2020-2021深圳市南山中英文学校高三数学下期末试卷(附答案)
2020-2021学年深圳南山中英文学校中学部高三英语下学期期末考试试卷及参考答案
2020-2021学年深圳南山中英文学校中学部高三英语下学期期末考试试卷及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项ANew events and changes of junior golf competition calendarNew eventsNotah BegayⅢJunior Golf National ChampionshipWhat does a junior golfer aim to pursue? One thing is to be noticed, ideally by a college coach. A remarkable opportunity will be offered by the Notah BegayⅢJunior Golf National Championship to its participants: an event broadcast by Golf Channel. Players aged between eight and 18 can compete in the new event; information about where and when it will be held will be released later.Barbasol Junior ChampionshipBeginning the career in the PGA Tour is something that a junior golfer tends to dream of. The Barbasol Junior Championship, which is scheduled to take place between June 29 and July 2 at Keene Trace Golf Club inNicholasville,Kentucky, will provide such an opportunity. Boys under 19 years old will qualify for this new 54-hole event, and the winner will be awarded a spot at the PGA Tour's Barbasol Championship in July.Changed eventsThunderbird International JuniorThe dates of the AJGA's Thunderbird International Junior have to be changed since the NCAA Championships move to Grayhawk Golf Club inScottsdale,Arizona, for the next three years. Generally, the Thunderbird is played at the end of May. However, this year it is scheduled on different dates for the first time, from April 9 to 12, which means, of course, that the finish date is on Masters Sunday.Gator InvitationalJunior golf intends to prepare for the following college golf. If this is the case, then it is crucial to simulate the higher-level experience as much as possible. Because of that, the Gator Invitational, as a junior boys' event, has made a significant decision on becoming a 54-hole event by adding a round this year. The new version will be played from March 13 to 15 at The Country Club of Jackson inJackson,Mississippi.1. Which event can be watched on TV?A. Notah BegayⅢJunior Golf National Championship.B. Barbasol Junior Championship.C. Thunderbird International Junior.D. Gator Invitational.2. When will the Thunderbird International Junior be played?A. At the end of May.B. From April 9 to 12.C. Between June 29and July 2.D. From March 13 to 15.3. What has been changed about the Gator Invitational?A. The award given to the winnerB. The place where it is played.C. The required age of the players.D. The number of rounds it has.BOne-year-old Tallulah turned purple and stopped moving after the sweet became stuck in her throat. Her mum Leigh-Anne said the drama began during a visit to her grandma’s house when her grandparents gave her older kids some sweets.“Then at about 4:45 pm, Tallulah started to choke—we all went into a panic.”“It seemed like it went on for ages. Not one of us knew what to do.”“I rang an ambulance while my grandma and granddad tried to get the sweet to come up.”“Tallulah was panicking at first but then she started to go purple—she almost had no oxygen left in her.”With her daughter limp (无力的) and time running out, Leigh—Anne knew she couldn’t afford to wait for the ambulance to arrive.“The only thing I could think was to go out into the street.” She said.“I rushed out and screamed for someone to help while my grandma rushed out crying with Tallulah.”At exactly the moment, Caitlin, who is studying public services atRedcarCollege, was passing byQueen Street. She said, “I was waiting to go to work when I heard someone screaming for help, so I ran straight over.”The 17-year-old girl added, “Something just clicked and I went into auto mode. The little girl was completely limp, so I checked her airways and tilted (使倾斜) her over and started hitting her back. I turned her round and tapped on her chest, then after what felt like forever she coughed up the sweet and spat it out.As soon as she started crying I felt a huge relief. I was just so pleased I was able to help.”Caitlin was taught her lifesaving skills when she joined the Army Cadets four years ago.4. When did Tallulah get choked?A. While eating sweets.B. While enjoying a drama.C. While having a meal.D. While taking some medicine.5. Why did the family go out into the street?A. To buy some needed tools.B. To search for timely help.C. To get a breath of fresh air.D. To wait for the ambulance to arrive.6. Which of the following can best describe Caitlin?A. Brave and selfless.B. Kind and energetic.C. Determined and generous.D. Quick-thinking and helpful.7. What may be the best title for the text?A. First aid skill sounds important.B. Screaming for help makes sense.C. Eating sweets endangers baby girl.D. Heroic teenager saves baby girl’s life.CIsraeli Paintings—Israeli artist Menashe Kadishman will hold a personal show named "Flock of Sheep" from November 26 to December 20 at the China National Art Museum On show are 550 colourful oil paintings of sheep heads.His works have been on show inthe Metropolitan Museum in New York and Tate Gallery in London over the past 30 years.Time: 9: 00 a.m.—4: 00 p.m., November 26—December 20.Place: China National Art Museum, 1 Wusi Dajie, Dongcheng District, Beijing.Tel: 6401-2252Russian Ballet—The Kremlin Ballet from Russia will perform two immortal classical ballets—"Swan Lake" and "The Nutcracker"—at the Beijing Beizhan Theatre. Set up in 1990, the theatre has a number of first-class ballet dancers. Most of their performances are classical.Time: 7: 15 p.m., December 5 and 6 ("Swan Lake"); 7: 15 p.m., December 7 ("The Nutcracker")Place: Beizhan Theatre, Xiwai Dajie, Xicheng District, Beijing.Tel: 6605-3388Folk Concert—The Central Conservatory of Music will hold a folk concert in memory of the late musician Situ Huacheng.On the programme are many popular folks such as "Moon Night on the Bamboo Tower", "Celebrating Harvest", "Deep and Lasting Friendship", "Golden Snake Dances Wildly" and "Children's Holiday".Time: 7: 30 p.m., November 25.Place: Beijing Concert Hall, 1 Beixinhuajie, Xicheng District, Beijing.Tel: 6605-58128.If a child is very fond of dancing, his parents should take him to ________.A.China National Art MuseumB.Beizhan TheatreC.Beijing Concert HallD.1 Wusi Dajie9.Menashe Kadishman is well known for painting ________.A.deerB.birdsC.sheepD.flowers10.Which of the following is TRUE?A.The folk concert will last three days.B.The ballet "The Nutcracker" will be put on once.C.The Israeli paintings will be on show for a month.D.China National Art Museum lies in Xicheng District.11.If you dial the telephone number 6605-3388 on Dec. 8, you can ________.A.go to the folk concertB.visit the Art MuseumC.watch the balletD.none of the aboveDAmerican football was the fastest-growing sport for US young players last year, according to a survey sponsored by the sport's governing body.But it was the game's no tackle variety that showed the biggest increase－a finding that may reflect concerns about injury. In American football, a tackle (抢断球) refers to an attempt to stop an opponent by forcing them to the ground.The number of participants in football grew in 2015 while most other sport, except baseball, posted a decline, USA Football said on Monday, citing(引用) the findings of a survey of 30,000 children and teenagers.Participation in flag football (a no-tackle type of football) increased by 8.7 percent among children aged 6 to 14, while tackle football rose by 1.9 percent. For that age group, the only other sport that grew was baseball, with a 3. 3 percent increase.In the 15-to-18 age group, flag football rose by 10. 5 percent, while tackle grew by 2.5 percent.Basketball was the third, with a 1. 1 percent increase. Participation in all other sports declined.Tom Farrey, executive director of the Aspen Institute's Sports & Society Program, said he was surprised that flag football participation rose so much.“The trend suggests that parents aremarching to the beat of a different drummer, in pursuing flagas analternative for their kids," he said.The findings come at a time of increasing concern about the risk associated with youth sports, particularly hockey (曲棍球) and football, where medical researchers have warned about the risk of concussions (damagesto the brain caused by violent blows to the head) and death linked to brain injury.USA Football, anIndianapolis,Indianabased nonprofit funded in part by the National Football League, believed that the increases resulted from better safety and health education."Football participation increases, even modest increases, may signal that programs such as our Heads Up Football program and practice guidelines are making a positive difference," said Scot Hallenbeck, USA Football chief executive, in a statement.Robert Cantu, aBostonUniversityneurosurgery professor and investigator at the school's chronic Traumatic Encephalopathy (CTE) Center said the increase in fag football participation signaled that more parents were directing children to a safe alternative12. What can we learn about the two age groups?A. Flag football grew the fastest in the 6-to-18 group.B. Tackle football grew he fastest in the 6-to-14 group.C. Participation in baseball declined the most in both groupsD. Participation in tackle football increased the most in both groups.13. The underlined part probably means ________.A working at a different paceB. behaving in a different wayC. ignoring the major differencesD. trying to accept different opinions14. The popularity of flag football is inked with the fact thatA. its rules have been adapted for young playersB. it receives more funds than other varietiesC. tackle football is an old-fashioned gameD. experts worry about children's safety15. What is the cause of football growth according to USA Football?A. Their safety programs are successful.B. More children show interest in the game.C. Football is less likely to cause concussions.D. There are different types of football to choose from.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2021届深圳南山中英文学校中学部高三英语下学期期末考试试题及答案解析
