数学小升初摸底质量检测卷（含参考答案解析）

六年级数学小升初摸底质量检测卷2025-2026学年北师大版六年级数学小升初摸底质量检测卷（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分题量：29题适用：小升初摸底题型选择题填空题计算题解决问题总分分值20202040100得分注意事项：1．本卷共四大题，满分100分。请先检查试卷页码和题号是否连续，再开始作答。2．选择题把正确选项填在题后括号内；填空题只写结果，必要时注明单位。3．计算题和解决问题要写出必要过程，能约分的分数要化为最简形式，小数计算要注意对齐。4．圆周率按3.14计算；单位换算、比例尺、百分数和几何问题均需看清题目条件。5．请保持卷面整洁，解题步骤写在对应作答区内，超出作答区时可在题目旁清楚标明。一、选择题（本大题共10小题，每小题2分，共20分。每题只有一个正确答案）1．在0.8、5/6、83%、0.805这四个数中，最大的数是（）。A．0.8B．5/6C．83%D．0.8052．一种商品先降价20%，又在降价后的价格基础上提价20%。现在的价格与原价相比，（）。A．不变B．提高4%C．降低4%D．降低20%3．一幅地图的比例尺是1∶2500000，甲、乙两地实际距离75千米，在图上的距离是（）。A．3厘米B．30厘米C．0.3厘米D．300厘米4．两个数的比是3∶5，它们的和是64，其中较大的数是（）。A．24B．32C．40D．485．一个圆柱的底面半径是3厘米，高是5厘米，它的体积是（）立方厘米。A．47.1B．94.2C．117.75D．141.36．如果x和y都是非零数，并且y=6÷x，那么x和y成（）。A．正比例B．无法确定C．反比例D．既成正比例又成反比例7．一个正方体的棱长扩大到原来的2倍，它的体积扩大到原来的（）。A．2倍B．4倍C．8倍D．16倍8．袋子里有3个红球、5个蓝球、2个黄球，任意摸出1个球，摸到的球不是蓝球的可能性是（）。A．1/5B．1/2C．3/5D．2/59．方程4x－1.5=10.5的解是（）。A．x=3B．x=2.25C．x=3.5D．x=410．一个三角形的底和高都扩大到原来的2倍，它的面积扩大到原来的（）。A．2倍B．3倍C．4倍D．8倍二、填空题（本大题共10小题，每小题2分，共20分）11．3.6平方米=（）平方分米；2.05升=（）毫升。12．把24∶36化成最简整数比是（），比值是（）。13．钟面上分针长6厘米，分针尖端走一圈经过的路程是（）厘米。14．一个数比它本身的25%多48，这个数是（）。15．如果5a=4b（a、b均不为0），那么a∶b=（）。16．一个圆锥的体积是37.68立方厘米，与它等底等高的圆柱体积是（）立方厘米。17．一项工程，甲单独做6小时完成，乙单独做9小时完成。两人合作1小时完成这项工程的（）。18．一个盒子里黑球和白球共有24个，黑球与白球个数的比是5∶3，黑球有（）个。19．一个圆柱的侧面展开图是长18.84厘米、宽10厘米的长方形，这个圆柱的体积是（）立方厘米。20．一组数据4、8、9、x、13的平均数是9，则x=（），这组数据的中位数是（）。三、计算题（本大题共4小题，每小题5分，共20分。请写出主要过程）21．直接计算或用简便方法计算。（1）7/8－2/5＋1/8（2）12.5×32×0.25（3）2/3÷4/9×3/5（4）[3/4＋（5/6－1/3）]×12作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．解方程或比例。（1）3x/5＋1.2=4.8（2）4∶x=5∶7（3）0.6x－25%x=7作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23．脱式计算，能简算的要简算。（1）5/9×7/11＋5/9×4/11（2）25×（4/5＋7/10）－3.5（3）7.2÷[0.8×（1.5－0.75）]作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24．