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闸北区2014学年度第一学期高三英语学科期末练习卷
（2014.12.30）
I. Listening Comprehension
Section A
Directions: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversation and the question will be spoken only once. After you hear the conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.
1. A. On University campus B. in a department store
C. In a Community Service D. On a street
2. A. Husband and wife B. Headmaster and teacher
C. Teacher and parent D. Shop assistant and customers
3.A. Spring B. Summer C. Autumn D. Winter
4. A. Interesting B. Positive C. Opposite D. Boring
5. A. She was terribly sick.
B. She arrived for work narrowly.
C. She walked to work every day.
D. She was always late for work.
6. A. The woman shouldn‟t let her daughter wear so scary clothes.
B. Her daughter‟s Halloween dress wasn‟t smart enough.
C. She couldn‟t have spent too much money on the dress.
D. She couldn‟t encourage her daughter to celebrate Halloween.
7. A. Playing tennis.
B. Writing term paper.
C. Gathering materials.
D. Holding a meeting.
8. A. Gaby was a good neighbour.
B. Gaby didn‟t think highly of his neighbours.
C. Gaby often told wrong stories.
D. Gary often quarrels with his neighbours.
9. A. 40. B. 60. C. 80. D. 120.
10. A. The woman pretends to be pregnant.
B. Men here are not polite enough.
C. Men aren‟t allowed to smoke here.
D. The woman shouldn‟t complain about the men here.
Section B
Directions: in Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.
Questions 11 through 13 are based on the following passage.
11. A. They cooked a meal excellently with given ingredients.
B. They were recommended by Manchester restaurant.
C. They were asked to replace two former high quality chefs.
D. They were selected by the school parents board.
12. A. The cost of the meal has risen.
B. Some pupils complained about the meal.
C. Children get bored with the meals at home.
D. The chefs can‟t handle so many meals a day.
13. A. Because they are from a famous restaurant.
B. Because they pay attention to what pupils like.
C. Because they are highly paid.
D. Because they are good at communicating with parents.
Questions 14 through 16 are based on the following passage.
14. A. Looking like humans. B. Having two wheels.
C. Being mobile and communicative. D. Having essential working ability.
15. A. 82. B. 86. C. 273. D. 300.
16. A. They got there through a land bridge.
B. They got there on foot.
C. They got there by the sea.
D. They got there following animals‟ footprints.
Section C
Directions: In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you hear.
Blanks 17 through 20 are based on the following conversation:
Blanks 21 through 24 are based on the following conversation:
II. Grammar and Vocabulary
Section A
Directions: Read the following two passages. Fill in the blanks to make the passage coherent. For the blanks with a given word, fill in each blank with the proper form of the given word. For the other blanks, fill in each blank with one proper word. Make sure that your answers are grammatically correct.
(A)
Are you on a diet? Then maybe you should consider (25)_________(sit) by the window the next time you eat out.
A new book claims that (26)________ you sit in a restaurant can affect how many you consume.
A New research found that people sitting farthest from the front door ate the fewest salads and were 73 percent (27)________(likely) to order dessert.
Those seated at a dark table ate heavier food and ordered more of it (28)______ diners seated at bright bar tables ordered more salads and fewer desserts.
According to the researchers, the darker it is, the more invisible you (29)______ feel, the less easy it is to see how much you‟re eating and the less guilty you are when you eat more.
In contrast, (30) ________(see) the sunlight, people or trees outside might make you more conscious of (31)________ you look, might make you think about walking or might make you want a green salad.
The researchers also noted that slim diners chewed around 15 times per mouthful, three chews more than heavier diners. By eating more slowly, the diner consumes less in the time
(32)_________ takes for the brain to register satisfaction.
(B)
Beijing‟s annoying smog(雾) seems to have hurt the city‟s appeal to tourists. Last year, Beijing Youth Daily reported that the number of visitors to Beijing (33)_________(fall) 50 percent since January. It‟s said that the city‟s bad air quality was to blame for the decline. It‟s also more difficult (34) _______(attract) high-end employees to work in Beijing, especially those with children.
However, the blanket of poisonous smog hasn‟t hurt Beijing‟s office market, (35)_______ has jumped up quickly on a global ranking to become the fourth-most-expensive location to rent office space in the world. According to a recent research, office space in Beijing‟s Central Business District costs (36)________ average $1,412 per square meter per year.