2021届深圳南山中英文学校中学部高三英语下学期期末考试试题及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AWe are proud to present a showcase for kid inventions from children chosen from the Kid's Forum at Blue Print Earth. We hope you enjoy the ideas expressed here and join us in supporting the next generation.Eater of Natural DisastersMy invention cansave your home by sucking up all-natural disasters. The government will not own this machine, but by you so there will be no taxes on it. Order Now! The Eater of Natural Disasters will run on renewable batteries. It will cost 50 dollars to make and I will sell it for just $ 75.Created by Matthew Szekeresh —Mt.WashingtonElementary, 5th Grade.Pick-up-Pollution BombMy invention is called the Pick-up-Pollution Bomb. It will just pick up pollution and it won't hurt anything else like people, animals, property, playgrounds, and parks. The reason why I made it is that I think there is too much pollution on the Earth. It sells for $100 apiece, and if you buy this now, I will send you another one for free.Created gratefully by Lauren Newberry — Mt. Washington Elementary, 5th GradeFlying HouseMy invention is a home that will blast off in space. For example, if there were an earthquake people would immediately blast off, or if there were a flood it would take off. Only for $ 400.99.Created by David Turner —Mt.WashingtonElementary, 5th GradeBug RobotMy invention is a robot that catches little bugs, eats little bugs, sucks up pollution, sucks up natural disasters, and turns them into food solving the problems of too many little bugs, natural disasters, pollution and starvation. My product is worth $500. My invention works on 2 triple — A batteries. And if you order one today I'll throw in 4 rechargeable triple-A batteries.Created by Cassie Courtey —Mt.WashingtonElementary, 5th Grade1. Why is the Flying House created?A. To explore the space.B. To clean the air.C. To prepare people for earthquakes.D. To help people escape from natural disasters.2. Which invention can turn pollution into food?A. The Bug Robot.B. The Pick-up-Pollution Bomb.C. The Flying House.D. The Eater of Natural Disasters.3. What can we infer about the four inventions?A. They are very easy to build.B. They are ideas from kids in the same school.C. They are expensive but of practical use.D. They are being used by people.BMost children who have suffered from ADHD still have it as teens. During teen years, especially as the hormonal changes of teenagers are going on and the demands of school and extra-curricular activities are increasing, ADHD may get worse.Because of problems with getting unfocused and poor concentration, many teens with ADHD have problems in school. Grades may fall, especially if the teen is not getting ADHD treatment. It’s not uncommon for teens with ADHD to forget their homework, lose textbooks, and become bored with their daily class work. Teens may become inattentive or extremely attentive, not waiting for their turn before blurting out answers. They may cut in on their teacher and classmates. Teens with ADHD may also befidgetyand find it hard to sit still in class.Often, teens with ADHD are so busy focusing on other things that they forget about the task at hand. This can be seen especially with homework and athletic skills and in relationships with their schoolmates. This lack of attention to what they’re doing often leads to bad grades on tests and being passed over for sports teams, after-school activities, and learning teams. Kids with ADHD can be targets for bullying, too. But, not all children with ADHD have trouble getting along with others. If your child does, you can take measures to help improve their social skills and relationships.ADHD affects all parts of a teenager’s life. As a parent you should discover your teen’s troubles as early as possible. The earlier your child’s troubles are discovered, the more successful the following steps can be.4. What does the author plan to do in paragraph 1?A. To list the types of ADHD.B. To introduce the main topic.C. To show the author’s opinion.D. To explain the causes of ADHD.5. What does the underlined word “fidgety” probably mean in paragraph 2?A. Clever.B. Noisy.C. Restless.D. Lazy.6. What is the text mainly about?A. Ways to deal with ADHD.B. Effects of ADHD on teens.C. Teens’ school performances.D. Demands of school work.7. What may the following paragraph talk about?A. How parents can help a teen with ADHD.B. The importance of healthy peer relationships.C. How many children are suffering from ADHD. D. Different opinions about treating ADHD in teens.CHi, Momis a hit inChina. Since its release in early February the movie has earned more than 5 billion yuan at the box office. It is currently the second-highest-grossing film ever released in the country, and may yet overtakeWolf Worrior2, an action film from 2017.Written and directed by Jia Ling, the film is adapted from her comedy routine from 2016 which explored her relationship with her mother, who died in an accident when Ms. Jia was 19. At a time when many people have been separated from their families, the themes of grief and filial piety (孝道) inHi, Mombring agreement.The film’s impressive box office income is also a reminder of the health of the industry inChinacompared withHollywood. In the West cinemas remain closed due to lockdown or operate at limited capacity; inChina, where many restrictions have been lifted, between 50% and 75% of seats are available to book. During the Spring Festival, Chinese cinemas made an estimated $1.5 billion in ticket sales – 71% of takings at the American box office in all of 2020.With cinemas shut, film-sales agent stopped bringingHollywoodmovies to market. That has given locally made films a chance to excel. Since 2013, domestic films have taken around 60% of total box office earnings. In 2021, that number may get closer to 100%.8. What can be inferred from the first paragraph aboutHi, Mom?A. It will be a success.B.Wolf Worrior2 will be released after it.C. It is better than Wolf Worrior 2.D. It may be the first-highest-grossing film inChina.9. Which statement is NOT true according to the text?A. The film industry inChinais developing better than that inHollywood.B. The film is based on a real story.C. You can’t go to cinema because there are many restrictions.D. Many people can’t see their families often nowadays.10. What is the author’s attitude towards local films?A. NegativeB. PositiveC. IndifferentD. Skeptical11. What can be a suitable title for the text?A. Local Movies Arise.B. China Film Industry.C. Comedy Time.D.Hi, Mom-China’s Latest Hit.DIf you ever find yourself trapped in the wilderness without food, you'llhave to figure out how to feed yourself. Many plants in the wild areedible, but many are also poisonous. So it is necessary to learn how to determine whether the plants you find can be eaten safely.Avoid using this method without careful planning. Some plants can be deadly, and even if you follow these guidelines perfectly, there is always a chance that a plant will make you seriously ill. Prepare yourself for wilderness outings by learning about the local plants, and carry a guidebook to help you identify plants. Even if you are unprepared and cannot find food you know to be safe, remember that, depending on your activity level, the human body can go for days without food, and you’re better off being hungry than being poisoned.Testing the plant in your mouth is dangerous, so go forward very slowly and carefully. First, hold a small portion of the prepared plant part against your lip for 3 minutes. Do not put the plant in your mouth. If you notice any burning, tingling (刺痛), or other reactions, discontinue testing. Second, place another small portion of the plant part on your tongue. Hold the plant on your tongue without chewing for 15 minutes. Discontinue testing if you notice any reaction. Third, chew the plant and holdit in your mouth for 15 minutes. Chew the plant well, and do not swallow. Discontinue testing if you notice any reaction. Fourth, swallow the small portion of the plant. Wait 8 hours. Do not eat or drink anything during this period except purified water. If you feel sick, immediately throw up what you eat and drink plenty of water. If activated charcoal (活性炭) is available, take that with the water.12. What’s the meaning of the underlined world “edible” in paragraph 1?A. Suitable for using as food.B. Widely spread.C. Existing in large quantities.D. Not widely known.13. What can we know from paragraph 2?A. Planning is unnecessary when using the method.B. Not all plants in the wild can serve as food generally.C. Suffering hunger can be more dangerous than testing plants.D. Following the method perfectly can ensure safety.14. Which is the correct order of testing plants in the mouth?① wait and see ② chew it in the mouth③ put it on the tongue④ put it against lips ⑤ swallow itA. ③④②①⑤B. ④③②①⑤C. ③④②⑤①D.④③②⑤①15. Where might the passage come from?A. A student’s diary.B. A science report.C. A guide book for camping.D. A doctor’ s notebook.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2020-2021深圳华南中英文学校高中三年级数学下期末一模试卷及答案
