2016崇明高三数学一模试卷及答案汇总

崇明县2015-2016学年第一次高考模拟考试试卷数学 2015.12

一．填空题（本大题满分56 分）本大题共有14 题，考生应在答题编号的空格内直接填写结 果，每个空格填对4 分，否则一律得零分． 1. 函数sin 2

()1x f x =

- cosx

的最小正周期是 . 2. 若集合 A ＝{x | ｜x ?1 ｜＜2}，B ＝2|

04x x x -??

，则 A B ＝

3. 已知 z ＝(a ?i )(1+i )（a ∈R ，i 为虚数单位），若复数 z 在复平面内对应的点在实轴 上，则a ＝ .

4. 已知cos 14α=

，且3(,2)2

παπ∈，则cos( 2π

α+)＝ . 5. 若log 21a b =-则a +b 的最小值为 .

6.10

()x a +的展开式中， x 7的系数为 15，则a = . (用数字填写答案)

7. 已知圆锥的母线长为5cm ，侧面积为15πcm 2，则此圆锥的体积是____________ cm 3 . 8. 已知 f (x )、g(x )分别是定义在R 上的偶函数和奇函数，且 f (x ) ?g(x ) ＝2x ＋x ，则

f (1) ＋g(1) ＝ .

9. 在上海高考改革方案中，要求每位高中生必须在理科学科：物理、化学、生物，文科学 科：政治、历史、地理这6 门学科中选择3 门学科参加等级考试.小王同学对理科学科 比较感兴趣，决定至少选择两门理科学科，那么小王同学的选科方案有___________种. 10. 有一列球体， 半径组成以1 为首项，

1

2

为公比的等比数列， 体积分别记为

11、在△ABC 中，AN ＝4，BC ＝62，∠CBA ＝4π

，.若双曲线Γ以 AB 为实轴，且过点C ，

则Γ的焦距为 .

12. 在矩形 ABCD 中， AB ＝2， AD ＝1，边DC （包含点 D 、C ）的动点 P 与 CB 延长

线

上（包含点B ）的动点Q 满足

的取值范围是____________.

13. 已知数列的各项均为正整数，对于，有

其中k 为使1n a +为奇数的正整数. 若存在， 当n ＞m 且n a 为奇数时，n a 恒为常数p ，

则p 的值为

14. 设函数 y ＝f （x ）的定义域为 D ，如果存在非零常数 T ，对于任意 x ∈D ，都有

f （x ＋T ）＝T ? f (x )，则称函数 y ＝f （x ）是“似周期函数”，非零常数T 为函数 y ＝f （ x ）

的“似周期”．现有下面四个关于“似周期函数”的命题：

①如果“似周期函数” y ＝f （ x ）的“似周期”为﹣1，那么它是周期为 2 的周期函数； ②函数 f （x ）＝x 是“似周期函数”；

③函数()2x

f x =是“似周期函数”；

④如果函数()cos f x x ω=是“似周期函数”，那么“k ωπ=，k ∈Z ”． 其中是真命题的序号是 ．（写出所有满足条件的命题序号）

二．选择题（本大题满分20 分）本大题共有4 题，每题有且仅有一个正确答案，考生应在 答题纸的相应编号上，将代表答案的小方格涂黑，每题选对得5 分，否则一律得零分． 15. “a ＜2”是“实系数一元二次方程x 2 ＋ax ＋1 ＝0有虚根”的

(A)必要不充分条件 (B)充分不必要条件 (C)充要条件 (D)既不充分也不必要条件 16. 要得到函数的图象，只需将函数 y ＝sin 2x 的图象（ ）

(A)向左平移

3π个单位 (B)向左平移6π个单位 (C)向右平移3π个单位 (D)向右平移6

π

个单位

17. 汽车的“燃油效率”是指汽车每消耗1 升汽油行驶的里程，下图描述了甲、乙、丙三辆汽车在不同速度下的燃油效率情况. 下列叙述中正确的是（）

(A)消耗1 升汽油，乙车最多可行驶5千米

(B)以相同速度行驶相同路程，三辆车中，甲车消耗汽油最多

(C)甲车以80 千米/小时的速度行驶1 小时，消耗10 升汽油

(D)某城市机动车最高限速80 千米/小时. 相同条件下，在该市用丙车比用乙车更省油

a a

18. 若a，b是函数的两个不同的零点，且a，b，?2这三个数可适当排序后成等差数列，也可适当排序后成等比数列，则p +q 的值等于（）(A)1 (B)4 (C)5 (D)9

三．解答题（本大题满分74 分）本大题共有5 题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤．

19. （本题满分12 分）本题共有2 个小题，第1 小题满分6 分，第2 小题满分满分6 分．如图，四棱锥S ?ABCD中，底面ABCD 为正方形，SA ⊥平面ABCD，AB=3，SA=4 （1）求异面直线SC 与AD 所成角；

（2）求点B 到平面SCD 的距离.

20. （本题满分14 分）本题共有2 个小题，第1 小题满分8 分，第2 小题满分满分6 分．如图，旅客从某旅游区的景点A 处下山至C 处有两种路径.一种是从A沿直线步行到

C ，另一种从A沿索道乘缆车到B ，然后从B 沿直线步行到C .

现有甲、乙两位游客从A 处下山，甲沿AC 匀速步行，速度为50米/分钟，在甲出发2

分钟后，乙从A 乘缆车到B ，在B 处停留1 分钟后，再从B 匀速步行到C . 假设缆车

匀速直线运动的速度为130 米/分钟，山路AC 长1260 米，经测量，

（1）求索道AB 的长；

（2）问乙出发后多少分钟后，乙在缆车上与甲的距离最短？

21. （本题满分14 分）本题共有2 个小题，第1 小题满分5 分，第2 小题满分满分9 分．已知△ABC的顶点A，B在椭圆x2＋3y2＝4上，C在直线l：y ＝x＋2上，且AB∥l．（1）当AB 边通过坐标原点O时，求AB的长及△ABC的面积；

（2）当∠ABC ＝90°，且斜边AC 的长最大时，求AB 所在直线的方程．

22. （本题满分16 分）本题共有3 个小题，第1 小题满分4 分，第2 小题满分满分6 分，第3 小题满分满分6 分．

已知函数f (x) ＝x ｜x ? a ｜＋b, x∈R.

（1）当b ＝0时，判断f (x)的奇偶性，并说明理由；

（2）当a ＝1,b ＝1时，若，求x的值；

（3）若－1≤b ＜0，且对任意x∈［0,1］不等式f (x) ＜0恒成立，求实数a的取值范围．

23. （本题满分18 分）本题共有3 个小题，第1 小题满分4 分，第2 小题满分满分6 分，第3 小题满分满分8 分．

设m 个正数依次围成一个圆圈．其中

(k＜m,k∈N*)是公差为d 的等差数列，而是公比为q 的等比数列．

⑴若，求数列的所有项的和S m；

⑵若，求m的最大值；

⑶当q ＝2时是否存在正整数k ，满足

？若存在，求出k 值；若不存

在，请说明理由．

13、1或5；14、①，③，④

二、选择题

15、A; 16、B；17、D；18、D

三、解答题

杨浦区2016年高三英语一模试卷

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