That‟s more expensive than No.5-rankes central Tokyo or No.6-rangked Madison & Fifth Avenues in New York. The research took into consideration both (37)________ (publish) rental rates and “additional costs,” which include agent fees and (38)_________costs to make the deal happen.
London (39)_________ (remain) the world‟s most expensive city in which to rent office space. Hong Kong, home to the priciest office space in Asia, comes in second globally. The cities
(40)___________(experience) the highest annual growth in office rental rates are both in South Africa with 40 percent rate rise for Durban and 44 percent for Sandton.
Section B
Directions: Complete the following passage by using the words in the box. Each word can be used only once. Note that there is one word more than you need.
Music has been playing a major role in the lives of teenagers for decades and today‟s teens are no ____41_____. Teens listen to over 2.5 hours of music per day. Earbuds, Mp3players, and smartphones make it easy for teens to listen to music while they go about much of their daily lives.
The digital world also means that parents must face new challenges when it comes to a teen‟s music. In the past---when music was ___42_____ through audio tape or CD, it was much easier for parents to be aware of a teen‟s musical ___43_____. But mow that teens have free access to millions of songs and music videos through the internet, parents are less likely to be ____44____ of what their teens are listening to.
Today, it‟s hard to believe that today‟s over-50-years people used to be ___45_____ against Elvis Presley‟s dance moves. Fast-forward to the present day and the society has certainly become more ____46____ of many strange forms of art.
As for parents, music is a powerful tool and certainly music with pro-social or warm lyrics(歌词) can be a(n)___47_____ influence in teens. It‟s important to take an active approach when ____48_____ your teen‟s musical interests. Get your teen to talk to you. Ask questions without passing ___49_____. Always be curious and inquire about what your teen looks for in music and talk about what ____50____ can be found in certain songs.
III. Reading Comprehension
Section A
Directions: For each blank in the following passage there are four words or phrases marked A, B,
C and D. Fill in each blank with the word or phrase that best fits the context.
Gallup used to conduct a poll(投票) that asked students to name the school subject that they considered to be the most difficult. Not ____51____, mathematics came out on top of the difficulty chart. So what is it about math that makes it difficult?
Dictionary.com defines the word “difficult” as “not easily or readily done; requiring much ____52___ or planning to be performed successfully.” This definition gets to the point of the problem when it comes to math. What makes math difficult is that it takes patience and persistence. For many students, math is not something that comes ___53_____. It takes effort. It is a subject that sometimes requires students to devote lots and lots of time and ___54_____.
This means, for many, the problem has little to do with brain power; it is mostly a matter of staying power. And since students don‟t make their own timelines, they can ___55____ the time as the teacher moves on to the next topic.
In fact, there is also an element of brain style in the big picture, according to many scientists. They believe that people are born with ___56____math understanding skills. Logical, left-brain thinkers tend to understand things in sequential bits, while artistic, intuitive, right-brainers are
more ___57____. They take in a lot of information at one time and allow time to let it “sink in”. so left-brain students may grasp concepts __58____ while right-brain students don‟t. To the right brain student, time loss can make them feel confused and behind. Unfortunately in busy classrooms with too many students, students are mot always ___59____ enough time. We have to move on, ready or not.
Math know-how is also cumulative(积累), which means it works much like a pile of building blocks. You have to gain enough ___60___ in one area before you can effectively go on to “build upon” another area. Our first mathematical building blocks are established in primary school, when we learn ____61___ for addition and multiplication, and those first concepts become our ___62__. These mathematical concepts or knowledge has to sink in and become ___63___ before students can move on to challenge the next stage of new concepts. However, teachers don‟t have time to ensure that every single student understands every single concept. So some students move to the next level with really shaky knowledge system. ___64____, as they climb the ladder, they may meet with more and more difficulties and might ___65_____ complete failure at some point.
