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贵州省贵阳市第一中学2021届高考数学适应性月考卷(六)文(扫描版)

贵州省贵阳市第一中学2021届高考数学适应性月考卷(六)文(扫描版)
贵州省贵阳市第一中学2021届高考数学适应性月考卷(六)文(扫描版)

贵州省贵阳市第一中学2021届高考数学适应性月考卷(六)文(扫描

版)

贵阳第一中学2021届高考适应性月考卷(六)

文科数学参考答案

一、选择题(本大题共12小题,每小题5分,共60分)

【解析】

1.{(01)(00)(01)(11)(10)(11)}A B =--,,,,,,,,,,,,故选C .

2.(2i)(i)3i y y y y ++=+,所以1

313

y x y ===,,故选D .

3.由已知4=a b ,222|2|4416-=-+=a b a a b b ,所以|2|4-=a b ,故选B . 4.p 真q 假p ??为假,q ?为真,①③为真命题,故选A .

5.未服药组的指标y 的取值相对集中,方差较小,所以B 说法不对,故选B .

6.由诱导公式2ππsin cos 36αα????+=+ ? ?????,所以ππ2π()63k k αα??

+=++∈ ???

Z (舍去)或

πππ2π()22π()sin 21632k k k k αααα????

+++=∈?=-+∈?=- ? ?

????

Z Z ,故选A .

7.OAB △是等腰直角三角形23OAB S m ?==△,在椭圆上,代入得2b =,故选B . 8.方法一:由图可知,π()sin 23f x x ??=+ ???,ππππ()sin 2sin 2612312g x x x f x ???

????

?=+=-+=

- ? ? ??????

???

??,

所以把()f x 的图象向右平移π

12

个单位得到()g x 的图象,故选D . 方法二:两个函数的振幅和周期相同,由图,点π112A ??

???,是()f x 图象的一个最高点,而由π203x -

=,得π16B ??

???

是()g x 图象的一个最高点,所以把()f x 的图象向右平移π12个单位得到()g x 的图象,故选D .

9.当BE CF =时,截面是矩形;当2BE CF =时,截面是菱形;当BE CF >时,截面是梯形,故选A .

10.取1n =,已经有111S a a ===,

即,不能进入循环,判断框应是i n <进入循环;进入循环后第一次加上的应该是2121a a =+,所以先算21a a =+,故选A .

11.依题意,一条渐近线是x 轴与另一条渐近线的对称轴,渐近线的倾斜角是60?或120?,所

32b c

a a

?=,故选C . 12.2()23f x x ax b '=++-,(1)0220f a b '=?+-=且21(()(1))a f x x '≠-≠-,(22)ab a a =-=

2

1112(1)222a a ???

?--≠-∈-∞ ? ????

?,,故选A . 二、填空题(本大题共4小题,每小题5分,共20分)

题号 13

14

15

16

答案

3 5π 3 2

【解析】

13.2()0(2)x f x x =?=,分别作(2)x y =与2y x =的图象,并注意到指数函数的增长速度

最终会远远超过幂函数的增长速度,所以两函数图象有3个交点,即()f x 有3个零点.

14.如图1,由已知,在底面ABCD 中,AB BC AD CD ⊥⊥,,由PA ⊥底

面ABCD ,易得PAC PBC PCD △,△,△都是Rt △,所以球心是

PC 的中点,5

R =

,5πS =. 15.如图2,设BD x =,则243

cos x A -=且2279BC x ==

22(43)2343cos x x

x A +---,解得1x =,3AB =∴.

16.由已知()f x 是以4为周期的奇函数,21511log (2)2222f f f a ??

????

=

-=-=-+=- ? ? ???????

,得2a =,又(2)(2)4(2)(2)0f f f f =-+-=(周期为)且(奇函数),所以(2)(2)0f f -==,所以()2a f a +=.

三、解答题(共70分.解答应写出文字说明,证明过程或演算步骤) 17.(本小题满分12分)

解:(1)高三备考学生每天完成数学作业的平均时间的平均值的估计值为

300.1400.18500.3600.25700.12800.0552.6?+?+?+?+?+?=,

图1

图2

完成数学作业的平均时间占自主学习时间的比例估计值为

52.6

0.18300

≈. ………………………………………………………………………(6分)

(2)由直方图,样本中高三备考学生每天完成数学作业的平均时间不超过45分钟的频率为0.28,

估计每个高三备考学生每天完成数学作业的平均时间不超过45分钟的概率为0.28.

…………………………………………………………………………(12分)

18.(本小题满分12分)

解:(1)设{}n a 的首项为1a ,公差为d ,取12n =,, 得1111114()14(2)()(2)1a a a d a d a d a d =++??+=+++?,,解得112a d =??=?,或1

1414

a d ?

=????=-??,,

当112a d ==,时,212121n n n a n a n S n +=-=+=,

,满足条件; 当111

44a d ==-,时,34311042

a a S =-=-=,,不满足条件,舍去,

综上,数列{}n a 的通项公式为21n a n =-. ………………………………………(6分) (2)

121892n n a n a n ++=--,记2110

()19292x f x x x

+==-+

--, ()f x 在( 4.5)-∞,与(4.5)+∞,上都是增函数(图象如

图3),

对数列18n n a a +????-??,当4n ≤时,18n n a a +??

