必修四复习测试

单元素养培优(一) Unit 1Ⅰ.单句语法填空1.As a teacher, he is respected for his good teaching.2.—Do you care for modern music?—No, I prefer classical music to modern music.3.This sentence does not seem to connect with the context.4.The audience was/were (be) no less than five thousand in the stadium.5.The woman scientist was awarded the Nobel Prize for Physics for those great achievements(achieve) made by her.6.The international agreement, intended to encourage(encourage) children not to smoke and help people kick the habit, was signed on February 27.7.He was unhappy because many people argued against his plan.8.You’d better write down the phone number of that restaurant for future reference (refer).9.Observation(observe), reason and experiment make up what we call the scientific method.10.All of the students in our school were inspired by the inspiring speech given by Professor Li in Tsinghua University last October.(inspire)Ⅱ.选词填空1.He decided to devote the rest of his life to scientific study.2.On my way to the museum, I came across one of my teachers.3.It started to rain harder, but we gathered our courage and carried on.4.By chance he found the very book he was always looking for.5.I worked out many problems in the exercise book.6.She tried to sleep, but too many thoughts crowded in on her.7.The days when the Chinese were looked down upon are gone forever.8.The patient leads a normal and healthy life following his doctor’s advice.9.The teacher referred to in my last letter has gone abroad.10.The car moved off before the boy had got into it.Ⅲ.完成句子1.It seems that he is an honest man.看起来他是个老实人。

高中数学必修4复习测试题一.选择题：1．角α的终边过点P （4，－3），则αcos 的值为（ ）A 、4B 、－3C 、54D 、53-2．若0cos sin <αα，则角α的终边在（ ）A 、第二象限B 、第四象限C 、第二、四象限D 、第三、四象限3.若a =(2,1)，b =(3,4)，则向量a 在向量b 方向上的投影为 （ ）A 、52B 、2C 、5D 、104．化简︒-160sin 1的结果是（ ）A 、︒80cosB 、︒-160cosC 、︒-︒80sin 80cosD 、︒-︒80cos 80sin 5．函数)sin(ϕω+=x A y 在一个周期内的图象如下，此函数的解析式为 （ ）A 、)322sin(2π+=x y B 、)32sin(2π+=x y C 、)32sin(2π-=x y D 、)32sin(2π-=x y6.已知平面向量(1,2)a =，(2,)b m =-，且a //b ， 则23a b +＝ （ ）A 、(5,10)--B 、(4,8)--C 、(3,6)--D 、(2,4)-- 7.已知(1,2),(3,2),a b ==-并且()(3)ka b a b +⊥-，则k 的值为 ( )A ．1119 B ．2- C ．13- D ．19 8．在ABC ∆中，已知sinC=2sin(B+C)cosB,那么ABC ∆一定是 ( )Ａ．等腰直角三角形 Ｂ．等腰三角形 Ｃ．直角三角形Ｄ．等边三角形9.已知函数)52cos(4)(ππ+=x x f ，如果存在实数1x 、2x ，使得对任意的实数x 都有)()()(21x f x f x f ≤≤成立，则21x x -的最小值是 ( )A ．6B ．4C ．2D ．110．已知函数2()(1cos2)sin ,f x x x x R =+∈，则()f x 是 （ ）A 、最小正周期为π的奇函数B 、最小正周期为2π的奇函数 C 、最小正周期为π的偶函数 D 、最小正周期为2π的偶函数二.填空题： 11．若21tan =α，则ααααcos 3sin 2cos sin -+= . 12．函数x x y sin 22cos -=的值域是 . 13. 已知向量(1,2)a =，(2,4)b =--，5||2c =，若()53a b c +⋅=，则a 与c 的夹角为 ； 14、已知函数()sin 2cos 2f x x k x =-的图像关于直线8x π=对称，则k 的值是．1521==，与的夹角为3π+= . 三．解答题16、已知函数2()sin sin 2f x x x m π⎡⎤⎛⎫=+-+ ⎪⎢⎥⎝⎭⎣⎦．（１）求()f x 的最小正周期；（２）若()f x 的最大值为3，求m 的值．17．设)1,3(=，)2,1(-=，OB OC ⊥，BC ∥OA ，试求满足OC OA OD =+的OD 的坐标（O 为坐标原点）。

t
12 3 ；当 k
2 时， 18 3
t
3 21
4
4
4
4
4
4
故船舶安全进港的时间段为 (0 : 45 3: 45) ， (9: 45 12: 45) ， (18: 45 21: 45)
21. 解: (1) f ( x) a b ( 3sin x, m cosx) (cos x, m cos x) 即 f ( x) 3sin x cosx cos2 x m2
第 1 页 共 11 页数学必修 4
一 . 选择题： 1. 的正弦值等于
3
数学必修 4
（
）
（ A） 3 2
（ B） 1 2
（ C） 3 2
1 （D）
2
2．215°是
（A）第一象限角
（B）第二象限角
（C）第三象限角
（D）第四象限角
3．角 的终边过点 P（ 4，－ 3），则 cos 的值为
（A）4
（B）－ 3
第 1 题．已知 A， B， C 三点的坐标分别是 A(3，0)， B(0，3)， C(cos ，sin ) ，其中 π 2
（ 1）若 AC BC ，求 的值；
（ 2）若 AC·BC
1 ，求 2sin 2 sin2 的值． 1 tan
解：（1 ）有 A(3，0)， B(0，3)， C(cos ，sin ) ．
x 2y x1 3 y2
x 14 OC (14,7)
y7
OD OC OA (11,6)
4
第 5 页 共 11 页数学必修 4
20. 解：（1）由表中数据可以看到：水深最大值为 13，最小值为 7， h 13 7 10 ， A 13 7 3

人教2019新版选择性必修四•Unit 2基础练一、词汇短语精练：用所给词的适当形式或填空。