51. A. surprisingly B. interestingly C. necessarily D. similarly
52. A. emotion B. labor C. curiosity D. money
53. A. regularly B. possibly C. automatically D. secretly
54. A. space B. confidence C. character D. energy
55. A. make up for B. run out of C. take advantage of D. add up to
56. A. steady B. abstract C. different D. sharp
57. A. negative B. global C. simple D. specific
58. A. quickly B. typically C. patiently D. strangely
59. A. reminded about B. exposed to C. blessed with D. accused of
60. A. praises B. scores C. material D. blocks
61. A. conditions B. rules C. aims D. choices
62. A. thought B. attitude C. foundation D. source
63. A. native B. accessible C. firm D. superior
64. A. In addition B. In contrast C. For example D. In result
65. A. realize B. acknowledge C. suffer D. regret
Section B
Directions: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have read.
(A)
October 17, 1989 is a day San Francisco will never forget. On that day, an uncommon number of tragedies took place. It was also a day when total strangers became linked. The story of Jim Betts and Julio Berumen is a moving example of one such meeting.
On that day, Petra Berumen took her daughter Cathy to the dentist. Also in the car was her son six-year-old Julio and their family friend Yolanda. Soon after Petra drove onto the highway, disaster struck. Without warning, the earth began to shake.
上海市闸北区2016届高三一模数学试卷
2015.12
一. 填空题（本大题共9题，每题6分，共54分） 1. (x2)(211)5的展开式中常数项为； 2x
ln(1x),x02. 函数f(x)的单调性为 ；奇偶性为 ； 1,x0ln1x
3. 一个正三棱锥的四个顶点都在半径为1的球面上，其中底面的三个顶点在该球的一个大圆上，则该正三棱锥的体积是 ；
DAB60，E为CD的中点，4. 在菱形ABCD中，AB1，则ABAE的值是 ；
5. 如图，靠山有一个水库，某人先从水坝的底部A测得水坝对面的山顶P的仰角为40，再沿坝面向上走80米到水坝的顶部B测得ABP56，若坝面与水平面所成的锐角为
30，则山高为 米；（结果四舍五入取整）
6. 将序号分别为1、2、3、4、5的5张参观券全部分给4人，每人至少1张，如果分给同一人的2张参观券连号，那么不同的分法种数是 ；（用数字作答）
7. 等差数列{an}的公差为d，关于x的不等式dx22a1x0的解集为[0,9]，则使数列 {an}的前n项和Sn最大的正整数n的值是
228.
过点My0)作圆O:xy1的切线，切点为N，如果OMN
6，那么y0的
取值范围是 ；
9. 如图，正方形ABCD的边长为2，O为AD的中点，射线OP从OA出发，绕着点O顺时针方向旋转至OD，在旋转的过程中，记AOP为x(x[0,])，OP所经过的在正方 形ABCD内的区域（阴影部分）的面积Sf(x)，那么对于函数f(x)有以下三个结论：
对任意x[0,]，都有f(x)f(x)4； 2223f(x1)f(x2)③ 对任意x1,x2(,)，且x1x2，都有0； 2x1x2①f()
其中所有正确结论的序号是 ；
二. 选择题（本大题共3题，每题6分，共18分）
y2
x21 10. “抛物线yax的准线方程为y2”是“抛物线yax的焦点与双曲线322
的焦点重合”的（ ）
A. 充分不必要条件 B. 必要不充分条件
C. 充要条件 D. 既不充分也不必要条件
11. 已知m,n是两条不同直线，,是两个不同平面，给出下列四个命题：
① 若,垂直于同一平面，则与平行；
② 若m,n平行于同一平面，则m与n平行；
③ 若,不平行，则在内不存在与平行的直线；
④ 若m,n不平行，则m与n不可能垂直于同一平面
其中真命题的个数为（ ）
A. 4 B. 3 C. 2 D. 1 *12. 已知i和j是互相垂直的单位向量，向量an满足：iann，jan2n1，nN，
设n为i和an的夹角，则（ ）
A.
