2017-2018学年度第一学期必修5 Modules1-3综合测试题

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2017-2018学年高中英语外研版必修五学业分层测评:Mod

2017-2018学年高中英语外研版必修五学业分层测评:Mod

学业分层测评Ⅰ.单句语法填空1.He faces the (tough)test of his leadership so far.2.In the last few years,China has (dramatic)improved relations with the region.3.Thanks to the competition,the two (compete)become good friends.4.Cao Cao's tomb is reported (find)in Anyang,which attracts nationwide attention.5.The moment the 30th Olympic Games (declare)open,the whole world cheered.6.When I came in,he saw me and rose his feet to greet me.7.He won this year's title with score of 9.687.8. is often said that human beings are naturally equipped to speak.9.With proper measures,the economy in China is picking again.10.Our house has reached the point so many things need putting up but it's so hard to find the time to fix it.【答案】 1.toughest 2.dramatically petitors 4.to have been found 5.were declared 6.to 7.a 8.It 9.up 10.whereⅡ.完成句子1.听到一个奇怪的声音,这个小男孩快速地站起来,跑了。

2017-2018学年(新课标)北师大版高中数学必修五模块检测试题及答案解析

2017-2018学年(新课标)北师大版高中数学必修五模块检测试题及答案解析

(新课标)2017-2018学年北师大版高中数学必修五模块检测(时间:120分钟 满分:150分)一、选择题(本大题共10小题,每小题5分,共50分) 1.已知数列{a n }的前n 项和S n =n 3,则a 5+a 6的值为( ). A .91 B .152 C .218 D .279 解析 a 5+a 6=S 6-S 4=63-43=152. 答案 B2.在△ABC 中,sin A ∶sin B ∶sin C =4∶3∶2,则cos A 的值是( ). A .-14B.14C .-23 D.23解析 由正弦定理得a ∶b ∶c =4∶3∶2,设a =4k ,b =3k ,c =2k ,则cos A = 9k 2+4k 2-16k 22×3k ×2k =-14.答案 A3.在正项等比数列{a n }中,a 1和a 19为方程x 2-10x +16=0的两根,则a 8·a 10·a 12等于( ).A .16B .32C .64D .256解析 ∵{a n }是等比数列且由题意得a 1·a 19=16=a 102(a n >0),∴a 8·a 10·a 12=a 103=64. 答案 C4.等差数列{a n }满足a 42+a 72+2a 4a 7=9,则其前10项之和为( ). A .-9 B .-15 C .15 D .±15解析 a 42+a 72+2a 4a 7=(a 4+a 7)2=9.∴a 4+a 7=±3, ∴a 1+a 10=±3,∴S 10=10(a 1+a 10)2=±15.答案 D5.在坐标平面上,不等式组⎩⎪⎨⎪⎧y ≥x -1,y ≤-3|x|+1所表示的平面区域的面积为( ).A. 2B.32C.322D .2解析 |CD|=1+1=2,⎩⎨⎧y =x -1,y =-3x +1,∴x A =12.⎩⎪⎨⎪⎧y =x -1,y =3x +1,∴x B =-1,∴S △CDA =12×2×12=12,S △CDB =12×2×1=1.故所求区域面积为32.答案 B6.如果不等式2x 2+2mx +m4x 2+6x +3<1对一切实数x 均成立,则实数m 的取值范围是( ).A .(1,3)B .(-∞,3)C .(-∞,1)∪(2,+∞)D .(-∞,+∞)解析 ∵4x 2+6x +3=⎝ ⎛⎭⎪⎫2x +322+34>0,∴原不等式⇔2x 2+2mx +m <4x 2+6x +3⇔2x 2+(6-2m)x +(3-m)>0,x ∈R 恒成立⇔Δ=(6-2m)2-8(3-m)<0,∴1<m <3. 答案 A7.△ABC 中,a ,b ,c 分别是内角A ,B ,C 的对边,且cos 2B +3cos(A +C)+2=0,b =3,则c ∶sin C 等于( ). A .3∶1 B.3∶1 C.2∶1 D .2∶1解析 cos 2B +3cos(A +C)+2=2cos 2B -3cos B +1=0, ∴cos B =12或cos B =1(舍).∴B =π3.∴c sin C =b sin B =332=2. 答案 D8.已知各项都为正数的等比数列{a n }的公比不为1,则a n +a n +3与a n +1+a n +2的大小关系是( ).A .a n +a n +3<a n +1+a n +2B .a n +a n +3=a n +1+a n +2C .a n +a n +3>a n +1+a n +2D .不确定的,与公比有关 解析 因为a n +a n +3=a n (1+q 3), a n +1+a n +2=a n (q +q 2),a n +a n +3-(a n +1+a n +2)=a n (1+q 3-q -q 2)= a n (1-q)(1-q 2)=a n (1-q)2(1+q)>0. 答案 C9.已知公差不为0的等差数列的第4,7,16项恰好分别是某等比数列的第4,6,8项,则该等比数列的公比是( ). A. 3 B.2C .±3D .± 2解析 等差数列记作{a n },等比数列记作{b n }, 则q 2=b 8b 6=b 6b 4=b 8-b 6b 6-b 4=a 16-a 7a 7-a 4=9d3d =3,∴q =± 3.答案 C10.若实数x ,y 满足不等式组⎩⎪⎨⎪⎧x +3y -3≥0,2x -y -3≤0,x -my +1≥0,且x +y 的最大值为9,则实数m 等于( ).A .-2B .-1C .1D .2 解析 如图,作出可行域,由⎩⎪⎨⎪⎧x -my +1=0,2x -y -3=0,得A ⎝⎛⎭⎪⎫1+3m -1+2m ,5-1+2m ,平移y =-x ,当其经过点A 时,x +y 取得最大值,即1+3m -1+2m +5-1+2m=9,解得m= 1. 答案 C二、填空题(本大题共5小题,每小题5分,共25分)11.正项等比数列{a n }满足a 2a 4=1,S 3=13,b n =log 3a n ,则数列{b n }的前10项和是________.解析 ∵{a n }成等比数列,a n >0,∴a 2a 4=a 32=1. ∴a 3=1,∴a 1q 2=1.①∵S 3=a 1+a 2+1=13,∴a 1(1+q)+1=13.② 由①②得,a 1=9,q =13,a n =33-n .∴b n =3-n.∴S 10=-25. 答案 -2512.如图所示,为测一树的高度,在地面上选取A 、B 两点,从A 、B 两点分别测得树尖的仰角为30°,45°,且A 、B 两点之间的距离为60 m ,则树高的高度为________.解析 ∵∠A =30°,∠ABP =45°,∴∠APB =15°,AB sin ∠APB =PA sin ∠PBA ,60sin 15°=PAsin 135°,∴PA =60(3+1),PQ =PA ·sin ∠A =60(3+1)·sin 30°=30(3+1).答案 (30+303)m13.设,x ,y 满足约束条件⎩⎪⎨⎪⎧2x -y +2≥0,8x -y -4≤0,x ≥0,y ≥0,若目标函数z =abx +y(a >0,b >0)的最大值为8,则a +b 的最小值为________.解析 如图所示,线性约束条件表示的区域为图中的阴影部分,A(0,2),B ⎝ ⎛⎭⎪⎫12,0,C(1,4),当直线l :y =-abx+z 过点C 时,z 取最大值8,即8=ab +4, ∴ab =4.又∵a >0,b >0,∴a +b ≥2ab =24=4(a =b =2时取等号).答案 414.在△ABC 中,D 为BC 边上一点,BC =3BD ,AD =2,∠ADB =135°,若AC =2AB ,则BD =________. 解析 如图,设AB =k , 则AC =2k ,再设BD =x , 则DC =2x.在△ABD 中,由余弦定理得 k 2=x 2+2-2·x ·2·⎝ ⎛⎭⎪⎫-22=x 2+2+2x ,① 在△ADC 中,由余弦定理得 2k 2=4x 2+2-2·2x ·2·22=4x 2+2-4x , ∴k 2=2x 2+1-2x.② 由①②得x 2-4x -1=0, 解得x =2+5(负值舍去). 答案 2+ 515.设x ,y ∈R ,a >1,b >1,若a x =b y =3,a +b =23,则1x +1y 的最大值为________.解析 因为a >1,b >1,a x =b y =3,a +b =23, 所以x =log a 3,y =log b 3.1x +1y =1log a 3+1log b 3=log 3a +log 3b =log 3ab ≤ log 3⎝⎛⎭⎪⎫a +b 22=log 3⎝ ⎛⎭⎪⎫2322=1,当且仅当a =b 时,等号成立.答案 1三、解答题(本大题共6小题,共75分)16.(12分)已知{a n }是首项为19,公差为-2的等差数列,S n 为{a n }的前n 项和. (1)求通项a n 及S n ;(2)设{b n -a n }是首项为1,公比为3的等比数列,求数列{b n }的通项公式及前n 项和T n .解 (1)∵{a n }是首项为a 1=19,公差为d =-2的等差数列,∴a n =19-2(n -1)=21-2n ,S n =19n +12n(n -1)×(-2)=20n -n 2.(2)由题意得b n -a n =3n -1,即b n =a n +3n -1,∴b n =3n -1-2n +21, ∴T n =S n +(1+3+…+3n -1)=-n 2+20n +3n -12.17.(12分)已知不等式ax 2-3x +6>4的解集为{x|x <1或x>b}, (1)求a ,b ;(2)解不等式ax 2-(ac +b)x +bc <0.解 (1)因为不等式ax 2-3x +6>4的解集为{x|x <1或x >b},所以x 1=1与x 2=b 是方程ax 2-3x +2=0的两个实数根,且b >1.由根与系数的关系,得⎩⎪⎨⎪⎧1+b =3a,1×b =2a.解得⎩⎪⎨⎪⎧a =1,b =2.所以a =1,b =2.(2)所以不等式ax 2-(ac +b)x +bc <0, 即x 2-(2+c)x +2c <0,即(x -2)(x -c)<0.当c >2时,不等式(x -2)(x -c)<0的解集为{x|2<x <c}; 当c <2时,不等式(x -2)(x -c)<0的解集为{x|c <x <2}; 当c =2时,不等式(x -2)(x -c)<0的解集为∅,综上,当c >2时,不等式ax 2-(ac +b)x +bc <0的解集为{x|2<x <c}; 当c <2时,不等式ax 2-(ac +b)x +bc <0的解集为{x|c <x <2}; 当c =2时,不等式ax 2-(ac +b)x +bc <0的解集为∅.18.(12分)在△ABC 中,a 比b 长2,b 比c 长2,且最大角的正弦值是32,求△ABC 的面积.解 据题意知a -b =2,b -c =2,∴边长a 最大,∴sin A =32, ∴cos A =±1-sin 2A =±12.∵a 最大,∴cos A =-12.又a =b +2,c =b -2,∴cos A =b 2+c 2-a 22bc =b 2+(b -2)2-(b +2)22b (b -2)=-12,解得b =5,∴a =7,c =3,∴S △ABC =12bcsin A =12×5×3×32=1534.19.(12分)已知某地今年年初拥有居民住房的总面积为a(单位:m 2),其中有部分旧住房需要拆除.当地有关部门决定每年以当年年初住房面积的10%建设新住房,同时也拆除面积为b(单位:m 2)的旧住房.(1)分别写出第一年末和第二年末的实际住房面积的表达式.(2)如果第五年末该地的住房面积正好比今年年初的住房面积增加了30%,则每年拆除的旧住房面积b 是多少?(计算时取1.15=1.6) 解 (1)第一年末的住房面积为 a ·1110-b =(1.1a -b)(m 2). 第二年末的住房面积为⎝ ⎛⎭⎪⎫a ·1110-b ·1110-b=a ·⎝⎛⎭⎪⎫11102-b ⎝ ⎛⎭⎪⎫1+1110=(1.21a -2.1b)(m 2).(2)第三年末的住房面积为⎣⎢⎡⎦⎥⎤a ·⎝ ⎛⎭⎪⎫11102-b ⎝ ⎛⎭⎪⎫1+1110·1110-b =a ·⎝⎛⎭⎪⎫11103-b ⎣⎢⎡⎦⎥⎤1+1110+⎝ ⎛⎭⎪⎫11102,第四年末的住房面积为 a ·⎝⎛⎭⎪⎫11104-b ⎣⎢⎡⎦⎥⎤1+1110+⎝ ⎛⎭⎪⎫11102+⎝ ⎛⎭⎪⎫11103,第五年末的住房面积为 a ·⎝⎛⎭⎪⎫11105-b ⎣⎢⎡⎦⎥⎤1+1110+⎝ ⎛⎭⎪⎫11102+⎝ ⎛⎭⎪⎫11103+⎝ ⎛⎭⎪⎫11104=1.15a -1-1.151-1.1b =1.6a -6b.依题意可知1.6a -6b =1.3a ,解得b =a 20,所以每年拆除的旧住房面积为a20 m 2.20.(13分)已知1≤x +y ≤5,-1≤x -y ≤3,求2x -3y 的取值范围.解 法一 作出一元二次方程组⎩⎪⎨⎪⎧1≤x +y ≤5-1≤x -y ≤3所表示的平面区域(如图)即可行域.考虑 z =2x -3y ,把它变形为y =23x -13z ,得到斜率为23,且随z 变化的一组平行直线,-13z 是直线在y 轴上的截距,当直线截距最大且满足约束条件时目标函数z =2x -3y 取得最小值;当直线截距最小且满足约束条件时目标函数z =2x -3y 取得最大值.由图可知,当直线z =2x -3y 经过可行域上的点A 时,截距最大,即z 最小.解方程组⎩⎪⎨⎪⎧x -y =-1,x +y =5,得A 的坐标为(2,3).所以z min =2x -3y =2×2-3×3=-5.解方程组⎩⎪⎨⎪⎧x -y =3,x +y =1,得B 的坐标为(2,-1),所以z max =2x -3y =2×2-3×(-1)=7. ∴2x -3y 的取值范围是[-5,7].法二 设2x -3y =m(x +y)+n(x -y)=mx +my +nx -ny =(m +n)x +(m -n)y则⎩⎪⎨⎪⎧m +n =2,m -n =-3,⇒⎩⎪⎨⎪⎧m =-12,n =52.则2x -3y =-12(x +y)+52(x -y)∵1≤x +y ≤5,-1≤x -y ≤3,∴-52≤-12(x +y)≤-12,-52≤52(x -y)≤152,∴-5≤2x -3y ≤7. 即2x -3y 的取值范围为[-5,7].21.(14分)某港口O 要将一件重要物品用小艇送到一艘正在航行的轮船上,在小艇出发时,轮船位于港口O 北偏西30°且与该港口相距20海里的A 处,并正以30海里/时的航行速度沿正东方向匀速行驶.假设该小艇沿直线方向以v 海里/时的航行速度匀速行驶,经过t 小时与轮船相遇.(1)若希望相遇时小艇的航行距离最小,则小艇航行速度的大小应为多少?(2)为保证小艇在30分钟内(含30分钟)能与轮船相遇,试确定小艇航行速度的最小值.解 (1)若相遇时小艇的航行距离最小,又轮船沿正东方向匀速行驶,则小艇航行方向为正北方向.如图所示,设小艇与轮船在C 处相遇.在Rt △OAC 中,OC =20cos 30°=103,AC =20sin 30°=10.又AC =30t ,OC =vt.此时,轮船航行时间t =1030=13,v =10313=303,即小艇以303海里/时的速度航行,相遇时小艇的航行距离最小.(2)如图所示,设小艇与轮船在B 处相遇.由题意,可得(vt)2=202+(30t)2-2·20·30t ·cos(90°-30°),化简,得v 2=400t 2-600t+900=400⎝ ⎛⎭⎪⎫1t -342+675.由于0<t ≤12,即1t≥2,所以当1t=2时,v 取得最小值1013,即小艇航行速度的最小值为1013海里/时.。

