1、數(shù)學(xué)試題第1頁(yè)(共4頁(yè))2021年普通高等學(xué)校招生全國(guó)統(tǒng)一考試模擬演練數(shù)學(xué)注意事項(xiàng)：答卷前，考生務(wù)必將自己的姓名、考生號(hào)、考場(chǎng)號(hào)、座位號(hào)填寫(xiě)在答題卡上?；卮疬x擇題時(shí)，選出每小題答案后，用鉛筆把答題卡上對(duì)應(yīng)題S的答案標(biāo)號(hào)涂 黑。如需改動(dòng)，用橡皮擦干凈后，再選涂其他答案標(biāo)號(hào)?；卮鸱沁x擇題時(shí)，將答案寫(xiě)在 答題卡上。寫(xiě)在本試卷上無(wú)效?？荚嚱Y(jié)束后，將本試卷和答題卡一并交回。一、選擇題：本題共8小題，每小題5分，共40分。在每小題給出的四個(gè)選項(xiàng)中，只 有一項(xiàng)是符合題目要求的。己知A/, 2V均為R的子集，且CRA/cAT,則MU(CrV) =0B. MC. ND. R在3張卡片上分別寫(xiě)上3位同學(xué)的學(xué)號(hào)后，

2、再把卡片隨機(jī)分給這3位同學(xué)，每人1張， 則恰有1位學(xué)生分到寫(xiě)有自己學(xué)號(hào)卡片的概率為3.關(guān)于x的方程x2axb = 0,有下列四個(gè)命題:甲：x = l是該方程的根；乙：x = 3是該方程的根；丙：該方程兩根之和為2;T：該方程兩根異號(hào).如果只有-個(gè)假命題，則該命題足A.甲B.乙C.丙D. T4.橢圓-+ 2 = 1(/w0)的焦點(diǎn)為巧，f2.上頂點(diǎn)為若則妍=m +1 mA. 1B.C. /3D. 25.已知單位向鐓1，辦滿(mǎn)足tf .A = 0，若向量c = j7a + !2b t則sin(a,c) =A.B.C.D.33996. (l + x)2+(l + x)十. + (l + x)9的展開(kāi)式

3、中x2的系數(shù)是A. 60B. 80C. 84D. 120己知拋物線(xiàn)上三點(diǎn)j(2,2), B, C，直線(xiàn)AB, /1C是圓(x-2)2+y = 1的 兩條切線(xiàn)，則直線(xiàn)BC的方程為x十2y + l = 0B. 3x + 6y + 4 = 0C. 2x + 6少+ 3 = 0D. x + 3y + 2 = 0己知a5且ae5 =5e, 64且be4 =4efe, c3 且ee3=3ec,則c b aB. b c aC. a c bD. a b c二、選擇題：本題共4小題，每小題5分，共20分。在每小題給出的選項(xiàng)中，有多項(xiàng)符合題目要求。全部選對(duì)的得5分，部分選對(duì)的得2分，有選錯(cuò)的得0分。己知函數(shù)/(x

4、) = xln(l + x),則/W在(0，w)單調(diào)遞增/(x)有兩個(gè)零點(diǎn)曲線(xiàn)y = /(x)在點(diǎn)(-丄，/(-丄)處切線(xiàn)的斜率為-l-ln22 2/(x)是偶函數(shù)設(shè)z2,之3為復(fù)數(shù)，Z 70 .下列命題中正確的是A.若|z21 = |z31 則 z2 =z3C.若z2=z3,貝izxz2=ztz3右圖是一個(gè)正方體的平面展幵圖AE/CDCH/BEDG1BHBG1DE設(shè)函數(shù),則2 + sinxcosxA. /(x) = /(x + 7t)B. /(x)的最大值為4D. /(x)在(0，1)單調(diào)遞減 4C. /(x)在(-,0)單調(diào)遞增4三、填空題：本題共4小題，每小題5分，共20分。圓臺(tái)上、下底

