(完整word版)山西省2017年对口升学考试真题

(完整word版)山西省2017年对口升学考试真题
(完整word版)山西省2017年对口升学考试真题

山西省2017年对口升学考试

数 学

一 单项选择题

1.用列举法表示“方程0652=+-x x 的所有解”构成的集合是( )

A {}2

B φ

C {}3

D {}32,

2.数列Λ,1,1,1,1,1,1---的一个通项公式为( )

A 1-=n a

B 1=n a

C n n a )1(-=

D 1

)1(--=n n a

3.5lg 2lg +的值是( )

A 2

B 1

C 3

D 4

4.下列哪对直线互相平行( )

A 5:,2:21=-=x l y l

B 52:,12:21-=+=x y l x y l

C 5:,1:21--=+=x y l x y l

D 53:,13:21--=+=x y l x y l

5 下列函数中,既是偶函数又在区间)0,(-∞上单调递减的是( ) A x y 1

= B x e y = C 12+-=x y D 23x y =

6.若,51

2sin =α则=αcos ( ) A 2523

- B 2523

C 51

D 54

7.在ABC ?中,,30,34,4?=∠==A b a 则C ∠的度数为( )

A ?30

B ?30或 ?90

C ?60

D ?60或?120

8.顶点在原点,对称轴是x 轴,焦点在直线01243=--y x 上的抛物线方程是( )

A x y 162=

B x y 122=

C x y 162-=

D x y 122-=

9.设向量)3,(),1,2(x b a =-=ρρ平行,则=x ( ) A 23

- B 23

C 6-

D 6

10.将5人排成一排照相,其中b a ,两人不能相邻的概率为( )

A 52

B 53

C 51

D 24

1 二 填空题

1.设集合{}{}R x x x Q P ∈≤==,24,3,2,1,,则=Q P I

2.等差数列{}n a 中,,298,3,11===n a d a 则=n

3.x y 2sin 2

1=的最小正周期=T 4.函数232x x y +-=的定义域

5.=-?)1(sin 256log 2

6.二项式12332)2

(x x +展开式的中间项为

7.抛物线)0(22>=p px y 的顶点到准线的距离为4,则=p

8.5)1234(转化为十进制数为

三 简答题

1(6分)设等差数列{}n a 的公差是正数,且4,125362-=+-=a a a a ,求前20项的和 2(6分)在ABC ?中,若,2

3,31==∠=?ABC S B BC π

,求角C 3 (6分) 已知b a ρρ,是平面上不共线的两个非零向量,且,1),3,4(=-=b a ρρ且0=?b a ρρ,求

向量b ρ的坐标

4.(6分)课外兴趣小组共有15人,包括9名男生,6名女生,其中1名为组长,现要选3人参加数学竞赛,分别求出满足下列各条件的不同选法种数

(1) 要求组长必须参加

(2)要求选出的3人中至少有1名女生

5.(8分)已知圆0864:2

2=++-+y x y x C ,求与直线012:=--y x l 平行的圆C 的切线方程

6.(6分)已知两点)4,(),6,2(-m B A ,其中),1(n M -为AB 的中点,求n m +

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