高三数学同步检测(四)
第一章单元检测(B)
说明：本试卷分为第Ⅰ、Ⅱ卷两部分,请将第Ⅰ卷选择题的答案填入题后括号内,第Ⅱ卷可在各题后直接作答.共100分,考试时间90分钟.
第Ⅰ卷(选择题共40分)
山东省淄博市2006―2007学年度第一次模拟考试高三数学（理科）
题号
一
二
三
总分
15
16
17
18
19
20
分数
本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，第Ⅰ卷1至2页，第Ⅱ卷3至9页，共150分。考试时间120分钟。考试结束，将本试卷和答题卡一并交回。
第Ⅰ卷（选择题 共40分）
注意事项：
1． 答第Ⅰ卷前，考生务必将自己的姓名、准考证号、考试科目涂写在答题卡上。
2． 每小题选出答案后，用铅笔把答题卡上对应题目的答案标号涂黑。如需改动，用橡皮擦干净后，再选涂其它答案标号。不能答在试卷上。
北京市人大附中2007届摸底考试数学试卷（理科）
命题人：罗 霞
本试卷分第I卷（选择题）和第II卷（非选择题）两部分，第I卷 1至2页，第II卷3至8页，共150分，考试时间120分钟.
第I卷（选择题共40分）
注意事项： 1．答第I卷前，考生务必将自己的姓名、班级、学号写在答题卡上；
2．每小题选出答案后，用铅笔把答题卡上对应题目的答案标号涂黑,如需改动,用橡皮擦干净后，再选涂其他答案标号；
3．考试结束，将答题卡和第II卷3至8页试卷一并交回.
北京市人大附中2007届摸底考试数学试卷（文科）
命题人：罗 霞
本试卷分第I卷（选择题）和第II卷（非选择题）两部分，第I卷 1至2页，第II卷3至8页，共150分，考试时间120分钟.
第I卷（选择题共40分）
注意事项： 1．答第I卷前，考生务必将自己的姓名、班级、学号写在答题卡上；
2．每小题选出答案后，用铅笔把答题卡上对应题目的答案标号涂黑,如需改动,用橡皮擦干净后，再选涂其他答案标号；
3．考试结束，将答题卡和第II卷3至8页试卷一并交回.
文科数学答案
一.选择题：每小题5分，共60分
题号
1
2
3
4
5
6
7
8
9
10
11
12
答案
B
D
B
B
B
B
B
D
A
D
D
C
二.填空题：每小题4分，共16分.
13． 64 14. 
15.－0.5
16.234
17.解：（1）方程
可化为：
，所以圆心
的坐标为
，半径
；（2）由直线
在两坐标轴是的截距相等，，设直线的方程为
，由直线与圆相切可得：
解得：
或
，所以所求直线的方程为
或
.
18.解：∵｛an｝为等差数列，｛bn｝为等比数列，∴a2＋a4＝
，a3＝
．由a1＝1，a3＝知｛an｝的公差为d＝
，∴
，由b1＝1，b3＝知｛bn｝的公比为q＝
或q＝
．当q＝时，
；当q＝时，
2S10＝
．当q＝时，
；当q＝时，
．
19.（1）证明：由
，且
得，
，又
，所以
；（2）过作
于
，连
，由（1）知，则
，于是
是二面角
的平面角.设
，由
得，
，
，因
为正三角形，所以
，
，于是
，所以二面角的大小为
.
20.解：（1）设袋中有白球
个，由题意可得：
，解得：
（舍去
），即袋中有3个白球；（2）记“取球2次终止”为事件
，
；
（3）记“甲到到白球” 为事件
，“第
次取出的球是白球”为事件
，因为甲先取，所以甲只有可能在第1次，第3次，第5次取球，所以
.
21.解：（1）
；（2）由
得，
，此时
，令
得：
或
，又
，
，
，
，所以
在
上的最大值为
，最小值为
；
（3）的图象为开口向上且过点
的抛物线，由条件得：
解得：
，所以
的取值范围为.
22.解：（1）令
，
得：
，由
得：
；
设
，则
，令
，
得：
，而，
，所以
；（2）设
，则
，由已知可得：
，所以
.又
，，所以
，即
，故在
上是减函数.
