高考新题型)链接训练 新人教版必修113
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高考语文根据语境填成语一姓名总分1李教授从来就(),临终前还叮嘱家人,将自己最后的一笔稿费赠给福利院的孩子们。
2一边是污染成因,一边是地球卫士,对待臭氧,要正确认识、区别看待,不能简单()。
3古人说:"沉舟可补,()",这话很有道理。
4()的人,总是能用爱心为他人带去快乐,让烦恼远离。
5野生菌只是当地积极修复生态的“副产品”,但通过小小的野生菌,大自然给予人们的回馈()。
6着力培养客观理性审视世界的技能与素养,需要当代大学生学会观察,尽可能全面准确地掌握热点事件的有关信息,避免()、以点带面。
7要胸怀群众感情,()为群众考虑,提高调查核实效率,能办的事情马上办,不能办的做好沟通解释工作。
8仁爱意味着(),底线要求是尊重他人权利,更高要求是扶危救困、见义勇为。
9个体境遇是时代注脚,切口虽小,但(),能够一窥社会发展现实图景。
10即便综合应用谈话、比对台账资料等多种措施,找出了问题,也因(),难以挽回后果。
11正因为样本检测对病例确诊有()的作用,所以检测质量极为重要,对取样手法、运送过程、保存要素都有非常严格的条件限制,只有按最严格的标准进行操作,才能保证得出的检测结果最精准。
12要看到,骗子虽打着不同的幌子,但万变不离其宗,就是巧立名目、()地钻空子,能骗一个是一个。
13日复一日间,刘师傅的雕刻技艺达到了()的地步。
14经历了又一次依法调查、听证等一系列程序后,案件()。
15这项工作对他来说简直就是(。
16经过长时间的练习,她终于可以()地进行脱稿演讲。
17要改变()的毛病,最好的办法就是多学习,多实践。
18他对本职工作(),受到上级领导的一致好评。
19谈到这里,他的险恶用心()。
20仔细读完,方知每一个专题之间(),不仅逻辑严密,而且自成体系。
21本公司具强大品牌设计团队,不断()颠覆时尚引领服装品牌潮流。
22老猴见多识广,对相机闪光灯早已(),反而更津津有味地吃着。
23现实生活中叶公好龙式的人()。
必修第一册高考题型综合训练一、阅读理解(一)If you are looking for apps to learn English for studying abroad, you might be confused. There are so many apps to choose from. How can you decide which English language learning app is right for you Our list of top four favourite apps to improve your English will help.Hello English — Best app for middle learnersIf you already understand the basics but want to improve your English, this app is for you. Hello English starts with a language test, and then serves up English lessons based on your test results. Hello English supports learners with 23 native languages and lets you play games, watch videos and listen to audio books, too.Fluent U — Best media-based appThis app sources English-language videos from the real world —including news, music videos and commercials — to help you learn English. Interactive captions (字幕) allow you to tap any word and see more information about it.Rosetta Stone — Most multi-use appThis award-winning English language learning app teaches vocabulary and English grammar. Rosetta Stone includes lessonson pronunciation so you can improve your English accent. You can also download audio lessons to learn offline.Duolingo — Most fun appThis personalised English-learning app turns studying into a game. Earn virtual coins to unlock new levels and spend them on fun upgrades. An animated owl (动画猫头鹰) keeps you company and encourages you as you learn. When you have questions, get help from fellow students inside the