2026届山东省济南市高三数学高考考前冲刺仿真模拟试卷B2卷（含答案详解、评分标准与学生作答区）

山东济南高三数学高考冲刺B2卷（含答案与评分标准）PAGE2026届山东省济南市高三数学高考考前冲刺仿真模拟试卷B2卷（含答案详解、评分标准与学生作答区）考试时间：120分钟满分：150分适用：高三考前冲刺打印：黑白可打印注意事项与答题要求1.答题前请填写姓名、班级和准考证号；选择题用规定方式填涂，非选择题写在对应作答区内。2.计算题须写出必要的推理、演算和结论；只写最终结果而无关键过程的题目，按评分标准扣分。3.本卷坚持临考稳分、综合提速与压轴分层突破；所有题目条件充分、结论唯一。4.卷面保持整洁，公式、区间端点、概率事件和几何关系请写清楚。题型结构与分值题型题号每题分值小计单项选择题1—85分40分多项选择题9—125分20分填空题13—165分20分解答题17题10分；18—22题各12分按小问给分70分选择题与填空题学生答题栏题号123456答案题号789101112答案题号13141516答案一、单项选择题：本大题共8小题，每小题5分，共40分。每小题只有一个选项符合题意。1.（5分）设全集U=R，A={x|-1≤x<3}，B={x|x^2-4x+3≤0}，则A∩B=（）A.[1,3]B.[1,3)C.(-1,1]D.(-1,3]2.（5分）已知复数z=(1+2i)/(1-i)，则|z|=（）A.√5/2B.√10/2C.5/2D.√103.（5分）函数f(x)=ln(x+1)-x/2在x=1处的切线斜率为（）A.-1/2B.0C.1/2D.14.（5分）等比数列{a_n}中，a_2=3，a_5=24，则其前5项和S_5=（）A.45B.46C.93/2D.48

5.（5分）若θ∈(0,π)，cosθ=-3/5，则sin2θ=（）A.-24/25B.-7/25C.7/25D.24/256.（5分）同时抛掷两枚质地均匀的骰子，点数和不小于10且至少有一枚为6的概率为（）A.1/9B.5/36C.1/6D.7/367.（5分）椭圆x^2/4+y^2/3=1的离心率为（）A.1/4B.1/3C.1/2D.√3/28.（5分）正方体ABCD-A_1B_1C_1D_1的棱长为2，则点A到平面BDC_1的距离为（）A.√3/3B.2√3/3C.√2D.2二、多项选择题：本大题共4小题，每小题5分，共20分。每小题有多个选项符合题意，全部选对得5分，部分选对得2分，有选错得0分。9.（5分）设f(x)=x^3-3x，下列说法正确的是（）A.f(x)是奇函数B.f(x)在(-∞,-1)和(1,+∞)上单调递增C.方程f(x)=0恰有两个实根D.f(x)在[-2,2]上的最大值为210.（5分）设向量a=(cosα,sinα)，b=(1,√3)，α∈[0,2π)，且a·b=1，下列判断正确的是（）A.α可以等于0B.α可以等于2π/3C.|a+b|=√6D.向量a与b的夹角为60°11.（5分）随机变量X服从二项分布B(4,1/2)，下列结论正确的是（）A.P(X=2)=3/8B.E(X)=2C.D(X)=1D.P(X≥3)=5/1612.（5分）抛物线C：y^2=4x，焦点为F，点P(t^2,2t)。当t为实数时，下列说法正确的是（）A.P一定在C上B.当t≠0时，C在P处切线斜率为1/tC.PF=t^2+1D.C在P处的法线经过同一个定点

三、填空题：本大题共4小题，每小题5分，共20分。请把答案填写在答题栏相应位置。13.（5分）二项式(x-2/x)^6展开式中的常数项为________。14.（5分）数列{a_n}的前n项和S_n=n^2+n，则a_10=________。15.（5分）双曲线x^2/a^2-y^2/3=1的一条渐近线方程为y=(√3/2)x，则a=________。16.（5分）袋中有3个红球、2个白球，任取2个，已知至少取到1个红球，则恰好取到1个红球的条件概率为________。四、解答题：本大题共6小题，共70分。解答应写出文字说明、证明过程或演算步骤。17.（10分）已知函数f(x)=2sinxcosx+2cos^2x-1。

（1）将f(x)化为Asin(2x+φ)的形式，其中A>0，0<φ<π/2；

（2）求方程f(x)=1在区间[0,π]内的所有解。学生作答区：__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

18.（12分）数列{a_n}满足a_1=1，a_{n+1}=2a_n+2^n（n∈N^*）。

（1）设b_n=a_n/2^{n-1}，证明{b_n}为等差数列，并求a_n；

（2）求T_n=a_1+a_2+...+a_n。学生作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

19.（12分）从编号为1，2，3，4，5的五个小球中不放回地随机取出2个，设两球编号之和为X，两球编号差的绝对值为Y。

（1）求X为偶数的概率；

（2）在X不小于7的条件下，求取出的两个编号中恰有一个偶数的概率；

（3）求E(Y)。学生作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

20.（12分）如图形关系所述，四棱锥P-ABCD中，底面ABCD为边长2的正方形，PA⊥平面ABCD，PA=2。

（1）证明BD⊥平面PAC；

（2）求平面PBD与平面ABCD所成锐二面角的余弦值；

（3）若M为PC的中点，求点A到平面BDM的距离。学生作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