2020-2021深圳华南中英文学校高中三年级数学下期末一模试卷及答案一、选择题1．设1i 2i 1i z -=++，则||z = A ．0 B ．12 C ．1 D ．22．某学校开展研究性学习活动，某同学获得一组实验数据如下表：x1.99 3 4 5.1 6.12 y 1.5 4.04 7.512 18.01对于表中数据，现给出以下拟合曲线，其中拟合程度最好的是( )A ．22y x =-B ．1()2x y =C ．2y log x =D ．()2112y x =- 3．设是虚数单位，则复数(1)(12)i i -+=（ ） A ．3+3iB ．-1+3iC ．3+iD ．-1+i 4．()()31i 2i i --+=（ ） A ．3i + B ．3i -- C ．3i -+ D ．3i - 5．设向量a r ，b r 满足2a =r ，||||3b a b =+=r r r ，则2a b +=r r （ ）A ．6B ．32C ．10D ．42 6．为美化环境，从红、黄、白、紫4种颜色的花中任选2种花种在一个花坛中，余下的2种花种在另一个花坛中，则红色和紫色的花不在同一花坛的概率是A ．13B ．12C ．23D ．567．如图是某高三学生进入高中三年来的数学考试成绩茎叶图，第1次到第14次的考试成绩依次记为1214,,A A A L ，下图是统计茎叶图中成绩在一定范围内考试次数的一个算法流程图，那么算法流程图输出的结果是（ ）A ．7B ．8C ．9D ．108．已知函数()(3)(2ln 1)x f x x e a x x =-+-+在(1,)+∞上有两个极值点，且()f x 在(1,2)上单调递增，则实数a 的取值范围是（ ）A ．(,)e +∞B ．2(,2)e eC ．2(2,)e +∞D ．22(,2)(2,)e e e +∞U 9．已知a 为函数f （x ）=x 3–12x 的极小值点，则a=A ．–4B ．–2C ．4D ．2 10．如图所示，网格纸上小正方形的边长为1，粗线画出的是由一个棱柱挖去一个棱锥后的几何体的三视图，则该几何体的体积为A ．72B ．64C ．48D ．32 11．若0,0a b >>，则“4a b +≤”是 “4ab ≤”的（ ）A ．充分不必要条件B ．必要不充分条件C ．充分必要条件D ．既不充分也不必要条件12．已知复数z 满足()12i z +=，则复数z 的虚部为（ ） A ．1B ．1-C ．iD ．i - 二、填空题13．若双曲线22221x y a b-=()0,0a b >>两个顶点三等分焦距，则该双曲线的渐近线方程是___________.14．已知曲线ln y x x =+在点()1,1处的切线与曲线()221y ax a x =+++相切,则a= ． 15．若三点1(2,3),(3,2),(,)2A B C m --共线，则m 的值为 ． 16．函数()22,026,0x x f x x lnx x ⎧-≤=⎨-+>⎩的零点个数是________． 17．若不等式|3|4x b -<的解集中的整数有且仅有1，2，3，则b 的取值范围是18．已知点()0,1A ，抛物线()2:0C y ax a =>的焦点为F ，连接FA ，与抛物线C 相交于点M ，延长FA ，与抛物线C 的准线相交于点N ，若:1:3FM MN =，则实数a 的值为__________．19．如图，用6种不同的颜色给图中的4个格子涂色，每个格子涂一种颜色，要求最多使用3种颜色且相邻的两个格子颜色不同，则不同的涂色方法共有 种（用数字作答）．20．幂函数y=x α,当α取不同的正数时,在区间[0,1]上它们的图像是一族美丽的曲线(如图).设点A (1,0),B (0,1),连接AB ,线段AB 恰好被其中的两个幂函数y=x α,y=x β的图像三等分,即有BM=MN=NA ,那么,αβ等于_____.三、解答题 21．已知向量()2sin ,1a x =+r ，()2,2b =-r ，()sin 3,1c x =-r ，()1,d k =u r (),x R k R ∈∈（1）若,22x ππ⎡⎤∈-⎢⎥⎣⎦，且()//a b c +r r r ，求x 的值. （2）若函数()f x a b =⋅r r ，求()f x 的最小值.（3）是否存在实数k ，使得()()a dbc +⊥+r u r r r ？若存在，求出k 的取值范围；若不存在，请说明理由.22．某小组共10人，利用假期参加义工活动，已知参加义工活动次数为1，2，3的人数分别为3，3，4，现从这10人中随机选出2人作为该组代表参加座谈会．()1设A 为事件“选出的2人参加义工活动次数之和为4”，求事件A 发生的概率； ()2设X 为选出的2人参加义工活动次数之差的绝对值，求随机变量X 的分布列和数学期望．23．如图，矩形ABCD 和菱形ABEF 所在的平面相互垂直，ABE 60∠=︒，G 为BE 的中点.(Ⅰ)求证：AG ⊥平面ADF ；(Ⅱ) 求AB 3=BC 1=，求二面角D CA G --的余弦值.24．已知矩形ABCD 的两条对角线相交于点20M （，），AB 边所在直线的方程为360x y --=，点11T -（，）在AD 边所在直线上. （1）求AD 边所在直线的方程；（2）求矩形ABCD 外接圆的方程.25．已知数列｛n a ｝的前n 项和Sn ＝n 2－5n (n∈N +）． （1）求数列｛n a ｝的通项公式；（2）求数列｛12n n a +｝的前n 项和Tn . 26．设O 为坐标原点，动点M 在椭圆C 22:12x y +=上，过M 作x 轴的垂线，垂足为N ，点P 满足2NP =u u u v u u u v .（1）求点P 的轨迹方程；（2）设点Q 在直线3x =-上，且1OP PQ ⋅=u u u v u u u v.证明：过点P 且垂直于OQ 的直线l 过C 的左焦点F .【参考答案】***试卷处理标记，请不要删除一、选择题1．C解析：C【解析】分析：利用复数的除法运算法则：分子、分母同乘以分母的共轭复数，化简复数z ，然后求解复数的模. 详解：()()()()1i 1i 1i 2i 2i 1i 1i 1i z ---=+=++-+ i 2i i =-+=，则1z =，故选c.点睛：复数是高考中的必考知识，主要考查复数的概念及复数的运算．要注意对实部、虚部的理解，掌握纯虚数、共轭复数这些重要概念，复数的运算主要考查除法运算，通过分母实数化转化为复数的乘法，运算时特别要注意多项式相乘后的化简，防止简单问题出错，造成不必要的失分.2．D解析：D【解析】【分析】根据,x y 的数值变化规律推测二者之间的关系，最贴切的是二次关系.【详解】根据实验数据可以得出，x 近似增加一个单位时，y 的增量近似为2.5，3.5，4.5，6，比较接近()2112y x =-，故选D. 【点睛】 本题主要考查利用实验数据确定拟合曲线，求解关键是观察变化规律，侧重考查数据分析的核心素养.3．C解析：C【解析】因为2(1)(12)1223i i i i i i -+=+--=+，故选 C.考点：本题主要考查复数的乘法运算公式. 4．B解析：B【解析】【分析】先分别对分子和分母用乘法公式化简，再分子分母同时乘以分母的共轭复数，化简即得最后结果.【详解】由题意得，复数()()()31i 2i 13i i 13i 3i i i i i --+-+⋅-+===----⋅．故应选B 【点睛】本小题主要考查复数的乘法和除法的运算，乘法的运算和实数的运算类似，只需要记住2i 1=-.除法的运算记住的是分子分母同时乘以分母的共轭复数，这一个步骤称为分母实数化，分母实数化的主要目的是将分母变为实数，然后将复数的实部和虚部求出来.属于基础题.5．D解析：D【解析】【分析】3=，求得2a b ⋅=-r r ，再根据向量模的运算，即可求解．【详解】∵向量a r ，b r 满足2a =r ，3b a b =+=r r r 3=，解得2a b ⋅=-r r ．则2a b +==r r ．故选D ．【点睛】本题主要考查了向量的数量积的运算，及向量的模的运算问题，其中解答中熟记向量的数量积的运算和向量的模的运算公式，合理、准确运算是解答的关键，着重考查了推理与运算能力，属于基础题．6．C解析：C【解析】试题分析：将4种颜色的花种任选2种种在一个花坛中，余下2种种在另一个花坛中，有6种种法，其中红色和紫色的花不在同一个花坛的种数有4种，故所求概率为23，选C. 【考点】古典概型【名师点睛】作为客观题形式出现的古典概型试题,一般难度不大,解答中的常见错误是在用列举法计数时出现重复或遗漏,避免此类错误发生的有效方法是按照一定的标准进行列举. 7．C解析：C【解析】【分析】根据流程图可知该算法表示统计14次考试成绩中大于等于90的人数，结合茎叶图可得答案．【详解】根据流程图所示的顺序，可知该程序的作用是累计14次考试成绩超过90分的次数．根据茎叶图可得超过90分的次数为9.故选：C ．【点睛】本题主要考查了循环结构，以及茎叶图的认识，解题的关键是弄清算法流程图的含义，属于基础题．8．C解析：C【解析】【分析】求得函数的导数()(2)()x xe a f x x x-'=-⋅，根据函数()f x 在(1,)+∞上有两个极值点，转化为0x xe a -=在(1,)+∞上有不等于2的解，令()xg x xe =，利用奥数求得函数的单调性，得到()1a g e >=且()222a g e ≠=，又由()f x 在(1,2)上单调递增，得到()0f x '≥在(1,2)上恒成立，进而得到x a xe ≥在(1,2)上恒成立，借助函数()x g x xe =在(1,)+∞为单调递增函数，求得2(2)2a g e >=，即可得到答案.【详解】由题意，函数()(3)(2ln 1)x f x x e a x x =-+-+， 可得2()(3)(1)(2)()(2)()x x xx a xe a f x e x e a x e x x x x -'=+-+-=--=-⋅， 又由函数()f x 在(1,)+∞上有两个极值点，则()0f x '=，即(2)()0x xe a x x--⋅=在(1,)+∞上有两解， 即0x xe a -=在在(1,)+∞上有不等于2的解，令()x g x xe =，则()(1)0,(1)xg x x e x '=+>>， 所以函数()xg x xe =在(1,)+∞为单调递增函数， 所以()1a g e >=且()222a g e ≠=， 又由()f x 在(1,2)上单调递增，则()0f x '≥在(1,2)上恒成立， 即(2)()0x xe a x x--⋅≥在(1,2)上恒成立，即0x xe a -≤在(1,2)上恒成立， 即x a xe ≥在(1,2)上恒成立，又由函数()x g x xe =在(1,)+∞为单调递增函数，所以2(2)2a g e >=， 综上所述，可得实数a 的取值范围是22a e >，即2(2,)a e ∈+∞，故选C. 【点睛】本题主要考查导数在函数中的综合应用，着重考查了转化与化归思想、逻辑推理能力与计算能力，对导数的应用的考查主要从以下几个角度进行：(1)考查导数的几何意义，求解曲线在某点处的切线方程；(2)利用导数求函数的单调区间，判断单调性；已知单调性，求参数；(3)利用导数求函数的最值(极值)，解决函数的恒成立与有解问题，同时注意数形结合思想的应用.9．D解析：D【解析】试题分析：()()()2312322f x x x x ==+'--，令()0f x '=得2x =-或2x =，易得()f x 在()2,2-上单调递减，在()2,+∞上单调递增，故()f x 的极小值点为2，即2a =，故选D.【考点】函数的导数与极值点【名师点睛】本题考查函数的极值点．在可导函数中，函数的极值点0x 是方程'()0f x =的解，但0x 是极大值点还是极小值点，需要通过这个点两边的导数的正负性来判断，在0x 附近，如果0x x <时，'()0f x <，0x x >时'()0f x >，则0x 是极小值点，如果0x x <时，'()0f x >，0x x >时，'()0f x <，则0x 是极大值点.10．B解析：B【解析】【分析】由三视图可知该几何体是一个底面边长为4的正方形，高为5的正四棱柱，挖去一个底面边长为4，高为3的正四棱锥，利用体积公式，即可求解。
2020-2021学年深圳南山外国语学校高三英语下学期期末试题及答案解析
2020-2021学年深圳南山外国语学校高三英语下学期期末试题及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AShopping centers，stadiums and universities may soon have a new tool to help fight crime.ACaliforniacompany called Knightscope says its robots can predict and prevent crime. Knightscope says the goal is to reduce crime by half in areas the robots guard.William Santana Li is the chief executive officer of Knightscope. He says，"These robot security guards will change the world. Our planet has more than seven billion people on it. It's going to quickly get to nine billion people. The security equipmentthat we have globally is just not going to develop that fast. The company's Autonomous Data Machines can become the eyes and ears of law enforcement（执法）.""You want them to be machines plus humans. Let. the machines do the heavy and sometimes dangerous work and let the humans do the strategic decision-making work，so it's always working all together."The machines do not carry weapons but they have day and night video cameras which are able to turn 360 degrees and can also sense chemical and biological weapons.Some people may become concerned about their privacy, especially in connection with the video recordings. Some people may worry that such recordings will appear on the Internet. Eugene Volokh, a law professor at the UCLA School of Law, says the machines have to be used in the right way and it will be interesting to see how state laws deal with this kind of video.William Santana Li says there is a long waiting list for the robots in theUS. Workers in the company are working overtime to meet the demands of the market. At least 25 other countries are also interested in these robot security guards.1. What can this new tool do for humans?A. Make strategic decisions.B. Keep watching day and night.C. Carry heavy weapons.D. Stop crime autonomously.2. Why are some people worried about the new robots?A. Their privacy may be let out.B. The robots are very expensive.C. Robots will replace humans.D. They will be out of work soon.3. Which of the following can be the best title of the text?A. Robots Are Becoming More PopularB. Robots Contribute aLotto the WorldC. Robots Are in Great Demand NowD. Security Robots Could Help Cut CrimeBMore than 10,000 people were made homeless in Ternang when the Sungai Mas overflowed its banks yesterday after six days of continuous heavy rain.The wooden bridge across the river has been washed away. The town is cut off by flood waters. At the fifth mile, Jalan Tengkn, the water is two meters deep. It is closed to all traffic. Flooding first happened at mid-afternoon yesterday along the river banks. People trying to get to higher ground were just in time to escape the destroying of the flood. Most of the flood victims(受害者) had to leave all their things behind.The National Flood Relief(救济) Center was reported to give its help and by early evening the whole town was moved out, helped by the army, police, Red Cross Society and volunteers(志愿者).The flood victims are now housed in different simple relief centers in the nearby town of Ternang. “Everything possible is being done to help the unlucky people,” a government spokesman said, “In fact, money, food and clothing have begun to come in from public organizations and helpful people. A Disaster Relief Fund(救灾基金会) will be started as soon as possible.”According to the latest reports it is still raining heavily at Ternang. The whole town is expected to be wholly covered by the water. So far no deaths have been reported.4. This passage is probably taken from______.A. a storybookB. a textbookC. a magazineD. a newspaper5. It seems that the flood happened just because ______.A. the banks were too lowB. the wooden bridge is solid (坚固)C. the river was too narrowD. they had had wet days for some time6.From the passage we know that ______.A. though the town was flooded, you could still go there by busB. as soon as the water flowed over the banks, people began to go to higher landsC. the government and the whole society are taking great care of the flood victimsD. the flood hasn't brought a large loss to the town as nobody died in the flood7. What is the best title for this passage?A. A Big FloodB. Ternang Is destroyedC. Over 10,000 People Are HomelessD. Rescue Team ArrivedCIn the Pacific Northwest during winter, 5:15 am might as well be the dead of night. The alarm goes off and the onlylight is the red glow from my clock. My body says, “Go back to bed.” But I don’t. I know my running partner will be waiting in the street and I’m not going to stand her up. Then I walk onto the road, complaining about the cold and wishing I were back under my warm covers.If you’d have asked me a year ago if I could see myself running at 5:15 on a winter morning, I’d have laughed. Morning just wasn’t my thing and running in the morning was something I didn’t even