app using the Duolingo message boards.1.What can we learn about Hello EnglishA.The users can chat with 23 native speakers.B.It may not suit English beginners.C.It provides lessons without a language test.D.The users can’t play games.2.What is special about DuolingoA.It only has the paid version.B.The users must pay in cash to upgrade.C.An owl can answer questions of the users.D.It combines English learning with entertainment.3.Which app best suits those who want to improve pronunciation A.Hello English. B.Fluent U. C.Rosetta Stone. D.Duolingo. 【答案】1.B 2.D 3.C【导语】这是一篇应用文,文章介绍了四种最受欢迎的提高英语的应用程序。
SectionⅢUsing Language,Assessing Your Progress&Video Time课后·训练提升一、单词拼写.Peter got a large s of money from his uncle..Mrs White is a quiet and g lady who likes reading in spare time.one of my old friends on the way to school this morning..Sue decided to apply for a p on her new invention of a practical item.(political).’s theory of (relative) is now generally accepted.a position at The New York Times.the circumstances we may say that man can conquer nature.the high standard of entries for the competition.1.我的老师看起来好像完全知道这件事了。
My teacher looked the thing2.据报道,这种产品已投入使用。
that the product has been put into use.3.我进去时发现一个陌生的女孩坐在角落里。
in the corner.4.这次会议总结了你们的经验。
your experience.5.音乐占广播节目的30%。
thirty percent of the broadcasting programmes.The journey my daughter Cathy has had with her swimming is as long as it is beautiful.Cathy suffered some terrible 1in her early childhood.After years of regular treatment,she finally became healthy.Two years ago,while Cathy was watching television,a dream came into her sweet little head—to be a st summer,she wanted to 2our local swim team.She practised hard and finally 3it.The team practice,however,was a rough start.She coughed and choked and could hardly 4her first few weeks.Hearing her coughing bitterly one night,I decided to pull her from it all.But Cathy woke me up early next morning,wearing her swimsuit 5to go!I told her she shouldn’t swim after a whole night’s coughing,but she refused to 6and insisted she go.From that day on,Cathy kept swimming and didn’t 7 a single practice.She had a 8 intention within herself to be the best she could be.My ten-year-old daughter was growing and changing right before my eyes,into this 9human being with a passion and a mission.There were moments of 10of course:often she would be the last