B. n随着n的增大而增大 n随着n的增大而减小
C. 随着n的增大，n先增大后减小
D. 随着n的增大，n先减小后增大
三. 解答题（本大题共4题，共18+20+20+20=78分）
13. 如图，在平面直角坐标系xOy中，角的顶点在原点，始边与x轴的非负半轴重合， 终边交单位圆于点A，且[,，将角的终边绕原点逆时针方向旋转
42
于点B，过B作BCy轴于点C；
（1）若点A
，交单位圆 3B的横坐标； （2）求△AOC的面积S的最大值；
14. 经过多年的运作，“双十一”抢购活动已经演变成为整个电商行业的大型集体促销盛宴；为迎接2015年“双十一”网购狂欢节，某厂家拟投入适当的广告费，对网上所售产品进行 促销；经调查测算，该促销产品在“双十一”的销售量p（万件）与促销费用x（万元） 20xa，a为正常数），已知生产该产品还需投入成本102p万 x1
20元（不含促销费用），每一件产品的销售价格定为(4)元，假定厂家的生产能力完全能 p满足p3
满足市场的销售需求；
（1） 将该产品的利润y（万元）表示为促销费用x（万元）的函数；
（2）促销费用投入多少万元时，厂家的利润最大？并求出最大利润的值；
15. 如图，已知动直线l交圆(x3)y9于坐标原点O和点A，交直线x6于点B；
（1
）若|OB|A、点B的坐标；
22（2） 设动点M满足OMAB，其轨迹为曲线C，求曲线C的方程F(x,y)0；
（3） 请指出曲线C的对称性、顶点和图形范围，并说明理由；
（4）判断曲线C是否存在渐近线，若存在，请直接写出渐近线方程；若不存在，说明理由；
16. 已知数列{an}的前n项和为Sn，且点(n,Sn)(nN*)在函数y2x12的图像上；
（1）求数列{an}的通项公式；
（2）设数列{bn}满足：b10，bn1bnan，求{bn}的通项公式；
（3）在第（2）问的条件下，若对于任意的nN，不等式bnbn1恒成立，求实数的取值范围；
*
参考答案
一. 填空题
1. 3； 2. 单调递增，奇函数；
3. ； 4. 1； 5. 176； 4
6. 96； 7. 5； 8. [1,1]； 9. ①②；
二. 选择题
10. A； 11. D； 12. B；
三. 解答题
13.（1）1；（2
24；（2）x1，ymax13； x114.（1）y16x
2412x3
215.（1）A(,)，B(6,3)；（2）y； 556x
（3）关于x轴对称；顶点(0,0)；x[0,6)，yR；（4）x6；
2n22n216.（1）an2；（2）n为奇数，bn；n为偶数，bn；（3）1； 33n
闸北区2014学年度第一学期高三英语学科期末练习卷
（2014.12.30）
I. Listening Comprehension
Section A
Directions: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversation and the question will be spoken only once. After you hear the conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.
1. A. On University campus B. in a department store
C. In a Community Service D. On a street
2. A. Husband and wife B. Headmaster and teacher
C. Teacher and parent D. Shop assistant and customers
3.A. Spring B. Summer C. Autumn D. Winter
4. A. Interesting B. Positive C. Opposite D. Boring
5. A. She was terribly sick.
B. She arrived for work narrowly.
C. She walked to work every day.
D. She was always late for work.
6. A. The woman shouldn‟t let her daughter wear so scary clothes.
B. Her daughter‟s Halloween dress wasn‟t smart enough.
C. She couldn‟t have spent too much money on the dress.
D. She couldn‟t encourage her daughter to celebrate Halloween.
7. A. Playing tennis.
B. Writing term paper.
C. Gathering materials.
D. Holding a meeting.
8. A. Gaby was a good neighbour.
B. Gaby didn‟t think highly of his neighbours.
C. Gaby often told wrong stories.
D. Gary often quarrels with his neighbours.
9. A. 40. B. 60. C. 80. D. 120.
10. A. The woman pretends to be pregnant.
B. Men here are not polite enough.
C. Men aren‟t allowed to smoke here.
D. The woman shouldn‟t complain about the men here.
Section B
Directions: in Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which ______________________________________________________________
跃龙学堂 您身边的中小学生辅导专家 1
one would be the best answer to the question you have heard.
Questions 11 through 13 are based on the following passage.