consider. “I prefer to work out in the middle of the morning or in the afternoon,” I’d say to my friends who go to the gym before work.Then, last fall I reconnected with an old neighborhood friend. She’d been running in the morning and taken off forty pounds that year. When I looked in the mirror, I knew I could benefit from the same kind of weight loss. I asked if I could join her. I knew I needed to change something if I was going to get back in shape.The first two months were especially hard, because we ran twice a week at 5:15 am and I slept till 7:00 the other mornings. But as I’ve adjusted to the routine of running, I’ve discovered great joys that make it even more worthwhile than a little weight loss.While I haven’t lost forty pounds yet, it’s amazing how much more energy I have and how much stronger I feel. Because of the morning run, the rest of my day is more productive. I wouldn’t say I’ve become a morning person, but I would say morning running is now my thing.8. What can we know about the author from paragraph 1?A. 5:15 is the ideal time for her to exercise.B. She prefers to run without any company.C. She takes the run with warm clothes on.D. She goes for a run in spite of the cold and early rise.9. What was the author’s attitude to morning running a year ago?A. Scared.B. Unfavorable.C. Supportive.D. Confused.10. What made the author begin to run in the morning?A. Her partner’s encouragement.B. Her friend’s suggestion.C. Realizing the benefits of running.D. Realizing the harm of being fat.11. What effect does morning runninghave on the author?A. She has become slim again.B. She has become more confident.C. She has become more energetic.D. She has become more exhausted.DWhen I was a child, I attained high grades in my academic study. However, I was physically uncoordinated because I was running too slowly. But for future college application, sport was a must. So I took up fencing (击剑) because I thought it required more strategy than athletic ability.Then I joined the school’s fencing team. My movements were clumsy compared to the seniors. One afternoon after a whole lesson’s failure, tears of frustration welled up in my eyes. One of my teammates approached me, “Could you tell me where your blade (剑) hit me?” She asked. I pointed to her right shoulder. She nodded and patted my stomach, “That’s where I hit you.” She had begun to walk away when I blurted out, “Want to practice together? Again?”We practiced until we both felt more confident. But it wasn’t just the two of us. All these girls were entirely willing to share their knowledge with everyone, helping each other to grow.That afternoon, I watched a senior fencer execute a flawless attack admiringly. Something inside me suddenly bloomed. I realized later that it was love for both fencing and the fencing team.During the city championship, I was selected to fence. My opponent was the best fencer on her school’s team. “Ready, fence.” The match began. Suddenly, my opponent’s blade hit me. The score was 1-0.At the moment I could hear my teammates shouting, “Keep distance!” And the team captain’s voice was clear and commanding, “Parry, then disengage!”Fencing, unlike academics, wasn’t something I could succeed in by myself—even during an individual match, my teammates were still giving me advice. Unathletic as I was, I was proud to be an athlete and a teammate.I saw my blade tip bury itself into my opponent’s shoulder and the judge signaling that it was my point. I could taste the sweat on my lips, which were breaking out into a smile.12. Why did the author start to learn fencing?A. Because she needed to train her coordination.B. Because she thought it would be easier for her.C. Because she could not succeed in any other sport.D. Because she wanted to enter the school fencing team.13. How did the girls improve their fencing skills?A. By observing flawless attacks.B. By practicing on their own.C. By offering guidance to each other.D. By competing with other teams.14. What distinguishes fencing from academics according to the author?A. Strong determination.B. Hard work.C. Athletic strategy.D. Team support.15. How did the author feel when she got her point?A. Unbeatable and respectful.B. Sweaty and ashamed.C. Energetic and secure.D. Proud and thankful.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2020-2021学年深圳南山深大附中高三英语期末考试试题及答案解析
2020-2021学年深圳南山深大附中高三英语期末考试试题及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AThe Rechargeable Go!☑The digital sound processing chip(芯片) provides clear sound and makes speech easier to understand with less whistling sound☑Never replace batteries again!Full Charge Gives 16 Hours of Use! (Free Charging Station Included)☑Easy On/ Off Button☑Automatic Noise Reduction and Feedback Canceler☑100% Money Back Guarantee5 Star Reviews☑☑☑☑☑Amazing!"My sisters had all given up hope that our elderly mother would hear us clearly again. And then we took a chance. We're so glad we did. They've been amazing for her, and for our entire family."-Karen M.The new HearClear GO Rechargeable Digital Hearing Aids feature advanced digital technology at an unbelievably affordable price! The GO has the same key elements that all high-end digital hearing aids share while leaving out fancy bells and whistles that increase cost and require expensive adjustments. You'll be happier saving much money!Your lightweight GO hearing aids are amazingly convenient! With the GO'S charging station, you won't have to keep replacing tiny hearing aid batteries, and the GO is pre-programmed for most mild to moderate hearing loss-no costly professional adjustments needed.You can spend thousands on an expensive hearing aid, or you can spend just $ 239 on a hearing aid that's great for most mild to moderate hearing loss (only $ 199 each when you buy a pair). We're so sure you'll be happy with your new hearing aids.1. Which is the feature of the GO?A. It removes noises.B. It has separate on/ off buttons.C. It includes small batteries.D. It focuses on practical functions.2. Why does the author refer to Karen?A. To prove the GO's popularity.B. To explain the GO'S function.C. To convey the family's amazement.D. To show the GO'S high performance.3. How much do you pay for a pair of the GO?A. $ 199.B. $ 239.C. $ 398.D. $ 478.BSince I was born and brought up in a rural town, I have a great interest in nature. Using the chance of studying abroad in my second year at college, I decided to go toCanadajust because I wanted to see the beautiful phenomena there So after I finished the study program, I went toYellowknifein theNorthwest Territories.I clearly remember the sixth night inYellowknife. Suddenly my host mother came to my room around 8 p.m. and told me to change clothes and go outside quickly carrying her camera.The northern lights were flickering (闪烁) in the sky! I was shocked and just stood there with my mouth open.I forgot to take pictures of the mysterious lights.Since that night, whenever it was sunny, I went outside at night and looked at the sky. It was so cold that I lost all feeling in myhands and feet.As I took pictures of the northern lights, I came to find a characteristic movement of the lights. They first appear in the north part of the sky and then they gradually come down to the south part of the sky. After that, suddenly, they come in the middle of the north and south only for a while, which is the time when the best northern lights can be seen. Since it is only a few seconds for the northern lights to come down to the middle of the sky, it is very hard to get good pictures.The stronger the sun acts, the better and stronger the northern lights flicker in the sky. That’s because they come about from the collisions (碰撞) between atmospheric gases and the solar wind. Much more solar wind comes to the earth when the sun is active, whichleads to the best northern lights. And the color1 s of the northern lights depend on the height of the collisions and the kinds of gases.4. Why did the host mother ask the author to go out?A. She wanted to take a picture of him.B. She wanted to take a walk with him.C. She wanted to tell him something important.D. She wanted him to see the northern lights.5. The author forgot to take pictures after going out because ______.A. the host mother didn’t remind him to take the cameraB. he was shocked by the wonderful sightC. the lights flickering in the sky disappeared too soonD. he lost all feeling in his hands and feet6. When is the best time to see the northern lights?A. When they appear in the north part of the sky.B. When they come down to the south part of the sky.C. When they are between the north and south.D. When they rise in the east part of the sky.7. What does the last paragraph mainly tell us?A. Waysto take good pictures.B. The relationship between the sun and the northern lights.C.The color1 s of the northern lights.D. The time of the best northern lights.CMany of us were delighted to learn that a high school senior Kwasi Enin was accepted to all eight Ivy League universities. To our surprise, he wasn't excited as expected, but appeared extra calm. He announced that he would revisit the universities to find the best suitable in music or medicine. He also wanted to compare their financial aid packages.Kwasi's success story is rare, but his reaction is not. After the admission letters arrive at home, students have 30 days to really think about what kind of school would help them grow as a person, which school would best prepare them for the future, and at which school they would be happiest. And they also have to think about whether they can afford the school they choose.But how to answer the questions about which school is the best suitable university? Some young people are attracted to large universities