swimmer in the race.It was difficult for Cathy to accept that she wasn’t a 11—ever.But that didn’t stop her from trying.Then came the final awards ceremony at the end of the year.Cathy didn’t expect any award but was still there to 12her friends and praise their accomplishments.As the ceremony was nearing the end,I suddenly heard the head coach 13,“The highest honour goes to Cathy!”Looking around,he continued,“Cathy has inspired us with her will and enthusiasm.14skills and talents bring great success,the most valuable asset(财富) one can hold is the heart.”It was the greatest 15of my daughter’s life.With all she had been through in her ten years,this was the hour of true triumph(成功).1.A.failure B.pressureD.illness“After years of regular treatment, she finally became healthy.”可知,Cathy在童年的时候患有某种严重的疾病。
模块综合训练(时间:120分钟满分:150分)一、选择题:本题共8小题,每小题5分,共40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.直线√3x-y-2 021=0的倾斜角等于()A.π6B.π3C.πD.不存在√3x-y-2021=0化为y=√3x-2021,则直线的斜率为√3,所以直线的倾斜角等于π3.故选B.2.(2020天津,7)设双曲线C的方程为x2a2−y2b2=1(a>0,b>0),过抛物线y2=4x的焦点和点(0,b)的直线为l.若C的一条渐近线与l平行,另一条渐近线与l垂直,则双曲线C的方程为()A.x24−y24=1B.x2-y24=1C.x24-y2=1 D.x2-y2=1双曲线x 2a2−y2b2=1的渐近线方程为y=±bax,y2=4x的焦点坐标为(1,0),l为yb+x1=1,即y=-bx+b,∴-b=-ba 且-b·ba=-1,∴a=1,b=1.故选D.3.若圆x2+y2-ax-2y+1=0关于直线x-y-1=0对称的圆的方程是x2+y2-4x+3=0,则a的值等于()A.0B.2C.1D.±2x2+y2-ax-2y+1=0的标准方程为(x-a2)2+(y-1)2=a24,圆心坐标为(a2,1),圆x2+y2-4x+3=0的标准方程为(x-2)2+y2=1,圆心坐标为(2,0),半径为1,连心线所在直线的斜率为1a2-2=2a-4,中点坐标为(a+44,1 2 ),由题意可得{a 24=1,2a -4·1=-1,a+44-12-1=0,解得a=2.4.如图,在棱长均相等的四面体O-ABC 中,点D 为AB 的中点,CE=12ED ,设OA⃗⃗⃗⃗⃗ =a ,OB ⃗⃗⃗⃗⃗ =b ,OC ⃗⃗⃗⃗⃗ =c ,则OE ⃗⃗⃗⃗⃗ =( )A.16a +16b +13c B.13a +13b +13c C.16a +16b -13cD.1a +16b +23cCE=12ED ,∴CE ⃗⃗⃗⃗⃗ =13CD ⃗⃗⃗⃗⃗ =13(CA ⃗⃗⃗⃗⃗ +AD ⃗⃗⃗⃗⃗ )=13(CA ⃗⃗⃗⃗⃗ +12AB ⃗⃗⃗⃗⃗ )=13CA ⃗⃗⃗⃗⃗ +16AB ⃗⃗⃗⃗⃗ , ∴OE⃗⃗⃗⃗⃗ =OC ⃗⃗⃗⃗⃗ +CE ⃗⃗⃗⃗⃗ =OC ⃗⃗⃗⃗⃗ +13CA ⃗⃗⃗⃗⃗ +16AB ⃗⃗⃗⃗⃗ =OC⃗⃗⃗⃗⃗ +13(OA ⃗⃗⃗⃗⃗ -OC ⃗⃗⃗⃗⃗ )+16(OB ⃗⃗⃗⃗⃗ -OA ⃗⃗⃗⃗⃗ ) =16OA ⃗⃗⃗⃗⃗ +16OB⃗⃗⃗⃗⃗ +23OC ⃗⃗⃗⃗⃗ =16a +16b +23c . 5.若双曲线C :x 2a 2−y 2b 2=1(a>0,b>0)的一条渐近线被圆(x-2)2+y 2=4所截得的弦长为2,则C 的离心率为 ( )A.2B.√3C.√2D.2√33bx ±ay=0,圆心(2,0)到渐近线距离为d=√22-12=√3, 则点(2,0)到直线bx+ay=0的距离为 d=√a 2+b2=2b c=√3,即4(c 2-a 2)c 2=3,整理可得c 2=4a 2,双曲线的离心率e=√c 2a 2=√4=2.6.如图,在几何体ABC-A 1B 1C 1中,△ABC 为正三角形,AA 1∥BB 1∥CC 1,AA 1⊥平面ABC ,若E 是棱B 1C 1的中点,且AB=AA 1=CC 1=2BB 1,则异面直线A 1E 与AC 1所成角的余弦值为( ) A.√1313B.2√1313C.