2017-2018学年度外研版必修5Module-3-单元试题

2017-2018学年度外研版必修5Module-3-单元试题

Module 3单元测试题第二部分:阅读理解(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,从每题所给的四个选项(A、B、C和D)中,选出最佳选项。

AThe first summer job is often a signal that you’re on your way to adulthood, and it’s also a method for earning money to pay for what you dream of. It’s never t oo early to start considering the future. Now, here are some good choices for you!Retail (零售) SalesRetail offers plenty of opportunity for teens who are looking for a job. This type of work can pay from $10 to $15 an hour depending upon the duty you are expected to take on. It can also be great for teens who are friendly and enjoy talking to other people. For more information, call us at 111-222-3333.Food ServiceA job in the food service industry is a natural fit for sociable teens who enjoy communicating with the public. It allows employees to work as part of a team while learning about following instructions. It also comes with the opportunity to earn between $8 and $10 per hour. Just call 111-222-3533 for more information.BabysitterThis job requires someone who is highly responsible (负责的). Though it pays generally between $6 and $8 hourly, it also requires a lot of patience. This is a great choice for teens who wish to make a career in teaching, child care, social work or any other field that makes use of social skills or requires interaction with kids. Got a question? Just call 111-222-3336.HousekeepingThis type of work can bring in about $5 an hour and it will allow teens to learn responsibility and develop their organizational skills. The summer sees an upswing in the tourism industry, so hotels are often looking for more housekeeping staff, and parks often need more people to assist with keeping public areas clean and organized as well. Telephone: 111-222-3330.21. How much can you earn at least in two hours as a retailer?A. $10.B. $12.C. $16.D. $20.22. Which of the following jobs may attract teens who want to be a teacher?A. Retail Sales.B. Food Service.C. Babysitter.D. Housekeeping.23. The underlined part “an upswing” in the last paragraph can best be replaced by “_____”.A. an increaseB. a limitC. a signD. a trick24. The text is mainly written for teens who _____.A. are faced with communication problemsB. want a part-time job in the summerC. dream of becoming a housekeeperD. plan to start their own businessBIn 1863, the great novelist (小说家) Jules Verne wrote a novel called Paris in the Twentieth Century. In the book he used the full power of his great ability to forecast the coming century. Unfortunately, the manuscript (手稿) was lost until his great-grandson happened to discover it lying in a safe where it had been carefully locked away for almost 130 years. Realizing what a treasure he had found, he arranged to have it published in 1994, and it became a bestseller at once.Back in 1863, kings still ruled the ancient world in Europe, with so many poor people performing backbreaking work in the fields. And steam power was just beginning to change the world. But Verne predicted that Paris in 1960 would have glass skyscrapers, air conditioning,TV, elevators, high-speed trains, gas-powered vehicles, and even something similar to the Internet. Verne described life in modern Paris almost without any mistakes.Just two years later Verne made another amazing prediction. He wrote From the Earth to the Moon, in which he predicted the details of the task that sent several astronauts to the moon more than 100 years later in 1969. He correctly predicted the size of the space capsule, the number of astronauts who would carry out the task, the length of time the journey would take, the weightlessness that the astronauts would experience, and the final landing in the ocean.How was Jules Verne able to predict 100 years into the future successfully? Although he was not a scientist himself, Verne often turned to scientists, asking them questions about their opinions of the future. He collected a vast amount of information about the great scientific discoveries of his time. Verne realized that science would make it possible for many amazing things to appear in the future. The secret of his successful prediction was his belief in the power of science to change society.25. Paris in the Twentieth Century is a novel that _____.A. people thought little of at firstB. took Jules Verne five years to finishC. didn’t sell well when published at firstD. was published long after it was finished26. The third paragraph is mainly about _____.A. the requirements of being an astronautB. what From the Earth to the Moon is aboutC. how From the Earth to the Moon was createdD. the differences between the earth and the moon27. According to the text, Jules Verne _____.A. showed strong interest in writing and scienceB. could predict what would happen to someoneC. was well-known as both a novelist and a scientistD. had Paris in the Twentieth Century published in 199428. What would be the best title for the text?A. The early life of Jules VerneB. Jules Verne’s opinions about scienceC. Jules Verne: A writer ahead of his timeD. Jules Verne’s inventions came trueCKnown as a radio host, Rush Limbaugh landed his first radio job when he was in high school. Then Limbaugh attended Southeast Missouri State University, where he showed interest in nothing but radio. After dropping out of college, Limbaugh went to work at a radio station, but he did not last long. For the next few years, he changed from station to station. Tom Leathers, publisher of The Squires, knew Limbaugh at the time and recalls, “Limbaugh was nothing special. He did not have that powerful personality you hear now. He was painfully shy.” Finally, under pressure from his father, who wanted him to give up radio, Limbaugh took a job as a public relations assistant for the Kansas City Royals (a Major League Baseball team).After five years, Limbaugh left the job because he wanted to work in radio. He soon landed a position at a Kansas City station as a talk show host and commentator. Ten months later, he was fired (解雇). In fact, he once admitted that he had been fired from all but two of the jobs he ever held. A year went by before a San Diego radio station agreed to give him a chance, mainly because it was in serious financial trouble. The job was exactly the chance he needed. Soon Limbaugh’s three-hour morning show became the most popular program in the city and spread to radio stations across the United States.In 2001, Limbaugh faced a new problem that threatened to take him off the air — deafness. Limbaugh went completely deaf in his left ear and had serious hearing loss in his right. At first, he made an effort to change the way he did his program to cover up his disability. Finally, he told the truth to his listeners and received a cochlear implant operation, which helped him regain(重新获得) some hearing in his left ear. As of 2008, Limbaugh’s radio show was still being broadcast on almost six hundred AM radio stations in the United States and on audio streams over the Internet. Limbaugh’s popularity is often said to have breathed new life into AM radio.29. What Tom Leathers said suggests that _____.A. Limbaugh’s hosting style was not attractiveB. Limbaugh was too shy to work as a radio hostC. Limbaugh used to be a man with a strong personalityD. Limbaugh shouldn’t have dropped out of college30. What’s the right order of the events about Rush Limbaugh?a. He worked as a public relations assistant.b. He had an operation because of hearing loss.c. He attended Southeast Missouri State University.d. He was offered a job by a San Diego radio station.e. He worked as a talk show host at a Kansas City station.A. c, a, d, e, bB. a, b, e, d, cC. c, a, e, d, bD. a, d, e, b, c31. What can we learn from Rush Limbaugh’s story?A. Think twice before you act.B. Where there is a will, there is a way.C. A good beginning makes a good ending.D. Don’t put off till tomorrow what should be done today.32. What is the text mainly about?A. Ways to help the deaf to hear.B. Rush Limbaugh’s career in radio.C. How to be an excellent radio host.D. Rush Limbaugh’s influence in the USA.DDon’t we all know a “Happy Meal” when we see one —the famous boxed meal that includes a hamburger, a kid-sized portion of fries, a side of fruits and milk, served with a toy that’s extremely popular with children who love to collect them?But collectors of these little toys will soon be in for a surprise. For the book lovers though, there is some good news. McDonalds will replace the plastic toys with books. However, each of these books will mainly pass on nutritional (营养的) messages.Do you know that McDonalds has been marketing the boxed kid’s meal since 1979? Happy Meals are extremely popular with kids, especially for its collectible toys, when you consider that over 1.3 billion of these packages are sold each year! These packages have been very controversial (有争议的). Health supporters believe that drawing kids to these meals with toys is a clever way of promoting unhealthy food choices. They see it as an advertising strategy (策略) of “catching its customers young” —a move that has paid off very well for the fast food company.Child development experts say that food habits get formed in children by age six and continue through to their adult life. Fatty and sugary foods such as those served in McDonalds’ Happy Meals are believed to play a big role in growing health problems such as obesity and diabetes. Public healthcare costs have gone up and untold amounts of money have been spent in caring for obesity and other health problems. In 2010, the State of California tried to ban toys in Happy Meals. But it was strongly opposed (反对) by some as being heavy-handed, and the ban was thrown out by the government.While some people believe that McDonalds, with its large following of children, can create a powerful message through the books, others believe its actions are contradictory (矛盾的). Anyway, the company is trying to spread the message of nutrition while it is serving food that is anything but healthy.33. Books will be added into Happy Meals to _____.A. encourage more kids to read booksB. introduce the history of McDonaldsC. have kids learn more about nutritionD. help young kids learn to read and write34. In the author’s opinion, Happy Meals _____.A. bring much fun to childrenB. are no good to children’s healthC. are popular with young and oldD. teach children a lot about nutrition35. The author’s purpose of writing the text is most likely to _____.A. discussB. advertiseC. entertainD. introduce第二节(共5小题;每小题2分,满分10分)根据短文内容,从短文后的选项中选出能填入空白处的最佳选项。

