2026版数学综合测评QS01仿真卷Org069（含答案解析与学生作答区）

通用数学综合测评QS01姓名：____________班级：____________考号：____________2026版数学综合测评QS01仿真卷Org069（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：请先检查试卷页码与题号是否完整；选择题在答题栏作答，填空题写出最终结果，解答题须写出必要的计算过程、推理依据和结论。本卷为黑白可打印版，答题时请保持书写清晰、步骤完整。

2026版数学综合测评QS01仿真卷Org069（含答案解析与学生作答区）姓名：________________班级：________________考号：________________考试时间：90分钟满分：100分答题说明：1.全卷共24题，满分100分；请按题号顺序作答。2.选择题每题只有一个正确选项，请在答题栏中填涂或填写字母。3.填空题只写最终答案，必要时保留根号、分数或百分数。4.解答题应写出主要步骤、公式、代入过程和结论，书写不规范或缺少依据将酌情扣分。选择题答题栏题号123456答案题号789101112答案一、选择题（本大题共12小题，每小题3分，共36分）下列每小题给出的四个选项中，只有一个选项符合题意。1.已知函数f(x)=x²-4x+3，则不等式f(x)<0的解集是（3分）A.x<1或x>3B.1<x<3C.x≤1或x≥3D.-1<x<32.若方程2x+a=3(x-1)的解为x=5，则a的值为（3分）A.-2B.2C.4D.83.在等腰三角形ABC中，AB=AC，∠A=40°，则∠B的度数为（3分）A.40°B.50°C.70°D.100°4.一个不透明袋中有2个红球、3个白球、1个蓝球，除颜色外完全相同。随机摸出1个球，摸到“不是白球”的概率为（3分）A.1/3B.1/2C.2/3D.5/65.等差数列{aₙ}中，a₁=3，公差d=2，则前10项和S₁₀为（3分）A.90B.100C.120D.1406.二次函数y=-2(x-1)²+5的最大值为（3分）A.5B.3C.1D.-27.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.4B.6C.7D.88.数据7，8，8，9，10，12的平均数和中位数分别为（3分）A.9，8B.9，8.5C.9.5，8.5D.9.5，99.不等式3(x-2)≤2x+5的解集是（3分）A.x≥11B.x≤-1C.x≥-1D.x≤1110.反比例函数y=k/x的图象经过点(2，-3)，则k的值为（3分）A.6B.-1C.-6D.-511.直线y=2x+1与坐标轴围成的三角形面积为（3分）A.1/4B.1/2C.1D.212.已知关于x的方程x²-mx+4=0有两个相等实根，则m的值可能是（3分）A.4B.-4C.0D.4或-4二、填空题（本大题共6小题，每小题3分，共18分）13.函数g(x)=√(x-2)+1/(x+1)的自变量x的取值范围是__________。（3分）14.边长为4的正六边形的面积是__________。（3分）15.某班40名学生中有12名学生佩戴眼镜，随机抽取1名学生，抽到佩戴眼镜学生的概率是__________。（3分）16.数列{aₙ}满足a₁=5，aₙ₊₁=aₙ+3，则a₈=__________。（3分）17.某商品原价为x元，按八折销售后再减16元，实际售价为64元，则原价x=__________元。（3分）18.不等式x²-5x+6≥0的解集是__________。（3分）

三、解答题（本大题共6小题，共46分）19.已知函数f(x)=x²-2x-3。（7分）（1）将f(x)因式分解，并求方程f(x)=0的两个根；（2）求方程f(x)=5的解；（3）结合函数图象或因式分解结果，写出不等式f(x)<0的解集。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

20.如图形关系所示，Rt△ABC中，∠C=90°，AC=6，BC=8，点D为AB的中点，点E在AC上，且AE=2。（7分）（1）求AB与CD的长；（2）证明DA=DB=DC；（3）求△BDE的面积。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