??-??

递增且都大

于1-,

当5n ≥时,18n n a a +??

??-??

递增且都小于1-,

数列18n n a a +??

??-?

?的最大项是第4项,值为9,最小项是第5项,值为11-. ………(12分)

19.(本小题满分12分)

(1)证明:设点11()A x y ,,22()B x y ,,(2)P b -,,

过点A ,P 的直线方程为111()2y y x x +=,同理过点B ,P 的直线方程为221()2

y y x x +=,

图3

因为点P 是两切线的交点,

所以1

(2)2y bx -=,即22y bx =+恒过(02),. ………………………………………(6

分)

(2)解:设直线AB 为2(2)y kx k b =+=,与抛物线方程联立得220x kx --=,其中0?>, 122x x =-,12x x k +=,

因为(21)M ,在AB 为直径的圆上,所以0MA MB =,

即11221212(21)(21)0(2)(2)(1)(1)0x y x y x x y y ----=?--+--=,, 1212(2)(2)(1)(1)0x x kx kx ?--+++=,

整理得21212(1)(2)()50k x x k x x ++-++=, 即2230k k +-=,解得1k =或3k =-,

当1k =时,122P ??- ???,,圆心为1522?? ???,,半径292r =,

圆的标准方程为2

2

159222x y ?

???-+-= ? ??

???;

当3k =-时,322P ??-- ???,,圆心为31322??

- ???

,,半径2852r =, 圆的标准方程为2

2

31385222x y ?

???++-= ? ?????

. …………………………………(12分)

20.(本小题满分12分)

(1)证明:如图4,设M 是AC 的中点,因为3DA DC ==, 所以DM AC ⊥,且22DM =

因为平面ACD ⊥平面ABC ,交线为AC ,DM ?平面ACD , 所以DM ⊥平面ABC ,又EF ⊥平面ABC , 所以DM EF ∥,且22DM EF == 四边形DEFM 是平行四边形,从而DE MF ∥,

在ABC △中,M F ,是AC BC ,的中点,所以MF AB ∥,

所以DE AB ∥,从而A B E D ,,,四点共面. …………………………………(6分)

图4

(2)解:由(1)1

2

DE AB DE AB =

∥且, 所以D 到平面BCE 的距离是A 到平面BCE 距离的

12

, EF ⊥平面ABC EF AC ?⊥,

又AC BC AC ⊥?⊥平面BCE , 所以D 到平面BCE 的距离为

1

12

AC =,

BCE △的面积1

2

S BC EF =?=

1

13B CDE D BCE V V --==?…………………………………………(12分) 21.(本小题满分12分)

解:(1)2()(1)(1)()f x x a x a x x a '=-++=--,

当1a =时,2()(1)0f x x '=-≥,()f x 在()-∞+∞,上单调递增;

当1a <时,在(1)a ,上,()0f x '<,()f x 单调递减;在()a -∞,和(1)+∞,上,()0f x '>,()f x 单调递增;

当1a >时,在(1)a ,上,()0f x '<,()f x 单调递减;在(1)-∞,和()a +∞,上,()0f x '>,()f x 单调递增;

综上,当1a =时,()f x 在()-∞+∞,上单调递增;

当1a <时,()f x 在(1)a ,上单调递减;在()a -∞,和(1)+∞,上单调递增; 当1a >时,()f x 在(1)a ,上单调递减;在(1)-∞,和()a +∞,上单调递增.

……………………………………………………………………………(6分)

(2)当1a ≠时,函数有两个极值2336()6a a b f a -+=和631

(1)6

b a f +-=,

若函数()f x 有三个不同的零点()(1)0f a f ?<,即32(36)(316)0a a b a b ---+>, 又因为a 的取值范围恰好是1(0)0(3)3??

-∞+∞ ???

,,, 所以令32()(36)(316)g a a a b a b =---+恰有三个零点1

033,,,

若3a =时,(3)6(68)0g b b b =-+=,或4

3

b =-;

当0b =时,2()(31)(3)0g a a a a =-->,解得1(0)0(3)3a ??

∈-∞+∞ ???

,,,符合题意;

当4

3

b =-时,32()(38)(39)0g a a a a =-+-=,

则32380a a -+=不存在1

3

这个根,与题意不符,舍去,

所以0b =. ……………………………………………………………(12分) 22.(本小题满分10分)【选修4?4:坐标系与参数方程】

解:(1)因为2

1sin ρ

θ

=

-,

所以sin 2ρρθ-=2y =, 两边平方整理得244x y =+.

P 点直角坐标cos 0x ρθ==,sin 1y ρθ==,

所以(01)

P ,. ……………………………………………………………(5分)

(2)设直线l 的参数方程为121x t y ?

=??