（3）由
，且在上是减函数，得
，由
得：
，因为
，即直线与圆
相切或相离，故
，解得：
，所以的取值范围为
.
2006―2007学年度上学期高三年级第一次月考
文科数学试卷
命题人：谢爱春 时间：120分钟 总分：150分
一.选择题：本大题共12小题，每小题5分，共60分.在每小题给出的四个选项中，只有一项是符合题目要求的.
1.下列各组命题构成“p或q”真，“p且q”假，“非P”为真的是（ ）
2.已知函数
在区间
上是减函数，则
的取值范围是（ ）
3.设
在映射
下的象是
，则
在下的原象是（ ）
4.已知
，
，则
的值为（ ）
5.已知
，
，
，若
，则
的值为（ ）
0 3 15 18
6.下列命题正确的是（ ）
7.已知双曲线与椭圆
共焦点，它们的离心率之和为
，那么双曲线方程为（ ）
8.已知直线a，b和平面
，下列命题是真命题的是（ ）
9.设
为奇数，则
被9除所得的余数为（ ）
8
7
2
0
10.设
若
，则
的取值范围是（ ）
11.已知
，则
（ ）
8
18
12.现代社会对破译密码的难度要求越来越高，有一种密码把英文的明文（真实文）按字母分解，其中英文的
…
的26个字母（不论大小写）依次对应1，2，3，…26这26个自然数（见下表）：
a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t
u
v
w
x
y
z
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
给出如下一个变换公式：
将明文转换成密文，如8→
=17，即将h变成q；5→
=3，即将e变成c.按上述规定，若将某明文译成密文是
，那么原来的明文是（ ）
lhho ohhl love eovl
二.填空题：本大题共4小题，每小题4分，共16分.把答案填在答题卡的相应位置.
13.集合
，
，可建立从A到B的映射个数有
.
14.已知集合
，
，若A是B的充分不必要条件，则m的取值范围是
.
15.设
是
上的奇函数，
，当
时；， 
，则
. 16.给出如下五个命题：1若
为实数，则函数
的值域为
；2在同一坐标系中，函数
与函数
关于直线
对称；3若
恒成立，则为周期函数；4若
，且
恒成立，则为偶函数；5函数
的单调递减区间是
.其中真命题的序号为
.
三.解答题：本大题共6小题，共74分，解答应写出文字说明、证明过程或演算步骤.
17.已知圆
.
（1）求圆心
的坐标及半径
的大小；
（2）已知不过原点的直线
与圆相切，且在两坐标轴的截距相等，求直线的方程.
18.（普通班做）设｛an｝为等差数列，｛bn｝为等比数列，a1＝b1＝1，a2＋a4＝b3，b2b4＝a3．求（1）｛an｝及｛bn｝的通项公式；（2）｛an｝及｛bn｝的前10项的和S10及T10．
（实验班做）已知函数
，
.（1）要得到的图象，只需要把
的图象经过怎样的变换？（2）求
的最大值及相应的的值.
19.如图，正
与
成直二面角，
，
.
（1）求证：
；
（2）求二面角
的大小.
20.袋中有黑球和白球共7个，从中任取2个球都是白球的概率为
，现有甲、乙两人从袋中轮流摸取1个球，甲先取，乙后取，然后甲再取……取后不放回，直到两人中有一人取到白球时终止，每个球在每一次取出的机会是等可能的.
（1）求袋中原有白球的个数；（2）求取球2次终止的概率；（3）求甲取到白球的概率.
21.已知为实数，
.
（1）求导数
；（2）若
，求在
上的最大值与最小值；
（3）若在
和
都是递增的，求的取值范围.
22.（普通班做）设函数定义在上，对任意实数
、恒有
，且
时，
.
（1）求证：
，且当
时，
；（2）求证：在上是减函数；
（3）设集合
，集合
，若
，求的取值范围.
（实验班做）在
平面上有一系列点
，
，…
，…对每个自然数，点
位于函数
的图象上，以点为圆心的⊙与轴相切，且⊙与⊙
又彼此外切. 若
，且
.（1）求证：数列
是等差数列；（2）设⊙的面积为
，
，求证：
2006~2007学年度上学期高三年级第一次月考
文科数学答题卷
一.选择题：每小题5分，共60分
题号
1
2
3
4
5
6
7
8
9
10
11
12
答案
二.填空题：每小题4分，共16分.