21.（12分）已知椭圆E：x^2/4+y^2=1，点T(0,2)，过T的动直线与E交于A，B两点，M为弦AB的中点。

（1）求椭圆E的离心率；

（2）当动直线斜率存在时，求其与E有两个公共点的斜率范围；

（3）求点M的轨迹方程。学生作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

22.（12分）已知函数f_a(x)=lnx-a(x-1)，定义域为(0,+∞)，其中a为实数。

（1）当a=1时，证明f_1(x)≤0，并指出等号成立条件；

（2）讨论方程lnx=a(x-1)在(0,+∞)内实根的个数；

（3）当a>0且a≠1时，设x_a为该方程除x=1外的另一个根，证明(x_a-1)(ax_a-1)>0。学生作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

山东济南高三数学高考冲刺B2卷参考答案与评分标准说明：选择题给出唯一答案或唯一正确组合；解答题按关键步骤给过程分，学生若采用其他正确方法，可按相应步骤酌情给分。题号123456789101112答案BBBCABCBABDABDABCDABC题号13141516答案-1602022/3分值每题5分一、选择题解析与评分标准1.答案B。考点为集合交集与一元二次不等式。B={x|1≤x≤3}，与A={x|-1≤x<3}相交得[1,3)。选项A右端点3取入，选项C、D端点与范围均不合。2.答案B。考点为复数除法和模。z=(1+2i)(1+i)/2=(-1+3i)/2，故|z|=√(1+9)/2=√10/2。3.答案B。考点为导数几何意义。f′(x)=1/(x+1)-1/2，f′(1)=0，故切线斜率为0。4.答案C。考点为等比数列。设公比为q，则3q^3=24，q=2，a_1=3/2，S_5=(3/2)(1+2+4+8+16)=93/2。5.答案A。考点为同角三角关系与二倍角。θ∈(0,π)且cosθ<0，所以sinθ=4/5，sin2θ=2sinθcosθ=-24/25。6.答案B。考点为古典概型。满足点数和不小于10且至少有一枚为6的有(4,6),(6,4),(5,6),(6,5),(6,6)共5个，样本总数36，概率为5/36。7.答案C。考点为椭圆离心率。a^2=4，b^2=3，c^2=1，e=c/a=1/2。8.答案B。考点为空间点面距离。设A(0,0,0)，B(2,0,0)，D(0,2,0)，C_1(2,2,2)，平面BDC_1为x+y-z-2=0，点A到该平面的距离为2/√3=2√3/3。9.答案ABD。考点为函数奇偶性、导数单调性和零点。f(-x)=-f(x)，A对；f′(x)=3x^2-3，在(-∞,-1)与(1,+∞)为正，B对；f(x)=x(x^2-3)有3个实根，C错；在[-2,2]比较端点与驻点值得最大值2，D对。10.答案ABD。考点为向量数量积与夹角。a·b=cosα+√3sinα=2cos(α-π/3)=1，α=0或2π/3，A、B对；|a+b|^2=|a|^2+|b|^2+2a·b=7，C错；cos夹角=1/(1·2)=1/2，D对。11.答案ABCD。考点为二项分布。P(X=2)=C_4^2(1/2)^4=3/8，E(X)=np=2，D(X)=np(1-p)=1，P(X≥3)=C_4^3/16+C_4^4/16=5/16。12.答案ABC。考点为抛物线参数点、切线与焦半径。P(t^2,2t)满足y^2=4x，A对；t≠0时由2yy′=4得y′=2/y=1/t，B对；F(1,0)，PF=√[(t^2-1)^2+4t^2]=t^2+1，C对；法线方程含t，不能经过同一定点，D错。二、填空题解析与评分标准13.答案-160。通项为C_6^kx^{6-k}(-2/x)^k，令6-2k=0得k=3，常数项C_6^3(-2)^3=-160。写出k=3得2分，算出系数得3分。14.答案20。a_n=S_n-S_{n-1}=n^2+n-[(n-1)^2+(n-1)]=2n，故a_10=20。列出通项关系得3分，代入得2分。15.答案2。双曲线x^2/a^2-y^2/3=1的渐近线为y=±(√3/a)x，由√3/a=√3/2得a=2。写出渐近线斜率得3分，求得a得2分。16.答案2/3。至少1个红球的概率为1-C_2^2/C_5^2=9/10，恰好1红1白的概率为C_3^1C_2^1/C_5^2=6/10，条件概率为(6/10)/(9/10)=2/3。事件计数正确得3分，条件概率正确得2分。

三、解答题参考答案、过程分与常见失分点17.（10分）

（1）f(x)=sin2x+cos2x=√2sin(2x+π/4)。（化简为sin2x+cos2x得3分，写成标准形式得2分）

（2）由√2sin(2x+π/4)=1，得sin(2x+π/4)=√2/2。因x∈[0,π]，故2x+π/4∈[π/4,9π/4]，取值为π/4，3π/4，9π/4，解得x=0，π/4，π。（列角范围得2分，求全解得3分）

常见失分点：漏掉端点x=0或x=π；把cos^2x化简时忘记2cos^2x-1=cos2x。18.（12分）

（1）b_{n+1}=a_{n+1}/2^n=(2a_n+2^n)/2^n=a_n/2^{n-1}+1=b_n+1，且b_1=1，所以{b_n}是首项1、公差1的等差数列，b_n=n，故a_n=n·2^{n-1}。（递推变形4分，结论2分）

（2）T_n=∑_{k=1}^nk2^{k-1}。设T_n=1+2·2+3·2^2+...+n2^{n-1}，则2T_n=1·2+2·2^2+...+n2^n，相减得-T_n=1+2+2^2+...+2^{n-1}-n2^n