辽宁省大连市2016年高三双基考试数学(理)试题(Word版,含答案)

2016年大连市高三双基测试卷

数 学（理科）

说明：1. 本试卷分第I 卷（选择题）和第II 卷（非选择题）两部分，其中第II 卷第22题～第24题为选考题，其它题为必考题．

2.考生作答时，将答案答在答题卡上，在本试卷上答题无效．考试结束后，将本试卷和答题卡一并交回．

参考公式：球的表面积公式：24R S π=，其中R 为半径.

第I 卷（选择题 共60分）

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.已知全集{2,4,6,8,10}U =，集合A ，B 满足(){8,10},{2}U U C A B A C B ==,则集合B =

（A ）{4,6}

(B) {4}

(C) {6}

(D)Φ

2.已知复数1z i =+，则4

z =

（A ）4i - (B) 4i (C) 4- (D) 4

3．已知函数()f x 定义域为R ，则命题p ：“函数()f x 为偶函数”是命题q ：

“000,()()x R f x f x ?∈=-”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．执行如图的程序框图，输出的C 的值为

（A ）3 （B ）5 （C ）8 （D ）13 5.已知互不重合的直线,a b ,互不重合的平面,αβ,给出下列四个命题，错．误．

的命题是 （A ）若a //

α，a //β，b αβ=，则a //b

(B)若βα⊥，a α⊥，β⊥b 则b a ⊥

(C)若βα⊥，γα⊥，a =γβ ，则a α⊥ (D)若α//β，a //

α，则a //β

6．《九章算术》是我国古代的数学名著，书中有如下问题：“今有五人分五钱，令上二人所得与下三

人等.问各得几何.”其意思为“已知甲、乙、丙、丁、戊五人分5钱，甲、乙两人所得与丙、丁、戊三人所得相同，且甲、乙、丙、丁、戊所得依次成等差数列.问五人各得多少钱？”（“钱”是古代的一种重量单位）.这个问题中，甲所得为 （A ）

54钱 （B ）43钱 （C ）32钱 （D ）53

钱 7．ABC ?中，2,3,60AB AC B ==∠=，则cos C =

（A

（B

） （C

） （D

8．已知点(,)x y 满足不等式组43021032190x y x y x y -+≤??

--≥??+-≤?

，则2z x y =-的最大值为

（A ）7- （B ）1- （C ）1 （D ）2

9．若抛物线2

4y x =上一点P 到其焦点F 的距离为2，O 为坐标原点，则OFP ?的面积为 （A ）

1

2

（B ）1 （C ）

32

（D ）2

10．已知直线m x y +=和圆12

2=+y x 交于B A 、两点，O 为坐标原点，若3

2

AO AB ?=

，则实数=m

（A ）1± （B ）23±

（C ）22± （D ）2

1± 11．在区间[]0,π上随机地取两个数x 、y ,则事件“sin y x ≤”发生的概率为

（A ）

1

π

（B ）

2

π

（C ）

2

1

π

（D ）

2

2

π

12．函数()f x 是定义在(0,)+∞上的单调函数，且对定义域内的任意x ，均有

3(()ln )2f f x x x --=，则()f e =

（A ）31e + （B ）32e + （C ）31e e ++ （D ）32e e ++

第Ⅱ卷(非选择题 共90分)

本卷包括必考题和选考题两部分，第13题第21题为必考题，每个试题考生

都必须做答．第22题第24题为选考题，考生根据要求做答． 二．填空题(本大题共4小题，每小题5分，共20分

)

13．双曲线22

21x y -=的渐近线方程为 . 14．10

1()2x x

-

的展开式中，4x 项的系数为 （用数字作答）. 15．数列{}n a 前n 项和2n n S =，则n a = .

16．如图，在小正方形边长为1的网格中画出了某多面体的三视图，则该多面体的外接球表面积为 .

三．解答题(本大题共6小题,共70分,解答应写出文字说明、证明过程或演算步骤) 17．（本小题满分12分） 已知函数()2sin()(0,||)f x x ω?ω?π=+><经过点7(,2),(

,2)12

12π

π-，且在区间7(,)1212

ππ

上为单调函数.

（Ⅰ）求,ω?的值； （Ⅱ）设*(

)()3

n n a nf n N π

=∈，求数列{}n a 的前30项和30S . 18.（本小题满分12分）

2015年“双十一”当天，甲、乙两大电商进行了打折促销活动，某公司分别调查了当天在甲、乙电商购物的1000名消费者的消费金额，得到了消费金额的频数分布表如下：

（Ⅰ）根据频数分布表，完成下列频率分布直方图，并根据频率分布直方图比较消费者在甲、乙电商消费金额的中位数的大小以及方差的大小（其中方差大小给出判断即可，不必说明理由）；

)

)

（第16题图）

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