一个长12厘米、宽8厘米的长方形纸片，从一端剪去一个以宽为直径的半圆。求剩余部分的面积和周长。（π取3.14）作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________四、解决问题（本大题共5小题，每小题8分，共40分。请列式并写出答语）25．书店开展小升初阅读活动，一套科普读物原价120元，现在按八五折出售。学校购买30套，结算时又符合“满3000元立减150元”的优惠条件。学校实际应付多少元？比原价一共节省多少元？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________26．六年级共有120名学生参加课后社团，科技社团、体育社团、艺术社团的人数比是3∶4∶5。艺术社团中女生占60%。科技社团有多少人？艺术社团女生有多少人？科技社团比体育社团少多少人？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________27．甲、乙两个工程队合修一条440米长的步道。甲队每天修40米，乙队每天修50米。甲队先修2天后，乙队加入一起修，剩下的部分还需要几天修完？全工程完成时甲队一共修了多少米？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________28．一个圆柱形水桶的内底面直径是20厘米，高30厘米，桶中原有水深18厘米。把一个底面积为157平方厘米、高12厘米的圆锥形铁块完全浸没在水中，水面会上升多少厘米？水会不会溢出？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________29．学校印刷A、B两种小升初摸底练习卷。A卷每份0.45元，B卷每份0.60元，两种卷共印600份，共用315元。A卷和B卷各印了多少份？如果再加印A卷原数量的1/5，每份价格仍为0.45元，还需要多少元？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________参考答案与解析说明：参考答案中的解法用于核对思路。计算题与解决问题只要数量关系正确、过程完整、结果准确，即可按评分点给分。一、选择题1．答案：B。解析：把各数统一化成小数比较。0.8=0.800，5/6≈0.8333，83%=0.83，0.805=0.805。因为0.8333大于0.83、0.805和0.800，所以最大的是5/6。关键点：本题考查分数、小数、百分数互化和大小比较。不能只看数字位数，要统一形式。2．答案：C。解析：设原价为1，降价20%后为1×（1－20%）=0.8；再在0.8的基础上提价20%，价格为0.8×（1＋20%）=0.96。现在价格是原价的96%，比原价降低4%。关键点：两次变化的单位“1”不同，第二次提价是在降价后的价格上进行，不是回到原价。3．答案：A。解析：比例尺1∶2500000表示图上1厘米代表实际2500000厘米。75千米=7500000厘米，图上距离=7500000÷2500000=3厘米。关键点：比例尺计算前要先统一单位，千米和厘米不能直接相除。4．答案：C。解析：两个数的比为3∶5，可看成3份和5份，共8份。每份为64÷8=8，较大的数占5份，所以较大的数是5×8=40。关键点：按比例分配时先求总份数，再求每份量，最后对应所求份数。5．答案：D。解析：圆柱体积公式是V=πr2h。代入r=3厘米，h=5厘米，V=3.14×32×5=3.14×9×5=141.3立方厘米。关键点：计算时不要把半径当直径，也不要漏乘高。6．答案：C。解析：由y=6÷x可得xy=6。两个相关联的量乘积一定时成反比例，所以x和y成反比例。关键点：正比例的特征是比值一定，反比例的特征是乘积一定。7．答案：C。解析：正方体体积=棱长×棱长×棱长。棱长扩大到原来的2倍，体积扩大到2×2×2=8倍。关键点：长度变化、面积变化和体积变化的倍数不同，要分清维度。8．答案：B。