with great school spirit and a list of offerings. But besides those advantages, many ofthese universities focus on graduate work and research, with undergraduates taught mostly by part-time instructors. Others are attracted to smaller boarding schools with discussion-based classes. But some of these schools will have much limitation for students who want a high-energy city life experience.Many students today seem to think they should pick the university where they will get the diploma that will help them get the most highly paid job. This is a sad misunderstanding of what a college education should provide.A good college education should prepare them to overcome any difficulty andthrivein society. It helps them to form the habit of creative mind and spirit that will continue to develop far beyond their university years. So when you choose college, you should consider if it is filled with useful learning to help create new spaces for different possibilities of growth.8. What can we know about Kwasi Enin from paragraph 1?A. He was from a very poor family.B. He would choose the top university.C. He was too excited to calm himself at the good news.D. He considered his interests when choosing his university.9. What can you infer from paragraph 2?A. Few students can be admitted to university.B. Many students face the choices like Kwasi.C. Top universities are the first choice for most students.D. American students can afford their university by themselves.10. Which of the following can best explain the underlined word “thrive” in paragraph 4?A. FailB. SucceedC. ResearchD. Work11. What should the best university be like according to the text?A. Very large and have good instructors.B. Small boarding schools with discussion-based classes.C. It will offerthe diploma to get the most highly paid job.D. It will help continue to develop far beyond university years.DContrary to the long-held belief that plants in the natural world are always in competition, new research has found that in severe environments adult plants help smaller ones and grow well as a result.The research, led by Dr Rocio, studied adult and seedling (幼苗)plants in the ecological desert in thesouth-east of Spain. Dr Rocio said, “If you're a seedling in a poor land — the top of a mountain or a sand hill, for example-and you’re lucky enough to end up underneath a big plant, your chances of survival are certainly better than if you landed somewhere on your own. What we have found, which was surprising, is an established large plant, called a ‘nurse’, protects a seedling; it also produces more flowers than the same plants of similar large size growing on their own.”Other benefits of nurse-seedling partnerships include that more variety of plants growing together can have a positive effect on the environment. For example, vegetation areas with nurse plants with more flowers might be able to attract higher numbers of pollinators(传粉者)in an area, in turn supporting insect and soil life and even provide a greater range of different fruit types for birds and other animals.“The biggest winner for this system of nursing a plant is biodiversity(生物多样性),” Dr Rocio said. “The more biodiversean area, the greater number of species of plants, insect life, mammals and birds, and the better the chances of long-term healthy functioning of the environment and ecosystems. ” This system is win-win for adult and seedling plants in unfavorable environments.The research is of value to those who manage and protect plants in tough environments. Most home gardeners and farmers plan to ensure their soil and conditions are the best they can be for plant growth, but the findings might be of value to those who garden in bare places.12. What is a common understanding of plants?A. They can help each other.B. They can survive ill conditions.C. They compete with each other.D. They grow well on their own.13. What will happen to seedling plants if they grow under adult plants?A. They will produce more flowers.B. They will die owing to competition.C. They will make adult plants larger.D. They will get support from adult plants.14. What is the effect of the nurse-seedling partnership?A. It leads to unfavorable environments.B. It produces long-term healthy chances.C. It attracts higher and larger pollinators.D It provides a more variety of plant types.15. Who will benefit from the new research?A. People studying organic farming.B. People protecting plants on sand hills.C. People wanting to change biodiversity.D. People keeping more animals on the farm.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2020-2021学年广东省深圳市新华中学高三数学文下学期期末试题含解析
2020-2021学年广东省深圳市新华中学高三数学文下学期期末试题含解析一、选择题：本大题共10小题，每小题5分，共50分。
在每小题给出的四个选项中，只有是一个符合题目要求的1. 如图，网格纸上小正方形的边长为1，粗线画出的是某三棱锥的三视图，则该三棱锥的体积为（）A．B．C．D．16参考答案：B2. 已知集合，，则（）（A）（B）（C）（D）参考答案：A3. 已知函数，且，若关于的方程有3个不同实根，则实数k的取值范围是（）A. B. C.D.参考答案：C4. 已知点,,,，则向量在方向上的投影为（）A．B．C．D．参考答案：A略5. 已知函数y＝f(x－1)的图象关于点(1，0)对称，且当x∈(－∞，0)时，f(x)＋xf′(x)<0成立(其中f′(x)是f(x)的导函数)，若a＝(30.3)·f(30.3)，b＝(logπ3)·f(logπ3)，c＝·f，则a，b，c的大小关系是()ks5uA．a>b>c B．c>a>b C．c>b>a D．a>c>b参考答案：B略6. 已知角的顶点为坐标原点，始边为轴的非负半轴，若是角终边上的一点，且，则的值为( )A． B． C．或 D．或参考答案：A略7. 已知等差数列的前项和为，若，则（）A． B． C．D．参考答案：C8. 若函数在为单调函数，则实数a的取值范围是( )A.(－∞,－1]∪[1,+∞)B. (－∞,－1]C. [1,+∞)D. [－1,1]参考答案：A9. 将函数的图象向右平移θ（θ＞0）个单位长度后，所得到的图象关于y轴对称，则θ的最小值是（）A．B．C．D．参考答案：D【考点】三角函数中的恒等变换应用；函数y=Asin（ωx+φ）的图象变换．【分析】y=cosx+sinx=2cos（x﹣），故将函数平移后得到y=2cos（x﹣﹣θ），由于平移后的新函数是偶函数，得cos（﹣x﹣﹣θ）=cos（x﹣﹣θ），即cos（x++θ）=cos（x﹣﹣θ）恒成立，于是x++θ=x﹣﹣θ+2kπ，解出θ=kπ﹣．【解答】解：∵y=cosx+sinx=2cos（x﹣），∴将函数平移后得到的函数为y=2cos（x﹣﹣θ），∵y=2cos（x﹣﹣θ）的图象关于y轴对称，∴cos（﹣x﹣﹣θ）=cos（x﹣﹣θ），即cos（x++θ）=cos（x﹣﹣θ）恒成立．∴x++θ=x﹣﹣θ+2kπ，解得θ=kπ﹣．∵θ＞0，∴当k=1时，θ取最小值．故选：D．10. 已知a、b是两条异面直线，c∥a，那么c与b的位置关系（）A.一定是异面B.一定是相交C.不可能平行 D.不可能相交参考答案：C略二、填空题:本大题共7小题,每小题4分,共28分11. 在平面直角坐标系xOy中，点M是椭圆（a＞b＞0）上的点，以M为圆心的圆与x轴相切于椭圆的焦点F，圆M与y轴相交于P，Q两点．若△PQM是钝角三角形，则该椭圆离心率的取值范围是．参考答案：12. 复数的实部为_________ ；虚部为___________.参考答案：【分析】直接利用复数代数形式的乘除运算化简得答案．【详解】＝＝.实部为，虚部为.故答案为：(1)；(2).【点睛】本题考查复数代数形式的乘除运算，考查复数的基本概念，是基础题．13. 已知F1为椭圆的左焦点，直线l：y=x﹣1与椭圆C交于A、B两点，那么|F1A|+|F1B|的值为．参考答案：【考点】椭圆的简单性质．【专题】计算题．【分析】由椭圆方程求出F1点的坐标，联立方程组求出A、B两点，然后利用两点间断距离公式求出|F1A|+|F1B|的值．【解答】解：把y=x﹣1代入椭圆，并整理，得3x2﹣4x=0，解得x1=0，y1=﹣1，，∴，F1（﹣1，0），∴|F1A|+|F1B|=+=．故答案为：．【点评】本题考查直线和椭圆的位置关系，解题时要认真审题，仔细挖掘题设中的隐含条件．14. 已知函数，，若与的图像上存在关于直线对称的点，则实数m的取值范围是________．参考答案：因为与的图像上存在关于直线对称的点，若关于直线对称的直线为，则直线与在上有交点，直线过定点，当直线经过点时，则直线斜率，，若直线与相切，设切点为，则，解得，时直线与在上有交点，即与的图象上存在关于直线对称的点，实数的取值范围是，故答案为．15. 从集合中随机选取一个数记为k，从集合中人随机选取一个数记为b,则直线不经过第四象限的概率为------------.参考答案：略16. 平行四边形ABCD中，已知AB=4，AD=3，∠BAD=60°，点E，F分别满足=2，=，则?= ．参考答案：﹣6【考点】平面向量数量积的运算．【分析】利用平行四边形法则，将分别利用平行四边形的相邻两边表示，然后利用已知计算向量的数量积．【解答】解：如图所示，由平行四边形可得：．∵，∴，，∴==3×4×cos120°+﹣+×3×4×cos60°=﹣6．17. （不等式选做题）若不等式对任意的实数x恒成立，则实数a的取值范圉是．参考答案：三、解答题：本大题共5小题，共72分。
2020届深圳南山外国语学校高三英语下学期期末考试试卷及答案
2020届深圳南山外国语学校高三英语下学期期末考试试卷及答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项ABook reading is certainly one of the most absorbing habits. For young adults who love to read, finding some good books to read is very essential. Writing a book review can help you to improve your language and writing skills.The Book ThiefListed onThe New York Times Children’s Best Seller List for over 100 weeks, The Book Thief by Markus Zusak is the story of a young girl in the Nazi camps set during World War II. So, if you love history and wish to learn how the life was during Adolf Hitler’s time, read this historic book.The Diary of Young GirlEven Anne Frank can not have imagined that her personal diary written during World War II would become such a popular book. It’s a must read that describes the situation of a family in the evils of wars through the eyes of a teenager.Animal FarmAnimal Farm is one of the most popular books by George Orwell. It is just a reflection of the Stalin and World War II period that has been so creatively presented in this book. It is an interesting example of how literature can be used to present conditions common in the society.Adventures of Huckleberry FinnMark Twain’s Adventures of Huckleberry Finn is one of the great American novels in history, and is certainly a great pick for young adults. Young Huck Finn and his mischief along with the color1 ful description of people around theMississippi Rivermake this novel a great book to read.1.Which book describes the author’s own experiences according to this passage?A.The Book ThiefB.The Diary of Young GirlC.Animal FarmD.Adventures of Huckleberry Finn2.What do the first three books have in common?A.All of them are about wars.B.All of them are about farms.C.All of them are intended for history lovers.D.All of them were written during World War II.3.The purpose of this passage is to _________.A.instruct youngsters how to improve skillsB.tell youngsters some wonderful reading habitsC.introduce several good books to youngstersD.give youngsters advice on writing a book reviewBYu Chenrui, 29, is a maker of automata (机关人偶) in Chengdu, Sichuan province. Automata are built to look like humans or animals and give the illusion (错觉) of being able to move on their own, “The art form amazes me, becauseit combines various skills, from storytelling to mechanics, and the pieces are built with a sense of humor,” Yu says. His creations have caught the attention of well-known artists and his fancy pieces of art have attracted collectors worldwide.Interested in handcrafts as a boy, Yu first encountered automata designed by Japanese artist Kazuaki at an exhibition in 2015 when he studied at the Communication University of China inBeijing. “It was like meeting a like-minded friend, ” Yu says, recalling the moment. As an art and design major, he began to learn the craft by himself and, with the support of his tutor, he kept studying and examining automata in school.When he graduated in 2016, Yu landed a job at an advertising agency inBeijing. He