2017-2018学年高中数学北师大版必修5课时作业:模块综合测试卷 Word版含答案

2017-2018学年高中数学北师大版必修5课时作业:模块综合测试卷 Word版含答案

模块综合测试卷班级__________ 姓名__________ 考号__________ 分数__________本试卷满分100分,考试时间90分钟.一、选择题:本大题共10题,每题4分,共40分.在下列各题的四个选项中,只有一个选项是符合题目要求的.1.已知{a n }是等比数列,a 2=2,a 5=14,则公比q =( ) A .-12 B .-2 C .2 D.122.设a ,b ,c ,d ∈R ,且a >b ,c >d ,则下列结论正确的是( )A. a +c >b +dB. a -c >b -dC. ac >bdD. a d >b c3.已知a ,b ,c 分别是△ABC 的三个内角A ,B ,C 所对的边,若A =45°,B =60°,a =6,则b 等于( ) A. 3 6 B. 3 2 C. 3 3 D. 2 6 4.设变量x ,y 满足⎩⎪⎨⎪⎧ x +y ≤1,x -y ≤1,x ≥0,则x +2y 的最大值和最小值分别为( )A .1,-1B .2,-2C .1,-2D .2,-15.已知数列{a n }是等比数列,且a n >0,a 2a 4+2a 3a 5+a 4a 6=25,那么a 3+a 5=( )A. 5B. 10C. 15D. 206.设a ,b ∈R ,a 2+2b 2=6,则a +b 的最小值是( )A .-2 2B .-533C .-3D .-727.在R 上定义运算 :x y =x (1-y ),若不等式(x -a ) (x +a )<1对任意实数x 成立,则( )A .-1<a <1B .0<a <2C .-12<a <32D .-32<a <128.已知0<x <1,则x (3-3x )取最大值时x 的值为( )A.13B.12C.34D.239.在△ABC 中,已知a 4+b 4+c 4=2c 2(a 2+b 2),则C 等于( )A .30° B.60° C.45°或135° D.120°10.设{a n }是任意等比数列,它的前n 项和,前2n 项和与前3n 项和分别为X ,Y ,Z ,则下列等式中恒成立的是( )A .X +Z =2YB .Y (Y -X )=Z (Z -X )C .Y 2=XZ D .Y (Y -X )=X (Z -X )二、填空题:本大题共3小题,每小题4分,共12分.把答案填在题中横线上.11.112+214+318+…+101210=________. 12.某公司一年购买某种货物400吨,每次都购买x 吨,运费为4万元/次,一年的总存储费用为4x 万,要使一年的总运费与总存储费用之和最小,则x =________吨.13.已知△ABC 的面积为12,sin A =14,则1b +2c的最小值是________. 三、解答题:本大题共5小题,共48分,其中第14小题8分,第15~18小题各10分.解答应写出文字说明、证明过程或演算步骤.14.已知△ABC 的内角A ,B ,C 所对的边分别为a ,b ,c ,且a =2,cos B =35. (1)若b =4,求sin A 的值;(2)若△ABC 的面积S △ABC =4,求b ,c 的值.15.某企业拟用集装箱托运甲、乙两种产品,甲种产品每件体积为5 m 2,重量为2吨,运出后,可获利润10万元;乙种产品每件体积为4 m 3,重量为5吨,运出后,可获利润20万元.集装箱的容积为24 m 3,最多载重13吨.求用该集装箱托运甲、乙两种产品能获得的最大利润.16.已知数列{a n }是等差数列,且a 1=2,a 1+a 2+a 3=12.(1)求数列{a n }的通项公式;(2)令b n =a n ²3n ,求数列{b n }的前n 项和的公式.17.若a 、b 、c 是不全相等的正数,求证:lga +b 2+lg b +c 2+lg c +a 2>lg a +lg b +lg c .18.同学们对正弦定理的探索与研究中,得到a sin A =b sin B =csin C=2R (R 为△ABC 外接圆的半径).请利用该结论,解决下列问题:(1)现有一个破损的圆块如图1,只给出一把带有刻度的直尺和一个量角器,请你设计一种方案,求出这个圆块的直径的长度.(2)如图2,已知△ABC 三个角满足(sin∠CBA )2+(sin∠ACB )2-(sin∠CAB )2=sin∠CBA ²sin∠ACB ,AD 是△ABC 外接圆直径,CD =2,BD =3,求∠CAB 和直径的长.。

