高三數學同步檢測(四)
第一章單元檢測(B)
說明：本試卷分為第Ⅰ、Ⅱ卷兩部分,請將第Ⅰ卷選擇題的答案填入題后括號內,第Ⅱ卷可在各題后直接作答.共100分,考試時間90分鐘.
第Ⅰ卷(選擇題共40分)
山東省淄博市2006―2007學年度第一次模擬考試高三數學（理科）
題號
一
二
三
總分
15
16
17
18
19
20
分數
本試卷分第Ⅰ卷（選擇題）和第Ⅱ卷（非選擇題）兩部分，第Ⅰ卷1至2頁，第Ⅱ卷3至9頁，共150分。考試時間120分鐘。考試結束，將本試卷和答題卡一并交回。
第Ⅰ卷（選擇題 共40分）
注意事項：
1． 答第Ⅰ卷前，考生務必將自己的姓名、準考證號、考試科目涂寫在答題卡上。
2． 每小題選出答案后，用鉛筆把答題卡上對應題目的答案標號涂黑。如需改動，用橡皮擦干凈后，再選涂其它答案標號。不能答在試卷上。
北京市人大附中2007屆摸底考試數學試卷（理科）
命題人：羅 霞
本試卷分第I卷（選擇題）和第II卷（非選擇題）兩部分，第I卷 1至2頁，第II卷3至8頁，共150分，考試時間120分鐘.
第I卷（選擇題共40分）
注意事項： 1．答第I卷前，考生務必將自己的姓名、班級、學號寫在答題卡上；
2．每小題選出答案后，用鉛筆把答題卡上對應題目的答案標號涂黑,如需改動,用橡皮擦干凈后，再選涂其他答案標號；
3．考試結束，將答題卡和第II卷3至8頁試卷一并交回.
北京市人大附中2007屆摸底考試數學試卷（文科）
命題人：羅 霞
本試卷分第I卷（選擇題）和第II卷（非選擇題）兩部分，第I卷 1至2頁，第II卷3至8頁，共150分，考試時間120分鐘.
第I卷（選擇題共40分）
注意事項： 1．答第I卷前，考生務必將自己的姓名、班級、學號寫在答題卡上；
2．每小題選出答案后，用鉛筆把答題卡上對應題目的答案標號涂黑,如需改動,用橡皮擦干凈后，再選涂其他答案標號；
3．考試結束，將答題卡和第II卷3至8頁試卷一并交回.
文科數學答案
一.選擇題：每小題5分，共60分
題號
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.填空題：每小題4分，共16分.
13． 64 14. 
15.－0.5
16.234
17.解：（1）方程
可化為：
，所以圓心
的坐標為
，半徑
；（2）由直線
在兩坐標軸是的截距相等，，設直線的方程為
，由直線與圓相切可得：
解得：
或
，所以所求直線的方程為
或
.
18.解：∵｛an｝為等差數列，｛bn｝為等比數列，∴a2＋a4＝
，a3＝
．由a1＝1，a3＝知｛an｝的公差為d＝
，∴
，由b1＝1，b3＝知｛bn｝的公比為q＝
或q＝
．當q＝時，
；當q＝時，
2S10＝
．當q＝時，
；當q＝時，
．
19.（1）證明：由
，且
得，
，又
，所以
；（2）過作
于
，連
，由（1）知，則
，于是
是二面角
的平面角.設
，由
得，
，
，因
為正三角形，所以
，
，于是
，所以二面角的大小為
.
20.解：（1）設袋中有白球
個，由題意可得：
，解得：
（舍去
），即袋中有3個白球；（2）記“取球2次終止”為事件
，
；
（3）記“甲到到白球” 為事件
，“第
次取出的球是白球”為事件
，因為甲先取，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，
，此時
，令
得：
或
，又
，
，
，
，所以
在
上的最大值為
，最小值為
；
（3）的圖象為開口向上且過點
的拋物線，由條件得：
解得：
，所以
的取值范圍為.
22.解：（1）令
，
得：
，由
得：
；
設
，則
，令
，
得：
，而，
，所以
；（2）設
，則
，由已知可得：
，所以
.又
，，所以
，即
，故在
上是減函數.
（3）由
，且在上是減函數，得
，由
得：
，因為
，即直線與圓
相切或相離，故
，解得：
，所以的取值范圍為
.