stayed on at the company for three years because, at that time, he was not sure that he could make a living out of his hobby. While working as a designer Yu kept exploring and advancing his skills in wood carving and mechanics. Eventually, despite the job’s good salary, it was not enough to make up for not following his true passion. Finally, in 2018, Yu quit his job and returned toChengduto open his automata workshop.To keep himself occupied while running his workshop, he planted blueberries, raspberries and cherries. He watered, weeded and added fertilizer (肥料) every day. “Daily routines helped me calm down and inspire my creativity, which resulted in an automaton called To Observe the Autumn,” Yu says.Over time, Yu’s reputation grew and his business flourished (兴旺). Many of Yu’s creations are built with a dash of wisdom, a sprinkle of humor and are inspired by observations of real life. Yu knows that there are many more creative ideas waiting to be expressed. “It feels quite good to be fully devoted to automata creation and I am still searching for myself.”4. What can we learn from the first paragraph?A. Yu is equipped with various skills.B. Yu is a person full of sense of humor.C. Yu is now gaining recognition worldwide.D. Yu is following the latest trend in handcraft.5. Why did Yu quit his job inBeijing?A. He couldn't make a living out of it.B. He wanted to pursue his own dream.C. He missed his family inChengdu.D. He thought he had a lot experience.6. According to Yu, what contributes to his creativity as an automata artist?A. The fruits he grows.B. Success of his business.C. His devotion to the job.D. Observation from daily life.7. Which of the following can best describe Yu’s story?A. There is no end to learning.B. Great hopes make great man.C. Actions speak louder than words.D. Experience is the mother of wisdom.CThe Gata used to look annoyed when they received power bills that routinely topped $200. Last September the couple moved into a 1,500-square-foot home in Premier Gardens, an area of 95 “zero-energy homes” (ZEH) just outside town. Now they're actually eager to see their electricity bills. The grand total over the 10 months they've lived in the three-bedroom house: $75. For the past two months, they haven’t paid a cent.ZEH communities are the leading edge of technologies that might someday create houses that produce as much energy as they consume. Premier Gardens is one of a half-dozen subdivisions (住宅开发项目) in California where every home cuts power consumption by 50%, mostly by using low power appliances and solar panels.Aside from the panels on the roof, Premier Gardens looks like a community of traditional homes. But inside, special windows cut power bills by blocking solar heat in summer and keeping indoor warmth winter.The rest of the energy savings comes from the solar units. They don't just feed the home they serve. If they generate more power than the home is using, the excess flows into the utility's power grid(电网). The residents are billed by “net metering”: they pay for the amount of power that they get from the grid, minus the kilowatts(千瓦) they feed into it. If a home generates more power than it uses, the bill is zero.That sounds like a bad deal for the power company, but it's not. Solar homes produce the most power on thehot sunny afternoons when everyone rushes home to turn up the air conditioner. "It helps us lower usage at peak power times," says solar expert Mike Keesee. “That lets us avoid building costly plants or buying expensive power at peak usage time.”What’s not to like? Mostly the costs. The special features can add $25,000 or more to the purchase price of a house. Tax breaks bring the cost down, especially in California, but in many states ZEHs can be extremely expensive. For the consumer, it's a matter of paying now for the hardware to save later on the power bill.8. Why is the Gata eager to see their electricity bills now?A. They want to cut down their utility' expenses.B. They want to know if they are able to pay.C. They want to see how much they have saved.D. They want to avoid being overcharged.9. What is special about the ZEH communities?A. They are built in harmony with the environment.B. They have created cutting edge technologies.C. They are subdivided into half a dozen sections.D. They aim to be independent in power supply.10. What does the "net metering" practice mean to the power company?A. More pressure at peak timeB. Reduced operational costs.C. Increased electricity output.D. Less profits in the short term.11. The author believes that buying a house in a ZEH community __________.A. is a worthy investment in the long runB. is but a dream for average consumersC. gives the owner great tax benefitsD. contributes toenvironmental protectionDSimply being quiet is a growing appeal. Lots of business have appeared to meet a rising demand for quiet time, from silent weekend getaways to silent dining, silent reading parties and even silent dating. Silence can mean different things to different people. We are usually silent only with those closest to us. So there is something almost radical(不同凡响的)about the recent trend towards enjoying silence with strangers.Mariel started a regular silent reading party inDundeejust under a year ago. Readers bring their books and meet in a bar, where they read together in silence for an hour or sometimes two and then put their books away to chat and have a drink. “When the reading party starts, everything goes quiet,” says Mariel, “ It’s a little bit surreal(超现实的), especially in what is usually a noisy bar. However, there is something special about sharing the silence with others. It offers a chance to escape from reality; everyone is so busy with work and with technology being ever present. An event like thisgives people the opportunity to escape these things for a while.”Honi Ryan is an artist based inBerlinwho began hosting silent dinner back in 2006. The rules of the dinner are: no talking, no using your voice, no reading or writing, trying to make as little noise as possible, not connecting with technology, and staying for at least two hours. So far she has taken her silent dinner project toMexico, theUS,AustraliaandChina. “It’s evident that the age-old connections we make over food do not depend on the words around it. Silence creates the space for the people and places involved to fill with whatever is needed;itis quite different from our usual social behaviors.”12. Why have lots of silent businesses appeared?A. To satisfy people’s demand for silence.B. To make people get close to each other.C. To appeal to young people.D. To change people’s old way of life.13. What can we learn about Mariel’s silent reading parties?A. Readers can use their voice while reading.B. Readers can be busy with their work.C. Readers can connect with technology.D. Readers can chat and drink after reading.14. The underlined word “it” in the last paragraph refers to .A. noiseB. spaceC. silenceD. food15. What can be a suitable title for the text?A. Escape from Reality.B. Enjoying Being Quiet.C. Silent Reading Parties.D. Silent Dining Projects.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2020-2021学年深圳南山外国语学校高三英语下学期期末考试试题及答案解析
2020-2021学年深圳南山外国语学校高三英语下学期期末考试试题及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项ALOI English—English Conversation ClassesTake English conversation classes with native English -speaking teachers from theUnited States,IrelandandAustralia, live, 1 - on - 1.This is by far the best way to improve your real spoken English and listening abilities and get to a level where you can use it in real - life situations. Our teachers mainly carry on conversations about work in different fields, such as business, finance, politics and travel. However, if you like, you can have normal day - to - day conversations about events, weather, etc. If you would like to learn some grammar during conversation, we can do that too!Our English Conversation classes：• Your conversations will always be with a native English speaker.• You can choose the time, day and teacher for each class.• The classes are made for each student individually. They will be at your level, studying what you need and what interests you.Packages10 Classes Package $ 229.90Interested in taking 10, 55 - minute conversation English classes?Schedule a first free class with LOI English and talk to the teacher about it. After that, you can arrange to take our 10 - class conversation English course.20 Classes Package $ 439,80Interested in taking 20, 55 - minute conversation English classes?Schedule a first free class with LOI English and talk to the teacher about it. After that, you can arrange to take our 20 - class conversation English course.1. What do the classes mainly focus on?A. Daily conversations.B. Work - related topics.C. Grammar rules.D. Area - based accents.2. Which is NOT offered to the students?A. Native English - speaking teachers.B. Personalized courses.C. Choice of class time and teacher.D. Offline learning materials.3. What should a student do first if he decides on either of the packages?A. Arrange a free class with LOI English.B. Bargain with LOI English for lower fees.C. Choose an experienced LOI English teacher.D. Make a promise to sit through each class.BIn ancient times, Chinese used plant leaves or bird feathers as a fan during the summer time. This was the earliest form of the fan. The first real fan was made back in the era of Yao and Shun period thousands of years ago. Since then,Chinese-made fans have become a vital part of Chinese art and culture. At the beginning, the fan functioned as a tool to generate a current of air in the hot weather. Now electric fans such as ceiling fans and other technological breakthroughs have taken the