5、面的圓周都在一個(gè)直徑為10的球面上，其上、下底面半徑分別為4和 5,則該圓臺(tái)的體積為 .若正方形一條對(duì)角線(xiàn)所在直線(xiàn)的斜率為2,則該正方形的兩條鄰邊所在直線(xiàn)的斜率 分別為 , .寫(xiě)出一個(gè)最小正周期為2的奇函數(shù)/(x)= .對(duì)一個(gè)物理M做次測(cè)量，并以測(cè)最結(jié)果的平均值作為該物理量的最后結(jié)果.已知 最后結(jié)果的誤差sn-N(0,-)t為使誤差么在(-0.5,0.5)的概率不小于0.9545,至少n要測(cè)量 次(若則P(|/-p|0,60）的左頂點(diǎn)為右焦點(diǎn)為動(dòng)點(diǎn)5在C上.當(dāng)5F 丄腳時(shí)，AF=BF.（1）求C的離心率；（2）若B在第一象限，證明：BFA = 2ZBAF.(12 分)己知函數(shù) /(x) = e

6、x - sin x - cosx, g(x) = ex +sinx + cosx 證明：當(dāng)x-/(X)彡0:4若g(x)2 +ax ,求a.2021年普通高等學(xué)校招生全國(guó)統(tǒng)一考試模擬演練數(shù)學(xué)注意事項(xiàng)：答卷前，考生務(wù)必將自己的姓名、考生號(hào)、考場(chǎng)號(hào)、座位號(hào)填寫(xiě)在答題卡上?；卮疬x擇題時(shí)，選出每小題答案后，用鉛筆把答題卡上對(duì)應(yīng)題S的答案標(biāo)號(hào)涂 黑。如需改動(dòng)，用橡皮擦干凈后，再選涂其他答案標(biāo)號(hào)?；卮鸱沁x擇題時(shí)，將答案寫(xiě)在 答題卡上。寫(xiě)在本試卷上無(wú)效?？荚嚱Y(jié)束后，將本試卷和答題卡一并交回。一、選擇題：本題共8小題，每小題5分，共40分。在每小題給出的四個(gè)選項(xiàng)中，只 有一項(xiàng)是符合題目要求的。己知A/, 2V

7、均為R的子集，且CRA/cAT,則MU(CrV) =A. 0B. MC. ND. R在3張卡片上分別寫(xiě)上3位同學(xué)的學(xué)號(hào)后，再把卡片隨機(jī)分給這3位同學(xué)，每人1張， 則恰有1位學(xué)生分到寫(xiě)有自己學(xué)號(hào)卡片的概率為3.關(guān)于x的方程x2axb = 0,有下列四個(gè)命題:甲：x = l是該方程的根；乙：x = 3是該方程的根；丙：該方程兩根之和為2;T：該方程兩根異號(hào).如果只有-個(gè)假命題，則該命題足A.甲B.乙C.丙D. T4.橢圓-+ 2 = 1(/w0)的焦點(diǎn)為巧，f2.上頂點(diǎn)為若則妍=m +1 mA. 1B.C. /3D. 25.已知單位向鐓1，辦滿(mǎn)足tf .A = 0，若向量c = j7a + !2b

8、 t則sin(a,c) =A.B.C.D.33996. (l + x)2+(l + x)十. + (l + x)9的展開(kāi)式中x2的系數(shù)是A. 60B. 80C. 84D. 120己知拋物線(xiàn)上三點(diǎn)j(2,2), B, C，直線(xiàn)AB, /1C是圓(x-2)2+y = 1的 兩條切線(xiàn)，則直線(xiàn)BC的方程為A. x十2y + l = 0B. 3x + 6y + 4 = 0C. 2x + 6少+ 3 = 0D. x + 3y + 2 = 0己知a5且ae5 =5e, 64且be4 =4efe, c3 且ee3=3ec,則A. c b aB. b c aC. a c bD. a b c二、選擇題：本題共4小

9、題，每小題5分，共20分。在每小題給出的選項(xiàng)中，有多項(xiàng)符合題目要求。全部選對(duì)的得5分，部分選對(duì)的得2分，有選錯(cuò)的得0分。己知函數(shù)/(x) = xln(l + x),則/W在(0，w)單調(diào)遞增/(x)有兩個(gè)零點(diǎn)曲線(xiàn)y = /(x)在點(diǎn)(-丄，/(-丄)處切線(xiàn)的斜率為-l-ln22 2/(x)是偶函數(shù)設(shè)z2,之3為復(fù)數(shù)，Z 70 .下列命題中正確的是A.若|z21 = |z31 則 z2 =z3C.若z2=z3,貝izxz2=ztz3右圖是一個(gè)正方體的平面展幵圖AE/CDCH/BEDG1BHBG1DE設(shè)函數(shù),則2 + sinxcosxA. /(x) = /(x + 7t)B. /(x)的最大值為4