2006―2007學年度上學期高三年級第一次月考
文科數學試卷
命題人：謝愛春 時間：120分鐘 總分：150分
一.選擇題：本大題共12小題，每小題5分，共60分.在每小題給出的四個選項中，只有一項是符合題目要求的.
1.下列各組命題構成“p或q”真，“p且q”假，“非P”為真的是（ ）
2.已知函數
在區間
上是減函數，則
的取值范圍是（ ）
3.設
在映射
下的象是
，則
在下的原象是（ ）
4.已知
，
，則
的值為（ ）
5.已知
，
，
，若
，則
的值為（ ）
0 3 15 18
6.下列命題正確的是（ ）
7.已知雙曲線與橢圓
共焦點，它們的離心率之和為
，那么雙曲線方程為（ ）
8.已知直線a，b和平面
，下列命題是真命題的是（ ）
9.設
為奇數，則
被9除所得的余數為（ ）
8
7
2
0
10.設
若
，則
的取值范圍是（ ）
11.已知
，則
（ ）
8
18
12.現代社會對破譯密碼的難度要求越來越高，有一種密碼把英文的明文（真實文）按字母分解，其中英文的
…
的26個字母（不論大小寫）依次對應1，2，3，…26這26個自然數（見下表）：
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
給出如下一個變換公式：
將明文轉換成密文，如8→
=17，即將h變成q；5→
=3，即將e變成c.按上述規定，若將某明文譯成密文是
，那么原來的明文是（ ）
lhho ohhl love eovl
二.填空題：本大題共4小題，每小題4分，共16分.把答案填在答題卡的相應位置.
13.集合
，
，可建立從A到B的映射個數有
.
14.已知集合
，
，若A是B的充分不必要條件，則m的取值范圍是
.
15.設
是
上的奇函數，
，當
時；， 
，則
. 16.給出如下五個命題：1若
為實數，則函數
的值域為
；2在同一坐標系中，函數
與函數
關于直線
對稱；3若
恒成立，則為周期函數；4若
，且
恒成立，則為偶函數；5函數
的單調遞減區間是
.其中真命題的序號為
.
三.解答題：本大題共6小題，共74分，解答應寫出文字說明、證明過程或演算步驟.
17.已知圓
.
（1）求圓心
的坐標及半徑
的大小；
（2）已知不過原點的直線
與圓相切，且在兩坐標軸的截距相等，求直線的方程.
18.（普通班做）設｛an｝為等差數列，｛bn｝為等比數列，a1＝b1＝1，a2＋a4＝b3，b2b4＝a3．求（1）｛an｝及｛bn｝的通項公式；（2）｛an｝及｛bn｝的前10項的和S10及T10．
（實驗班做）已知函數
，
.（1）要得到的圖象，只需要把
的圖象經過怎樣的變換？（2）求
的最大值及相應的的值.
19.如圖，正
與
成直二面角，
，
.
（1）求證：
；
（2）求二面角
的大小.
20.袋中有黑球和白球共7個，從中任取2個球都是白球的概率為
，現有甲、乙兩人從袋中輪流摸取1個球，甲先取，乙后取，然后甲再取……取后不放回，直到兩人中有一人取到白球時終止，每個球在每一次取出的機會是等可能的.
（1）求袋中原有白球的個數；（2）求取球2次終止的概率；（3）求甲取到白球的概率.
21.已知為實數，
.
（1）求導數
；（2）若
，求在
上的最大值與最小值；
（3）若在
和
都是遞增的，求的取值范圍.
22.（普通班做）設函數定義在上，對任意實數
、恒有
，且
時，
.
（1）求證：
，且當
時，
；（2）求證：在上是減函數；
（3）設集合
，集合
，若
，求的取值范圍.
（實驗班做）在
平面上有一系列點
，
，…
，…對每個自然數，點
位于函數
的圖象上，以點為圓心的⊙與軸相切，且⊙與⊙
又彼此外切. 若
，且
.（1）求證：數列
是等差數列；（2）設⊙的面積為
，
，求證：
2006~2007學年度上學期高三年級第一次月考
文科數學答題卷
一.選擇題：每小題5分，共60分
題號
1
2
3
4
5
6
7
8
9
10
11
12
答案
二.填空題：每小題4分，共16分.
13． 14. 15. 16.
三.解答題：本大題共6小題，共74分，解答應寫出文字說明、證明過程或演算步驟.
17.已知圓.
