題目列表(包括答案和解析)
A． “Better road design and training hold the key to cycle safety”, the new Transport Secretary said today as he pledged to restore Britain’s safety record. Patrick McLoughlin told Conservative Party Conference that while cycling was enjoying a post-Olympics boom, the number of casualties among cyclists was also rising. “But the number of accidents has gone up too. That means it needs better design and better education too.” Mr McLoughlin said in his first speech as Transport Secretary.
B. Cycling in the UK will become safer through “sheer weight of numbers,” the founder of one of the world’s leading cycle brands has said as he backed The Times’s Cyclesafe campaign. Simon Mottram, founder and chief executive of Rapha, has added his support to 40 cross-party MPs who have signed a letter urging David Cameron to use his speech at the Conservative Party Conference to promote measures to make the streets safer for cyclists.
C. Commuters who cycle to work face an increased danger as the casualty toll during peak hours rose by 10 percent last year. The rate at which cyclists were killed or seriously injured rose sharply last year, official figures showed yesterday.
D. In future decades, Londoners will look back on the way cyclists jostled with buses and lorries on major roads as an absurd anachronism. Some risks are unavoidable. But other risks survive only because we are too slow to embrace bold solutions. That is the message from designers who are proposing an ambitious plan to create cycle lanes suspended above London’s busiest streets. London is one of the most dangerous places in the world for cycling. “SkyCycle” would remedy that problem by attaching dedicated cycle paths to existing railway viaducts.
E. Money should be apportioned from the funding for major transport projects, such as the new Forth Crossing, to create a pot of cash for cycling, campaigners have told MSPs. Cycle groups have given warning that not enough money is being put into routes and promotion. They want the Scottish government to take a percentage of the funding allocated to key national projects and create an “active transport” fund to be distributed gradually.
F. We’d like you to tell us why you love cycling by sending a photo of yourself, a family member or friend with their bike and a note about why it is so brilliant. To take part, instagram your photo with the hashtag #ilovemybike or email it to us at ilovemybike@thetimes.co.uk. We’ll post the best pictures here ilovemybike.tumblr.com.
請閱讀以下信息，并為他們匹配合適的新聞內容。
【小題1】“Cycle lanes in the sky” answer to traffic danger
【小題2】More cyclists are seriously injured on Britain’s roads
【小題3】Share a picture of you and your bike and help us promote the fun and freedom of cycling
【小題4】“Weight of numbers” will bring safe cycling
【小題5】Transport Secretary calls for better road design and training to help cyclists
A．DETECTIVES ABROAD
Read about the lives of real detectives. This monthly magazine brings you up-to-date true stories about real life of detectives as they chase criminals across continents. Find out how some of the most dangerous criminals in the world are caught by some of world’s finest detectives. Follow their routes on the free map which comes with every issue.
B. WORLD TRAVEL
This weekly magazine can bring the world to your home. Have you ever wondered what the Chinese eat for breakfast? Did you know that the Sahara Desert is getting bigger every year? This fascinating magazine, full of color photographs, is your window on the world.
C. ONLY 16
Every week well-known writers bring you the latest teenage love stories. Each magazine carries three full-length stories as well as cartoons and color pictures of your favorite film stars.
D. EUROPE NEWS
The weekly magazine keeps you in touch with what’s happening. Filled with facts and figures about almost everything you can think of, plus articles by our regular writers on the week’s most interesting news stories. Special back page sums up the news for the busy readers.
E. OLD SCHOOLHOUSE
The magazine is approximately 200 pages, full color, and packed with support and fun! Columns: Creation Answers with AiG’s Ken Ham, Resource Room for special needs home schooling with Christine Field, Diana Waring’s History column, our Finishing the Race (High School) department, and Show and Tell – where readers share their own detailed methods and curriculum choices.
F. CRIME AND CRIMINALS
These exciting short stories are written by well-known crime writers. Every magazine brings you the best in criminal thrillers, stories are so good that you won’t be able to put the magazine down. And every month we leave one crime unanswered so that you, that reader, can play detective.
請閱讀以下讀者的信息，然后匹配讀者和適合他/她的雜志：
【小題1】Emi is a university student studying Italian and Politics. She doesn’t have much time to read anything very detailed but she is looking for something with plenty of news and information.