10、D. /(x)在(0，1)單調(diào)遞減 4C. /(x)在(-,0)單調(diào)遞增4三、填空題：本題共4小題，每小題5分，共20分。圓臺(tái)上、下底面的圓周都在一個(gè)直徑為10的球面上，其上、下底面半徑分別為4和 5,則該圓臺(tái)的體積為 .若正方形一條對(duì)角線(xiàn)所在直線(xiàn)的斜率為2,則該正方形的兩條鄰邊所在直線(xiàn)的斜率 分別為 , .寫(xiě)出一個(gè)最小正周期為2的奇函數(shù)/(x)= .對(duì)一個(gè)物理M做次測(cè)量，并以測(cè)最結(jié)果的平均值作為該物理量的最后結(jié)果.已知 最后結(jié)果的誤差sn-N(0,-)t為使誤差么在(-0.5,0.5)的概率不小于0.9545,至少n要測(cè)量 次(若則P(|/-p|0,60）的左頂點(diǎn)為右焦點(diǎn)為動(dòng)點(diǎn)5在C上.當(dāng)5

11、F 丄腳時(shí)，AF=BF.（1）求C的離心率；（2）若B在第一象限，證明：BFA = 2ZBAF.(12 分)己知函數(shù) /(x) = ex - sin x - cosx, g(x) = ex +sinx + cosx 證明：當(dāng)x-/(X)彡0:4若g(x)2 +ax ,求a.2021八省適應(yīng)性考試（數(shù)學(xué)）答案一、選擇題BCACDDBD二、多選題AC BC BD AD三、堝空題Glpi去.-3sin7：z16.32四、解符題17.(1 )2 += 3(a + an=2-3*，則-3a,=-(an-3an_1) = (a2-3a.).(-1 廣1 = 0，a = 30= +.3n18.BC = aw

12、ZBZX? = /3- I19.(1)P= 1-0.9x0.8 = 0.18X0123p0.5(M0.398(1.092O.(MK)E(X) = ().620.2jc*4-&c = 2c設(shè)多面體有a個(gè)頂點(diǎn)，6條梭，c個(gè)面，各個(gè)面分別是么.fe,么邊型， 明I 面用和為 K(ki 2) + ir(kj 2) + (62),又 + A+.“+fc/ = 2bt則總曲率為 2na n(ki +kb 2c) = 2na jt(26 2c) = 2n(a-b-c) =4r21.(1)|BF| = |AF|.= a + c.則e =三=2.aa2j/”(Jo + a) (z+a)2- UnZBFX =題沒(méi)

13、等價(jià)于證明tanZBFA = tan2ZBXF.即 j=叫+aci 1-( 一 v x 注總判/() = U.,hj x (子 -y時(shí)/(工)=r s2in(x + y) 0;23 x (), + oo)吋 J(x) = c binx cosx e z 1 Xk ，ll xE (吋 fM = 一 cosx + sinx,/*() = 0,2021年普通高等學(xué)校招生全國(guó)統(tǒng)一考試模擬演練注意事項(xiàng)：答卷前，考生務(wù)必將自己的姓名、考生號(hào)、考場(chǎng)號(hào)、座位號(hào)填寫(xiě)在答題卡上?；卮疬x擇題時(shí)，選出每小題答案后，用鉛筆把答題卡上對(duì)應(yīng)題B的答案標(biāo)號(hào)涂 黑。如需改動(dòng)，用橡皮擦干凈后，再選涂其他答案標(biāo)號(hào)?；卮鸱沁x擇題時(shí)，

14、將答案寫(xiě)在 答題卡上，寫(xiě)在本試卷上無(wú)效?？荚嚱Y(jié)束后，將本試卷和答題卡一并交回。第一部分聽(tīng)力（共兩節(jié)，滿(mǎn)分30分）做題時(shí)，先將答案標(biāo)在試卷上。錄音內(nèi)容結(jié)束后，你將冇兩分鐘的時(shí)間將試卷上的 答案轉(zhuǎn)涂到答題卡上。第一節(jié)（共5小題：每小題1.5分，滿(mǎn)分7.5分）nip胡妒聽(tīng)下面5段對(duì)話(huà)。每段對(duì)話(huà)后有一個(gè)小題，從題中所給的A、B、C三個(gè)選項(xiàng)中選 出最佳選項(xiàng)。聽(tīng)完每段對(duì)話(huà)后，你都有10秒鐘的時(shí)間來(lái)回答有關(guān)小題和閱讀下一小題。 每段對(duì)話(huà)僅讀一遍。例:How much is the shirt?A. 19.15.B.9.18.C. 9.15.答案是C。Why does the woman refuse to

15、go to the gym?C. She has to work.C. A new restaurant.C. Potatoes.C. Buying a cupboard.A. She is sick.B. She needs a rest.What are the speakers talking about?A. A kind of food.B. A close relative.What will the woman probably eat?A. Beef.B. Grapes.What is the womans suggestion?A. Repairing the sofa.B.