（1）求圓心的坐標及半徑的大小；
（2）已知不過原點的直線與圓相切，且在兩坐標軸的截距相等，求直線的方程.
18. （普通班做）設｛an｝為等差數列，｛bn｝為等比數列，a1＝b1＝1，a2＋a4＝b3，b2b4＝a3．求（1）｛an｝及｛bn｝的通項公式；（2）｛an｝及｛bn｝的前10項的和S10及T10．
（實驗班做）已知函數，.（1）要得到的圖象，只需要把的圖象經過怎樣的變換？（2）求的最大值及相應的的值.
19.如圖，正與成直二面角，，.
（1）求證：；
（2）求二面角的大小.
20.袋中有黑球和白球共7個，從中任取2個球都是白球的概率為，現有甲、乙兩人從袋中輪流摸取1個球，甲先取，乙后取，然后甲再取……取后不放回，直到兩人中有一人取到白球時終止，每個球在每一次取出的機會是等可能的.
（1）求袋中原有白球的個數；
（2）求取球2次終止的概率；
（3）求甲取到白球的概率.
.
21.已知為實數，.
（1）求導數；
（2）若，求在上的最大值與最小值；
（3）若在和都是遞增的，求的取值范圍.
22. （普通班做）設函數定義在上，對任意實數、恒有，且時，.
（1）求證：，且當時，；（2）求證：在上是減函數；
（3）設集合，集合，若，求的取值范圍.
（實驗班做）在 大余中學2006―2007學年度高三第一次考試試題
理科數學 2006.9
（考試時間120分鐘 ， 滿分150分） 命題人：賴彌春平面上有一系列點，
2006-2007學年度上學期大余中學高三第一次月考
英語試題
第二部分 英語知識應用
Ⅰ.單項選擇。(15分)
21．He worked hard. ________, he won the first prize.
A．As a whole B. As a rule C. As well D. As a consequence
22. Do you know _______ expense the trip will be?
A. at which B. in which C. at whose D. in whose
23.Teaching year after year, he gradually ________much experience.
A. calculated B. accumulated C. abandoned D. appointed
24.It’s said that _______ of the students _______ absent.
A. three-fifth, are B. three-fifths, is C. third-fifth, is D. three-fifths, are
25.Some animals hibernate in the snow, which can ______ the cold.
A. keep out B. keep off C. keep up D. keep back
26. The flowers
____ sweet in the botanic garden attract the visitors to the beauty of nature.
A. smelling B. to smell C. smelt D. to be smelt
27.Feeling very _______, he felt _______ he should take some actions.
A. angry, strong B. angry, strongly C. angrily, strong D. angrily, strongly
28.It was seven o’clock ______ I got to school this morning, _______ made our teacher very angry.
A. when, that B. that, that C. when, which D. that, when
29.
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(紫羅蘭) 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 (絲帶) 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.閱讀理解 40分
A
New York was very proud of its electric trolleys(無軌電車) 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 (擋風玻璃). 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 (根據) 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 (搖晃) 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（挑戰）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
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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（批評）have been theorizing（理論化）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：寫作（共兩節，滿分35分）
第一節，短文改錯（共10小題；每小題1分，滿分10分）
此題要求改正所給短文中的錯誤。對標有題號的每一行作出判斷；如無錯誤，在該行右邊橫線上畫一個勾（√）；如有錯誤（每行只有一個錯誤），則按下列情況改正：
該行多一個詞：把多余的詞用（\）劃掉，在該行右邊橫線上寫出該詞，并也用斜線劃掉。
該行缺一個詞：在缺詞處加一個漏字符號（∧），在該行右邊橫線上寫出該加的詞。
該行錯一個詞：在錯的詞下劃一橫線，在該行右邊橫線上寫出改正后的詞。
注意：原行沒有錯的不要改。
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.
第二節：書面表達（共25分）
假定你在參加一場英語辯論賽。你是正方辯手，試用英語簡要地表明自己的觀點。
主題
Shall a senior student take a part―time job in holidays?
觀點
1．高中生重視功課，而對社會知道甚少。
2．假期做a part―time job 是很好的社會實踐。
3．通過書本學到的東西不如通過實踐學到的東西有效。
4．通過社會實踐，我們可以在知識和能力兩個方面取得進步。
5．假期做a part―time job 的報酬或多或少有些幫助。
結論
高中生……
高三英語月考試題答案
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（刪去） 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.
大余中學2006―2007學年度高三年級第一次考試
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