1. He was fond of ________ (dive) from an early age and he enjoys the wonderful creatures on the ocean floor.2. She is old enough to have the________ (free) to do what she likes.3. The carnival held in our school last week________(sponsor) by several famous graduates.4. The charity organized the ______ (distribute) of food and clothing in the disaster area.5. Road accidents have decreased in ________ (frequent) in this region during the past decade.6. You should keep your ________ (capable) to deal with all kinds of problems.7. Modern science makes it possible for us to be in contact ________ each other much more easily.8. California _________ (refer) to as the Golden State, as you know.9. He picked up a handful ____ gravel (石子) and drew back his arm to throw.10. The organization is called Root Shoots because roots move slowly under the ground to make a firm ________ (found).二、题型精练：阅读理解On September 15, El Salvador, Guatemala, and Honduras celebrate their own independence days. On October 16, Mexico follows suit. Each country above has its own nature, but what combines them is local traditions and Spanish culture. Here are four destinations worthy of planning a trip.Tazumal, El SalvadorEl Salvador is home to some rather impressive Mayan ruins that show off this once great civilization. Tazumal is one such place, which is believed to be more than 7,000 years old and was left abandoned sometime around the 13th century. However, large areas were extensively restored in the 40s’ and 50s’, giving visitors a taste of the past.Antigua, GuatemalaThe 16th-century city of Antigua is surrounded by volcanoes, churches, and Baroque buildings, combining European style with pre-Hispanic traditions, making its way to the list of UNESCO World Heritage Sites. It’s possible to visit most of its attractions on foot, including the Arco de Santa Catalina, the Central Park, and the Palacio del Ayuntamiento.Comayagua, HondurasHonduras may be well-known for its beaches, and one worthy of your travels is the city that was once the capital: Comayagua. Founded in the early 1500s, a visit here is like traveling back in time. Several museums showcase the cultural richness and the must-see clock in the central square, which is the oldest clock in the continent, dating back to the 12th century.Veracruz, MexicoVeracruz is a natural beauty with beaches that stretch for as far as the eye can see, deep blue waves and powerful waterfalls. When visiting Veracruz, stop by the Zocalo in Downtown Veracruz, where locals gather to listen to “son jarocho”, a regional folk music style that started right here. Couples also gather to dance in the square. But not just any dance, rather they take part in Danzόn, a traditional couples dance iconic (标志性的) to this particular state.1. Which place has the potential to be a UNESCO World Heritage Site?A. Tazumal.B. Antigua.C. Comayagua.D. Veracruz.2. What can visitors do in Veracruz?A. Learn to sing folk music.B. Watch unique dances.C. Go in for water sports.D. Walk on man-made beaches.3. What do the listed places have in common?A. They share the same traditional culture.B. They have beautiful long beaches.C. They are home to famous ancient ruins.D. They celebrate independence days the same day.三、语法填空Carrying a message of peace and friendship, the flame for the 2022 Winter Olympic Games arrived to a warm welcome in Beijing on Wednesday.Witnessed by organizers, sports 1(figure), performers and students, the flame housed in a red lantern 2(draw) crowds of onlookers as it was accompanied by volunteers into a ceremony held at Beijing’s Olympic Tower. The flame arrived early on Wednesday after 3 (fly) from Greece, the birthplace of the Olympics, where it was lit two days 4 (early).Public exhibitions of the torch and the traditional national relay (接力) in the host country have been simplified for the Beijing Games due 5 COVID-19 precautionary measures. The relay will take place in three host areas and involve about 1,200 torchbearers, 6 scheduled for Feb 2 to Feb 4, with the route 7 (connect) landmarks, historical sites and major tourism attractions in Beijing and Zhangjiakou. The shortened torch relay with reduced crowds, will help ensure the health and 8 (safe) of all participants as well as that of local communities.