11. A. They cooked a meal excellently with given ingredients.
B. They were recommended by Manchester restaurant.
C. They were asked to replace two former high quality chefs.
D. They were selected by the school parents board.
12. A. The cost of the meal has risen.
B. Some pupils complained about the meal.
C. Children get bored with the meals at home.
D. The chefs can‟t handle so many meals a day.
13. A. Because they are from a famous restaurant.
B. Because they pay attention to what pupils like.
C. Because they are highly paid.
D. Because they are good at communicating with parents.
Questions 14 through 16 are based on the following passage.
14. A. Looking like humans. B. Having two wheels.
C. Being mobile and communicative. D. Having essential working ability.
15. A. 82. B. 86. C. 273. D. 300.
16. A. They got there through a land bridge.
B. They got there on foot.
C. They got there by the sea.
D. They got there following animals‟ footprints.
Section C
Directions: In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you hear.
Blanks 17 through 20 are based on the following conversation:
Blanks 21 through 24 are based on the following conversation:
______________________________________________________________ 2 跃龙学堂 您身边的中小学生辅导专家
II. Grammar and Vocabulary
Section A
Directions: Read the following two passages. Fill in the blanks to make the passage coherent. For the blanks with a given word, fill in each blank with the proper form of the given word. For the other blanks, fill in each blank with one proper word. Make sure that your answers are grammatically correct.
(A)
Are you on a diet? Then maybe you should consider (25)_________(sit) by the window the next time you eat out.
A new book claims that (26)________ you sit in a restaurant can affect how many you consume.
A New research found that people sitting farthest from the front door ate the fewest salads and were 73 percent (27)________(likely) to order dessert.
Those seated at a dark table ate heavier food and ordered more of it (28)______ diners seated at bright bar tables ordered more salads and fewer desserts.
According to the researchers, the darker it is, the more invisible you (29)______ feel, the less easy it is to see how much you‟re eating and the less guilty you are when you eat more.
In contrast, (30) ________(see) the sunlight, people or trees outside might make you more conscious of (31)________ you look, might make you think about walking or might make you want a green salad.
The researchers also noted that slim diners chewed around 15 times per mouthful, three chews more than heavier diners. By eating more slowly, the diner consumes less in the time
(32)_________ takes for the brain to register satisfaction.
(B)
Beijing‟s annoying smog(雾) seems to have hurt the city‟s appeal to tourists. Last year, Beijing Youth Daily reported that the number of visitors to Beijing (33)_________(fall) 50 percent since January. It‟s said that the city‟s bad air quality was to blame for the decline. It‟s also more difficult (34) _______(attract) high-end employees to work in Beijing, especially those with children.
However, the blanket of poisonous smog hasn‟t hurt Beijing‟s office market, (35)_______ has jumped up quickly on a global ranking to become the fourth-most-expensive location to rent office space in the world. According to a recent research, office space in Beijing‟s Central Business District costs (36)________ average $1,412 per square meter per year.
That‟s more expensive than No.5-rankes central Tokyo or No.6-rangked Madison & Fifth Avenues in New York. The research took into consideration both (37)________ (publish) rental rates and “additional costs,” which include agent fees and (38)_________costs to make the deal happen.
London (39)_________ (remain) the world‟s most expensive city in which to rent office ______________________________________________________________
跃龙学堂 您身边的中小学生辅导专家 3
space. Hong Kong, home to the priciest office space in Asia, comes in second globally. The cities
(40)___________(experience) the highest annual growth in office rental rates are both in South Africa with 40 percent rate rise for Durban and 44 percent for Sandton.
Section B
Directions: Complete the following passage by using the words in the box. Each word can be used only once. Note that there is one word more than you need.
Music has been playing a major role in the lives of teenagers for decades and today‟s teens are no ____41_____. Teens listen to over 2.5 hours of music per day. Earbuds, Mp3players, and smartphones make it easy for teens to listen to music while they go about much of their daily lives. The digital world also means that parents must face new challenges when it comes to a teen‟s music. In the past---when music was ___42_____ through audio tape or CD, it was much easier for parents to be aware of a teen‟s musical ___43_____. But mow that teens have free access to millions of songs and music videos through the internet, parents are less likely to be ____44____ of what their teens are listening to.
Today, it‟s hard to believe that today‟s over-50-years people used to be ___45_____ against Elvis Presley‟s dance moves. Fast-forward to the present day and the society has certainly become more ____46____ of many strange forms of art.