2017-2018学年高中数学北师大版必修5:模块综合测评 含解析 精品

2017-2018学年高中数学北师大版必修5:模块综合测评 含解析 精品

模块综合测评(时间120分钟,满分150分)一、选择题(本大题共12小题,每小题5分,共60分.在每小题给出的四个选项中,只有一项是符合题目要求的)1.已知等差数列{a n}满足a2+a4=4,a3+a5=10,则它的前10项的和S10=()A.138B.135C.95 D.23【解析】由a2+a4=4,a3+a5=10得a1=-4,d=3,所以S10=10×(2a1+9d)2=10×(-8+27)2=5×19=95.【答案】 C2.在△ABC中,已知a、b和锐角A,要使三角形有两解,则应该满足的条件是()A.a=b sin A B.b sin A>aC.b sin A<b<a D.b sin A<a<b【解析】当a=b sin A时,有一解,当b sin A<a<b时,有两解,当a>b 时有一解.【答案】 D3.已知不等式x2+ax+4<0的解集为空集,则a的取值范围是()A.-4≤a≤4 B.-4<a<4C.a≤-4或a≥4 D.a<-4或a>4【解析】欲使不等式x2+ax+4<0的解集为空集,则Δ=a2-16≤0,∴-4≤a≤4.【答案】 A4.已知等差数列的前n项和为18,若S3=1,a n+a n-1+a n-2=3,则n的值为()A.9 B.21C.27 D.36【解析】 ∵S 3=a 1+a 2+a 3=1, 又a 1+a n =a 2+a n -1=a 3+a n -2, ∴3(a 1+a n )=1+3,∴a 1+a n =43.又S n =n (a 1+a n )2=23n =18,∴n =27,故选C.【答案】 C5.关于x 的不等式ax -b >0的解集是(1,+∞),则关于x 的不等式(ax +b )(x -3)>0的解集是( )A .(-∞,-1)∪(3,+∞)B .(-1,3)C .(1,3)D .(-∞,1)∪(3,+∞) 【解析】 (ax +b )(x -3)>0等价于 ⎩⎨⎧ ax +b >0,x -3>0或⎩⎨⎧ax +b <0,x -3<0, ∴⎩⎨⎧x >-1,x >3或⎩⎨⎧x <-1,x <3. ∴x ∈(-∞,-1)∪(3,+∞). 【答案】 A6.“神七”飞天,举国欢庆,据科学计算,运载“神舟七号”飞船的“长征2号”系列火箭,点火1分钟内通过的路程为2 km ,以后每分钟通过的路程比前一分钟增加2 km ,在到达离地面240 km 的高度时,火箭与飞船分离,则这一过程大约需要的时间是( )A .10分钟B .13分钟C .15分钟D .20分钟【解析】 由题设条件知,火箭每分钟通过的路程构成以a 1=2为首项,公差d =2的等差数列,∴n 分钟内通过的路程为S n =2n +n (n -1)2×2=n 2+n =n (n +1).检验选项知,n =15时,S 15=240 km.故选C.【答案】 C7.在△ABC 中,内角A 、B 、C 满足6sin A =4sin B =3sin C ,则cos B =( ) A.154 B.34 C.31510D.1116【解析】 由6sin A =4sin B =3sin C 得sin A ∶sin B ∶sin C =2∶3∶4,设△ABC 中角A 、B 、C 的对边分别为a ,b ,c ,则由正弦定理知a ∶b ∶c =2∶3∶4.不妨设a =2k ,b =3k ,c =4k (k >0), 则cos B =a 2+c 2-b 22ac =(22+42-32)k 22×2k ×4k =1116.【答案】 D8.设变量x ,y 满足约束条件⎩⎨⎧x -y +2≥0,2x +3y -6≥0,3x +2y -9≤0,则目标函数z =2x +5y 的最小值为( )【导学号:47172142】A .-4B .6C .10D .17【解析】 由约束条件作出可行域如图所示,目标函数可化为y =-25x +15z ,在图中画出直线y =-25x ,平移该直线,易知经过点A 时z 最小. 又知点A 的坐标为(3,0), ∴z min =2×3+5×0=6.故选B. 【答案】 B9.y =3+x +x 21+x(x >0)的最小值是( )A .2 3B .-1+2 3C .1+2 3D .-2+2 3【解析】 y =3+x +x 21+x =31+x +x =31+x +x +1-1≥23-1,当且仅当31+x =1+x ,即x =3-1时取等号,故y 有最小值23-1.【答案】 B10.对于每个自然数n ,抛物线y =(n 2+n )x 2-(2n +1)x +1与x 轴交于A n ,B n 两点,以|A n B n |表示该两点间的距离,则|A 1B 1|+|A 2B 2|+…+|A 2 015B 2 015|的值是( )A.2 0142 015 B.2 0162 015 C.2 0152 014D.2 0152 016【解析】 |A n B n |=|x 1-x 2|=⎝ ⎛⎭⎪⎫2n +1n 2+n 2-4n 2+n =1n 2+n =1n ·(n +1)=1n -1n +1, ∴|A 1B 1|+|A 2B 2|+…+|A 2 015B 2 015|=⎝ ⎛⎭⎪⎫1-12+⎝ ⎛⎭⎪⎫12-13+…+⎝ ⎛⎭⎪⎫12 015-12 016=2 0152 016.【答案】 D11.设f (x )=3ax -2a +1,若存在x 0∈(-1,1)使f (x 0)=0,则实数a 的取值范围是( )A .-1<a <15 B .a <-1 C .a <-1或a >15D .a >15 【解析】 由于f (x )=3ax -2a +1,故f (x )一定是一条直线,又由题意,存在x 0∈(-1,1),使得f (x 0)=0,故直线y =3ax -2a +1在x =-1和x =1时的函数值异号,即f (-1)f (1)<0,得(1-5a )(a +1)<0,解得a <-1或a >15.【答案】 C12.已知圆C :(x -a )2+(y -b )2=1,平面区域Ω:⎩⎨⎧x +y -7≤0,x -y +3≥0,y ≥0.若圆心C ∈Ω,且圆C 与x 轴相切,则a 2+b 2的最大值为( ) 【导学号:47172143】A .5B .29C .37D .49【解析】 作出可行域,如图,由题意知,圆心为C (a ,b ),半径r =1,且圆C 与x 轴相切,所以b =1.而直线y =1与可行域的交点为A (6,1),B (-2,1),目标函数z =a 2+b 2表示点C 到原点距离的平方,所以当点C 与点A 重合时,z 取到最大值,z max =37.【答案】 C二、填空题(本大题共4个小题,每小题5分,共20分.将答案填在题中的横线上)13.已知二次函数f (x )=ax 2-3x +2,不等式f (x )>0的解集为{x |x <1或x >b },则b =________.【解析】 由题意知1,b 是方程ax 2-3x +2=0的两根, 由根与系数的关系得⎩⎪⎨⎪⎧1+b =3a ,1×b =2a ,∴⎩⎨⎧a =1,b =2.【答案】 214.在△ABC 中,B =120°,AC =7,AB =5,则△ABC 的面积为________.【导学号:47172144】【解析】 设AB =c ,BC =a ,AC =b ,由余弦定理b 2=a 2+c 2-2ac cos B ,得49=a 2+25-2×5a ⎝ ⎛⎭⎪⎫-12,解得a =3,∴S △ABC =12ac sin B =12×3×5×sin120°=1534. 【答案】 153415.若x ,y 满足约束条件⎩⎨⎧x -y +1≥0,x -2y ≤0,x +2y -2≤0,则z =x +y 的最大值为________.【解析】 画出可行域如图所示.由⎩⎨⎧x -2y =0,x +2y -2=0, 得⎩⎪⎨⎪⎧x =1,y =12.∴A ⎝ ⎛⎭⎪⎫1,12. 由z =x +y ,得y =-x +z ,平移直线l 0:x +y =0. 当直线过点A 时,z 最大,z max =1+12=32. 