2016-2017学年浙江省杭州市地区(含周边)重点中学高三(上)期中数学试卷

2016-2017学年浙江省杭州市地区(含周边)重点中学高三(上)期中数学试卷
2016-2017学年浙江省杭州市地区(含周边)重点中学高三(上)期中数学试卷

2016-2017学年浙江省杭州市地区(含周边)重点中学高三(上)

期中数学试卷

一、选择题:本大题共8个小题,每小题5分,共40分.在每小题给出的四个选项中,只有一项是符合题目要求的.

1.(5分)已知全集为R,集合A={x|2x≥1},B={x|x2﹣6x+8≤0},则A∩(?R B)=()

A.{x|x≤0}B.{x|2≤x≤4}C.{x|0≤x<2或x>4} D.{x|x<2或x>4} 2.(5分)已知a,b∈R,且a>b,则下列不等式恒成立的是()

A.a2>b2B.>1 C.lg(a﹣b)>0 D.()a<()b

3.(5分)在△ABC中,“sinB=1”是“△ABC为直角三角形”的()

A.充分不必要条件 B.必要不充分条件

C.充要条件D.既不充分也不必要条件

4.(5分)设函数y=xcosx﹣sinx的图象上的点(x0,y0)处的切线的斜率为k,若k=g(x0),则函数k=g(x0)的图象为()

A.B.C.

D.

5.(5分)若+=,则sinαcosα=()

A.﹣ B.C.﹣或1 D.或﹣1

6.(5分)已知函数f(x)=﹣kx2(k∈R)有四个不同的零点,则实数k的

取值范围是()

A.k<0 B.k<1 C.0<k<1 D.k>1

7.(5分)已知实数对(x,y),设映射f:(x,y)→(,),并定义|(x,

y)|=,若|f[f(f(x,y))]|=4,则|(x,y)|的值为()

A.4 B.8 C.16D.32

8.(5分)在△ABC中,角A、B、C所对的边分别为a、b、c,c﹣b=6,c+b﹣a=2,且O为此三角形的内心,则?=()

A.4 B.5 C.6 D.7

二、填空题(共7个小题,满分21分,将答案填在答题纸上)

9.(3分)若a=3,b=log43,则log3a=,a与b的大小关系是.10.(3分)已知函数y=log a(x﹣1)+3,(a>0且a≠1)的图象恒过点P,则P 的坐标是,若角α的终边经过点P,则sin2α﹣sin2α的值等于.11.(3分)将函数f(x)=sin(x+)图象上各点的横坐标缩短到原来的倍(纵坐标不变),再把得到的图象向右平移个单位,得到的新图象的函数解析式为g(x),g(x)的单调递减区间是.

12.(3分)已知x∈R,函数f(x)=为奇函数,则t=,g(f (﹣2))=.

13.(3分)已知△ABC中,AB=4,AC=2,|λ+(2﹣2λ)|(λ∈R)的最小值为2,若P为边AB上任意一点,则?的最小值是.

14.(3分)在等腰△ABC中,AB=AC,AC边上的中线BD长为6,则当△ABC的面积取得最大值时,AB的长为.

15.(3分)记max{m,n}=,设F(x,y)=max{|x2+2y+2|,|y2﹣2x+2|},其中x,y∈R,则F(x,y)的最小值是.

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