2019届苏州大学高考考前指导卷 (2)

2019届苏州大学高考考前指导卷 (2)
2019届苏州大学高考考前指导卷 (2)

2019届苏州大学高考数学指导卷(2)

一、填空题(本大题共14小题,每小题5分,共计70分.不需要写出解答过程,请将答案填写在答题卡相应的位置上.........

.) 1、已知集合},1{a A =,3}{2,=B ,{3}=B A ,则=B A _______.

2、已知i 是虚数单位,复数i

i

z ++=

243的虚部为_______. 3、某公司共有1000名员工,下设若干部门,现采用分层抽样方法,从全体员工中抽取一个

容量为80的样本,已知广告部门被抽取了4个员工,则广告部门的员工人数为_______.

4、已知)

,(02是双曲线)0(122

2

>=-b b

y x 的一个焦点,则b 的值是_______. 5、右图是一个算法的程序框图,当输入值x 为8时,则其输出,输出y 的结果是_________.

6、函数)1lg()(-=

x x f 的定义域为___________.

7、在不透明的布袋中有大小相同的白球、黑球各1个,红球2个.现从中随机摸出2个球, 则其颜色不同的概率是___________.

8、若数列}{n a 满足151=a ,且 2331-=+n n a a ,则使01<+k k a a 的k 值为_______. 9、已知一个凸多面体共有9个面,所有棱长均为1,其平面展开图如图所示,则该凸名面体的体积I=____________.

10、已知函数x x x f cos 3sin )(-=, 且4)()(21-=?x f x f , 则 21x x +的最小值为__________.

11、 已知α,β均为锐角,且ββαtan 6)tan(=+,则αsin 的最大值为__________.

12、设函数 ?????>≤+=0,log 0

,1)(4x x x x x f ,若关于x 的方程a x f =)(有四个不同的解

4321,,,x x x x ,且4321x x x x <<<,则4

2

32131

)(x x x x x +

+的取值范围是_________. 13、如图,等边△ABC 的边长为2,顶点B , C 分别在x 轴的非负半轴,y 轴的非负半轴

上滑动,M 为AB 的中点,则M O A O

?的最大值为_________.

14、已知函数)(2

1)(2

R a x ae x f x

∈-

= .若函数)(x f 有两个极值点21,x x , 212≥x x ,

则实数a 的取值范围为_________.

二、解答题(本大题共6小题,共计90分.请在答题纸指定区域.......

内作答,解答应写出文字说明,证明过程或演算步骤.) 15、(本小题满分14分)

已知函数)20)(2sin(2)(π??<<+=x x f 的图象过点,-2)2

(

π

.

(1)求?的值;

(2)若56)2

(=

α

f ,02<<-απ,求 )6

2sin(π

α-的值

16、(本小题满分14分)

如图,在四棱锥ABCD P -中,底面ABCD 为平行四边形,E 为侧棱PA 的中点,O 为AC 与BD 的交点,CD DE ⊥, AD PD =.

(1)求证:直线∥OE 平面PCD ; (2)求证:平面APD ⊥平面PAB .

17、(本小题满分14分)

在平面直角坐标系xoy 中,已知圆C 过点(1,1)P ,且与圆M :

)0()2()2(222>=-+-r r y x 关于直线02=++y x 对称.

(1)求 圆 C 的方程;

(2)过点P 作两条相异直线分别与圆C 相交于B A ,两点,设直线PA 与直线PB 的倾斜角分别为)(,βαβα≠ ,且满足 βαsin sin = ,试判断直线AB 的斜率是否为定值,井说明理由.

18、(本小题满分16分)

在一片生态草原上,某花卉观赏区的边界道路是圆弧CD , B A ,为两处游客中心,其中 ABCD 为矩形,

且km AB 8= ,km BC 24= .圆弧CD 以AB 的中点M 为园心,MC 为半径.为了保护草原的生态环境,方便游客观赏游览,考虑在草原上修建道路。现提供两种设计方案:方案在弧CD 上取中点N ,建造NO BO AO ,,三条道路,其中点O 在线段NM 上(不包括两端点);方案二:在弧CD 上任取点 N ,直接修建两条道路BN AN , ;方案二

中每公里道路的造价是方案一中的每公里道路造价的

2

3

倍。 (1)若在方案一中,点N 这在弧CD 的中点时的建造费用与方案二建造费用相等,求此时方案一中O 点的位置:

(2)从节省费用的角度考息,试问两种方案中哪种方案更合理,请说明理由

19、(本小题满分16分)

已知函数)0,,(4)(2

3

≠∈-+=a R b a a bx ax x f 且.

(1)若函数)(x f 恰有两个零点,求a

b

的值;

(2)若对任意的]1,4[--∈x , 2

4)(0x x f ≤≤恒成立,求b a +的取值范围。

20、(本小题满分16分)

如果数列}{n c 满足“对任意正整数j i j i ≠,,, 都存在正整数k ,使得j i k c c c ?= , 则称数列}{n c 为“封闭数列"”。已知等差数列}{n a 的首项01>a ,公差为d .

(1)若3,21==d a ,试判断数列}{n a 是否为“封闭数列”,并说明理由;

(2)若数列}{n a 为“封闭数列”,且存在正整数k ,使得 3=k a ,求数列}{n a 的通项公 式.

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