【小題2】Carrie is sixteen years old and loves spending time listening to pop music and lying on her bed reading. She is always interested in finding out more about some of the stars in the world of pop and fashion.
【小題3】Bill travels a lot when he was younger. Now that he has stopped his work, he enjoys reading about foreign people, places and customs even if he has already visited that part of the world.
【小題4】 Leroy used to be a detective. He still takes an active interest in the work of the police, but these days he enjoys reading fictions after years spent chasing real criminals.
【小題5】Brigitte has a five-year-old daughter and after several talks with her husband, she is considering to educate their daughter at home. She would like a magazine to learn about this new trend.
| A．The great impact and progress in genetic engineering B．Worries about privacy protection C．Worries about medical use of genetic engineering D．Genetic knowledge helps to predict diseases E．Genetic knowledge may not be properly used AB．The application of genetic engineering in the medical fields |
A．American & British Classics
A classic is a literary work which has stood the test of time. Generations of readers have turned to classics to discover that which is ever-lasting. Through both the works themselves and the people they mirror, we may better be able to see ourselves.
B. Creative Writing
Creating Writing does not only provide us with an opportunity to express ourselves, but also holds our attention to word choice, paragraph development, and other skills useful in writing.
C. Technical Writing
It's a course which can help you to improve your communication skills in, for arid through technology.
D. Journalism
It's a course for seniors, in which we will cover how 10 gather, write and report the news. We will discuss how information is, or can be organized.
E. Non-fiction
The course is a study of non-fiction through reading many different types of non-fiction. The course will also be about the possible changes in journalistic reporting and the sharing of personal stories of various people on various topics such as travel and adventure.
請閱讀以下學生的相關信息，然后匹配和他/她擬要選擇的課程：
【小題1】______. Lucy .wants to become a famous reporter in the world. She is eager to have the course which can help her to realize her dream.
【小題2】_____. Sally's vocabulary is very large, but she can not organize what she write well, which makes her writing illogically. She wants to get some more skill of it.
【小題3】_____. Lily can not know how to communicate with others as a. writer. She needs to improve the skill of it badly.
【小題4】_______. Jenny wants to become a writer of biography. Therefore, she wants to choose a course connected with it.
【小題5】_______. Mary is interested in Mark Twain, especially his novels which arc full of humors. She really want to know some other writers who were born in the same country as Mark Twain was.
A．American & British Classics
A. classic is a literary work which has stood the test of time. Generations of readers have turned to classics to discover that which is ever-lasting. Through both the works themselves and the people they mirror, we may better be able to see ourselves.
B. World Literature
World Literature examines the common people found in quality literature worldwide, in these worlds, we find not only what is unique to each culture but what is universal,
C. Creative Writing
Creating Writing does not only provide us with an opportunity to express ourselves, but also holds our attention to word choice, paragraph development, and other skills useful in writing.
D. Technical Writing
It's a course which can help you to improve your communication skills in, for arid through technology.
E. Journalism
It's a course for seniors, in which we will cover how 10 gather, write and report the news. We will discuss how information is, or can be organized.
F. Non-fiction
The course is a study of non-fiction through reading many different types of non-fiction. The course will also be about the possible changes in journalistic reporting and the sharing of personal stories of various people on various topics such as travel and adventure.
請閱讀以下學生的相關信息，然后匹配和他/她擬要選擇的課程：
【小題1】Lucy .wants to become a famous reporter in the world. She is eager to have the course which can help her to realize her dream.
【小題2】Sally's vocabulary is very large, but she can not organize what she write well, which makes her writing illogically. She wants to get some more skill of it.
【小題3】Lily can not know how to communicate with others as a. writer. She needs to improve the skill of it badly.
【小題4】Jenny wants to become a writer of biography. Therefore, she wants to choose a. course connected with it.
【小題5】Mary is interested in Mark Twain, especially his novels which arc full of humors. She really want to know some other writers who were born in the same country as Mark Twain was.
1．解析：
，故選A。
2．解析：∵
，
故選B。
3．解析：由
，得
，此時
，所以，
，故選C。
4．解析：顯然，若
與
共線，則
與
共線；若與共線，則
，即
，得
，∴與共線，∴與共線是與共線的充要條件，故選C。
5．解析：設公差為
，由題意得，
；
，解得
或
，故選C。
6．解析：∵雙曲線
的右焦點到一條漸近線的距離等于焦距的
，∴
，又∵
，∴
，∴
，∴雙曲線的離心率是
。故選B.