解析：共有3+5+2=10个球。不是蓝球的有红球和黄球，共3+2=5个，所以可能性是5/10=1/2。关键点：“不是蓝球”包含红球和黄球，不能只算某一种颜色。9．答案：A。解析：4x－1.5=10.5，等式两边同时加1.5，得4x=12；两边再除以4，得x=3。关键点：解方程要保持等式两边同时进行同一种运算。10．答案：C。解析：三角形面积=底×高÷2。底扩大2倍，高扩大2倍，面积扩大2×2=4倍，与除以2无关，因为原式和变化后的式子都有÷2。关键点：面积与两个长度量有关，两个长度量同时扩大时，面积倍数要相乘。二、填空题11．答案：360；2050。解析：1平方米=100平方分米，所以3.6平方米=3.6×100=360平方分米；1升=1000毫升，所以2.05升=2.05×1000=2050毫升。关键点：从大单位化成小单位用乘法，进率分别是100和1000。12．答案：2∶3；2/3。解析：24和36的最大公因数是12，把比的前项和后项同时除以12，得2∶3。比值是24÷36=2/3。关键点：化简比得到的是两个数的比，比值是一个数，写法不同。13．答案：37.68。解析：分针尖端走一圈的轨迹是圆，半径为6厘米。圆周长C=2πr=2×3.14×6=37.68厘米。关键点：此题求路程，不是求圆面积。14．答案：64。解析：“比它本身的25%多48”表示这个数减去它的25%等于48，也就是这个数的75%是48。因此这个数=48÷75%=64。关键点：找到单位“1”是这个数本身，剩下的百分率是1－25%=75%。15．答案：4∶5。解析：由5a=4b可知a/b=4/5，所以a∶b=4∶5。也可以把a看作4份，b看作5份，代入后5×4份=4×5份成立。关键点：比例变形时要注意对应关系，不要把a∶b写反。16．答案：113.04。解析：等底等高的圆柱体积是圆锥体积的3倍，所以圆柱体积=37.68×3=113.04立方厘米。关键点：圆锥体积是等底等高圆柱体积的1/3。17．答案：5/18。解析：甲的工作效率是1/6，乙的工作效率是1/9。两人合作1小时完成1/6+1/9=3/18+2/18=5/18。关键点：工程问题中工作总量常看作1，合作效率等于各自效率之和。18．答案：15。解析：黑球和白球的总份数是5+3=8份，每份为24÷8=3个。黑球占5份，所以黑球有5×3=15个。关键点：按比例分配时，先用总数除以总份数。19．答案：282.6。解析：侧面展开图的长18.84厘米是圆柱底面周长，底面半径=18.84÷3.14÷2=3厘米；宽10厘米是圆柱高。体积=3.14×32×10=282.6立方厘米。关键点：侧面展开图的长通常对应底面周长，宽对应高。20．答案：11；9。解析：五个数的平均数是9，总和为9×5=45。已知四个数之和为4+8+9+13=34，所以x=45－34=11。排序后是4、8、9、11、13，中间的数是9。关键点：求中位数必须先按大小排序。三、计算题21．答案：（1）3/5；（2）100；（3）9/10；（4）15。解析：（1）7/8－2/5＋1/8=7/8+1/8－2/5=1－2/5=3/5。先把同分母的7/8和1/8相加，计算更简便。（2）12.5×32×0.25=12.5×8×4×0.25=（12.5×8）×（4×0.25）=100×1=100。把32拆成8×4，可凑整。（3）2/3÷4/9×3/5=2/3×9/4×3/5。约分后计算，2与4约成1和2，3与9可配合化简，结果为9/10。（4）[3/4+（5/6－1/3）]×12。括号内5/6－1/3=5/6－2/6=3/6=1/2，3/4+1/2=3/4+2/4=5/4，5/4×12=15。评分点：每小题方法正确、计算准确可得相应分；能使用运算定律简算且结果正确，过程完整。22．答案：（1）x=6；（2）x=28/5或5.6；（3）x=20。解析：（1）3x/5+1.2=4.8，先移项得3x/5=3.6，再用3.6÷3/5=3.6×5/3=6，所以x=6。（2）4∶x=5∶7，根据比例基本性质，内项积等于外项积，得5x=4×7=28，所以x=28/5。（3）0.6x－2