2026版数学综合测评QS01仿真卷Bloom012（含答案解析与学生作答区）

通用数学综合测评QS01第页2026版数学综合测评QS01仿真卷Bloom012（含答案解析与学生作答区）考试时间：90分钟总分：100分适用对象：全国通用数学综合测评训练答题说明：本卷为闭卷限时测评；请先检查试卷页码与题号，按题号顺序作答；书写规范，计算题须写出必要过程。

2026版数学综合测评QS01仿真卷Bloom012（含答案解析与学生作答区）姓名班级考号得分考试时间：90分钟满分：100分答题说明：1.本卷共三大题、24小题，满分100分。2.选择题请先在题旁判断，再填写答题栏；填空题将答案写在横线上；解答题需写出必要的推理、计算和结论。3.作图、证明与建模题应书写清楚，单位与范围不可遗漏。选择题答题栏123456789101112一、选择题（本大题共12小题，每小题3分，共36分）1.已知集合A={x｜x^2-5x+6=0}，B={2，3，4}，则A∩B为（3分）A.{2}B.{3}C.{2，3}D.{4}2.已知f(x)=2x-1，g(x)=x^2+1，则(g∘f)(2)的值为（3分）A.10B.9C.7D.53.方程3(2x-1)=4x+5的解为（3分）A.x=1B.x=2C.x=3D.x=44.一个三角形的三边长分别为6、8、10，则该三角形的面积为（3分）A.20B.22C.24D.305.一组数据4，6，6，8，10的平均数是（3分）A.6.4B.6.8C.7.0D.7.26.袋中有3个红球和2个蓝球，随机不放回依次摸出2个球，第一次为红球且第二次为蓝球的概率为（3分）A.1/5B.3/10C.2/5D.1/27.二次函数y=x^2-4x+1的顶点坐标是（3分）A.(−2，−3)B.(2，3)C.(2，−3)D.(4，1)8.不等式2x−3>5的解集是（3分）A.x>4B.x<4C.x>1D.x<19.等差数列{a_n}中，a_1=2，公差d=3，则a_8=（3分）A.20B.21C.22D.2310.经过点(1，2)和(5，8)的直线斜率为（3分）A.1/2B.1C.3/2D.211.某商品先降价20%，再在降价后的基础上提价25%，则最终价格与原价相比（3分）A.降低5%B.相等C.提高5%D.提高10%12.圆x^2+y^2=25与直线y=3的交点个数是（3分）A.0个B.2个C.1个D.无数个二、填空题（本大题共6小题，每小题3分，共18分）13.解方程组2x+y=7，x−y=2，则x+y=答：____________________________（3分）14.因式分解：x^2−9=答：____________________________（3分）15.一次函数f(x)=kx+2的图象经过点(3，11)，则k=答：____________________________（3分）16.同时掷两枚均匀骰子，点数和为7的概率是答：____________________________（3分）17.数列a_n=n^2−n，则a_6=答：____________________________（3分）18.矩形的一条边长为5，对角线长为13，则另一条边长为答：____________________________（3分）三、解答题（本大题共6小题，共46分）19.已知函数f(x)=x^2−2mx+m^2−4。

（1）当m=3时，解方程f(x)=0；

（2）若方程f(x)=0的两个实数根都在区间[0，6]内，求m的取值范围。（7分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

20.如图形关系所示，在△ABC中，AB=AC，D为BC的中点，AB=10，BC=12。

（1）证明AD⊥BC；

（2）求AD的长和△ABC的面积。（7分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

21.某校对50名学生每天课外数学练习时间进行调查，得到如下频数表。

请根据表中数据完成问题。（8分）练习时间t（小时）[0，1)[1，2)[2，3)[3，4)[4，5]频数61218104（1）用组中值估计这50名学生每天课外数学练习时间的平均数；

（2）随机抽取1名学生，估计其每天练习时间不少于3小时的概率；

（3）从这50名学生中不放回随机抽取2名学生，求两人练习时间都不少于3小时的概率。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

22.已知数列{a_n}满足a_1=3，a_{n+1}=a_n+2n（n为正整数）。

（1）写出a_n的通项公式；

（2）证明：对任意正整数n，都有a_n≥2n+1；

（3）求满足a_n>100的最小正整数n。（8分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

23.某培训机构为学生购买练习本和签字笔共70件。练习本每本6元，签字笔每支4元，总费用为360元。

（1）求练习本和签字笔各购买多少件；

（2）若下次按同样数量购买，练习本单价下降10%，签字笔单价不变，则总费用比本次节省多少元；

（3）结合结果说明费用变化主要来自哪一类物品。（8分）____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24.在平面直角坐标系中，A(0，4)，B(6，0)，点P(t，0)在线段OB上，且0<t<6。

（1）用含t的式子表示△APB的面积S；

（2）当S=8时，求t的值；

（3）求AP^2+PB^2的最小值，并说明此时点P的位置。（8分）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2026版数学综合测评QS01仿真卷Bloom012（含答案解析与学生作答区）参考答案与解析一、选择题答案与解析1.C。x^2−5x+6=(x−2)(x−3)，故A={2，3}，与B的公共元素为2、3。2.A。先求f(2)=3，再代入g(x)得g(3)=3^2+1=10。3.D。6x−3=4x+5，移项得2x=8，所以x=4。4.C。6^2+8^2=10^2，为直角三角形，面积为1/2×6×8=24。5.B。平均数为(4+6+6+8+10)÷5=34÷5=6.8。6.B。第一次红球概率为3/5，第二次蓝球概率为2/4，乘得3/10。7.C。y=x^2−4x+1=(x−2)^2−3，顶点为(2，−3)。8.A。2x−3>5，得2x>8，所以x>4。9.D。a_8=a_1+7d=2+7×3=23。10.C。斜率k=(8−2)/(5−1)=6/4=3/2。11.B。设原价为1，变化后为1×0.8×1.25=1，与原价相等。12.B。将y=3代入圆方程得x^2+9=25，x=±4，有2个交点。二、填空题答案与解析