As for parents, music is a powerful tool and certainly music with pro-social or warm lyrics(歌词) can be a(n)___47_____ influence in teens. It‟s important to take an active approach when ____48_____ your teen‟s musical interests. Get your teen to talk to you. Ask questions without passing ___49_____. Always be curious and inquire about what your teen looks for in music and talk about what ____50____ can be found in certain songs.
III. Reading Comprehension
Section A
Directions: For each blank in the following passage there are four words or phrases marked A, B,
C and D. Fill in each blank with the word or phrase that best fits the context.
Gallup used to conduct a poll(投票) that asked students to name the school subject that they considered to be the most difficult. Not ____51____, mathematics came out on top of the difficulty chart. So what is it about math that makes it difficult?
Dictionary.com defines the word “difficult” as “not easily or readily done; requiring much ____52___ or planning to be performed successfully.” This definition gets to the point of the problem when it comes to math. What makes math difficult is that it takes patience and persistence. For many students, math is not something that comes ___53_____. It takes effort. It is a subject that sometimes requires students to devote lots and lots of time and ___54_____.
This means, for many, the problem has little to do with brain power; it is mostly a matter of ______________________________________________________________ 4 跃龙学堂 您身边的中小学生辅导专家
staying power. And since students don‟t make their own timelines, they can ___55____ the time as the teacher moves on to the next topic.
In fact, there is also an element of brain style in the big picture, according to many scientists. They believe that people are born with ___56____math understanding skills. Logical, left-brain thinkers tend to understand things in sequential bits, while artistic, intuitive, right-brainers are more ___57____. They take in a lot of information at one time and allow time to let it “sink in”. so left-brain students may grasp concepts __58____ while right-brain students don‟t. To the right brain student, time loss can make them feel confused and behind. Unfortunately in busy classrooms with too many students, students are mot always ___59____ enough time. We have to move on, ready or not.
Math know-how is also cumulative(积累), which means it works much like a pile of building blocks. You have to gain enough ___60___ in one area before you can effectively go on to “build upon” another area. Our first mathematical building blocks are established in primary school, when we learn ____61___ for addition and multiplication, and those first concepts become our ___62__. These mathematical concepts or knowledge has to sink in and become ___63___ before students can move on to challenge the next stage of new concepts. However, teachers don‟t have time to ensure that every single student understands every single concept. So some students move to the next level with really shaky knowledge system. ___64____, as they climb the ladder, they may meet with more and more difficulties and might ___65_____ complete failure at some point.
51. A. surprisingly B. interestingly C. necessarily D. similarly
52. A. emotion B. labor C. curiosity D. money
53. A. regularly B. possibly C. automatically D. secretly
54. A. space B. confidence C. character D. energy
55. A. make up for B. run out of C. take advantage of D. add up to
56. A. steady B. abstract C. different D. sharp
57. A. negative B. global C. simple D. specific
58. A. quickly B. typically C. patiently D. strangely
59. A. reminded about B. exposed to C. blessed with D. accused of
60. A. praises B. scores C. material D. blocks
61. A. conditions B. rules C. aims D. choices
62. A. thought B. attitude C. foundation D. source
63. A. native B. accessible C. firm D. superior
64. A. In addition B. In contrast C. For example D. In result
65. A. realize B. acknowledge C. suffer D. regret
Section B
Directions: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have read.