??=??,

,(t 为参数)与曲线C 的方程244x y =+联立,

得2320t --=,其中12t t +=,1232t t =-, 11||||PA PB +=1211

||||

t t +12121212||||||||||

t t t t

t t t t +-==,

12||t t

-

所以

1212||11||||||t t PA PB t t -+==…………………………………………………(10分) 23.(本小题满分10分)【选修4?5:不等式选讲】

解:(1)22

2242()24022240x x x f x x x x x x ?--?

=-+<

,,,≤,

当0x ≤时,2224x x -++<0?1x <-; 当02x <<时,2402x x -+矛盾; 当2x ≥时,2224012x x x --

综上,1x <-. ……………………………………………………………(5

分)

(2)对任意的1x >时,因为()0f m =,()0()f x f m >=, 所以x m >,则1m ≤, 当1m ≤,1x >时,0x m ->,

则()()(2)()0f x x m x x x m =-++->恒成立,

所以m 的取值范围是1m ≤. …………………………………………………(10分)

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15. The girl wants __________noodles. A. beef B. mutton C. chicken 16. The bank is on__________. A. Garden Street B. Fifth Avenue C. Green Street 17. They're talking about__________. A. polar bears B. manatees C. monkeys 18. Larry likes music that he can__________. A. dance to B. play instrument with C. sing along with D. 听对话及问题,根据对话内容选择正确的答案,并将答题卡该选项涂黑。(读两遍) 19. A. English. B. Physics. C. Chinese. 20. A. A doctor. B. A dentist. C. A nurse. 21. A. A chess club. B. A music club. C. An art club. 22. A. A wallet. B. A belt. C. A watch. 23. A. Once. B. Twice. C. Three times. 24. A. For 2 years. B. For 3 years. C. For 4 years. D. 听下面的独白及问题,根据其内容选择正确答案,并将答题卡上该选项涂黑。(读三遍) 25. A. She's 14. B. She's 15. C. She's 16. 26. A. Her hobby. B. Her family. C. Her school. 27. A. Nina's teacher. B. Nina's mother. C. Nina's sister. 28. A. Last month. B. Last week. C. Last year. 29. A. 1 hour. B. 2 hours. C. 3 hours. 30. A. By working hard. B. By reading more. C. By watching TV. II. 单项选择(本大题共15分,每小题1分) 根据语境或句意,选择可填入句子的最佳答案,并将答题卡上该选项涂黑。 31. "Cindy, do you have ________e-mail address? I want to send you some photos. " "Yes, I do. It's cindy]26@ sohu. com. " A. a B. an C. the 答案:B 【解析】e-mail是以元音音素开头的单词,其前应用不定冠词an。故选B。 32. It is our duty _________our hometown clean and beautiful. We must do something for it. A. to keep B. keeps C. keeping 答案:A 【解析】这里考查的是it is + 名词+ to do sth.结构。故选A。 33. "Excuse me, how can I get to the nearest bus stop?" "Go down this road. It's about_________ walk A. five minute's B. five minutes' C. five-minutes 答案:B 【解析】这里考查的是表示时间、距离时,使用含数词的名词所有格形式作定语。名词应用其复数形式的所有格。故选B。 34. "Marcia, could you please_________my dog when I'm on vacation?" "Yes, sure.” A. look after B. look at C. look for 答案:A 【解析】根据句意:Marcia,当我度假的时候,你能帮我照看一下我的狗吗?是的,可以。look after照顾;look at看;look for寻找。故选A。

2017年贵州省贵阳市中考英语试卷

绝密★启用前 贵州省贵阳市2017年初中毕业生学业考试 英 语 (满分150分,考试时间120分钟) 第Ⅰ卷(选择题,共110分) Ⅰ.听力测试(本大题共30分,每小题1分) A .听对话,选择与对话内容相符的图。(读一遍) 1. A B C 2. A B C 3. A B C 4. A B C 5. A B C 6. A B C B. 听句子,根据所听句子,选择最佳应答。(读一遍) 7. A. By bus. B. It’s fine. C. Thanks. 8. A. It’s Okay. B. It’s an orange. C. It’s sunny today. 9. A. See you. B. Sounds good. C. You’re welcome. 10. A. English. B. Koalas. C. Carrots. 11. A. Sure, I’d love to. B. It’s a nice day. C. Here you are. 12. A. Mooncakes. B. Dumplings. C. Zongzi. C. 听对话,根据对话内容,选择最佳选项完成句子。(读两遍) 13. Scott loves ________ music. A. pop B. rock C. country 14. Jack likes ________ because they are healthy. A. apples B. noodles C. vegetables 15. Jane’s telephone number is ________. A. 543-4721 B.876-3721 C.635-2721 16. Bill used to be ________. A. shy and friendly B. kind and quiet C. shy and quiet 17. Mary thinks a good friend should ________. A. make her laugh B.be a good listener C. care about her 18. Mr. Green is going to ________ next year. A. take guitar lessons B. get lots of exercise C. get good grades D. 听对话及问题,根据对话内容,选择最佳答案。(读两遍) 19. A. At 6:30. B. At 7:30. C. At 8:30. ------------- 在 --------------------此 -------------------- 卷--------------------上 -------------------- 答-------------------- 题--------------------无 --------------------效---------------- 毕业学校_____________ 姓名________________ 考生号________________ ________________ ___________

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