【答案】 3216.若a >0,b >0,且a 2+14b 2=1,则a 1+b 2的最大值为________.【解析】 a 1+b 2=12·2a 1+b 2≤4a 2+1+b 24=54,当且仅当⎩⎨⎧4a 2=1+b 2,4a 2+b 2=4时等号成立, 即a =104,b =62时成立.【答案】 54三、解答题(本大题共6小题,共70分,解答应写出文字说明,证明过程或演算步骤)17.(本小题满分10分)已知△ABC 的周长为2+1,且sin A +sin B =2sin C . (1)求边AB 的长;(2)若△ABC 的面积为16sin C ,求C 的度数. 【解】 (1)由题意△ABC 的周长为2+1, ∴AB +BC +AC =2+1.由正弦定理,得 BC +AC =2AB ,∴AB =1.(2)由△ABC 的面积为12BC ·AC ·sin C =16sin C ,得BC ·AC =13.由(1)知BC +AC =2,由余弦定理,得cos C =AC 2+BC 2-AB 22AC ·BC =12,∴C =60°.18.(本小题满分12分)已知等比数列{a n }中,a 2=2,a 5=128,若b n =log 2a n ,数列{b n }前n 项的和为S n .(1)若S n =35,求n 的值; (2)求不等式S n <2b n 的解集.【导学号:47172145】【解】 (1)由a 2=a 1q =2,a 5=a 1q 4=128得q 3=64, ∴q =4,a 1=12,∴a n =a 1q n -1=12·4n -1=22n -3, ∴b n =log 2a n =log 222n -3=2n -3. ∵b n +1-b n =[2(n +1)-3]-(2n -3)=2,∴{b 1}是以b 1=-1为首项,2为公差的等差数列, ∴S n =(-1+2n -3)n 2=35,n 2-2n -35=0,(n -7)(n +5)=0,即n =7.(2)∵S n -2b n =n 2-2n -2(2n -3)=n 2-6n +6<0, ∴3-3<n <3+3, ∵n ∈N +,∴n =2,3,4,即所求不等式的解集为{2,3,4}.19.(本小题满分12分)如图1,矩形ABCD 是机器人踢球的场地,AB =170 cm ,AD =80 cm ,机器人先从AD 中点E 进入场地到点F 处,EF =40 cm ,EF ⊥AD .场地内有一小球从点B 向点A 运动,机器人从点F 出发去截小球.现机器人和小球同时出发,它们均作匀速直线运动,并且小球运动的速度是机器人行走速度的2倍.若忽略机器人原地旋转所需的时间,则机器人最快可在何处截住小球?图1【解】 设该机器人最快可在点G 处截住小球,点G 在线段AB 上.连接FG .设FG =x cm.根据题意,得BG =2x cm.则AG =AB -BG =(170-2x )cm.连接AF ,在△AEF 中,EF =AE =40 cm ,EF ⊥AD , 所以∠EAF =45°,AF =402cm , 于是∠F AG =45°.在△AFG 中,由余弦定理,得 FG 2=AF 2+AG 2-2AF ·AG cos ∠F AG ,所以x 2=(402)2+(170-2x )2-2×402×(170-2x )×cos 45°, 解得x 1=50,x 2=3703.所以AG =170-2x =70 cm 或AG =-2303cm(不合题意,舍去). 即该机器人最快可在线段AB 上离A 点70 cm 处截住小球.20.(本小题满分12分)解关于x 的不等式ax 2-2≥2x -ax (a ∈R ).【导学号:47172146】【解】 原不等式可化为ax 2+(a -2)x -2≥0⇒(ax -2)(x +1)≥0. (1)当a =0时,原不等式化为x +1≤0⇒x ≤-1. (2)当a >0时,原不等式化为⎝ ⎛⎭⎪⎫x -2a (x +1)≥0⇒x ≥2a 或x ≤-1; (3)当a <0时,原不等式化为⎝ ⎛⎭⎪⎫x -2a (x +1)≤0.①当2a >-1,即a <-2时,原不等式的解集为-1≤x ≤2a ; ②当2a =-1,即a =-2时,原不等式的解集为x =-1; ③当2a <-1,即-2<a <0时,原不等式的解集为2a ≤x ≤-1. 综上所述,当a <-2时,原不等式的解集为⎣⎢⎡⎦⎥⎤-1,2a ;当a =-2时,原不等式的解集为{-1}; 当-2<a <0时,原不等式的解集为⎣⎢⎡⎦⎥⎤2a ,-1;当a =0时,原不等式的解集为(-∞,-1];当a >0时,原不等式的解集为(-∞,-1]∪⎣⎢⎡⎭⎪⎫2a ,+∞.21.(本小题满分12分)某汽车运输公司购买了一批豪华大客车投入运营.据市场分析,每辆客车运营的总利润y (单位:十万元)与运营年数x 满足二次函数的关系:y =-a (x -6)2+11,且该二次函数图像过点(4,7).问每辆客车运营多少年,运营的年平均利润最大?最大值为多少?(年平均利润=总利润年数) 【解】 设年平均利润为z 十万元,依题意, ∵二次函数y =-a (x -6)2+11的图像过点(4,7), ∴7=-a (4-6)2+11, ∴a =1,∴y =-(x -6)2+11,z =y x =-(x -6)2+11x=-x 2+12x -25x =-x -25x +12=-⎝ ⎛⎭⎪⎫x +25x +12.∵x >0,∴x +25x ≥10, ∴-⎝ ⎛⎭⎪⎫x +25x ≤-10,∴-⎝ ⎛⎭⎪⎫x +25x +12≤2,∴z ≤2,当且仅当x =25x 即x =5时,z 有最大值为2十万元.即每辆客车运营5年,运营的年平均利润最大,最大值为2十万元. 22.(本小题满分12分)已知数列{a n }是首项为a 1=14,公比q =14的等比数列,设b n +2=3log 14a n (n ∈N +),数列{c n }满足c n =a n ·b n .(1)求证:{b n }是等差数列; (2)求数列{c n }的前n 项和S n ;(3)若c n ≤14m 2+m -1对一切正整数n 恒成立,求实数m 的取值范围.【导学号:47172147】【解】 (1)证明:由题意知,a n =⎝ ⎛⎭⎪⎫14n (n ∈N +),∵b n =3log 14a n -2,b 1=3log 14a 1-2=1,∴b n +1-b n =3log 14a n +1-3log 14a n =3log 14a n +1a n =3log 14q =3,∴数列{b n }是首项b 1=1,公差d =3的等差数列. (2)由(1)知,a n =⎝ ⎛⎭⎪⎫14n ,b n =3n -2(n ∈N +),∴c n =(3n -2)×⎝ ⎛⎭⎪⎫14n (n ∈N +),∴S n =1×14+4×⎝ ⎛⎭⎪⎫142+7×⎝ ⎛⎭⎪⎫143+…+(3n -5)×⎝ ⎛⎭⎪⎫14n -1+(3n -2)×⎝ ⎛⎭⎪⎫14n ;于是14S n =1×⎝ ⎛⎭⎪⎫142+4×⎝ ⎛⎭⎪⎫143+7×⎝ ⎛⎭⎪⎫144+…+(3n -5)×⎝ ⎛⎭⎪⎫14n +(3n -2)×⎝ ⎛⎭⎪⎫14n +1,两式相减得34S n =14+3⎣⎢⎡⎦⎥⎤⎝ ⎛⎭⎪⎫142+⎝ ⎛⎭⎪⎫143+…+⎝ ⎛⎭⎪⎫14n -(3n -2)×⎝ ⎛⎭⎪⎫14n +1=12-(3n +2)×⎝ ⎛⎭⎪⎫14n +1. ∴S n =23-12n +83×⎝ ⎛⎭⎪⎫14n +1(n ∈N +). (3)∵c n +1-c n =(3n +1)·⎝ ⎛⎭⎪⎫14n +1-(3n -2)·⎝ ⎛⎭⎪⎫14n =9(1-n )·⎝ ⎛⎭⎪⎫14n +1(n ∈N +), ∴当n =1时,c 2=c 1=14, 当n ≥2时,c n +1<c n ,即c 1=c 2>c 3>c 4>…>c n ,∴当n =1或2时,c n 取得最大值是14.又c n ≤14m 2+m -1对一切正整数n 恒成立,∴14m 2+m -1≥14,即m 2+4m -5≥0,解得m ≥1或m ≤-5.故实数m 的取值范围为{m |m ≥1或m ≤-5}.。