13． 14. 15. 16.
三.解答题：本大题共6小题，共74分，解答应写出文字说明、证明过程或演算步骤.
17.已知圆.
（1）求圆心的坐标及半径的大小；
（2）已知不过原点的直线与圆相切，且在两坐标轴的截距相等，求直线的方程.
18. （普通班做）设｛an｝为等差数列，｛bn｝为等比数列，a1＝b1＝1，a2＋a4＝b3，b2b4＝a3．求（1）｛an｝及｛bn｝的通项公式；（2）｛an｝及｛bn｝的前10项的和S10及T10．
（实验班做）已知函数，.（1）要得到的图象，只需要把的图象经过怎样的变换？（2）求的最大值及相应的的值.
19.如图，正与成直二面角，，.
（1）求证：；
（2）求二面角的大小.
20.袋中有黑球和白球共7个，从中任取2个球都是白球的概率为，现有甲、乙两人从袋中轮流摸取1个球，甲先取，乙后取，然后甲再取……取后不放回，直到两人中有一人取到白球时终止，每个球在每一次取出的机会是等可能的.
（1）求袋中原有白球的个数；
（2）求取球2次终止的概率；
（3）求甲取到白球的概率.
.
21.已知为实数，.
（1）求导数；
（2）若，求在上的最大值与最小值；
（3）若在和都是递增的，求的取值范围.
22. （普通班做）设函数定义在上，对任意实数、恒有，且时，.
（1）求证：，且当时，；（2）求证：在上是减函数；
（3）设集合，集合，若，求的取值范围.
（实验班做）在平面上有一系列点，</b></p><p>21．He worked hard. ________, he won the first
prize.</p><p>A．As a whole
B. As a rule C. As
well D. As a consequence</p><p>22. Do you know
_______ expense the trip will be?</p><p>A. at which B. in which C. at whose D. in whose</p><p>23.Teaching year
after year, he gradually ________much experience.</p><p>A. calculated B. accumulated C. abandoned D. appointed</p><p>24.It’s
said that _______ of the students _______ absent.</p><p>A. three-fifth, are B. three-fifths, is C. third-fifth,
is D. three-fifths, are</p><p>25.Some animals
hibernate in the snow, which can ______ the cold.</p><p>A. keep out B. keep off C. keep up D. keep back</p><p>26. The flowers
____ sweet in the botanic garden attract the visitors to the beauty of nature.<br>
A. smelling B. to smell C. smelt D. to be smelt<br>
27.Feeling very _______, he felt _______ he should take some actions.</p><p>A. angry,
strong B. angry,
strongly C. angrily, strong D. angrily, strongly</p><p>28.It was seven
o’clock ______ I got to school this morning, _______ made our teacher very
angry.</p><p>A. when, that B. that, that C. when, which D. that, when</p><p>29.<st1:country-region
w:st=)
A. that B. where C. what D. the place
30.Maybe you have
been to many countries, but nowhere else_______ such a beautiful palace .
A. can you find B. you could
find C. you can find D. could you find
31.____with the size of the whole earth , the biggest ocean does not seem big at all .
A．Compare B．When comparing C．Comparing D．When compared
32. Had I got to the airport earlier, I _______ you.
A. might not miss to see B. would not have missed seeing
C. should not miss seeing D. would not have missed to see
33. All the employees except the manager ______to work online at home.
A. encourages B. encourage C. is encouraged D. are encouraged
34. The teacher, with 6 girls and 8 boys of her class, _______ visiting a museum when the earthquake struck.
A. was B. were C. had been D. would be
35.---John, there is ______ Mr. Wilson on the phone for you.
---I'm in ______ bath.
A. a; the B. the; a C. a;不填 D. the;不填
Ⅱ.完形填空 30分
Mrs White was a wealthy lady. She lived
Mrs Green was an experienced doctor. She knew old people
became set in their ways and don’t like to be 40
what to do. She decided
to get to know Mrs White before she said anything.
