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2016学年浙江省温州中学高一下学期期末数学试卷及参考答案

2016学年浙江省温州中学高一下学期期末数学试卷及参考答案
2016学年浙江省温州中学高一下学期期末数学试卷及参考答案

2015-2016学年浙江省温州中学高一(下)期末数学试卷

一、选择题:本大题共10小题.每小题4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.(4分)已知集合A={2,3,4},B={2,4,6,8},C={(x,y)|x∈A,y∈B,且log x y∈N*},则C中元素个数是()

A.9 B.8 C.3 D.4

2.(4分)已知△ABC的内角A,B,C满足sin2A+sin(A﹣B+C)=sin(C﹣A﹣B)+,面积S满足1≤S≤2,记a,b,c分别为A,B,C所对的边,在下列不等式一定成立的是()

A.bc(b+c)>8 B.ab(a+b)>16C.6≤abc≤12 D.12≤abc≤24 3.(4分)若函数f(x)=x2+e x﹣(x<0)与g(x)=x2+ln(x+a)图象上存在关于y轴对称的点,则a的取值范围是()

A.(﹣)B.()C.()D.()4.(4分)函数y=sin(2x+φ)的图象沿x轴向左平移个单位后,得到一个偶函数的图象,则φ的一个可能的值为()

A. B.C.0 D.

5.(4分)在平面直角坐标系中,O是坐标原点,两定点A,B满足||=||=?=2,则点集{P|=λ+μ,|λ|+|μ|≤1,λ,μ∈R}所表示的区域的面积是()

A.B.C.D.

6.(4分)下列说法正确的是()

A.存在α∈(0,),使sinα+cosα=

B.y=tanx在其定义域内为增函数

C.y=cos2x+sin(﹣x)既有最大、最小值,又是偶函数

D.y=sin|2x+|的最小正周期为π

7.(4分)如图,半径为1的半圆O与等边三角形ABC夹在两平行线l1,l2之间,

l∥l1,l与半圆相交于F,G两点,与三角形ABC两边相交于E,D两点.设弧

的长为x(0<x<π),y=EB+BC+CD,若l从l1平行移动到l2,则函数y=f(x)的图象大致是()

A.B.C.

D.

8.(4分)在如图所示的空间直角坐标系O﹣xyz中,一个四面体的顶点坐标分别为(0,0,2),(2,2,0),(1,2,1),(2,2,2),给出的编号为①,②,③,④的四个图,则该四面体的正视图和俯视图分别为()

A.①和②B.③和①C.④和③D.④和②

9.(4分)设等差数列{a n}满足:

=1,公差d∈(﹣1,0).若当且仅当n=9时,数列{a n}的前n项和S n取得最大值,则首项a1取值范围是()A.(,)B.(,)C.[,]D.[,] 10.(4分)已知二次函数f(x)=ax2+bx(|b|≤2|a|),定义f1(x)=max{f(t)|﹣1≤t≤x≤1},f2(x)=min{f(t)|﹣1≤t≤x≤1},其中max{a,b}表示a,b

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