2026版数学综合测评QS01仿真卷Org214（含答案解析与学生作答区）

通用数学综合测评QS01第1页2026版数学综合测评QS01仿真卷Org214（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：通用数学综合测评备考学生、教师组卷与可打印练习使用答题说明：请按题号作答，选择题填入答题栏，计算题与证明题写出必要过程。

2026版数学综合测评QS01仿真卷Org214（含答案解析与学生作答区）姓名：________________班级：________________考号：________________考试时间90分钟总分100分适用对象通用数学综合测评备考学生、教师组卷与可打印练习使用答题说明请先检查试卷；按题号顺序作答；选择题填入答题栏；计算题、证明题写出必要过程；书写清楚，结果准确。答题说明：1.本卷共24题，满分100分，考试时间90分钟。2.选择题每题只有一个正确答案。3.解答题须写出必要的演算、证明或建模过程。4.作图与书写应规范清楚，结果用最简形式表示。选择题答题栏123456789101112填空题作答栏（请将答案直接写在题后横线上）一、选择题（本大题共12小题，每小题3分，共36分）1.计算2³+√16的结果是（3分）A.10B.11C.12D.142.函数y=(x-1)²+2的最小值为（3分）A.1B.2C.-1D.03.方程2x²-5x-3=0的两个根是（3分）A.3，-1/2B.-3，1/2C.1，-3/2D.-1，3/24.不等式-2(x-3)≤4的解集是（3分）A.x≤1B.x<1C.x≤-1D.x≥1

5.已知△ABC中，点D在AB上，点E在AC上，DE∥BC，AD:AB=2:5，BC=10，则DE的长为（3分）A.3B.4C.5D.66.袋中有编号1到6的6个大小相同的小球，随机摸出1个，编号为偶数的概率是（3分）A.1/6B.1/3C.1/2D.2/37.等差数列{aₙ}中，a₁=5，公差d=-2，则a₆等于（3分）A.-5B.-3C.5D.158.一组数据7，8，8，9，10，下列说法正确的是（3分）A.平均数为8B.众数为9C.中位数为9D.平均数为8.4，中位数为89.半径为5的圆中，一条弦到圆心的距离为3，则该弦长为（3分）A.6B.8C.10D.1210.一次函数f(x)=kx+b经过点(-1,5)和(2,-1)，则f(3)等于（3分）A.-5B.-4C.-3D.311.两个相似三角形的对应边长之比为2:3，则它们的面积之比为（3分）A.2:3B.3:2C.8:27D.4:912.某地出租车3km内收费10元，超过3km后每千米加收2.4元。乘坐8km的车费为（3分）A.20元B.22元C.24元D.29.2元二、填空题（本大题共6小题，每小题3分，共18分）13.因式分解：x²-9=________________。（3分）14.若x=2，y=-1，则3x-2y=________________。（3分）15.反比例函数y=3/x中，当x=6时，y=________________。（3分）16.袋中有3个红球、2个蓝球，随机不放回连续摸出2个球，先红后蓝的概率为________________。（3分）17.等差数列首项a₁=2，公差d=3，则前10项和S₁₀=________________。（3分）18.平面直角坐标系中，A(-2,3)，B(4,-5)，则AB=________________。（3分）三、解答题（本大题共6小题，共46分）19.函数与方程（7分）已知二次函数f(x)=x²-4x+1。（1）写出该函数图象的顶点坐标，并求最小值；（2）解方程f(x)=0；（3）写出不等式f(x)<0的解集。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

20.几何证明与计算（7分）在△ABC中，AB=AC，点D在BC上，且∠BAD=∠CAD，AD=6，BD=4。（1）证明△ABD≌△ACD；（2）求BC的长与△ABC的面积。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

21.统计概率建模（8分）某学习小组记录了30天图书馆自习人数，整理如下表：人数区间20—2930—3940—4950—59天数49125（1）用各组组中值估计这30天的平均自习人数；（2）写出出现天数最多的人数区间；（3）从这30天中随机抽取1天，估计自习人数不少于40人的概率；（4）若一个学期按80天估计，预测自习人数不少于40人的天数。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

22.数列与不等式（8分）数列{aₙ}满足a₁=3，aₙ₊₁=aₙ+2n+1（n为正整数）。（1）求a₂、a₃、a₄；（2）猜想aₙ的通项公式，并用归纳思路说明其正确性；（3）求满足aₙ<102的正整数n的最大值。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

23.应用题数量关系（8分）一个水箱初始有18L水，同时进水与排水。进水速度为4L/min，排水速度为1.5L/min，水箱最大容量为70L。设经过t分钟后水箱中的水量为VL。（1）写出V关于t的函数关系式；（2）求水量达到58L所需时间；（3）若持续运行24分钟，判断是否溢水，并说明理由。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

24.函数综合与面积模型（8分）在平面直角坐标系中，抛物线y=-x²+4x+5与x轴交于A、B两点，与y轴交于C点。点P(t，-t²+4t+5)在抛物线上，且0<t<5。（1）求抛物线的顶点坐标和最大值；（2）求A、B两点坐标，并写出△PAB的面积S关于t的关系式；（3）求△PAB面积的最大值；（4）当S=24时，求t的值。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2026版数学综合测评QS01仿真卷Org214（含答案解析与学生作答区）参考答案与解析一、选择题题号答案解析要点1C2³=8，√16=4，二者相加为12。2B配方式y=(x-1)²+2，顶点为(1,2)，最小值为2。3A2x²-5x-3=(2x+1)(x-3)，根为3和-1/2。4D-2(x-3)≤4，化简得-2x≤-2；不等号变向，x≥1。5BDE∥BC，△ADE∽△ABC，AD/AB=2/5，所以DE/BC=2/5，DE=4。6C共有6个球，偶数球有2、4、6共3个，概率为3/6=1/2。7A等差数列a₆=a₁+5d=5+5×(-2)=-5。8D数据7、8、8、9、10的中位数为8，平均数为42/5=8.4。9B半径5，弦心距3，半弦长√(5²-3²)=4，弦长8。10C直线斜率为(-1-5)/(2-(-1))=-2，b=3，f(3)=-3。11D相似比为2:3，面积比为4:9。12B超过3km部分为5km，车费10+2.4×5=22元。二、填空题题号答案解析要点13(x-3)(x+3)平方差公式a²-b²=(a-b)(a+b)。148代入3x-2y=3×2-2×(-1)=6+2=8。151/2y=3/x，x=6时y=3/6=1/2。163/10不放回抽取：P=3/5×2/4=3/10。17155S₁₀=10/2×[2×2+(10-1)×3]=155。1810两点距离√[(4+2)²+(-5-3)²]=√100=10。三、解答题19.函数与方程（7分）参考答案：顶点为(2,-3