During the visit, Dr. Green asked Mrs White to give
her a 41 of the house. Mrs
White was 42 her house and happily agreed. As they
walked from room to room, Dr. Green 43 that there were a lot of violets(紫罗兰) in every window. She asked, “ 44 do you have so many violets?” Mrs White replied, “I love these 45 and they 46 so fast that I have more and more.” When
the tour of the house was over, Dr. Green said “I have one suggestion to make.
Whenever you
Mrs White said 50 about the doctor’s advice and for a few months 51 the visit, she didn’t give away any of her violets. Then one day she was invited to the 52 of her neighbor’s daughter. She put a ribbon (丝带) on one of her potted plants and took it to the party. Later one of her friends was sick so she took a violet plants and took it to the hospital. 53 she began to give more and more of her potted violets to her neighbors. Over the years she 54 so many that she became known as the 55 lady.
36.A. well B. alone C. quietly D. happily
37.A. cheerful B. delighted C. unhappy D. disappointed
38.A. money B. children C. big house D. old age
39.A. talked B. thought C. worried D. learned
40.A. told B. ordered C. wanted D. invited
41.A. tour B. view C. sight D. picture
42.A. proud of B. familiar with C. interested in D. anxious about
43.A. looked B. showed C. noticed D. watched
44.A. How B. Why C. When D. Where
45.A. rooms B. windows C. children D. flowers
46.A. grow B. make C. become D. produce
47.A. ask B. get C. hear D. want
48.A. ill B. sad C. excited D. pleased
49.A. it B. me C. you D. them
50.A. nothing B. anything C. something D. everything
51.A. before B. after C. during D. until
52.A. lecture B. graduation C. celebration D. wedding
53.A. Usually B. Continuously C. Gradually D. Regularly
54.A. sold out B. gave away C. grew D. kept on
55.A. old B. violet C. rich D. famous
Ⅲ.阅读理解 40分
A
New York was very proud of its electric trolleys(无轨电车) at the turn of the century. They were the latest way
to get around. But Mary Anderson, who visited
It was not that the drivers were bad. It was the
windshields (挡风玻璃). In those days, drivers rubbed their
windshields with damp tobacco. This was supposed to help off rain and snow. But
it did not work too well.
Back in Alabama, Anderson made the first windshield wiper by fixing handle （把手）to a rubber blade (片). This, in turn, was fixed to the windshield. The drivers had to turn the handle back and forth by hand to make the blade wipe off the rain. But it worked. And travel in bad weather was made a little safer for everyone.
56.Which of the following best gives the main idea of this passage?
A.How Mary Anderson visited
B.How drivers cleaned their windshields?
C.How the first windshield wiper came into being?
D.How windshield wiper was made?
57.Though New Yorkers had great pride in electric trolleys, Mary disliked them because she thought ______________.
A. they were dangerous B.they kept off rain and snow
C.their windshields were not good D.their drivers were inexperienced
58.To stop rain and snow coming on the windshields, a trolley driver had to _______.
A. work hard B.see out of them clearly
C.struggle in the trolleys D.use damp tobacco to clean them
59.Which of the following is NOT true according to the passage?
A. The windshield wiper helped keep off the rain.
B. The windshield wiper was turned by the driver.
C. The rubber blade was fixed to the windshield.
D. The windshield wiper was made in
Marlin Perkins’ keen interest in animals, especially
snakes, brought him a lot of trouble when he was young. His landlady never
excused him for keeping snakes in his closet. After two years of college, he
left school and found a job in a zoo, sweeping the sidewalks for $
Through his snake-hunting expeditions, Perkins won his fame as a snake expert. His love for snakes is such that he thinks of them in terms of (根据) personalities. However, snakes do not have the universal appeal as he wishes. Even Perkins’ most favorite animal Bushman, the 550-pound toughest African ape, was frightened by snakes. Bushman once escaped from his cage. Nothing could draw him back. Finally a keeper went to the reptile house, got three little snakes, and dangled (摇晃) them toward Bushman. The great ape nearly tore the place apart getting back to the safety of his cage.
Perkins likes all animals and takes more interest in them than many parents take in their own children. He keeps daily records on all the baby animals, takes their temperature and watches their diet strictly. Speaking about his success, Perkins sums up his philosophy of life as follows: “My life has taught me that the surest path to success is to find out what you most enjoy doing, then set out to do it.”
60.Perkins’ first zoo job was __________.