2018最新试题资料-新人教版高中语文必修五模块综合测试卷(含解析)

2018最新试题资料-新人教版高中语文必修五模块综合测试卷(含解析)

新人教版高中语文必修五模块综合测试卷(含解析)
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新人教版高中语必修五模块综合测试卷(含解析)
(测试时间150分钟评价分值150分)
一、(本大题共4小题,每小题3分,共12分。

)
1.下列词语中加点的字,每对读音都不相同的一组是( )
A.坎坷/窠臼嗔怪/缜密供稿/供应
B.怠慢/逮捕誊写/家眷扁舟/扁平
c.侥幸/矫健脸颊/要挟驻扎/扎实
D.骁勇/肖像针砭/贬谪果脯/胸脯
解析D项,xiā/xià,biān/biǎn,fǔ/pú;A项,ě/ē,chēn/zhěn,gōng;B项,dài,téng/uàn,piān/biǎn;c项,iǎ,iá/xié,zhā。

答案D
2.下面语段中画线的词语,使用不恰当的一项是( )
安部第123号令规定“闯黄灯”也要被罚款扣分。

此新规一出台便引起轩然大波。

这条新规实施前没有广泛征求意见,涉及的问题在闭门造车中被掩盖,争议和置疑都被推到了实施之后,使得此法规陷入进退维谷的境地。

“黄灯”对我们的改革也有着深刻的隐喻,我们生活中处处都有规则,如何划定合法与非法的界限,这一次的争论是很生动的一。

A.轩然大波 B.闭门造车
c.置疑 D.进退维谷
解析c项,置疑怀疑(多用于否定式)。

此处应该用“质疑”。

质疑提出疑问。

A项,轩然高高涌起的样子。

高高涌起的波涛。

比喻大的纠纷或乱子,指不好的影响。

B项,闭门造车关上门造车,比喻只凭主观办事,不管客观实际。

D项,进退维谷进退两难(谷,比喻困难的境地)。

最新-2018届高考英语 Modules 1-3复习模块能力检测 外

2018届英语复习模块能力检测:Modules 1-3(外研版必修5)高考体验1(2018福建卷)29.-It’s nice. Never before____ such a special drink!-I’m glad you like it.A.I have hadB. I hadC. have I hadD. had IC2. Little _________ about her own safety, though she was in great danger herself.[2018陕西,18]A. did Rose careB. Rose did careC. Rose does careD. does Rose care【解析】选A。

