华师大二附中高三数学综合练习试卷(共十套)

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上海市华师大二附中高三年级综合练习[1]

数学

一、填空题 (本大题满分48分) 本大题共有12题，只要求直接填写结果，每个空格填对得4分，否则一律得零分。

1．函数))((R x x f y ∈=图象恒过定点)1,0(，若)(x f y =存在反函数)(1

x f y -=，则1)(1

+=-x f

y 的图象必过

定点 。

2．已知集合{}

R x y y A x

∈-==,12，集合{

}

R x x x y y B ∈++-==,322

，则集合{}

B x A x x ?∈且=

。

3．若角α终边落在射线)0(043≤=-x y x 上，则=??

?

??

?

-+)22arccos(

tan α 。 4．关于x 的方程)(01)2(2

R m mi x i x ∈=+++-有一实根为n ，则

=+ni

m 1

。

5．数列{}n a 的首项为21=a ，且))((2

1

211N n a a a a n n ∈+++=+Λ，记n S 为数列{}n a 前n 项和，则n S = 。 6．（文）若y x ,满足?????

??-≥-

≤-≥+

≤+

1

315

y x y x y x y x ，则目标函数y x s 23-=取最大值时=x 。 （理）若)(13N n x x n

∈??? ?

?

-的展开式中第3项为常数项，则展开式中二项式系数最大的是第 项。

7．已知函数)20,0)(2sin()(π??<<>+=A x A x f ，若对任意R x ∈有)12

5

()(πf x f ≥成立，则方程0)(=x f 在[]π,0上的解为 。

8．某足球队共有11名主力队员和3名替补队员参加一场足球比赛，其中有2名主力和1名替补队员不慎误服违禁药物，依照比赛规定，比赛后必须随机抽取2名队员的尿样化验，则能查到服用违禁药物的主力队员的概率为 。（结果用分数表示） 9．将最小正周期为

2π的函数)2,0)(sin()cos()(π?ω?ω?ω<>+++=x x x g 的图象向左平移4

π个单位，得到偶函数图象，则满足题意的?的一个可能值为 。

10．据某报《自然健康状况》的调查报道，所测血压结果与相应年龄的统计数据如下表，观察表中数据规律，并将

最适当的数据填入表中括号内。

年龄（岁） 30

35

40

45

50

55

60

65

……

收缩压

（水银柱/毫米）

110

115

120

125

130

135

145

……

舒张压

（水银柱/毫米）

70

73

75

78

80

73

85

……

11．若函数?

???

??+=x x x f 24

1log ,log 3min )(，其中{}q p ,m in 表示q p ,两者中的较小者，

则2)(

12．如图，1P 是一块半径为1的半圆形纸板，在1P 的左下端剪去一个半径为

2

1

的半圆得到图形2P ，然后依次剪去一个更小的半圆（其直径是前一个被剪掉半圆的半径）可得图形ΛΛ,,,,43n P P P ，记纸板n P 的面积为n S ，则=∞

→n n S lim 。

二、选择题 (本大题满分16分) 本大题共有4题，每题都给出代号为A 、B 、C 、D 的四个结论，其中有且只有一个结论是正确的，必须把正确结论的代号写在题后的圆括号，选对得4分，不选、错选或者选出的代号超过一个(不论是否都写在圆括号内)，一律得零分。

13．已知c b a ,,满足0<<

A 、ac ab >

B 、0)(>-a b c

C 、2

2

ca cb < D 、0)(<-c a ac

14．下列命题正确的是（ ）

A 、若A a n n =∞

→lim ，B b n n =∞

→lim ，则)0(lim

≠=∞→n n

n n b B A

b a 。

B 、函数)11(arccos ≤≤-=x x y 的反函数为R x x y ∈=,cos 。

C 、函数)(1

2

N m x y m m

∈=-+为奇函数。

D 、函数21)

3

2(sin )(2

+

-=x

x x f ，当2004>x 时，2

1

)(>x f 恒成立。 15．函数1

1)(2

-+-=x x a x f 为奇函数的充要条件是（ ）

A 、10<

B 、10≤

C 、1>a

D 、1≥a 16．不等式)10(2sin log ≠>>a a x x a 且对任意)4

,

0(π

∈x 都成立，则a 的取值范围为（ ）

A 、)4,0(π

B 、)1,4(π

C 、)2

,1()1,4(π

π? D 、)1,0(

三、解答题 (本大题满分86分) 本大题共有6题，解答下列各题必须写出必要的步骤。 17．（本题满分12分）

ABC ?中角C B A ,,所对边分别为c b a ,,，若,2,32==c a b

c

tgB tgA 21=+

，求ABC ?的面积S 。

18．（本题满分12分）

设复数)0,,(1≠∈+=y R y x yi x z ，复数)(sin cos 2R i z ∈+=ααα，且112

1,2z R z z ∈+在复平面上所对应

点在直线x y =上，求21z z -的取值范围。

19．（本题满分14分）

已知关于x 的不等式

05

2<--a

x ax 的解集为M 。

（1）当4=a 时，求集合M ；（2）若M M ?∈53且，求实数a 的取值范围。

20．（本题满分14分）

如图，一个计算装置有两个数据输入口Ⅰ、Ⅱ与一个运算结果输出口Ⅲ，当Ⅰ、Ⅱ分别输入正整数n m ,时，输出结果记为),(n m f ， 且计算装置运算原理如下：

①若Ⅰ、Ⅱ分别输入1，则1)1,1(=f ；②若Ⅰ输入固定的正整数，Ⅱ输入的正整数增大1，则输出结果比原来增大3；③若Ⅱ输入1，Ⅰ输入正整数增大1，则输出结果为原来3倍。试求：

（1）)1,(m f 的表达式)(N m ∈； （2）),(n m f 的表达式),(N n m ∈；

求出相应

（3）若Ⅰ,Ⅱ都输入正整数n ,则输出结果),(n n f 能否为2006？若能,的n ;若不能,则请说明理由。

21．（本题满分16分）

对数列{}n a ，规定{}n a ?为数列{}n a 的一阶差分数列，其中)(1N n a a a n n n ∈-=?+。 对

自然数k ，规定{}

n k a ?为{}n a 的k 阶差分数列，其中)(1

111n k n k n k n k a a a a --+-??=?-?=?。

（1）已知数列{}n a 的通项公式),(2N n n n a n ∈+=，试判断{}n a ?，{}

n a 2

?是否为等差或等比数列，为什么？

（2）若数列{}n a 首项11=a ，且满足)(212N n a a a n

n n n ∈-=+?-?+，求数列{}n a 的通项公式。

（3）（理）对（2）中数列{}n a ，是否存在等差数列{}n b ，使得n n

n n n n a C b C b C b =+++Λ2211对一切自然N

n ∈都成立？若存在，求数列{}n b 的通项公式；若不存在，则请说明理由。

广东省华南师大附中2020┄2021届高三考前热身三模 英语试题Word版

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