A. collecting snakes B. sweeping sidewalks
C. looking after an ape D. taking notes on animals
61.Bushman’s reaction (反映) suggests that ___________.
A. he was easy to be nervous B. most people dislike animals
C. even animals dislike snakes D. he was a tough animal to manage
62.Perkins believes the best way to success is to __________.
A. do what you like most B.work hard at it
C.do what people don’t like D.be brave enough
63. According to the passage, Marlin Perkins entered his life work through ______.
A. help B.chance C.choice D.necessity
64.A good title for the passage would be ________.
A.Lovely Snakes B.A Good Expert
C.Marlin Perkins’ world D.Human’s Friend---Animal
C
Women’s roles have changed throughout the world in recent years, but nowhere so obviously as in America .As the roles of women have changed ,so have men’s .In many American homes today ,the husband still carries on his traditional role of breadwinner ,while his homemaker wife is in charge of the home and child―raising. But it is more and more common to find that the children are left in day ?care centers or nursery schools while both parents work .The woman may earn as much or more money than her husband. At home ,household duties are shared in varying degrees by all family members .It is not unusual to find father cooking dinner ,cleaning the living room or changing the baby .Mother might be outside mowing the lawn or washing the car .Children have responsibilities ,too .One of the goals of the Women’s Liberation Movement has been to have both men and women share in childcare, housework and financial responsibility. Today many American women will not marry a man who is not willing to share equally in household responsibilities.
The high cost of living has made it necessary for many women to have jobs outside the home ,but women often choose to have jobs in order to use their skills and education or to seek a more fulfilling and interesting life .Many American women enjoy the independence that an outside job and the salary give men and even some women―sometimes are not for women working outside the home ,and in some cases ,a woman might be paid less than a man who performs the same job .American women ,however ,have met challenges（挑战）since pioneer days ,and they continue to work for true equality.
65．Many American women go out to work in order to .
A．earn enough money to support the family
B．make their husbands share in the housework
C．enjoy independence
D．get more money than their husbands
66．What does sex discrimination mean, EXCEPT ?
A．It’s harder for women to get a same job as men
B．Women get less paid than men at the same position
C．Women do most of the housework
D．Women have jobs outside house
67． for the women to win true equality.
A．It’s impossible B．It takes a long time
C．It’s greatly successful D．It’s not difficult
68．From the text we known .
A．women’s roles in the world have changed a lot but men’s roles haven’t changed
B．American women continued to work for their true equality
C．in all areas of American men and women got paid equally
D．most women began to work outside the home
D
THE FINANCIAL TRAINING COMPANY
CFA 2002 SEMINAR
Come to our FREE information seminar and learn about the Cartered Financial Analyst (CFA) Program ,study materials and how to plan for your study.
Date: 28 January 2002(Monday)
Time :7:30 pm
Venue:
Jing An Hilton Hotel(
Language : English
For reservation（预定），visit www.ftcasiapacific.com
For enquiries （问询）,email cfainfo@financialtrainins.com..hk
Or
call (852) 25263686(
69．Here is an advertisement in China Daily .After we read it ,we can know that the word
“Seminar” refers to a .
A．school of English B．company of information
C．hotel for students in vacation D．class for research and discussion
70．If we read the advertisement ,we draw a conclusion that .
A．CFA is another name of the company
B．suppose someone wants to visit the head office of the company in person ,probably he
ought
to go to
C．only English is used in this company
D．a branch of the company will be set up in
E
Shakespeare ,more perhaps than any other writer ,made full use of the greatest resources of the English Language .Most of us use about five thousand words in our normal employment of English ;Shakespeare in his works used about twenty―five thousand! There is probably no better way for a foreigner to appreciate the richness and variety of the English language than by studying the various ways in which Shakespeare uses it .Such a study is well worth the effort, even though some aspects of English usage ,and the meaning of many words ,have changed since Shakespeare’s day.
However
,it is surprising that we should know comparatively little about the life of
the greatest English author. We know that Shakespeare was born in
However ,what is important about Shakespeare’s life is not its incidental details but its products , the plays and the poems .For many years scholars have been trying to add a few facts about Shakespeare’s life to the small number we already possess and for an equally long tine critics（批评）have been theorizing（理论化）about the plays .Sometimes ,indeed ,it seems that the poetry of Shakespeare will disappear under the great mass of comment that has been written upon it .
