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海珠区2014学年高三综合测试（二）

数学（理科）

2014.11

本试卷共4页，21小题，满分150分。考试用时120分钟。注意事项：

1．答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名和考生号、试室号、座位号填写在答题卡上。

2．选择题每小题选出答案后，用2B 铅笔把答题卡上对应题目选项的答案信息点涂黑，如需改动，用橡皮擦干净后，再选涂其他答案，答案不能答在试卷上。

3．非选择题必须用黑色字迹钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅笔和涂改液。不按以上要求作答的答案无效。

4．考生必须保持答题卡的整洁。考试结束后，将答题卡交回。参考公式：锥体体积公式Sh V 3

,其中S 为锥体的底面积，h 为锥体的高. 一、选择题：本大题共8小题，每小题5分，满分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．已知集合{}{}

4),(,2),(=-==+=y x y x B y x y x A ，那么集合A B 为

A ．(){}1,3-

B ．()3,1-

C ．{

}3,1- D ．(){}3,1-

2．若复数z 满足()1i z i -=,则z 在复平面内对应的点位于

A ．第一象限

B ．第二象限

C ．第三象限

D ．第四象限

3．函数cos 2sin 2y x x =-的一条对称轴为 A. 4

x p

B. 8x p =

C. 8x p =-

D. 4

x p =-

4．已知向量,a b 的夹角为120，2a =，且8a b ?=-，则b =

A ．6

B ．7

C ．8

D ．9

5．函数ln y x =

与y =-

6．阅读如图所示的程序框图，输出的结果S 的值为

A ．0

D ．7．已知椭圆22

19x y +=与双曲线22221x y a b

共焦点12,F F ，设它们在第一象限的交点为P ，且120PF PF ?=，则双曲线的渐近线方程为

A ．y =

B ．y x =

C ．y x =

D ．y x = 8．若实数,,,a b c d 满足222(3ln )(2)0b a a c d +-+-+=，则22()()a c b d -+-的最小

值为

A ．8

B ．

C ．2 D.

二、填空题：本大题共7小题，考生作答6小题，每小题5分，满分30分．（一）必做题（9～13题）

9．已知{}n a 是等差数列，124a a +=，91028a a +=，则该数列前10项和10S = ． 10．一个几何体的正（主）视图和侧（左）视图都是边长为2的等边

三角形，俯视图如图所示，则这个几何体的体积为 . 11．不等式13x x +-≤的解集是．

12．从5种不同的书中买3本送给3名同学，每人各1本，则不同的送法

有种（用数字作答）． 13．给出下列四个命题：

①已知ξ服从正态分布()

2,0σN ，且()4.022=≤≤-ξP ，则()2.02=>ξP ； ②“2450x x --=”的一个必要不充分条件是“5x =”；

③函数()3132

f x =x x +-在点()()2,2f 处的切线方程为3y =-；

④命题:,tan 1p x x ?∈=R ；命题2:,10q x x x ?∈-+>R ．则命题“()p q ∧?”是

假命题．

其中正确命题的序号是．

（二）选做题（14、15题，考生只能从中选做一题）

14．（坐标系与参数方程选做题）在极坐标中，圆

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