place.Long ago, fans caught the attention of ancient Chinese artists by chance. Thereafter, a unique fan art gradually took shape in the history of Chinese culture. Fan art usually includes Chinese calligraphy, paintings, or poems on the sectors（扇区）. Special skills are needed to write or paint on them.Due to its history and partly because of its unique shape, Chinese would soon develop the tradition of using fans as ornaments（装饰品）. Fans are made in different sizes and different color1 s to meet the needs of each request. Other Chinese ornaments, such as the Chinese knot, the green jade, and the Spring Festival picture, are often combined in each design.The value of fans depends mainly on the materials used and the level of craftsmanship that is involved during the process. Feather, paper, jade, bamboo and silk have all been used as ideal materials to make fans. Ancient Chinese even made iron fans to serve as deadly weapons（武器）in Chinese martial arts. Fans made by famous craftsmen are often characterized by pretty designs and detailed workmanship, and thus become favorites of collectors. Fans with masterpiece fine art like calligraphy or paintings are even more valuable.4.What is the first paragraph mainly about?A. The origin of fans.B. The materials of fans.C. The popularity of fans.D. The production of fans.5. Why do Chinese use fans as ornaments?A. They are made of valuable materials.B. They reflect the beauty of Chinese culture.C. They convey literature works on the sectors.D. They are often combined with other ornaments.6. Which of the following makes a fan favored by most collectors?A. Its advanced function.B. Its complex character.C. Its artistic handicraft.D. Its various applications.7. What can we infer about the fan from the text?A. Chinese send fans to their friends as gifts.B. Chinese ornaments can meet different requests.C. Traditional fans have lost their functional value.D. The fan plays different roles with the change of time.CIn someareas ofCalifornia, it’s so dry that farmers aren’t willing to plant crops this season. Growers, north ofSan Francisco, have begun pulling out of local farmers markets.CountyLineHarvest, which farms more than 30 acres inPetaluma, hasn’t had enough water to grow all the peppers, lettuces and other produce for a long time, according to a video on its Instagram page. Nearby farms arc saying the same, emphasizing (强调) the effect of theextendeddry periods.Californiagrows a third of theUnited States' vegetables and two-thirds of the nation's fruits and nuts. If dry weather prevents farmers from growing plants, that could lead to pushing up the price of food that's already starting to affect theU.S.economy.“Due to severe drought, for the first time in 21 years, we will not be able to grow this summer inPetaluma,"CountyLinesaid in its post.Drew Lerner, president of World Weather Inc. inKansas, saidCalifornia“missed the rainy season" and won't see much moisture (水分) over the next several months.A La Nina weather pattern in the Pacific pushed winter storms north and away from the state, leaving it with less moisture than usual. AsCaliforniagets most of its water from winter storms, little relief is expected before October.That has left growers such as Shao Shan Fann in a bind. The business can’t offer the selection of Asian vegetables and Bay Area staples it usually grows at its Bolinas location, according to its website.Nearby, Green Valley Community Farm has access to only about 5% of the water it usually relies on, owner David Plescia said. He’s looking for new land with enough water to use, and also has a permit in the works to grow cannabis to make up for the lost income. If it doesn’t make it, he’ll leave the fields empty.“It’s part of our generation’s cross to bear, figuring out how to run small — or medium-scale farm businesses in this kind of atmosphere of highly variable rainfall,” Andrew said.8. What does the underlined word “extended” in the second paragraph mean?A. Hot.B. Short.C. Long.D. Wonderful.9. Which is the result if the dry weather stops famers from planting crops?A. Theincreaseinthe priceof food.B. The growth of economy inU.S.C.Lessmoisture than usual.D. The low price of Asian vegetables.10. From what Andrew said, we can infer (推断) all of the following statements EXCEPT that________.A. The climate is not very goodB. It is part of the burden for people of his generationC. It is hard for him to run his farm businesses insuch bad climateD. He is sure that the serious drought will come to an end soon11. What does the passage mainly talk about?A. How do the famers run businesses inCalifornia.B. How does the owner look for new land with enough waterC. California farmers facing drought choose not to plant crops.D. The farm economy of theUnited Stateshas changed a lot.DAs a 51-year-old first-aid responder since 1984, Jeffrey never knows what type of situation he might walk into, or who he'll meet along the wayTen years into the job, Jeffrey received a call that reported that a man in his early 30s had fallen down in the Mall of America. When Jeffrey and his partner arrived at the scene, they found the young male face down on the ground. He had gone unconscious, making weak attempts to breathe. His wife stood beside him holding their small son in horror. They quickly rushed to calm the man to keep him under control and offer necessary first aid. After Jeffrey dropped the patient off at the neighboring hospital, he thought about the man and his family for a long time.Jeffrey thought he had experienced everything under the sun until one random visit to Office Max three yearsago, where he met a man repeatedly walking back and forth while staring at him. As it turned out, the man was the patient he had saved 20 years earlier."You gave me 20 years more than I ever thought I'd have," the man said. He thanked Jeffrey repeatedly and told him he had someone he wanted him to meet. He stepped around the corner and reappeared with a 20-something-year-old man. Jeffrey instantly knew that it was the son he had seen standing by his mother all those years ago"That day changed my life," Jeffrey said. "Before that, everything was about work…When I talk to my beginner-training class, I tell them you never know the effect you can have on someone's life."12. What did Jeffrey do with the young man?A. He cured the man at the scene.B. He took care of the man's wife and son.C. He only sent the man to hospital.D. He did what was needed13. What did Jeffrey think of the encounter with the man at Office Max?A. It was a common routine.B. It was troublesomeC. It was unbelievableD. It was a dangerous situation.14. Why was the man thankful to Jeffrey?A. Jeffrey helped bring up his little sonB. Jeffrey donated to support his family.C. Jeffrey's help gave him the present happy life.D. Jeffrey's kindness taught his son to be a new doctor.15. How did the meeting change Jeffrey's life?A. He was rewarded with much moneyB. He changed his attitude to his job.C. He got a promotion to be a team leader.D. He took up teaching work to train newcomers.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
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2020-2021深圳市南山中英文学校高三数学下期末试卷(附答案)一、选择题1．123{3x x >>是12126{9x x x x +>>成立的（ ） A ．充分不必要条件B ．必要不充分条件C ．充要条件D ．即不充分也不必要条件 2．在“一带一路”知识测验后，甲、乙、丙三人对成绩进行预测． 甲：我的成绩比乙高．乙：丙的成绩比我和甲的都高．丙：我的成绩比乙高．成绩公布后，三人成绩互不相同且只有一个人预测正确，那么三人按成绩由高到低的次序为A ．甲、乙、丙B ．乙、甲、丙C ．丙、乙、甲D ．甲、丙、乙3．设集合2{|20,}M x x x x R =+=∈，2{|20,}N x x x x R =-=∈，则M N ⋃=（ ） A ．{}0B ．{}0,2C ．{}2,0-D ．{}2,0,2- 4．一个容量为80的样本中数据的最大值是140,最小值是51,组距是10,则应将样本数据分为( )A ．10组B ．9组C ．8组D ．7组5．函数()()2ln 1f x x x =+-的一个零点所在的区间是( ) A ．()0,1 B ．()1,2 C ．()2,3D ．()3,4 6．在下列区间中，函数()43x f x e x =+-的零点所在的区间为（ ）A ．1,04⎛⎫- ⎪⎝⎭B ．10,4⎛⎫ ⎪⎝⎭ C ．11,42⎛⎫ ⎪⎝⎭ D ．13,24⎛⎫ ⎪⎝⎭7．已知集合1}{0|A x x -≥=，{0,1,2}B =，则A B =IA ．{0}B ．{1}C ．{1,2}D ．{0,1,2}8．函数()()sin 22f x x πϕϕ⎛⎫=+< ⎪⎝⎭的图象向右平移6π个单位后关于原点对称，则函数()f x 在,02π⎡⎤-⎢⎥⎣⎦上的最大值为（） A． BC ．12D ．12- 9．如图是一个正方体的平面展开图，则在正方体中直线AB 与CD 的位置关系为( )A ．相交B ．平行C ．异面而且垂直D ．异面但不垂直10．设A （3，3，1），B （1，0，5），C （0，1，0），AB 的中点M ，则CM = A ．534 B ．532 C ．532 D ．13211．《九章算术》是我国古代的数学名著，书中有如下问题：“今有五人分五钱，令上二人所得与下三人等．问各得几何．”其意思为“已知甲、乙、丙、丁、戊五人分5钱，甲、乙两人所得与丙、丁、戊三人所得相同，且甲、乙、丙、丁、戊所得依次成等差数列．问五人各得多少钱？”（“钱”是古代的一种重量单位）．这个问题中，甲所得为（ ） A ．54钱 B ．43钱 C ．32钱 D ．53钱 12．函数()f x 的图象如图所示，()f x '为函数()f x 的导函数，下列数值排序正确是（ ）A ．()()()()02332f f f f ''<<<-B ．()()()()03322f f f f ''<<-<C ．()()()()03232f f f f ''<<<-D ．()()()()03223f f f f ''<-<<二、填空题13．在ABC ∆中，角,,A B C 的对边分别为,,a b c ，4c =，42a A =，且C 为锐角，则ABC ∆面积的最大值为________.14．在ABC ∆中，内角A ，B ，C 所对的边分别为a ，b ，c ，若3A π=，3a =b=1,则c =_____________15．已知点()0,1A ，抛物线()2:0C y ax a =>的焦点为F ，连接FA ，与抛物线C 相交于点M ，延长FA ，与抛物线C 的准线相交于点N ，若:1:3FM MN =，则实数a 的值为__________．16．在平面上，若两个正三角形的边长的比为1：2，则它们的面积比为1：4，类似地，在空间内，若两个正四面体的棱长的比为1：2，则它们的体积比为 ▲17．已知直线：与圆交于两点，过分别作的垂线与轴交于两点.则_________. 18．若x ，y 满足约束条件220100x y x y y --≤⎧⎪-+≥⎨⎪≤⎩，则32z x y =+的最大值为_____________．19．34331654+log log 8145-⎛⎫+= ⎪⎝⎭________. 20．如图，正方体1111ABCD A B C D -的棱长为1，线段11B D 上有两个动点,E F ，且2EF =，现有如下四个结论： AC BE ①⊥；//EF ②平面ABCD ；③三棱锥A BEF -的体积为定值；④异面直线,AE BF 所成的角为定值，其中正确结论的序号是______．三、解答题21．在直角坐标系xOy 中，曲线C 的参数方程为2221141t x t t y t ⎧-=⎪⎪+⎨⎪=⎪+⎩，（t 为参数），以坐标原点O 为极点，x 轴的正半轴为极轴建立极坐标系，直线l 的极坐标方程为2cos 3sin 110ρθρθ++=．（1）求C 和l 的直角坐标方程；（2）求C 上的点到l 距离的最小值．22．如图，四边形ABCD 为矩形，平面ABEF ⊥平面ABCD ，//EF AB ，90BAF ∠=︒，2AD =，1AB AF ==，点P 在线段DF 上.（1）求证：AF ⊥平面ABCD ；（2）若二面角D AP C --的余弦值为6，求PF 的长度. 23．十九大以来，某贫困地区扶贫办积极贯彻落实国家精准扶贫的政策要求，带领广大农村地区人民群众脱贫奔小康.经过不懈的奋力拼搏，新农村建设取得巨大进步，农民收入也逐年增加.为了更好的制定2019年关于加快提升农民年收入力争早日脱贫的工作计划，该地扶贫办统计了2018年50位农民的年收入并制成如下频率分布直方图：附：参考数据与公式 6.92 2.63≈，若 ()2~,X N μσ，则① ()0.6827P X μσμσ-<+=…；② (22)0.9545P X μσμσ-<+=…；③ (33)0.9973P X μσμσ-<+=….（1）根据频率分布直方图估计50位农民的年平均收入x （单位：千元）（同一组数据用该组数据区间的中点值表示）；（2）由频率分布直方图可以认为该贫困地区农民年收入 X 服从正态分布 ()2,N μσ，其中μ近似为年平均收入2,x σ 近似为样本方差2s ，经计算得：2 6.92s =，利用该正态分布，求：（i ）在2019年脱贫攻坚工作中，若使该地区约有占总农民人数的84.14%的农民的年收入高于扶贫办制定的最低年收入标准，则最低年收入大约为多少千元?