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高考最新-执信中学2018二模试卷 精品

高考最新-执信中学2018二模试卷 精品
高考最新-执信中学2018二模试卷 精品

2018执信中学二模试卷

2018.4

第Ⅰ卷(选择题 共60分)

注意事项:

1.答第Ⅰ卷前,考生务必将自己的姓名、准考号、考试科目用铅涂写在答题卡上。 2.每小题选出答案后,用铅笔把答题卡上对应题目的答案标号涂黑,如需改动,用橡 皮擦干净后,再选涂其它答案,不能答在试题卷上。

参考公式:

如果事件A 、B 互斥,那么

球的表面积公式

P (A+B )=P (A )+P (B ) 24R S π=

其中R 表示球的半径

如果事件A 、B 相互独立,那么 球的体积公式

P (A ·B )=P (A )·P (B )

33

4

R V π= 其中R 表示球的半径

如果事件A 在一次试验中发生的概率是P.

那么n 次独立重复试验中恰好发生k 次的概

率 k n k

k n n P P C k P --=)1()(

一、选择题(每题只有一个正确答案,每小题5分,共60分)

1.已知集合,},3|||{},02|{2R B A a x x B x x x A =?<-=>--=若集合,则实数a 的取值 范围是 ( ) A .[1,2] B .(-1,2) C .[-1,2] D .(-2,1) 2.sin2490°= ( )

A .-21

B .21

C .-23

D .2

3

3.在数列*)(233,15,}{11N n a a a a n n n ∈-==+中,则该数列中相邻两项的乘积是负数的

( ) A .2221a a ?

B .a 22·a 23

C .a 23·a 24

D .a 24·a 25

4.要使函数]2,1[122

在+-=ax x y 上存在反函数,则a 的取值范围是 ( )

A .1≤a

B .2≥a

C .1≤a 或2≥a

D .21≤≤a 5.≤||x 2的必要非充分条件是 ( )

A .3|1|≤+x

B .2|1|≤+x

C .1|1|≤+x

D .1|1|≤-x

6.已知椭圆1),0(122

222222=->>=+b

y a x b a b y a x 双曲线和抛物线)0(22>=p px y 的离

心率分别为e 1、e 2、e 3,则 ( ) A .e 1e 2> e 3 B .e 1e 2= e 3 C .e 1e 2< e 3 D .e 1e 2≥e 3

7.已知长方体ABCD -A 1B 1C 1D 1中,AB=BC=4,CC 1=2,则直线BC 1和平面DBB 1D 1所成 角的正弦值为 ( )

A .23

B .25

C .510

D .10

10

8.函数123+--=x x x y 在闭区间[-1,1]上的最大值是 ( )

A .2732

B .2726

C .0

D .-27

32

9.随机变量ξ的概率分布规律为),4,3,2,1()

1()(=+=

=n n n a

n P ξ其中a 是常数,则 )25

21(<<ξP 的值为 ( )

A .32

B .43

C .54

D .6

5

10.设a 、b 是方程0cos cot 2

=-+θθx x 的两个不相等的实数根,那么过点A (a ,a 2)和 B (b ,b 2)的直线与圆122=+y x 的位置关系是 ( )

A .相离

B .相切

C .相交

D .随θ的值变化而变化

11.对于项式)()1

(

3+∈+N n x x

n ,四位同学作出了四种判断: ①存在n ∈N +,展开式中有常数项; ②对任意n ∈N +,展开式中没有常数项; ③对任意n ∈N +,展开式中没有x 的一次项; ④存在n ∈N +,展开式中有x 的一次项. 上述判断中正确的是 ( ) A .①与③ B .②与③ C .②与④ D .④与①

12.已知定义在R 上的函数y=f(x)满足下列三个条件:①对任意的x ∈R 都有);()4(x f x f =+②对

于任意的2021≤<≤x x ,都有),()(21x f x f <③)2(+=x f y 的图象关于y 轴对称,则下列结论中,正确的是 ( ) A .)7()5.6()5.4(f f f << B .)5.6()7()5.4(f f f << C .)5.6()5.4()7(f f f <<

D .)5.4()5.6()7(f f f <<

第ll 卷

二、填空题:本大题共4小题,每小题4分,共16分.

13.在数列{}n a 中,31=a ,且对任意大于1的正整数n ,点(),1-n n a a 在直线

03=--y x 上,则=+∞→2

)1(lim

n a n

n .

14.已知n

x

x )1(-

的展开式中所有二项式系数的和为512,则展开式中3x 项的系数为 . 15.在△ABC

中,有命题①;=-②=++;③若

0)()(=-?+,则△ABC 为等腰三角形;④若0>?,则△ABC 为锐角

三角形. 上述命题正确的是 .

16.已知四个面都是直角三角形的三棱锥,其中三个面展开后构成

一直角梯形ABCD ,如图AD ⊥AB ,AD ⊥DC ,AB=2,BC=3, CD=1,则这个三棱锥外接球的表面积是 (结果可含π).

三、解答题:(本大题共6小题,共74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c bx ax x x f +++=23)(有极大值)(αf 和极小值)(βf . (1)求)(αf +)(βf 的值;

(2)设曲线y=f(x)的极值点为A 、B ,求证:线段AB 的中点在y=f(x)上.

D C

A B

18、(本小题满分12分)

已知函数f (x )=3x +k (k 为常熟),A(-2k,2)是函数y=)(1

x f -图像上一点

(Ⅰ)求实数k 的值及函数y=)(1

x f -的解析式

(Ⅱ)将y=)(1

x f -的图像沿x 轴向右平移3个单位得到的y=g(x)图像,求函数

F(x)=2)(1

x f --g(x)的最小值.

19.(本小题满分12分)

如图,PA⊥平面AC,四边形ABCD是矩形,E、F分别是AB、PD的中点.

(Ⅰ)求证:AF∥平面PCE;

CD=3,求点F到平面PCE的距离.

20.(本小题满分12分) 设函数.],

1,0(,1)(2

+∈∈+++-=R a x a x x a x f

(Ⅰ)若]1,0()(在x f 上是增函数,求a 的取值范围; (Ⅱ)求]1,0()(在x f 上的最大值.

21.(本题满分12分)

某医药研究所开发一种新药,如果成人按规定的剂量服用,据监测:服药后每毫升血液中的含药量y与时间t之间近似满足如图所示的曲线.

(1)写出服药后y与t之间的函数关系式;

(2)据测定:每毫升血液中含药量不少于4微克时治疗疾病有效,假若某病人一天中第一次服药时间为上午7:00,问一天中怎样安排服药的时间(共4次)效果最佳?

(22)(本小题满分14分)

若数列{n a }的通项21n a n =-,设数列{n b }的通项1

1n n

b a =+,又记n T 是数列{n b } 的前n 项的积.

(Ⅰ)求1T ,2T ,3T 的值; (Ⅱ)试比较n T 与1+n a 的大小,并证明你的结论.

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