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四川省2019年普通高校职教师资和高职对口招生统一考试数学试题

四川省2019年普通高校职教师资和高职对口招生统一考

试数学试题

本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。第Ⅰ卷1至2页,第Ⅱ卷3至4页,共4页。满分150分,考试时间120分钟。考生作答时,须将答案答在答题卡上,在本试卷、草稿纸上答题无效。考试结束后,将本试题卷和答题卡分别收回。

第Ⅰ卷(选择题 共60分)

注意事项:

1、选择题必须使用2B 铅笔在答题卡上将所选答案对应的标号涂黑.

2、第Ⅰ卷共1大题,15小题,每小题材4分,共用60分.

一、选择题(本大题共15小题,每小题4分,共60分。每小题给出A,B,C,D 四个选项,其中只

有一项是符合题目要求的。 1. 设集合{}{}2,2,1,2A B =-=-,则A B =

{}

{}

{}

{}

.2.2,1.2,2.2,1,2A B C D -----

2.

sin 26ππ?

?+= ???函数(

)f x =的定义域

()

()

()

()

.1,1.1,.,1.1,A B C D --+∞-∞+∞

3. 已知角α的终边经过点()1,1-,则cos α=

11 (2222)

A B C D -

-

4. 已知平面向量()()()5,43,2,7,6===a ,b c ,则a +b -c =

()()()()

.0,0.1,0.0,1.1,1A B C D

5. 绝对值不等式34x -<的解集为 ()

()

()

()

()

.,1.7,.1,7.,17,A B C D -∞-+∞--∞-+∞

6. 函数()sin 23f x x π?

?=+ ??

?在区间[],ππ-上的图像大致为

7. 与直线3270x y --=垂直的直线的斜率是 2

233....

3

3

2

2

A B C D -

-

8. 椭圆22

143

x y +=的焦点坐标是

()(

)

(

))

()(

)

(

))

.1,0,1,0.,

.2,0,2,0.,

A B C D --

9. 已知球的半径为6cm ,则它的体积为 3

3

33

.36.144.288.864A cm B cm C cm D cm ππππ

10. 计算:1

4

1lg5lg 2016-??

++= ?

??

.1.2.3.4A B C D

11. “0x >”是“1x >”的

....A B C D 充分且不必要条件必要且不充分条件

充要条件既不充分也不必要条件

12. 某科技公司从银行贷款500万元,贷款期限为6年,年利率为005.76,利息按“复利计息法”(把当年的本金与利息的和作为次年的本金来计算利息的方法)计算. 如果6年后一次性还款,那么这家科技公司应偿还银行的钱是

5656.5000.9424.5000.9424.500 1.0576.500 1.0576A B C D ????万元万元万元

万元

13. 已知31211

ln ,2,log 23

a b c -===,则,,a b c 的大小关系为

....A b c a B b a c C c b a

D c a b >>>>>>>>

14.已知甲、乙两个城市相距120千米,小王开汽车以100千米/时匀速从甲城市驶往乙城市,到达乙城

市后停留1小时,再以80千米/时匀速返回甲城市.汽车从甲城市出发时,时间x (小时)记为0.在这辆汽车从甲城市出发至返回到甲城市的这段时间内,该汽车离甲城市的距离y (千米)表示成时间x (小

时)的函数为

100,0 1.2,

.80, 1.2.x x A y x x ≤≤?=?>? 100,0 1.2,.12080, 1.2.x x B y x x ≤≤?=?->? 100,

0 1.2,.120, 1.2 2.212080 2.2 3.7

x x C y x x x ≤≤??

=<≤??-<≤?

100,0 1.2,.120,

1.2

2.229680 2.2

3.7x x D y x x x ≤≤??=<≤??-<≤? 15.函数()()()()()2222

12310f a a a a a =-+-+-+???+-的单调区间为

[)[)[)[).5,.5.5,.6,.6.5,A B C D +∞+∞+∞+∞

第 Ⅱ 卷(非选择题 共90分)

注意事项:

1. 必须使用0.5毫米的黑色墨迹签字笔在答题卡上题目所指示的答题区域内作答,不得超出题框区域。答在试题卷、草稿纸上答题无效。

2. 第Ⅱ卷共2个大题,11小题,共90分。

二、填空题(本大题共5小题,每小题4分,共20分)。

16. 已知平面向量()()2,13,2---a =,b =,则?a b = ▲ . 17. 双曲线2

213

y

x -

=的离心率为 ▲ . 18. 二项式6

21x x ?

?+ ??

?的展开式中常数项为 ▲ .(用数字作答)

19. 为落实精准扶贫工作,某单位计划从7名优秀干部中任选3名到贫困村驻村工作,不同的选派

方案有 ▲ 种.

20.

计算:0000tan 20tan 4020tan 40+= ▲ .(用数字作答)

三、解答题(本大题共6小题,共70分,解答应写出必要的文字说明、证明过程或推演步骤)。 21.(本小题满分10分)

设等差数列{}n a 的前n 项和为n S ,5492,108a a S ==,求数列{}n a 的通项公式.

22.(本小题满分12分)

为了弘扬勤俭节约的中华传统美德,某校开展了节约用水教育与问卷调查.调查得知某地区300居民某月的用水量(单位:吨),将这些数据按照[)[)[)[)[)[]0,1,1,2,2,3,3,4,4,5,5,6分成6组,制成了如图所示的频率直方图.

⑴求频率直方图中a 的取值;

⑵若每组中居民的用水量用该组的中间值来估计(如[)0,1的中间 值为0.5),试估计该地区居民这个月的人均用水量(单位:吨).

23.(本小题满分12分)

在ABC ?中,内角,,A B C 的对边分别为,,a b c ,且2,tan 2a C ==-,ABC ?的面积为2.

⑴求边b 的长; ⑵求cos B 的值.

24.(本小题满分12分)

如图,已知在长方体1111ABCD A B C D -

中,11,AB BC AA ===E 为 1AA 的中点.

⑴证明: ∥平面 ;

⑵求 与平面 所成的角的大小.

25.(本小题满分12分)

已知圆O 的方程是2

2

1x y +=,三点()()()

222,2,,2,,2A B b b C c c --互不重合,直线AB 与圆O

相切.

⑴求证:2

3410b b +-=;

⑵若直线AC 与圆O 相切,证明:直线BC 与圆O 也相切.

26.(本小题满分12分)

已知函数()f x 的定义域为R ,并且对一切实数x ,都有()()()()0,2f x f x f x f x -+=--=-成 立 .当()0,1x ∈时,()sin 1f x x π=+. (1).求()()0,1f f 的值;

(2).当()11,13x ∈时,求()f x 的解析式.

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