Fortunately this is not likely to happen .Shakespeare’s people have long delighted not just the English but lovers of literature everywhere ,and will continue to do so after the scholars and critics and all their works have been forgotten.
71．This passage is about .
A．the great length of each chapter
B．the great varieties in writing styles
C．the richness of the content in Shakespeare’s works
D．the rich English language used by Shakespeare in his works
72．According to the writer ,which of the following remains uncertain about Shakespeare?
A．His date of birth.
B．His marriage.
C．His life in the
D．His date of death.
73．It can be inferred from
A．not all the comments on Shakespeare’s works have produced good effects
B．scholars have successfully collected facts about Shakespeare’s life
C．critics are more interested in Shakespeare’s play than his poetry
D．the details of Shakespeare’s life are more important than his literary works
74．What does the last sentence in
A．People don’t think the poetry of Shakespeare good any more.
B．People pay more attention to the comment than the poetry of Shakespeare.
C．People can’t see the poetry of Shakespeare any more.
D．The comment is printed on the poetry of Shakespeare.
75．“Shakespeare’s
people” in
A．the characters in Shakespeare’s products
B．the people whose native language is English
C．the people living in Shakespeare’s day
D．the readers of Shakespeare’s works
第二卷（共35分）
第四部分：写作（共两节，满分35分）
第一节，短文改错（共10小题；每小题1分，满分10分）
此题要求改正所给短文中的错误。对标有题号的每一行作出判断；如无错误，在该行右边横线上画一个勾（√）；如有错误（每行只有一个错误），则按下列情况改正：
该行多一个词：把多余的词用（\）划掉，在该行右边横线上写出该词，并也用斜线划掉。
该行缺一个词：在缺词处加一个漏字符号（∧），在该行右边横线上写出该加的词。
该行错一个词：在错的词下划一横线，在该行右边横线上写出改正后的词。
注意：原行没有错的不要改。
Mr. Smith had neither wife nor children. He liked nothing but 76．
drinking.He almost spent all of his money drinks .Sometimes he 77．
was hungry but had to borrow some money to buy a little food. 78．
One evening he met a friend of him in the street .The man 79．
asked him to have dinner in a restaurant .He was very happy 80．
that he drank too much .His friend stopped a taxi and ask 81．
the driver to take him home .Soon they reached in the door of 82．
his house .The taxi went away .But he couldn’t put the key into 83．
the keyhole .Just then a policeman went up ,offering to help him 84．
but he refused . “The house is circled now. If you can stop it 85．
moving ,I can open the door myself,” he said.
第二节：书面表达（共25分）
假定你在参加一场英语辩论赛。你是正方辩手，试用英语简要地表明自己的观点。
主题
Shall a senior student take a part―time job in holidays?
观点
1．高中生重视功课，而对社会知道甚少。
2．假期做a part―time job 是很好的社会实践。
3．通过书本学到的东西不如通过实践学到的东西有效。
4．通过社会实践，我们可以在知识和能力两个方面取得进步。
5．假期做a part―time job 的报酬或多或少有些帮助。
结论
高中生……
高三英语月考试题答案
1-5 BACCA 6-10 CCBBC 11-15 AABAA 16-20 CBBBB
21―25 DCBDA 26---30ABCCA 31---35DBDAC 36---40BCDCA
41---45AACBD 46---50ACADA 51---55 BDCBB
56---60 CADAB 61---65 CACCC 66---70BBBDB 71---75DCABA
76．wife→a wife 77．money ∧→on 78．but→and
79．him→his 80．very→so 81．ask→asked 82．in（删去） 83．√
84．went→came 85．circled→circling
One possible version:
Dear friends,
Here are my points .We students of today have to pay much attention to our lessons and know little of society though it’s not out fault .A holiday is the best time to make up for that .Taking a part―time job is a good form of social practice. What is learned in books can’t have the same deep effect on us as what is learned through experience .In social practice ,we can surely make progress in both knowledge and ability .Besides ,taking a part―time job ,we may get paid more or less to help our family .Thus ,I will say a senior school student should take a part―time job in holidays ,if possible ,of course.
大余中学2006―2007学年度高三年级第一次考试