16、 Cleaning the kitchen.英語(yǔ)試題第丨頁(yè)（共12頁(yè)）What does the man think of the movie?A. Top quality.B. Above average.C. Surprisingly bad.第二節(jié)（共15小題：每小題1.5分，滿(mǎn)分22.5分）聽(tīng)下面5段對(duì)話(huà)或獨(dú)白。每段對(duì)話(huà)或獨(dú)白后有幾個(gè)小題，從題中所給的A、B、C 三個(gè)選項(xiàng)中選出最佳選項(xiàng).聽(tīng)每段對(duì)話(huà)或獨(dú)白前，你將有時(shí)間閱讀各個(gè)小題，每小題5 秒鐘：聽(tīng)完后，各小題將給出5秒鐘的作答時(shí)間。每段對(duì)話(huà)或獨(dú)白讀兩遍。聽(tīng)第6段材料，回答第6、7題。Where are the speakers?A.

17、In a restaurant.B. In a bookstore.What does the man have to do now?A. Sign his name.B. Wait his tum.聽(tīng)第7段材料，回答第8至10題。When does the man plan to check in?A. Three days later.B. Four days later.What kind of room does the man take?One with one bed and a kitchen.One with two beds and a kitchen.One with tw

18、o beds and no kitchen.10. How much will the man pay?A. $400.B. $800.C. In a supermarket.C. Call his friend.C. Seven days later.C.S1200.聽(tīng)第8段材料，回答第n至13題。What did Susan do right before the conversation?A. She visited her brother. B. She called John Reeves. C. She toured the company.What does Susan thin

19、k of the place?A. Ifs big.B. Its famous.C. Its crowded.Who is Michael?A. Johns boss.B. Tara*s husband.C. Susans brother.聽(tīng)第9段材料，回答第14至16題。What did the woman do last night?A. She went to school.B. She listened to a talk.C. She decorated her home.What does the woman suggest the man do with his big tabl

20、e?A. Replace it.B. Have it painted.C. Make good use of it.英語(yǔ)試題第2頁(yè)（共12頁(yè)）英語(yǔ)試題第 頁(yè)（共12頁(yè)）What is a benefit of decorating a house by oneself?Saving money.B. Suiting personal taste. C. Strengthening family ties.聽(tīng)第10段材料，回答第17至20題。What is special about a live concert?The whole experience is unique.The sound

21、quality is outstanding.The performance can be recorded.What does the speaker say about concerts by university performing groups?They are expensive.They are often of high quality.They are covered by the local media.What does the speaker suggest doing before the concert?Listening to the works to be pe

22、rformed.Checking information at the box office.Reading something about the concert hall.What is the speaker?A news reporter.B. A theater designer.C. A college teacher.第二部分 閱讀（共兩節(jié)，滿(mǎn)分50分）第一節(jié)（共15小題；每小題2.5分，滿(mǎn)分37.5分）閱讀下列短文，從每題所給的A、B、C、D四個(gè)選項(xiàng)中選出最佳選項(xiàng)。 A Non-Credit CoursesThe Pre-College Program offers non-c

23、redit courses. Students will experience college-level courses given by some of our colleges leading experts and will receive written feedback （反 饋）on their work at the end of the course. Pre-College students will also receive a grade of Satisfactory/Unsatisfactory and a certificate of completion at

24、the conclusion of the program.All non-credit courses meet from 9:00 a.m. 一 11:30 a.m. daily and may have additional requirements in the afternoons or evenings.COURSE: Case Studies in NeuroscienceJune 11 - July 2Leah RoeschUsing student-centered, active-learning methods and real-world examples, this

25、course is designed to provide a fuller understanding of how the human brain works.COURSE: Psychology of CreativityJune 15 - June 28Marshall DukeWhy arc certain people so creative? Is it genetic （遺傳的），or a result of childhood experience? Are they different from everyone else? This popular psychology