7.解析：∵
、
為正實數，∴
，∴
；由均值不等式得
恒成立，
，故②不恒成立，又因為函數
在
是增函數，∴
，故恒成立的不等式是①③④。故選C.
8．解析：∵
，∴
在區間
上恒成立，即
在區間上恒成立，∴
，故選D。
9．解析：∵
，此函數的最小值為
，故選C。
10．解析：如圖，∵正三角形
的邊長為
，∴
，∴
，又∵
，∴
，故選D。
11．解析：∵
在區間
上是增函數且
，∴其反函數
在區間上
是增函數，∴
，故選A
12．解析：如圖，①當
或
時，圓面
被分成2塊，涂色方法有20種；②當
或
時，圓面被分成3塊，涂色方法有60種；
③當
時，圓面被分成4塊，涂色方法有120種，所以m的取值范圍是
，故選A。
13．解析：做出
表示的平面區域如圖，當直線
經過點
時，
取得最大值5。
14.解析：∵
，∴
時，
，又
時，
滿足上式，因此，
，
∴
。
15．解析：設正四面體的棱長為，連
，取的中點
，連
，∵
為
的中點，∴
∥，∴
或其補角為與
所成角，∵
，
，∴
，∴
，又∵
，∴
，∴與所成角的余弦值為
。
16．解析：∵
，∴
，∵點
為
的準線與
軸的交點，由向量的加法法則及拋物線的對稱性可知，點
為拋物線上關于軸對稱的兩點且做出圖形如右圖，其中
為點
到準線的距離，四邊形
為菱形，∴
，∴
，∴
，∴
，∴
，∴向量
與
的夾角為
。
17．(10分)解析：（Ⅰ）由正弦定理得，
，
，…2分
∴
，
，………4分
（Ⅱ）∵
，
，∴
，∴
，………………………6分
又∵
，∴
，∴
，………………………8分
∴
。………………………10分
18.解析：（Ⅰ）∵
，∴
；……………………理3文4分
（Ⅱ）∵三科會考不合格的概率均為
，∴學生甲不能拿到高中畢業證的概率
；……………………理6文8分
（Ⅲ）∵每科得A，B的概率分別為
，∴學生甲被評為三好學生的概率為
。……………………12分
（理）∵
，
，
，
。……………………9分
∴
的分布列如下表：
0
1
2
3
∴的數學期望
。……………………12分
19．(12分)解析：（Ⅰ）
時，
，
，
由
得，
或
………3分
+
0
－
0
+
遞增
極大值
遞減
極小值
遞增
，
………………………6分
（Ⅱ）
在定義域
上是增函數，
對
恒成立，即
………………………9分
又
（當且僅當
時，
）
………………………4分
20．解析：（Ⅰ）∵
∥
，
，∴
，∵
底面
，∴
，∴
平面
，∴
，又∵
平面
，∴
，∴
平面
，∴
。………………………4分
（Ⅱ）∵平面，∴
，
，∴
為二面角
的平面角，………………………6分
，
，∴
，又∵平面，
，∴
，∴二面角的正切值的大小為
。………………………8分
（Ⅲ）過點
做
∥，交于點，∵平面，∴
為在平面內的射影，∴
為與平面所成的角，………………………10分
∵
，∴
，又∵∥，∴和與平面所成的角相等，∴與平面所成角的正切值為
。………………………12分
解法2：如圖建立空間直角坐標系，（Ⅰ）∵，
，∴點
的坐標分別是
，
，
，∴
，
，設
，∵平面，∴
，∴
，取
，∴
，∴。………………………4分
（Ⅱ）設二面角的大小為
，∵平面的法向量是，平面
的法向量是
，∴
，∴
，∴二面角的正切值的大小為。………………………8分
（Ⅲ）設與平面所成角的大小為，∵平面的法向量是
，
，∴
，∴
，∴與平面所成角的正切值為。………………………12分
21.（Ⅰ） 解析：如圖，設右準線
與軸的交點為
，過點
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