“As 9 iconic (偶像) cultural element of the Olympic Games, the torch relay plays a10 (extreme) significant role in promoting the host’s international image while spreading the message of peace and friendship,” said Zhang Jiandong, a vice-mayor of Beijing.提升练四、阅读理解Best places to visit in the UKLondon: The UK's All-in-One DestinationWhile it's possible to plan a trip to the UK without visiting London, it's certainly not to beadvised. The nation's capital offers plenty of attractions to keep you busy. For those interested in learning more about the UK's rich history, one of the top things to do in London is visit the Tower of London. Located beside the Tower Bridge on the banks of the River Thames, this former palace and prison includes highlights such as the iconic 1,000-year-old White Tower, with its fascinating displays of armor and weaponry, and the Jewel House, home to the Crown Jewels.Edinburgh; Scotland's CapitalOne of Scotland's most attractive cities, the capital city of Edinburgh is also one of the UK's most visited destinations. Popular for its many well-preserved historic buildings, Edinburgh is perhaps best known as the home of the Edinburgh Castle.Other Edinburgh highlights include broad Princes Street, popular for its shopping and dining, as well as for the Royal Botanical Garden and the National Gallery of Scotland.Medieval (中世纪的) York and its MinsterOne of northern England's most popular tourist destinations, the medieval city of York, long the ecclesiastical (教会的) capital of the Church of England, boasts one of the country's most magnificent cathedrals (教堂). The country's largest medieval church, York Minster can trace its roots back to the spread of Christianity in the 3rd century, although the splendid present Gothic structure was built almost 1,000 years later.Highlights of a tour include the opportunity to view its 14th-century stained glass windows, plus the richly decorated interiors of the choir and north transept. Also worth a visit is the crypt, which contains parts of the original 11th-century church the cathedral now stands on.Plan your sightseeing adventures with our list of the best places to visit in the UK. Click here for more information.1. If you are interested in UK's rich history; where would you go?A. Tower BridgeB. River ThamesC. Tower of LondonD. White Tower2 Which of the following is Edinburgh best known for?A. Edinburgh CastleB. Princes StreetC. National GalleryD. Royal Botanical Garden3. Which of the following about York is true?A. It was the capital of the Church of England.B. York boasts UK's most magnificent cathedrals.C. York Minster is the country's largest medieval church.D. The present Gothic structure was built almost 1000 years ago.4. Where would you probably read this article?A. On a sports magazine.B. On a travel website.C. On a science report.D. On a geography book.五、七选五The Sahara DesertLocationFilling nearly all of northern Africa, the Sahara Desert measures approximately 3,000 miles from east to west and between 800 and 1,200 miles from north to south. 1 The Sahara Desert is bordered in the west by the Atlantic Ocean, in the north by the Atlas Mountains and the Mediterranean Sea, in the east by the Red Sea, and in the south by the Sahel.LandscapeThe Sahara Desert features iconic sand dune (沙丘) fields, which cover about 15 percent of the entire desert’s surface and lie primarily in the north-central region. 