26、course highlights the different theories of creativity.COURSE: Creative StorytellingJune 21 - July 3Edith FreniThis college-level course in creative storytelling functions as an introduction to a variety of storytelling techniques that appear in different forms of creative writing, such as short fic

27、tion and playwriting.COURSE: Sports EconomicsJuly 19 - August 1Christina DePasqualeIn this course we will analyze many interesting aspects of the sports industry: sports leagues, ticket pricing, salary negotiations, discrimination, and NCAA policies to name a few.Who is the text intended for?The gen

28、eral public.B. College freshmen.C. Educational experts.D. High school students.Which course can you take if you are free only in June?Sports Economics.B. Creative Storytelling.C. Psychology of Creativity.D. Case Studies in Neuroscience.Whose course should you choose if you are interested in creative

29、 writing?Leah Roeschs.B. Edith Freni*s.C. Marshall Dukes.D. Christina DePasquales.In my everyday life, I am on an ongoing journey to figure out different ways to reduce my carbon footprint on the planet. A carbon footprint is the measure of influence our activities have on the environment, in partic

30、ular climate change. It is calculated by the amount of greenhouse gas we produce in our daily lives. Fortunately, nowadays it is much easier to make eco-friendly lifestyle choices than, lets say，20 years ago. But one question has been on my mind a lot lately: is it better to buy new eco-friendly pro

31、ducts or used traditionally produced goods?After doing some research, I have decided that some things are better new and others are better used. Let me try to explain.A carbon footprint is made up of two parts, the primary footprint and the secondary footprint. The primary footprint is a measure of

32、our direct emissions （j非放）of carbon dioxide （CO2） from the burning of fuels, including household energy consumption and transportation. The secondary footprint is a measure of the indirect CO2 emissions from the whole lifecycle of products we use - those related to their production and breakdown.Bas

33、ed on this understanding, we have a good deal of control and responsibility over our carbon footprint. Things like dishes, clothes and furniture fall into the secondary footprinf group, so less is more and we can focus on finding used goods to avoid the added production. However, for the car and the

34、 other appliances （設(shè)備）that we need we can go with new, energy-saving models. I heard somewhere that electronics and appliances give off 90% of their carbon footprint after they leave the factory. So it seems most reasonable to go for the energy-saving models. The main concern here is the amount of e

35、nergy that goes into the making of new products and whether or not that extra carbon is worth the footprint the product will make once it gets to you.What is the text mainly about?What appliances to buy to save energy.What a carbon footprint means in our life.How to identify different carbon footpri

36、nts.How to make eco-friendly lifestyle choices.What do we know about the secondary carbon footprint?It is related to our consumption of fuels.It is made when we are buying the products.It is less harmful than the primary carbon footprint.It is counted as ours though not directly made by us.Which of

37、the following helps reduce our carbon footprint according to the author?Using second-hand textbooks.Using old and expensive cars.Buying new but cheap clothes.Buying new wooden furniture.“The footprint” underlined in the last sentence refers to the CO2 produced in using the productB. recycling the pr

38、oductC. making the productD. transporting the productMagic is a form of entertainment that is based on pretending to do things that are impossible. The magician is a specially trained actor. He tries to make the audience believe that he has the power to do things which are against the laws of nature

39、.Magic shows are entertaining as long as the audience does not discover how the tricks are done. The magician usually depends on his skill with his hands, on his knowledge of psychology, and, sometimes, on mechanical devices （機(jī)械裝置）.Since magic performance is meant to trick people, the use of psychol

40、ogy is important. The magician must keep people from noticing all the movements of his hands and from thinking about the secret parts of his equipment. He must also lead the audience to draw false conclusions. The magicians success depends on the fact that many things seen by the eye are not the thi

41、ngs that matter.Two basic magic tricks are making objects seem to appear and making objects seem to disappear. A combination of these two tricks makes for some interesting effects. For example, the magician puts a small ball under one of several cups. The ball then seems to jump from one cup to anot

42、her or to change colour. What actually happens is that the magician, employing quick hand movements or a mechanical device, hides one ball. While doing this he talks to the audience and waves a brightly coloured cloth with one hand. The audience is too busy watching the cloth and listening to the ma

43、gicians words to notice that his other hand is hiding the ball.Another favourite trick is to cut or bum something, and then make it appear whole again. What actually happens is that the magician makes the cut or burned object disappear by quickly hiding it while the audience watches something else.

