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山西大学附中高中数学（高三二轮）导学设计 编号42 选择填空专项训练（四十二） 一、选择题（本大题共12小题，每小题

5分，共60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．复数2(1i z i i

-=+是虚数单位）在复平面内对应的点位于象限为( ) A ．第一象限 B ．第二象限 C ．第三象限 D ．第四象限

2．已知函数()y f x =的图象关于直线1x =-对称，且当(0,)x ∈+∞时，有1()f x x

=，当(,2)x ∈-∞-时，()f x 的解析式为( )

A ．1()f x x =-

B ．1()2f x x =--

C ．1()2f x x =+

D ．1()2

f x x =-+ 3．设曲线2y ax =在点(1,)a 处的切线与直线260x y --=平行，则(a = )

A ．1

B ．12

C ．12

- D ．1- 4．设x ，y 满足约束条件10103x y x y x -+??++???

，则23z x y =-的最小值是( )

A ．7-

B ．6-

C ．5-

D ．3-

5．将直径为2的半圆绕直径所在的直线旋转半周而形成的曲面所围成的几

何体的表面积为( )A ．2π B ．3π C ．4π D ．6π

6．运行如图所示的程序框图，若输出的y 值为2-，则判断框中应填写的

条件是( )

A ．5i >？

B ．3i >？

C ．6i >？

D ．4i >？

7．直线20x y ++=分别与x 轴，y 轴交于A ，B 两点，点P 在圆

22(2)2x y -+=上，则ABP ?面积的取值范围是( )

A ．[2，6]

B ．[4，8]

C ．[2，32]

D ．[22，32]

8．如图是一个几何体的三视图，根据图中数据，可得该几何体的表面积是( )

A ．9π

B ．10π

C ．11π

D ．12π

9．关于统计数据的分析，有以下几个结论：

①将一组数据中的每个数据都减去同一个数后，方差没有变化；

②绘制频率分布直方图时，各小长方形的面积等于相应各组的

组距；③一组数据的方差一定是正数；

④如图是随机抽取的200辆汽车通过某一段公路时的时速分布直方图，根据这个直方图，

可以得到时速在(50,60)的汽车大约是60辆．则这4种说法中错误的个数是( )

A ．1

B ．2

C ．3

D ．4

10．双曲线22221(0,0)x y a b a b

-=>>的左、右焦点分别为1F ，2F ，过1F 作倾斜角为60?的直线与y 轴和双曲线的右支分别交于A ，B 两点，若点A 平分线段1F B ，则该双曲线

的离心率是( )

A B ．2 C ．2 D 1

11．已知定义在R 上的函数()f x 满足2()()42f x f x x +-=+，设2()()2g x f x x =-，若

()g x 的最大值和最小值分别为M 和m ，则(M m += )

A ．1

B ．2

C ．3

D ．4

12．等比数列{}n a 的前n 项和为n S ，已知1S ，22S ，33S 成等差数列，则数列{}n a 的公

比为( )

A ．12

B ．13

C ．25

D ．49

二、 填空题（本大题共4小题，每小题5分，共20分．）

13．已知函数()cos(3)()2

f x x x R π=+∈，给出如下结论： ①函数()f x 的最小正周期为23

π； ②函数()f x 是奇函数； ③函数()f x 的图象关于点(,0)3

π对称；④函数()f x 在区间[0,]3π

上是减函数． 其中正确命题的序号是 ．（写出所有正确命题的序号）

14．已知命题:(0)p x R x ?∈≠，12x x +，则:p ? ． 15．在ABC ?中，角A ，B ，C 所对的边分别为a ，b ，c ，已知222a b c -=，且

cos 3cos a B b A =，则边c = ． 16．给定两个长度为1的平面向量OA 和OB ，它们的夹角为120?．如图所示，点C 在

以O 为圆心的圆弧AB 上变动．若OC xOA yOB =+，其中x ，y R ∈，则52

x y +的最大值是 ．

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