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2019年上海市春季高考数学模拟试题及答案

2019年上海市春季高考数学模拟试题及答案
2019年上海市春季高考数学模拟试题及答案

2019年上海市春季高考数学模拟试题

1. 设集合{1,2,3}A =,集合{3,4}B =,则A

B = ; 2. 不等式|1|3x -<的解集为 ;

3. 若复数z 满足2136z i -=+(i 是虚数单位),则z = ;

4. 若1cos 3α=,则sin()2

πα-= ; 5. 若关于x 、y 的方程组2436

x y x ay +=??+=?无解,则实数a = ;

6. 若等差数列{}n a 的前5项的和为25,则15a a += ;

7. 若P 、Q 是圆222440x y x y +-++=上的动点,则||PQ 的最大值为 ;

8. 已知数列{}n a 的通项公式为3n n a =,则123lim n n n

a a a a a →∞+++???+= ; 9. 若2

()n

x x +的二项展开式的各项系数之和为729,则该展开式中常数项的值为 ; 10. 设椭圆2

212

x y +=的左、右焦点分别为1F 、2F ,点P 在该椭圆上,则使得△12F F P 是 等腰三角形的点P 的个数是 ;

11. 设1a 、2a 、…、6a 为1、2、3、4、5、6的一个排列,则满足1234||||a a a a -+-+ 56||3a a -=的不同排列的个数为 ;

12. 设a 、b R ∈,若函数()a f x x b x

=+

+在区间(1,2)上有两个不同的零点,则(1)f 的取 值范围为 ;

13. 函数2()(1)f x x =-的单调递增区间是( )

A. [0,)+∞

B. [1,)+∞

C. (,0]-∞

D. (,1]-∞

14. 设a R ∈,“0a >”是“10a

>”的( )条件 A. 充分非必要 B. 必要非充分 C. 充要 D. 既非充分也非必要

15. 过正方体中心的平面截正方体所得的截面中,不可能的图形是( )

A. 三角形

B. 长方形

C. 对角线不相等的菱形

D. 六边形

16. 如图所示,正八边形12345678A A A A A A A A 的边长为2,若

P 为该正八边形边上的动点,

则131A A A P ?的取值范围为( )

A. [0,8+

B. [-+

C. [8--

D. [8--+

三. 解答题(本大题共5题,共14+14+14+16+18=76分)

17. 如图,长方体1111ABCD A BC D -中,

2AB BC ==,13AA =; (1)求四棱锥

1A ABCD -的体积;

(2)求异面直线1AC 与1DD 所成角的大小;

18. 设a R ∈,函数2()21

x x a f x +=+; (1)求a 的值,使得()f x 为奇函数;

(2)若2()2a f x +<

对任意x R ∈成立,求a 的取值范围;

2019年上海市春考高考英语试卷(精校Word版含答案)

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普通高校春季高考数学试卷(附答案)

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2017上海春考英语卷解析

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上海市春季高考数学试题

上海市春季高考数学试题

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= 5.(3分)(2013?上海)已知向量,.若,则实数k= . ,得﹣ 故答案为: ,则6.(3分)(2013?上海)函数y=4sinx+3cosx的最大值是5. (sinx+cosx== 7.(3分)(2013?上海)复数2+3i(i是虚数单位)的模是. ,代入计算即可得出复数

= 故答案为: 8.(3分)(2013?上海)在△ABC中,角A,B,C所对边长分别为a,b,c,若a=5,c=8,B=60°,则b=7. 9.(3分)(2013?上海)正方体ABCD﹣A1B1C1D1中,异面直线A1B与B1C所成角的大小为60°.

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