考查倒装语序。

句意为:虽然身处险境,Rose却丝毫不在乎她个人的安危。

little是否定副词,否定副词置于句首时,句子用部分倒装;再依据后面的“was”一词,可知事情发生在过去,用过去时,所以A项正确。

3. For a moment nothing happened. Then ________ all shouting together.[2018福建,25]A. voices had comeB. came voicesC. voices would comeD. did voices come【解析】选B。

考查倒装结构。

句意为:那一会儿,什么都没发生。

随后大家一起欢呼起来。

表示时间的副词now, then及表示方位的副词here, there等位于句首,与位移性动词come, go, arrive等连用,且主语不是人称代词,此时用完全倒装。

从前一句可知此处描述的是过去的事情,所以用一般过去时。

4. Not until I came home last night ________ to bed.[2018四川, 16]A. Mum did goB. did Mum goC. went MumD. Mum went【解析】选B。

20172018学年高中英语模块综合测评新人教版必修3

模块综合测评(用时:120分钟满分:150分)第一部分听力(共两节,满分30分)第一节(共5小题;每小题1.5分,满分7.5分)听下面5段对话。

每段对话后有一个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。

听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

W:Excuse me,could you tell me the way to the railway station?M:Sorry,I don’t know.I’m a stranger here.1.What is the relationship between the two speakers?A.Strangers.B.Friends.C.Brother and sister.答案:AM:Excuse me,where is the closest place to eat?W:Down the street about four blocks.I can take you there if you like.2.What’s the man going to do?A.He is going to have dinner.B.He is looking for a hotel.C.He is trying to find the nearest street.答案:AW:Excuse me.Which is the nearest hospital?M:Go along this street.At the end of the street,you can find it on your left. W:Thank you.3.Where does the woman want to go?A.The farm.B.The factory.C.The hospital.答案:CW:Excuse me,could you tell me which bus goes to the town centre?M:Oh,dear,I’m sorry.I don’t know.I’m a stranger here myself.Why don’t you ask someone in the shop centre?4.What does the woman want to do?A.She wants to take a bus.B.She wants to buy something.C.She wants to make friends with the man.答案:AW:Excuse me.Can you tell me where the People’s Theatre is?M:Of course.Let me see.Oh,go straight down the street,and then turn right at the first crossing.And then walk on.You will see it on your left.5.What is the woman probably going to do?A.She may be going to buy a book.B.She may be going to watch a play.C.She may be going to watch a football match.答案:B第二节(共15小题;每小题1.5分,满分22.5分)听下面5段对话或独白。

必修五 Modules 1~3综合技能测试

必修五Modules 1~3综合技能测试本卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。

满分150分,考试时间120分钟。

第Ⅰ卷(选择题共115分)第一部分:听力(共两节,满分30分)做题时,先将答案标在试卷上,录音内容结束后,你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节(共5小题;每小题1.5分,满分7.5分)听下面5段对话。

每段对话后有一个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。

听完每段对话后,你将有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1.What is the weather like?A.Rainy. B.Sunny. C.Cloudy.2.Where does the conversation probably take place?A.In the street. B.In the school.C.In the office.3.Where does the woman live now?A.In HiltonB.In New Y ork.C.In California.4.What does the man want to have designed?A.A history museum. B.A car museum.C.An art museum.5.What are the two speakers going to do?A.Watch a football match.B.Go out for a walk.C.Watch TV at home.第二节(共15小题;每小题1.5分,满分22.5分)听下面5段对话或独白。

每段对话或独白后有几个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。

听每段对话或独白前,你将有时间阅读各个小题,每小题5秒钟;听完后,各小题将给出5秒钟的作答时间。

2017-2018学年度必修五综合测试卷

必修五综合测试卷一、选择题(每题5分,共50分)1.不等式x -1x +2>1的解集是( ) A .{x |x <-2} B .{x |-2<x <1} C .{x |x <1}D .{x |x ∈R } 2.下列说法正确的是( )A .a >b ⇒ac 2>bc 2B .a >b ⇒a 2>b 2C .a >b ⇒a 3>b 3D .a 2>b 2⇒a >b 3.若,,a b c R ∈,且a b >,则下列不等式中一定成立的是( )A.a b b c +≥-B.ac bc ≥C.20c a b>- D 2()0a b c -≥ 4.对于任意实数,,,a b c d ,命题①若,0,a b c ><则ac bc >;②若a b >,则22ac bc >;③若22ac bc <,则a b <;④若a b >,则 11a b <;⑤若0,0a b c d >>>>,则a c b d >。

其中正确的个数是( ) A.1 B.2 C.3 D.45.若x +23x -5<0,化简y =25-30x +9x 2-(x +2)2-3的结果为( ) A .y =-4x B .y =2-x C .y =3x -4 D .y =5-x6.已知不等式250ax x b -+>的解集为{|32}x x -<<,则不等式250bx x a -+>的解集为( ) A.11{|}32x x -<< B.11{|}32x x x <->或 C.{|32}x x -<< D.{|32}x x x <->或 7.对于任意实数x,不等式04)2(2)2(2<----x a x a 恒成立,则实数a 的取值范围是( )A.()2,∞-B.]2,(-∞C.]2,2(-D.)2,2(-8.已知n S 为数列}{n a 的前n 项和,若n n S S a 2,313==+,则=4a ( )A.6B.12C.16D.249.已知}{n a 是递减的等比数列,且5,2312=+=a a a ,则)(13221*+∈+++N n a a a a a a n n 的取值范围是( )A.[12,16)B.[8,16)C.)332,8[D.)332,316[ 10.正项数列}{n a 中,)2(2,2,12121221≥+===-+n a a a a a n n n ,则=6a ( )A.16B.8C.22D.4二、填空题(每题5分,共30分)11.ABC ∆中,oB b x a 45,2,===,若ABC ∆有两解,则x 的取值范围是12.等比数列}{a n 中,===n n n S S S 32,60,4813.若14,24a b <<-<<,则2a b -的取值范围是14.若x R ∈,则2x 与1x -的大小关系是15(A )对于x ∈R ,式子1kx 2+kx +1恒有意义,则常数k 的取值范围是_________. (B )不等式log 12(x 2-2x -15)>log 12(x +13)的解集是_________. 16.(A )=-++-+-22222212979899100(B )数列{}n a 的前n 项和为n S ,若)34()1(--=n a n n ,则n S =_________.三、解答题(13题10分,其余每题12分)17.在ABC ∆中,已知1)cos(32cos =+-C A A(1)求角A 的大小(2)若ABC ∆的面积5,35==b S ,求C B sin sin 的值18.设数列{}n a 的前n 项和为n S ,已知24,111+==+n n a S a(1)设n n n a a b 21-=+,证明数列{}n b 是等比数列(2)求数列{}n a 的通项公式19.在公差为d 的等差数列{}n a 中,已知101=a ,且3215,22,a a a +成等比数列(1)求n a (2)若0<d ,求na a a a ++++ 32120.(12分)已知m ∈R ,试解关于x 的不等式:(m +3)x 2-(2m +3)x +m >0.21.(1)若不等式049)1(220822>+++++-m x m mx x x 对任意实数x 都成立,求实数m 的取值范围(2)已知函数122++=ax ax y 的定义域为R ,解关于x 的不等式022<+--a a x x22. 正项数列}{n a 中,)(111,21,12121*++∈⋅===N n a a a a a n n n (1)求n a (2)求数列{}2+⋅n n a a 的前n 项和。

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必修5 Modules1-3综合测试题第一部分阅读理解(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,从每题所给的四个选项(A、B、C和D)中,选出最佳选项。

