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2017-2018年上海市华师大二附中高三(上)期中数学试卷及参考答案

2017-2018年上海市华师大二附中高三(上)期中数学试卷及参考答案
2017-2018年上海市华师大二附中高三(上)期中数学试卷及参考答案

2017-2018学年上海市华师大二附中高三(上)期中数学试卷

一、填空题

1.已知集合A={1,3,2m﹣1},B={3,m2},若B?A,则实数m=.2.若组合数C=,则实数m=.

3.不等式≤3的解集为.

4.如图,在直三棱柱ABC﹣A1B1C1中,∠ACB=90°,AA1=2,AC=BC=1,则异面直线A1B与AC所成角的大小是(结果用反三角函数值表示).

5.若复数z满足3z+=1+i,期中i为虚数单位,则|z|=.

6.已知抛物线y2=16x的焦点恰好是双曲线﹣=1的右焦点,则双曲线的渐

近线方程为.

7.三阶行列式第2行第1列元素的代数余子式为﹣10,则k=.

8.已知函数f(x)是定义在R上的周期为2的奇函数,当0<x<1时,f(x)=8x,则f(﹣)=.

9.给出四个函数:①y=cosx;②y=x2;③y=2x;④y=log x,从其中任选2个,则事件A:“所选2个函数图象有且仅有2个公共点”的概率是.

10.设等比数列{a n}的前n项和为S n,若a4,a3,a5成等差数列,且S k=33,S k+1=﹣63,其中k∈N*,则S k

的值为.

+2

11.如图所示,正八边形A1A2A3A4A5A6A7A8的边长为2,若P为该正八边形上的动点,则?的取值范围.

12.在平面直角坐标系中,定义d(A,B)=max{|x1﹣x2|,|y1﹣y2|}为两点A (x1,y1)、B(x2,y2)的“切比雪夫距离”,又设点P及l上任意一点Q,称d(P,Q)的最小值为点P到直线l的“切比雪夫距离”,记作d(P,l),给出四个命题,正确的是

①对任意三点A、B、C,都有d(C,A)+d(C,B)≥d(A,B);

②到原点的“切比雪夫距离”等于1的点的轨迹是正方形;

③已知点P(3,1)和直线l:2x﹣y﹣1=0,则d(P,l)=;

④定点F1(﹣c,0)、F2(c,0),动点P(x,y)满足|d(P,F1)﹣d(P,F2)|=2a(2c>2a>0),则点P的轨迹与直线y=k (k为常数)有且仅有2个公共点.

二、选择题

13.数列{a n}中,a n=,则数列{a n}的极限为()

A.0 B.1 C.0或1 D.不存在

14.“ω=1”是“函数f(x)=sin2ωx﹣cos2ωx的最小正周期为π”的()

A.充分必要条件B.充分不必要条件

C.必要不充分条件 D.既不充分又必要条件

15.下列命题中真命题是()

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