21.某校对40名学生一周课外数学阅读时间进行抽样调查，整理成如下频数表：（8分）阅读时间x（分钟）0≤x<3030≤x<6060≤x<9090≤x<120频数410188（1）用组中值估计这40名学生一周课外数学阅读时间的平均数；（2）从样本中随机抽取1名学生，估计其一周阅读时间不少于60分钟的概率；（3）若该校共有800名学生，请估计一周阅读时间不少于60分钟的学生人数，并说明这种估计的前提。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

22.已知数列{aₙ}的通项公式为aₙ=3n-1，前n项和为Sₙ。（8分）（1）求a₁、a₁₂；（2）用n表示Sₙ；（3）求满足Sₙ≥100的最小正整数n，并说明判断过程。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

23.某研学小组购买成人票和学生票共32张。成人票每张60元，学生票每张40元，合计付款1560元。（8分）（1）成人票和学生票各购买多少张？（2）若改用线上购票，成人票按九折，学生票按九五折，仍购买相同张数，应付款多少元？比原来节省多少元？学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

24.在平面直角坐标系中，抛物线y=-x²+4x-3与x轴交于点A、B（A在B左侧），点P为抛物线上位于x轴上方的一点，点P的横坐标为t，且1<t<3。（8分）（1）求A、B的坐标及抛物线顶点坐标；（2）用含t的式子表示△PAB的面积，并求该面积的最大值；（3）当△PAB的面积为3/4时，求t的值。学生作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2026版数学综合测评QS01仿真卷Org069（含答案解析与学生作答区）参考答案与解析一、选择题题号123456789101112答案BBCBCADBDCAD1.答案：B。解析：f(x)=(x-1)(x-3)，开口向上，函数值小于0时自变量在两个零点之间，所以为1<x<3。2.答案：B。解析：把x=5代入2x+a=3(x-1)，得10+a=12，故a=2。3.答案：C。解析：AB=AC，所以∠B=∠C；由三角形内角和得∠B=(180°-40°)/2=70°。4.答案：B。解析：不是白球共有2+1=3个，总数为6个，概率为3/6=1/2。5.答案：C。解析：S₁₀=10/2×[2×3+(10-1)×2]=5×24=120。6.答案：A。解析：函数写成顶点式y=-2(x-1)²+5，开口向下，最大值为5。7.答案：D。解析：过圆心作弦的垂线平分弦，半弦长为√(5²-3²)=4，所以弦长为8。8.答案：B。解析：平均数为(7+8+8+9+10+12)/6=9；中位数为第3、4个数的平均值，即(8+9)/2=8.5。9.答案：D。解析：3x-6≤2x+5，移项得x≤11。10.答案：C。解析：把(2，-3)代入y=k/x，得-3=k/2，所以k=-6。11.答案：A。解析：直线与y轴交于(0，1)，与x轴交于(-1/2，0)，面积为1/2×1×1/2=1/4。12.答案：D。解析：两个相等实根要求判别式m²-16=0，得m=4或m=-4。二、填空题13.答案：x≥2。解析：根式要求x-2≥0，且分母x+1≠0；当x≥2时分母条件自动满足。14.答案：24√3。解析：正六边形可分成6个边长为4的等边三角形，面积为6×(√3/4×4²)=24√3。15.答案：3/10或0.3。解析：概率为12/40=3/10。16.答案：26。解析：这是公差为3的等差数列，a₈=5+(8-1)×3=26。17.答案：100。解析：由0.8x-16=64，得0.8x=80，x=100。18.答案：x≤2或x≥3。解析：x²-5x+6=(x-2)(x-3)，开口向上，大于等于0在两根外侧。

三、解答题19.答案与过程：（1）f(x)=x²-2x-3=(x-3)(x+1)，所以方程f(x)=0的两个根为x=3，x=-1。（2）f(x)=5，即x²-2x-3=5，整理得x²-2x-8=0，分解为(x-4)(x+2)=0，故x=4或x=-2。（3）由(x-3)(x+1)<0，得-1<x<3。评分点：因式分解2分；零点1分；列出并解出f(x)=5方程2分；不等式解集2分。常见失分提醒：不要把