AAre you planning for your first ever international trip? No worries! We have a list of places that are perfect for first-time getaways.BaliBali is ever charming. Photographs cannot describe the beauty of its beaches, coral reefs, temples and forest areas. The temples, especially Tanah Lot, are quite a sight. The Kit. Batur is another amazing experience.Top attractions: Tanah Lot, Kuta Beach, Nusa Dua and Jimbaran Beach.MaldivesMaldives is an amazing beach destination. Here you can spend quality time away from the city life. Its bright blue shoreline, clean air and white sand can make you start feeling as if you had landed in heaven, then you get on a seaplane to the hotel that you have booked. The seaplane journey is an adventure that helps you see some of the most beautiful islands.Top attractions: water sports, beach and outdoor activities, local markets and more.MauritiusWhether you are into scenic beauty, adventure, or food, this island will not disappoint you. Mark Twain said, "Mauritius was made first and then heaven.” You can spend an evening in Port Louis and have dinner in Namaste Restaurant. Spend all the other days visiting only the beaches. If you are visiting lie Aux Cerfs, ensure you reach the island as early as possible as it closes at 4 pm.Top attractions: Grand Bay, Blue Bay, skydiving and bird watching.SingaporeClassical buildings stand tall with elegant skyscrapers (摩天大楼) all around the island, city, mixing perfectly with fancy shopping malls. This small country has good enough places for your 5-6 days‟ stay.Top attractions: shopping, street foods, museums and theme parks.1. If you are interested in water skiing, which place is the best choice?A. Bali.B. Maldives.C. Mauritius.D. Singapore.2. What do we know about Mauritius?A. Mark Twain loved Mauritius more than his country.B. Port Louis is not open at daytime.C. Only beaches are worth visiting in Mauritius.D. You can visit lie Aux Cerfs at night.3. What can we learn from this text?A. You‟re not allowed to take pictures in Bali.B. People take seaplanes rather than ships in Maldives.C. Singapore combines the classical and modem culture.D. Summer is the best time to visit the four places.BAs a mom who had already lost her son, a Houston nurse became concerned when she heard about the popular Netflix show 13 Reasons Why. By then her 15-year-old daughter had already been attracted to it. In the show, the main character feels hopeless and kills herself.Mental health experts believe that the show's messages on suicide (自杀) are dangerous. Educators have warned parents that it glamorizes the idea of suicide and could lead to an increase in imitation (模仿) among student s. They‟re worried about children watching it alone without parents beside them. Employees from some elementary and middle schools have seen an increase in self-harm among students since the show began.Netflix believed that the show has helped bring up important conversations in many families. Though some parents loved the show, for the nurse‟s family, it was a disaster. Her daughter has been suffering from depression since her brother‟s death. With treatment, things got better until she watched the series. “If I‟d known about the show beforehand I would have monitored (监视) her Netflix account,” said the nurse. “If kids have a history of depressio n or suicidal thoughts, I don ‟t think they need to watch it. ”The show‟s creators said they did make part of t he show painful to watch because they wanted to make it clear that there is nothing worthwhile about suicide. Before its release, a producer sought the support of the JED Foundation, a teen suicide prevention group. “I think they were looking for us to say it was a great educational tool, or that they handled the issues in a psychologically helpfu l way,” said a medical officer. The group issued a guide about the show, advising people who choose to watch it to view it with someone else and to take breaks between episodes (剧集).4. What does the underlined word “glamorizes” in Paragraph 2 mean?A. Makes something become more strange.B. Makes something seem more attractive.C. Makes something become more fearful.D. Makes something seem more touching.5. What do we know about the nurse?A. She‟d known about the TV show before her daughter watched it.B. The show has helped improve her family relationship.C. She didn‟t suggest teens with self-harm thoughts watch the show.D. She has been monitoring her daughter‟s Netflix account.6. The creators may agree that the show ________.A. includes dangerous messagesB. encourages self-harmC. is pleasant to watchD. is educational and helpful7. What is the passage mainly about?A. The story of a mom and her daughter.B. A TV show that caused discussion.C. An educational TV show.D. Some common teen problems.CAn “exercise pill” that could reduce the need for visits to the gym is a step closer. A study found that preventing production of the protein myostatin (肌肉抑制素) increases muscle. Although the research was conducted in mice, the team hopes it will lead to human treatments (治疗)Lead researcher Dr Joshua Butcher, from Augusta University in Georgia, the US, said, "Finally, the goal of our research would be to create a pill that mimics the effect of exercise and protects against obesity. A pill that stops myostatin could also be used for muscle-wasting diseases, such as cancer, muscle dystrophy and AIDS. Myostatin is known to be a powerfu l …brake‟ that holds back muscle growth.”Studies suggest that obese people produce more of the protein myostatin, making it harder for them to exercise and build up muscle. “Given that exercise is one of the most effective ways to deal with obesity, this creates a cycle by which a perso n becomes trapped in obesity,”said Dr Butcher.The researchers got four groups of thin and obesemice that were genetically programmed either to produce unlimited levels of myostatin or to be completely lacking in the protein. As expected, mice with no myostatin became markedly more muscular. Obese mice unable to produce myostatin remained fat, but they were also stronger and showed signs of heart and metabolic (新陈代谢) health compared with the thin mice. They were in greatly better shape than obese mice with unlimited myostatin production.Dr Butcher added, “In our muscular obese mice, despite full presentation of obesity, it appears that several of these key points are prevented. While much more research is needed, at this point, myostatin appears to be a very promising way for protection against some heart problems caused by obesity.” The research was presented at the American Physiological Society‟s annual meeting, Experimental Biology 2017, in Chicago, the US.8. What b enefit will the ''exercise pill” bring to people?A. Consumers will look much younger than before.B. Users can keep in good shape without going to the gym.C. Patients don‟t have to be treated in hospital at all.D. It offers more opportunities to take exercise outdoors.9. The underlined word “mimics” in Paragraph 2 means ________.A. lacksB. reducesC. is similar toD. is limited to10. The cycle mentioned in the third paragraph should be ________.①It‟s harder to exercise.②Obesity appears.③People tend to be fatter and fatter.④More myostatin is produced.A. ②④①③B. ①④③②C. ④③②①D. ③②①④11. How did researchers reach the conclusion?A. By analyzing causes.B. By referring to documents.C. By turning to scientists.D. By making comparisons.DSometimes “you” doesn‟t mean “you”, a new study finds.People often say “you” to make it easier to talk about a negative personal experience. For example, people may say “You win some, you lose some.” when they have just failed at a task. By using “you” instead of “I”, they explain that failure can happen to anyone. The “you” here used to refer to people in general rather than a specific (特定的) audience is called “generic-you”. Researchers conducted a series of experiments, asking 2,500 people to write about personal experiences and answer questions. In one experiment, a group of participants were asked to write about a negative (消极的) personal experience and another group of participants were asked to write about a neutral (中立的) personal experience. Researchers noted that people in the negative group used the ……generic-you” more in their responses.When they use “you”to describe the event, it allows them to move beyond the negative experience and helps them feel better.In another experiment, all participants were asked to write about a negative experience. One group focused on lessons they had learned, while another group wrote about the emotions they felt. Researchers found that peop le who focused on lessons used “you” more than those who focused on emotions. Besides, the people who used “you” said they felt further away from the event than those who used “I”. This suggests that “generic-you” is a way for people to give meaning t o an experience.Researchers concluded that the “generic-you” provides a way to normalize one‟s negative experiences and find meaning from personal experiences.12. When people say “You win some, you lose some.”, failure actually happened to __________.A. the listenerB. the speakerC. anyoneD. nobody13. Which of the following is an example of “generic-you”?A. Do you believe it?B. When will you be ready to go?C. You don‟t know how long I‟ve waited for you.D. Treat others as you hope they will treat you.14. In the first experiment, the “generic-you” _________.A. is only used in a neutral situationB. is only used in a negative situationC. helps leave good impressions on othersD. helps overcome a negative situation15. What do we know about the second experiment?A. “Lessons” group used “you” less than “emotions” group.B. “Emotions” group was less affected by negative experiences.C. People tend to use “you” to explain lessons they've learned.D. People never use “you” to express personal feelin gs.第二节(共5小题;每小题2分,满分10分)根据短文内容,从短文后的选项中选出能填入空白处的最佳项。

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