(A)
______________________________________________________________
跃龙学堂 您身边的中小学生辅导专家 5
闸北区2015学年度第一学期高三数学（文科）期末练习卷
考生注意：
1. 本次测试有试题纸和答题纸，解答必须在答题纸上，写在试题纸上的解答无效． 2. 答卷前，考生务必在答题纸上将姓名、学校、考试号，以及试卷类型等填写清楚，并在规定区域内贴上条形码．
3. 本试卷共有16道试题，满分150分．考试时间120分钟．
一、填空题（54分）本大题共有9题，要求在答题纸相应题序的空格内直接填写结果，每
个空格填对得6分，否则一律得零分．
1a
1．若二项式2x的展开式中3的系数是84，则实数a的值为 ．
xx
7
x1x,x0,
2．函数fx的单调性为_________；奇偶性为
x1x,x0
3．一个正三棱锥的四个顶点都在半径为1的球面上，其中底面的三个顶点在该球的一个大圆 上，则该正三棱锥的体积是 ．
4．在菱形ABCD中，AB1，DAB60，E为CD的中点，则ABAE的值是 ．
5．已知log2alog2b1，则39的最小值为________．
6．将序号分别为1,2,3,4,5的5张参观券全部分给4人，每人至少1张.如果分给同一人的2 张参观券连号，那么不同的分法种数是 ． 7
．过点M
ab
y0作圆O:x2y21的切线，切点为N，如果y00，那么切线的斜率
是 ．
8．等差数列{an}的公差为d，关于x的不等式dx22a1x0的解集为0,9，则使数列
{an}的前n项和Sn最大的正整数n的值是 ．
9．如图，正方形ABCD的边长为2，O为AD的中点，射线OP从OA出发，绕着点O顺时 针方向旋转至OD，在旋转的过程中，记AOP为x（x[0,]），OP所经过的在正方 形ABCD内的区域（阴影部分）的面积Sf(x)，那么对于函数f(x)有以下三个结论：
3
【2016年闸北区高三英语一模答案】
②对任意x0,，都有fxfx4；
222
f(x1)f(x2)
③对任意x1,x2,，且x1x2，都有0.
x1x22
①f
其中所有正确的结论的序号是 ．
二、选择题（18分）本大题共有3题，每题都给出四个结论，其中有且只有一个结论是正确
的，必须把答题纸上相应题序内的正确结论代号涂黑，选对得6分，否则一律得零分.
1y22
x21焦点重合”的 【 】10．“a”是“抛物线yax的焦点与双曲线
83
A．充分不必要条件； B．必要不充分条件； C．充要条件； D．既不充分也不必要条件．
11．已知m，n是两条不同直线，，是两个不同平面，则下列命题正确的是【 】
A．若,垂直于同一平面，则与平行； B．若m,n平行于同一平面，则m与n平行；
C．若,不平行，则在内不存在与平行的直线； D．若m,n不平行，则m与n不可能垂直于同一平面．
12．已知i和j是互相垂直的单位向量，向量an满足：ann，an2n1，nN，
设n为i和an的夹角，则 【 】
A．n随着n的增大而增大；
B．n随着n的增大而减小；
C．随着n的增大，n先增大后减小； D．随着n的增大，n先减小后增大．
三、解答题（本题满分78分）本大题共有4题，解答下列各题必须在答题纸的规定区域（对
应的题号）内写出必要的步骤．
13．（本题满分18分，第1小题8分，第2小题10分）【2016年闸北区高三英语一模答案】
如图，在平面直角坐标系xOy中，角的顶点在原点，始边与x轴的非负半轴重合， 终边交单位圆于点A，且
,，将角的终边绕原点逆时针方向旋转，交单位
342
圆与点B，过B作BCy轴于点C． （1）若点A
B
（2）求AOC的面积S的最大值．
14．（本题满分20分，第1小题10分，第2小题10分）
有一块铁皮零件，其形状是由边长为30cm的正方形 截去一个三角形ABF所得的五边形，其中AF8cm，
BF6cm，如图所示，现在需要用这块材料截取矩形铁
皮DMPN，使得矩形的相邻两边分别落在CD,DE上，另 一个顶点P落在边CB或BA边上，设DMxcm，矩形
DMPN的面积为ycm2．
A
（1）试求出矩形铁皮DMPN的面积y关于x的函数解析式，并写出定义域； （2）试问如何截取（即x取何值时），可使得到的矩形DMPN的面积最大？ 15．（本题满分20分，第1小题5分，第2小题6分，第3小题9分）
如图，已知动直线ykx交圆(x3)2y29于 坐标原点O和点A，交直线x6于点B． （1）试用k表示点A、点B的坐标；
（2）设动点M满足OMAB，其轨迹为曲线C，
求曲线C的方程F(x,y)0；
（3）请指出曲线C的顶点、对称性和图形范围，并
说明理由．
16．（本题满分20分，第1小题4分，第2小题8分，第3小题8分）