2 A few examples include crescent (新月形的) dunes, linear dunes, transverse dunes and star dunes. These dunes, with their various forms, raise many questions about the dynamics of their formation.Water3 Its age-old rivers are the Nile and the Niger. The Nile rises south of the Sahara and empties into the Mediterranean. The Niger rises southwest of the Sahara and flows northeastward into Mali.4 It is the expansive but shallow Lake Chad, a body of water that lies at the southernmost edge of the Sahara. Other lakes hold a salty stew of undrinkable water.ClimateAcross the Sahara Desert, the annual average rainfall equals no more than a few inches or fewer. In the summer, daytime air temperatures often soar to over 100 degrees Fahrenheit, with the hottest air temperature meteorologists have ever recorded — 136 degrees — occurring at EL Azizia, Libya, on September 13, 1922. 5 In the winter, freezing temperatures may occur in the northern Sahara Desert, and milder temperatures across the southern Sahara Desert. Snow may fall occasionally in some of the higher mountain ranges and rarely, on the desert floor.A. No rain at all may fall for several more years.B. It has a total area of some 3,320,000 square miles.C. The dunes usually take on varied and complex forms.D. Star dunes form under winds that blow from several directions.E. The Sahara Desert has some lakes, but only one with drinkable water.F. The Sahara Desert has only two permanent rivers and a handful of lakes.G. Under the clear skies, the temperature may fall 40 degrees or more during an evening.六、完形填空According to a Chinese saying, he who doesn’t reach the Great Wall of China is never a great man. Growing up in Beijing I 1 historical sites and natural attractions (吸引) perfectly well. However, I’d 2climbed the Great Wall before until recently. I, along with my friends, aimed for the top. We soon discovered that the hike (远足) was much more 3 than we had imagined. But we didn’t 4. It took us about two hours to finally reach where we had wanted to get to.As I 5 at the top of the Great Wall, I looked back at the waves (浪) of 6 walking to the top. At that moment, I saw an amazing view that would forever change my opinion on humans’ limits. I saw young couples carrying their children, walking 7but surely towards the top. They would stop once in a while to take a 8 under the hot sun.As I stood there, I began to 9 words that can describe us humans. If one would like to describe Giraffes (长颈鹿), he/she would use words such as 10and long-necked—But what about us? I took another look down below and my 11 began to gather, persevering (坚持不懈的), determined, and strong... As these words came into my mind, I12 that it was not appearance (外貌) or physical characteristics that should define (定义) us humans, but the 13 that we share.I don’t know if I became a great man after returning from this 14 according to the Chinese saying, 15 I surely returned as a more thoughtful person.1. A. show B. accept C. imagine D. know2. A. still B. also C. never D. already3. A. expensive B. interesting C. difficult D. important4. A. break up B. give up C. keep up D. look up5. A. shook B. lay C. walked D. stood6. A. children B. sights C. people D. foreigners7. A. dangerously B. slowly C. worriedly D. strangely8. A. break B. tip C. step D. note9. A. care about B. make up C. tell about D. think of10. A. healthy B. tall C. fat D. scary11. A. thoughts B. emotions C. rules D. plans12. A. worried B. argued C. feared D. realized13. A. dreams B. qualities C. concerns D. experiences14. A. trip B. country C. vacation D. risk15. A. but B. as C. unless D. so七、书面表达假如你是李华，你远在英国的朋友Peter对历史文化名城扬州很感兴趣，发邮件来询问详细信息。