（ii ）为了调研“精准扶贫，不落一人”的政策要求落实情况，扶贫办随机走访了1000位农民.若每个农民的年收入相互独立，问：这1000位农民中的年收入不少于12.14千元的人数最有可能是多少?24．如图：在ABC ∆中，10a =，4c =，5cos C =.（1）求角A ；（2）设D 为AB 的中点，求中线CD 的长.25．已知A 为圆22:1C x y +=上一点，过点A 作y 轴的垂线交y 轴于点B ，点P 满足2.BP BA =u u u v u u u v（1）求动点P 的轨迹方程；（2）设Q 为直线:3l x =上一点，O 为坐标原点，且OP OQ ⊥，求POQ ∆面积的最小值.26．如图，边长为2的正方形ABCD 中，E 、F 分别是AB 、BC 边的中点，将AED V ，DCF V 分别沿DE ，DF 折起，使得A ，C 两点重合于点M ．(1) 求证：MD EF ⊥；(2) 求三棱锥M EFD -的体积．【参考答案】***试卷处理标记，请不要删除一、选择题1．A解析：A【解析】试题分析：因为123{3x x >>12126{9x x x x +>⇒>，所以充分性成立；1213{1x x ==满足12126{9x x x x +>>，但不满足123{3x x >>，必要性不成立，所以选A.考点：充要关系2．A解析：A【解析】【分析】利用逐一验证的方法进行求解.【详解】若甲预测正确，则乙、丙预测错误，则甲比乙成绩高，丙比乙成绩低，故3人成绩由高到低依次为甲，乙，丙；若乙预测正确，则丙预测也正确，不符合题意；若丙预测正确，则甲必预测错误，丙比乙的成绩高，乙比甲成绩高，即丙比甲，乙成绩都高，即乙预测正确，不符合题意，故选A ．【点睛】本题将数学知识与时政结合，主要考查推理判断能力．题目有一定难度，注重了基础知识、逻辑推理能力的考查．3．D解析：D【解析】【分析】【详解】试题分析：M ＝{x|x 2＋2x ＝0，x ∈R}＝{0，-2}，N ＝{x|x 2－2x ＝0，x ∈R}＝{ 0，2}，所以 M N ⋃={-2,0,2}，故选D ．考点：1、一元二次方程求根；2、集合并集的运算．4．B解析：B【解析】由题意知，(14051)108.9-÷=，所以分为9组较为恰当，故选B.5．B解析：B【解析】【分析】先求出(1)(2)0,f f <根据零点存在性定理得解.【详解】由题得()21ln 2=ln 2201f =--<， ()22ln3=ln3102f =-->， 所以(1)(2)0,f f <所以函数()()2ln 1f x x x=+-的一个零点所在的区间是()1,2. 故选B【点睛】本题主要考查零点存在性定理，意在考查学生对该知识的理解掌握水平，属于基础题.6．C解析：C【解析】【分析】先判断函数()f x 在R 上单调递增，由104102f f ⎧⎛⎫< ⎪⎪⎪⎝⎭⎨⎛⎫⎪> ⎪⎪⎝⎭⎩,利用零点存在定理可得结果. 【详解】因为函数()43x f x e x =+-在R 上连续单调递增， 且114411221143204411431022f e e f e e ⎧⎛⎫=+⨯-=-<⎪ ⎪⎪⎝⎭⎨⎛⎫⎪=+⨯-=-> ⎪⎪⎝⎭⎩, 所以函数的零点在区间11,42⎛⎫ ⎪⎝⎭内，故选C. 【点睛】本题主要考查零点存在定理的应用，属于简单题.应用零点存在定理解题时，要注意两点：（1）函数是否为单调函数；（2）函数是否连续.7．C解析：C【解析】【分析】由题意先解出集合A,进而得到结果．【详解】解：由集合A 得x 1≥,所以{}A B 1,2⋂=故答案选C.【点睛】本题主要考查交集的运算，属于基础题．8．B解析：B【解析】【分析】由条件根据函数()sin y A ωx φ=+的图象变换规律，正弦函数的图象的对称性可得3πφk π-+=，k z ∈，由此根据||2ϕπ<求得ϕ的值，得到函数解析式即可求最值． 【详解】函数()()sin 22f x x πϕϕ⎛⎫=+< ⎪⎝⎭的图象向右平移6π个单位后， 得到函数sin 2sin 263ππy x φx φ⎡⎤⎛⎫⎛⎫=-+=-+ ⎪ ⎪⎢⎥⎝⎭⎝⎭⎣⎦的图象， 再根据所得图象关于原点对称，可得3πφk π-+=，k z ∈， ∵||2ϕπ<，∴3πϕ=，()sin 23πf x x ⎛⎫=- ⎪⎝⎭， 由题意,02x ⎡⎤∈-⎢⎥⎣⎦π，得42,333πππx ⎡⎤-∈--⎢⎥⎣⎦，∴21,32πsin x ⎡⎛⎫-∈-⎢ ⎪⎝⎭⎣⎦，∴函数()sin 23πf x x ⎛⎫=-⎪⎝⎭在区间,02π⎡⎤-⎢⎥⎣⎦的最大值为2， 故选B ．【点睛】本题主要考查函数()sin y A ωx φ=+的图象变换规律，正弦函数的图象的对称性，考查了正弦函数最值的求法，解题的关键是熟练掌握正弦函数的性质，能根据正弦函数的性质求最值，属于基础题． 9．D解析：D【解析】解：利用展开图可知，线段AB 与CD 是正方体中的相邻两个面的面对角线，仅仅异面，所成的角为600，因此选D10．C解析：C【解析】试题分析：先求得M （2,32，3）点坐标，利用两点间距离公式计算得CM =，故选C ．考点：本题主要考查空间直角坐标系的概念及空间两点间距离公式的应用．点评：简单题，应用公式计算． 11．B解析：B【解析】设甲、乙、丙、丁、戊所得钱分别为2,,,,2a d a d a a d a d --++,则22a d a d a a d a d -+-=++++,解得6a d =-,又225,a d a d a a d a d -+-+++++=1a \=,则4422633a a d a a ⎛⎫-=-⨯-== ⎪⎝⎭,故选B.12．B解析：B【解析】【分析】根据导数的几何意义可对比切线斜率得到()()032f f ''<<，将()()32f f -看作过()()22f ,和()()3,3f 的割线的斜率，由图象可得斜率的大小关系，进而得到结果.【详解】由()f x 图象可知，()f x 在2x =处的切线斜率大于在3x =处的切线斜率，且斜率为正，()()032f f ''∴<<，()()()()323232f f f f --=-Q ，()()32f f ∴-可看作过()()22f ,和()()3,3f 的割线的斜率，由图象可知()()()()3322f f f f ''<-<，()()()()03322f f f f ''∴<<-<.故选：B .【点睛】本题考查导数几何意义的应用，关键是能够将问题转化为切线和割线斜率大小关系的比较，进而根据图象得到结果.二、填空题13．【解析】【分析】由利用正弦定理求得再由余弦定理可得利用基本不等式可得从而利用三角形面积公式可得结果【详解】因为又所以又为锐角可得因为所以当且仅当时等号成立即即当时面积的最大值为故答案为【点睛】本题主解析：4+【解析】【分析】由4c =，a A =，利用正弦定理求得4C π=.，再由余弦定理可得2216a b =+，利用基本不等式可得(82ab ≤=+，从而利用三角形面积公式可得结果.【详解】因为4c =，又sin sin c a C A ==所以sin 2C =，又C 为锐角，可得4C π=.因为(2222162cos 2a b ab C a b ab =+-=+≥，所以(82ab ≤=+，当且仅当a b =时等号成立，即1sin 42ABC S ab C ab ∆==≤+即当a b ==时，ABC ∆面积的最大值为4+. 故答案为4+.【点睛】本题主要考查余弦定理、正弦定理以及基本不等式的应用，属于简单题. 对余弦定理一定要熟记两种形式：（1）2222cos a b c bc A =+-；（2）222cos 2b c a A bc +-=，同时还要熟练掌握运用两种形式的条件.另外，在解与三角形、三角函数有关的问题时，还需要记住30,45,60o o o 等特殊角的三角函数值，以便在解题中直接应用.14．2【解析】【分析】根据条件利用余弦定理可建立关于c 的方程即可解出c【详解】由余弦定理得即解得或（舍去）故填2【点睛】本题主要考查了利用余弦定理求三角形的边属于中档题解析：2【解析】【分析】根据条件，利用余弦定理可建立关于c 的方程，即可解出c.【详解】由余弦定理2222cos a b c bc A =+-得231c c =+-，即220c c --=，解得2c =或1c =-（舍去）.故填2.【点睛】本题主要考查了利用余弦定理求三角形的边，属于中档题.15．【解析】依题意可得焦点的坐标为设在抛物线的准线上的射影为连接由抛物线的定义可知又解得点睛：本题主要考查的知识点是抛物线的定义以及几何性质的应用考查了学生数形结合思想和转化与化归思想设出点在抛物线的准【解析】依题意可得焦点F 的坐标为04a ⎛⎫ ⎪⎝⎭，， 设M 在抛物线的准线上的射影为K ，连接MK 由抛物线的定义可知MF MK =13FM MN =Q ∶∶ 221KN KM ∴=∶∶又01404FN K a a --==-， 22FN KN K KM==-422a-∴=-，解得2a = 点睛：本题主要考查的知识点是抛物线的定义以及几何性质的应用，考查了学生数形结合思想和转化与化归思想，设出点M 在抛物线的准线上的射影为K ，由抛物线的定义可知MF MK =，再根据题设得到221KN KM =∶∶，然后利用斜率得到关于a 的方程，进而求解实数a 的值16．1：8【解析】考查类比的方法所以体积比为1∶8解析：1：8 【解析】考查类比的方法，11111222221111314283S hV S h V S h S h ⋅⨯＝＝＝＝，所以体积比为1∶8. 17．4【解析】试题分析：由x-3y+6=0得x=3y-6代入圆的方程整理得y2-33y+6=0解得y1=23y2=3所以x1=0x2=-3所以|AB|=(x1-x2)2+(y1-y2)2=23又直线l 的解析：4 【解析】 试题分析：由，得，代入圆的方程，整理得，解得，所以，所以．又直线的倾斜角为，由平面几何知识知在梯形中，．【考点】直线与圆的位置关系【技巧点拨】解决直线与圆的综合问题时，一方面，要注意运用解析几何的基本思想方法（即几何问题代数化），把它转化为代数问题；另一方面，由于直线与圆和平面几何联系的非常紧密，因此，准确地作出图形，并充分挖掘几何图形中所隐含的条件，利用几何知识使问题较为简捷地得到解决．18．6【解析】【分析】首先根据题中所给的约束条件画出相应的可行域再将目标函数化成斜截式之后在图中画出直线在上下移动的过程中结合的几何意义可以发现直线过B 点时取得最大值联立方程组求得点B 的坐标代入目标函数解析：6 【解析】 【分析】首先根据题中所给的约束条件，画出相应的可行域，再将目标函数化成斜截式3122y x z =-+，之后在图中画出直线32y x =-，在上下移动的过程中，结合12z 的几何意义，可以发现直线3122y x z =-+过B 点时取得最大值，联立方程组，求得点B 的坐标代入目标函数解析式，求得最大值. 【详解】根据题中所给的约束条件，画出其对应的可行域，如图所示：由32z x y =+，可得3122y x z =-+， 画出直线32y x =-，将其上下移动， 结合2z的几何意义，可知当直线3122y x z =-+在y 轴截距最大时，z 取得最大值， 由2200x y y --=⎧⎨=⎩，解得(2,0)B ，此时max 3206z =⨯+=，故答案为6.点睛：该题考查的是有关线性规划的问题，在求解的过程中，首先需要正确画出约束条件对应的可行域，之后根据目标函数的形式，判断z 的几何意义，之后画出一条直线，上下平移，判断哪个点是最优解，从而联立方程组，求得最优解的坐标，代入求值，要明确目标函数的形式大体上有三种：斜率型、截距型、距离型；根据不同的形式，应用相应的方法求解.19．【解析】试题分析：原式=考点：1指对数运算性质解析：278【解析】 试题分析：原式=344332542727log log 134588-⎡⎤⎛⎫+⨯=+=⎢⎥ ⎪⎝⎭⎢⎥⎣⎦ 考点：1.指对数运算性质.20．【解析】【分析】对于①可由线面垂直证两线垂直；对于②可由线面平行的定义证明线面平行；对于③可证明棱锥的高与底面积都是定值得出体积为定值；对于④可由两个特殊位置说明两异面直线所成的角不是定值【详解】对 解析：①②③【解析】 【分析】对于①，可由线面垂直证两线垂直；对于②，可由线面平行的定义证明线面平行；对于③，可证明棱锥的高与底面积都是定值得出体积为定值；对于④，可由两个特殊位置说明两异面直线所成的角不是定值． 【详解】对于①，由1,AC BD AC BB ⊥⊥，可得AC ⊥面11DD BB ，故可得出AC BE ⊥，此命题正确；对于②，由正方体1111ABCD A B C D -的两个底面平行，EF 在平面1111D C B A 内，故EF 与平面ABCD 无公共点，故有//EF 平面ABCD ，此命题正确；对于③，EF 为定值，B 到EF 距离为定值，所以三角形BEF 的面积是定值，又因为A 点到面11DD BB 距离是定值，故可得三棱锥A BEF -的体积为定值，此命题正确； 对于④，由图知，当F 与1B 重合时，此时E 与上底面中心为O 重合，则两异面直线所成的角是1A AO ∠，当E 与1D 重合时，此时点F 与O 重合，则两异面直线所成的角是1OBC ∠，此二角不相等，故异面直线,AE BF 所成的角不为定值，此命题错误．综上知①②③正确，故答案为①②③ 【点睛】本题通过对多个命题真假的判断，综合考查线面平行的判断、线面垂直的判断与性质、棱锥的体积公式以及异面直线所成的角，属于难题.这种题型综合性较强，也是高考的命题热点，同学们往往因为某一处知识点掌握不好而导致“全盘皆输”，因此做这类题目更要细心、多读题，尽量挖掘出题目中的隐含条件，另外，要注意从简单的自己已经掌握的知识点入手，然后集中精力突破较难的命题.三、解答题21．（1）22:1,(1,1]4y C x x +=∈-；:2110l x ++=；（2【解析】 【分析】（1）利用代入消元法，可求得C 的直角坐标方程；根据极坐标与直角坐标互化原则可得l 的直角坐标方程；（2）利用参数方程表示出C 上点的坐标，根据点到直线距离公式可将所求距离表示为三角函数的形式，从而根据三角函数的范围可求得最值. 【详解】 （1）由2211t x t -=+得：210,(1,1]1x t x x -=≥∈-+，又()2222161t y t =+ ()()222116141144111xx y x x x x x -⨯+∴==+-=--⎛⎫+ ⎪+⎝⎭整理可得C 的直角坐标方程为：221,(1,1]4y x x +=∈-又cos x ρθ=，sin y ρθ=l ∴的直角坐标方程为：2110x ++=（2）设C 上点的坐标为：()cos ,2sin θθ则C 上的点到直线l的距离d ==当sin 16πθ⎛⎫+=- ⎪⎝⎭时，d 取最小值则min d = 【点睛】本题考查参数方程、极坐标方程与直角坐标方程的互化、求解椭圆上的点到直线距离的最值问题.求解本题中的最值问题通常采用参数方程来表示椭圆上的点，将问题转化为三角函数的最值求解问题. 22．（1）见解析；（2【解析】（1）先证明AB AF ⊥，又平面ABEF ⊥平面ABCD ，即得AF ⊥平面ABCD ；（2）以A 为原点，以AB ，AD ，AF 为x ，y ，z 轴建立如图所示的空间直角坐标系，由题得26cos ,21411m AB m AB m ABλλ⋅===⎛⎫⋅++ ⎪-⎝⎭u u u vu u u v u u u v ，解方程即得解.【详解】（1）证明：∵90BAF ∠=︒，∴AB AF ⊥，又平面ABEF ⊥平面ABCD ，平面ABEF I 平面ABCD AB =，AF ⊂平面ABEF ， ∴AF ⊥平面ABCD .（2）以A 为原点，以AB ，AD ，AF 为x ，y ，z 轴建立如图所示的空间直角坐标系， 则()0,0,0A ，()1,0,0B ，()1,2,0C ，()0,2,0D，()0,0,1F ，∴()0,2,1FD u u u v =-，()1,2,0AC =u u u v，()1,0,0AB =u u u r由题知，AB ⊥平面ADF ，∴()1,0,0AB =u u u r为平面ADF 的一个法向量， 设()01FP FD λλ=≤<u u u v u u u v ，则()0,2,1P λλ-，∴()0,2,1AP λλ=-u u u v，设平面APC 的一个法向量为(),,x y z =m ，则0m AP m AC ⎧⋅=⎨⋅=⎩u u u v u u u v ， ∴()21020y z x y λλ⎧+-=⎨+=⎩，令1y =，可得22,1,1m λλ⎛⎫=- ⎪-⎝⎭， ∴26cos ,21411m AB m AB m ABλλ⋅===⎛⎫⋅++ ⎪-⎝⎭u u u vu u u v u u u v ，得13λ=或1λ=-（舍去），∴5PF =.【点睛】本题主要考查空间垂直关系的证明，考查二面角的求法，意在考查学生对这些知识的理解掌握水平和分析推理能力.23．（1）17.4；（2）（i ）14.77千元（ii ）978位【分析】（1）用每个小矩形的面积乘以该组中点值，再求和即可得到平均数； （2）（i ）根据正态分布可得：0.6827()0.50.84142P X μσ>-=+≈即可得解；（ii ）根据正态分布求出每个农民年收入不少于12.14千元的事件概率为0.9773，利用独立重复试验概率计算法则求得概率最大值的k 的取值即可得解. 【详解】（1）由频率分布直方图可得：120.04140.12160.28180.36200.1220.06240.0417.4x =⨯+⨯+⨯+⨯+⨯+⨯+⨯=；（2）（i ）由题()~17.4,6.92X N ，0.6827()0.50.84142P X μσ>-=+≈， 所以17.4 2.6314.77μσ-=-=满足题意，即最低年收入大约14.77千元；（ii ）0.9545(12.14)(2)0.50.97732P X P X μσ≥=≥-=+≈， 每个农民年收入不少于12.14千元的事件概率为0.9773，记这1000位农民中的年收入不少于12.14千元的人数为X ，()1000,0.9773X B : 恰有k 位农民中的年收入不少于12.14千元的概率()()100010000.997310.9973kkk P X k C -==-()()()()10010.97731110.9773P X k k P X k k =-⨯=>=-⨯-得10010.9773978.2773k <⨯=，所以当0978k ≤≤时，()()1P X k P X k =-<=，当9791000k ≤≤时，()()1P X k P X k =->=，所以这1000位农民中的年收入不少于12.14千元的人数最有可能是978位. 【点睛】此题考查频率分布直方图求平均数，利用正态分布估计概率，结合独立重复试验计算概率公式求解具体问题，综合性强.24．（1）4A π=；（2【解析】 【分析】（1）通过cos C 求出sin C 的值，利用正弦定理求出sin A 即可得角A ；（2）根据()sin sin B A C =+求出sin B 的值，由正弦定理求出边b ，最后在ACD ∆中由余弦定理即可得结果. 【详解】（1）∵cos C =，∴sin C ===. 由正弦定理sin sin a c A C==.得sin A =cos 0C =<，∴C 为钝角，A 为锐角， 故4A π=.（2）∵()B A C π=-+，∴()sin sin sin cos cos sin B A C A C A C =+=+22⎛=⨯+= ⎝⎭. 由正弦定理得sin sin b a B A==得b = 在ACD ∆中由余弦定理得：2222cos CD AD AC AD AC A =+-⋅⋅24222=+-=，∴CD =. 【点睛】本题主要考查了正弦定理和余弦定理在解三角形中的应用，考查三角函数知识的运用，属于中档题.25．(1) 2214x y += (2) 3.2【解析】 【分析】（1）设出A 、P 点坐标，用P 点坐标表示A 点坐标，然后代入圆方程，从而求出P 点的轨迹；（2）设出P 点坐标，根据斜率存在与否进行分类讨论，当斜率不存在时，求出POQ ∆面积的值，当斜率存在时，利用点P 坐标表示POQ ∆的面积，减元后再利用函数单调性求出最值，最后总结出最值. 【详解】解：（1） 设(),P x y ， 由题意得：()()1,,0,A x y B y ， 由2BP BA =u u u v u u u v，可得点A 是BP 的中点， 故102x x +=，所以12x x =， 又因为点A 在圆上，所以得2214x y +=，故动点P 的轨迹方程为2214x y +=.（2）设()11,P x y ，则10y ≠，且221114x y +=，当10x =时，11y =±，此时()33,0,2POQ Q S ∆=； 当10x ≠时，11,OP y k x = 因为OP OQ ⊥, 即11,OQ x k y =- 故1133,x Q y ⎛⎫-⎪⎝⎭，OP ∴=OQ ==，221111322POQx y S OP OQ y ∆+==⋅①， 221114x y +=代入① 2111143334322POQy S y y y ∆⎛⎫-=⋅=- ⎪ ⎪⎝⎭()101y <≤设()()4301f x x x x=-<≤ 因为()24f x 30x '=--<恒成立， ()f x ∴在(]0,1上是减函数， 当11y =时有最小值，即32POQ S ∆≥, 综上：POQ S ∆的最小值为3.2【点睛】本题考查了点的轨迹方程、椭圆的性质等知识，求解几何图形的长度、面积等的最值时，常见解法是设出变量，用变量表示出几何图形的长度、面积等，减元后借助函数来研究其最值.26．（1）见解析；（2）13【解析】 【分析】（1）在正方形ABCD 中，有AB AD ⊥，CD BC ⊥，在三棱锥M DEF -中，可得MD MF ⊥，MD ME ⊥，由线面垂直的判定可得MD ⊥面MEF ，则MD EF ⊥； （2）由E 、F 分别是AB 、BC 边的中点，可得1BE BF ==，求出三角形MEF 的面积，结合()1及棱锥体积公式求解． 【详解】（1）证明：Q 在正方形ABCD 中，AB AD ⊥，CD BC ⊥，∴在三棱锥M DEF -中，有MD MF ⊥，MD ME ⊥，且ME MF M ⋂=，MD ∴⊥面MEF ，则MD EF ⊥；（2）解：E Q 、F 分别是边长为2的正方形ABCD 中AB 、BC 边的中点， 1BE BF ∴==，111122MEF BEF S S V V ∴==⨯⨯=，由（1）知，111123323M DEF MEF V S MD -=⋅=⨯⨯=V ．【点睛】本题考查线面垂直的判定定理及性质定理的应用，考查棱锥体积的求法，是中档题．。