已知数列{an}的前n项和为Sn，且点n,Sn（nN）在函数y2x12的图象上．
（1）求数列{an}的通项公式；
（2）设数列{bn}满足：b10，bn1bnan，求b6的值，并求其通项bn；
（3）在第（2）问的条件下，若对于任意的nN不等式bnbn1恒成立，求实数的
取值范围．
【2016年闸北区高三英语一模答案】
闸北区2015学年度第一学期高三数学（文科）期末练习卷参考答案
一．填空题：
1、1； 2、增函数；奇函数 3
4、1； 5、18； 6、96； 7
、二．选择题：
8、5； 9、① ②
10.A11.D12.B
三．解答题：
13．（本题满分18分，第（1）小题8分，第（2）小题10分） （1）由定义得，A(cos,sin)，Bcos
……………………………… ,sin，
33
3分
依题意知sin
3分
所以点B的横坐标为
，,，所以，………………………………………
342
21
coscos，……………………………………… 2分
332
（2）
|OA|1,|OC|sin,AOC， ……………………………………
32
……… 2分
S
1分
1
|OA||OC|sinAOC ………………………………………………………………… 2
11
…………………………………… 3sinsinsin223243
分
,，42
54
∴2,，…………………………………………………… 1分
363
5
∴当2，即时，sin2取最大值
3643
1
……………………………… 2分 2，
∴S
的最大值为1………………………………………………………………………… 1分
8.
∵
14．（本题满分20分，第（1）小题10分，第（2）小题10分） 解（1）依据题意并结合图形，可知：
10 当点P在线段CB上y30x；…………………………………………… 2分 20 当点P在线段BA上，即24x
，即
0x24
时，
3时0，由
PQBF
，得
QAFA
QA40
于
4
x．……………… 2分 3
是
，
yDMPMDMEQ62x
42
x．………………………………………………………3分 3
所以，
03x 0<x,
y42
6xx x.3
22
44
定
义
3
域
D(
（
2
0．…………………………………… 3分
0x24）由(1)知，当时，
0y7……………………………………………………… 3分 ；
当时，30x40449328832883
，…………………… 4分 y62xx2(x)2
33444
当
且
仅
当
x
93
4
时，等号成
立．………………………………… 2分
2883
． 4
93
cm，然后过点M作DE的垂线交BA于点P，再过点答：先在DE上截取线段DM4
P作DE的平行线交DC于点N，最后沿MP与PN截铁皮，所得矩形面积最大，最大面
2883
cm2．…… 1分 积为4
因此，y的最大值为
15．（本题满分20分，第1小题5分，第2小题6分，第3小题9分） 解：（1）A
2412
,（3分），B6,3（2分）. 55
6k2
x26k26k31k
,)，则点M的参数方程为（2）OMAB(（k为参数）, 223
1k1ky6k
1k2k消去参数，得
2
. ……………………………………………………………6分 x3xy6y0
（3）① 关于轴对x
称； ……………………………………………………………………………1分
将方程中的(x,y)换成(x,y)，方程的形式不变，则曲线C关于x轴对
称. …………2分
② 曲
线C的顶点为（0，
闸北区2015学年度第一学期高三化学学科期末练习卷2015.12
参考答案及评分标准
三、选择题(本题共20分)，每小题4分，每小题有一个或两个正确选项，只有一个正确选23．2，2（各1分，共2分）
24．N2（g）+3H2（g）2NH3（g）+2（b — a）
mol（2分） 25．该温度下催化剂的活性最好；14.5%（各2分，共4分）
27．晶体硅；它属于原子晶体，而硫化铵属于离子晶体；（各1分，共2分）
，
33．2MgCO3·3CaCO3+10CH3COOH →3 Ca+2Mg+10CH3COO+5CO2↑+5H2O（2分）； 34．SiO2（1分）；实验过程中苯酚被空气中的氧气氧化，最终变为褐色物质 （1分）； 35．吸附性（1分）； 36．b（2分）；调节钙、镁离子的物质的量之比（2分），除去过量的乙酸（2分）； 37．蒸发结晶（1分）
－
七、（本题共12分）
38．Na2SO3+H2SO4→Na2SO4+SO2↑+H2O（2分）或Na2SO3+2H2SO4→2NaHSO4+SO2↑+H2O； 39．玻璃棒、漏斗、烧杯（1分），cd（2分）；
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