44、Then he “magically” makes it appear whole again by displaying （展示）another object that has not been cut or burned.What is the authors main purpose in wr: A. To promote a magic show.C. To explain the art of magic.Which of the following is important for A. Moving stage equipment.C. Applying high techno

45、logy.What does the author focus on in the A. Providing examples.C. Drawing comparisons.What can we infer from the text?ing the text?To teach people to be magicians.To praise the talents of magicians, successful magic trick?Directing the audiences attention.Keeping the performance in secret, two para

46、graphs?Making a summary.Explaining a concept.A. Mechanical devices are expensive.It takes practice to perform magic.Most magicians employ assistants.D. Small objects are magicians favourite.The average bear, it seems，is getting ever smarter. First，it turned out that at least one can use a comb. Now

47、it appears that some can count, too.Jennifer Vonk，of Oakland University, in Michigan, and Michael Beran, from Georgia State University, set three American black bears the task of distinguishing between numerically larger and smaller groups of dots （點(diǎn)）on a computer screen. In return for a food reward

48、 one bear, Brutus, would touch the more heavily dotted pattern with his nose. The others, Bella and Dusty, would touch the screen with their claws （爪子）.As the researchers report in Animal Behavior，the bears did best with patterns where the coloured dots did not move and where more of them also took

49、up a larger coloured area. This could be explained by the bears distinguishing the different areas of colour rather than truly counting the dots. However, the three bears managed to pick out the bigger number of dots even in pairs of patterns where fewer dots took up a larger area.Moving patterns, w

50、here each dot followed its own path around the screen, were more of a challenge. But Brutus，at least, was not defeated. He seemed to be counting mobile dots even when the scientists tried to mislead him by moving the total coloured area of the dots at the same time.It is not entirely surprising that

51、 bears should have a high degree of intelligence. They face a lot of challenges when trying to get food. They are, however, always alone, and so do not have the complex social systems that contribute to animal smarts. Perhaps, then, their maths skill developed because they cannot count on their frie

52、nds for help.What task did the scientists set for the three bears?Distinguishing different dot patterns.Figuring out different colours of dots.Putting the dots into differently coloured groups.Picking out the group with a larger number of dots.For the bears, the task was easier when .A. the coloured

53、 dots were moving slowlyB. the dot patterns were regular in shapethe dots followed a path on the screenD. more dots covered a larger coloured areaWhat may explain the bears* high degree of intelligence?A. They leam skills from other animals.They feed on a diverse range of food.What can be a suitable

54、 title for the text? A. Bears Taught to Distinguish ColoursThree Bears Learned How to CountThey face life challenges on their own. D. They have complex social networks.B. New Evidence of Bear Intelligence FoundThe Smartest American Black Bear Brutus第二節(jié)(共5小題：每小題2.5分，滿(mǎn)分12.5分)閱讀下面短文，從短文后的選項(xiàng)中選出可以填入空白處的最

55、佳選項(xiàng)。選項(xiàng)中有兩項(xiàng) 為多余選項(xiàng)。Apps (short for applications) are becoming increasingly popular nowadays, and for good reason. They can help you out in just about every area of your life, whether ifs keeping fit, communicating with friends, or even learning a language. 36 Heres what you should think about before d

56、ownloading an app for language learning.Learn from diverse sources (not just apps)Any seasoned language learner will tell you that the beauty of mastering a foreign language is the world which it opens up to you. This is a world of diverse sources (來(lái)源)of information, from newspapers and books to TV,

57、 radio, music and even real people. Would you limit yourself to one medium in your native language? 37Establish your purpose and plan your habitsDo you want to be fluent in weeks or are you in it for the brain training? The good apps are designed to help you fit your studies around your timetable. 3

58、8 These apps encourage habit building, because the successful formation of a habit ensures your safe and regular return.Make it social39 I mean social for real. I owe the speed of progress I made in Italian to the support from Jim, my partner in study time. Find a friend to accompany you. Take an ev

59、ening class. Borrow a book. Buy a book. Book a week away and attend a language school. Just dont forget your phone!If I may speak sincerely, the combination of app, language school, Jim, evenings out, and a choice book or two proved extremely effective. 40I recommend it.Remember that an app is just

60、a tool.No, I dont mean posting your progress online.I encourage you to use apps as often as you can.Probably not, so why do so in your new language?The best apps adapt themselves based upon your behavior.However, you need to know how to use them properly to really benefit.第三部分 語(yǔ)言運(yùn)用（共兩節(jié)，滿(mǎn)分30分）第-節(jié)（共15