√2613D.2√2613C 为原点,在平面ABC 内过C 作BC 的垂线为x 轴,CB 为y 轴,CC 1为z 轴,建立空间直角坐标系,设AB=AA 1=CC 1=2BB 1=2,则A 1(√3,1,2),A (√3,1,0),C 1(0,0,2),B 1(0,2,1),E (0,1,32),A 1E ⃗⃗⃗⃗⃗⃗⃗ =(-√3,0,-12),AC 1⃗⃗⃗⃗⃗⃗⃗ =(-√3,-1,2),设异面直线A 1E 与AC 1所成角为θ,则cos θ=|A 1E ⃗⃗⃗⃗⃗⃗⃗⃗ ·AC1⃗⃗⃗⃗⃗⃗⃗⃗ ||A 1E ⃗⃗⃗⃗⃗⃗⃗⃗ ||AC1⃗⃗⃗⃗⃗⃗⃗⃗ |=√134·√8=√2613. ∴异面直线A 1E 与AC 1所成角的余弦值为√2613.7.已知抛物线C :y 2=8x ,圆F :(x-2)2+y 2=4(点F 为其圆心),直线l :y=k (x-2)(k ≠0)自上而下顺次与上述两曲线交于M 1,M 2,M 3,M 4四点,则下列各式结果为定值的是( ) A.|M 1M 3|·|M 2M 4|B.|FM 1|·|FM 4|C.|M 1M 2|·|M 3M 4|D.|FM 1|·|M 1M 2|,设M 1,M 2,M 3,M 4四点的横坐标分别为x 1,x 2,x 3,x 4,由题意知y 2=8x 的焦点坐标与圆F 的圆心(2,0)相同,准线l 0:x=-2. 由定义得|M 1F|=x 1+2. 又|M 1F|=|M 1M 2|+2,∴|M 1M 2|=x 1,同理,|M 3M 4|=x 4.将y=k (x-2)代入抛物线方程,得k 2x 2-(4k 2+8)x+4k 2=0, ∴x 1x 4=4,∴|M 1M 2|·|M 3M 4|=4.故选C .8.如图,已知F 1,F 2是椭圆T :x 2a2+y 2b 2=1(a>b>0)的左、右焦点,P 是椭圆T 上一点,且不与x 轴重合,过F 2作∠F 1PF 2的外角的平分线的垂线,垂足为Q ,则点Q 在 上运动.( )A.直线B.圆C.椭圆D.抛物线F 2Q 与F 1P 的延长线交于点M ,连接OQ (图略).因为PQ 是∠F 1PF 2的外角的平分线,且PQ ⊥F 2M ,所以在△PF 2M 中,|PF 2|=|PM|,且Q 为线段F 2M 的中点.又O 为线段F 1F 2的中点,由三角形的中位线定理,得|OQ|=12|F 1M|=12(|PF 1|+|PF 2|).由椭圆的定义,得|PF 1|+|PF 2|=2a ,所以|OQ|=a ,所以点Q 在以原点为圆心,a 为半径的圆上运动.二、选择题:本题共4小题,每小题5分,共20分.在每小题给出的选项中,有多项符合题目要求.全部选对的得5分,有选错的得0分,部分选对的得3分. 9.(2020山东,9)已知曲线C :mx 2+ny 2=1.( ) A.若m>n>0,则C 是椭圆,其焦点在y 轴上 B.若m=n>0,则C 是圆,其半径为√nC.若mn<0,则C 是双曲线,其渐近线方程为y=±√-mn xD.若m=0,n>0,则C 是两条直线mx 2+ny 2=1,∴x 21m+y 21n=1.∵m>n>0,∴1n >1m >0,∴C 是焦点在y 轴上的椭圆,A 正确; ∵m=n>0,∴x 2+y 2=1n ,即C 是圆, ∴r=√nn ,B 错误; 由mx 2+ny 2=1,得x21m+y 21n=1,∵mn<0,1m 与1n 异号,∴C 是双曲线,令mx 2+ny 2=0,可得y 2=-mn x 2,即y=±√-mn x ,C 正确;当m=0,n>0时,有ny 2=1,得y 2=1n ,即y=±√nn ,表示两条直线,D 正确,故选ACD .10.如图,在长方体ABCD-A 1B 1C 1D 1中,AA 1=AB=4,BC=2,M ,N 分别为棱C 1D 1,CC 1的中点,则下列说法正确的是( )A.A ,M ,N ,B 四点共面B.平面ADM ⊥平面CDD 1C 1C.直线BN 与B 1M 所成的角为60°D.BN ∥平面ADMA,由图显然AM 、BN 是异面直线,故A ,M ,N ,B 四点不共面,故A 错误;对于B,由题意AD ⊥平面CDD 1C 1,故平面ADM ⊥平面CDD 1C 1,故B 正确;对于C,取CD 的中点O ,连接BO ,ON ,可知B 1M ∥OB ,三角形BON 为等边三角形,故C 正确;对于D,BN ∥平面AA 1D 1D ,显然BN 与平面ADM 不平行,故D 错误.11.在正方体ABCD-A 1B 1C 1D 1中,给出下列四个结论,其中正确的结论是( ) A.(A 1A ⃗⃗⃗⃗⃗⃗⃗ +A 1D 1⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ +A 1B 1⃗⃗⃗⃗⃗⃗⃗⃗⃗ )2=3A 1B 1⃗⃗⃗⃗⃗⃗⃗⃗⃗ 2B.A 1C ⃗⃗⃗⃗⃗⃗⃗ ·(A 1B 1⃗⃗⃗⃗⃗⃗⃗⃗⃗ −A 1A ⃗⃗⃗⃗⃗⃗⃗ )=0 C.向量AD 1⃗⃗⃗⃗⃗⃗⃗ 与向量A 1B ⃗⃗⃗⃗⃗⃗⃗ 的夹角为60°D.正方体ABCD-A 1B 1C 1D 1的体积为|AB ⃗⃗⃗⃗⃗ ·AA 1⃗⃗⃗⃗⃗⃗⃗ ·AD ⃗⃗⃗⃗⃗ |中,设正方体的棱长为1,则(A 1A ⃗⃗⃗⃗⃗⃗⃗ +A 1D 1⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ +A 1B 1⃗⃗⃗⃗⃗⃗⃗⃗⃗ )2=A 1C ⃗⃗⃗⃗⃗⃗⃗ 2=3,3A 1B 1⃗⃗⃗⃗⃗⃗⃗⃗⃗ 2=3,故A 正确;B 中,A 1B 1⃗⃗⃗⃗⃗⃗⃗⃗⃗ −A 1A =AB 1⃗⃗⃗⃗⃗⃗⃗ ,由AB 1⃗⃗⃗⃗⃗⃗⃗ ⊥A 1C ⃗⃗⃗⃗⃗⃗⃗ ,故B 正确;C 中,A 1B 与AD 1两异面直线所成角为60°,但AD 1⃗⃗⃗⃗⃗⃗⃗ 与A 1B ⃗⃗⃗⃗⃗⃗⃗ 的夹角为120°,故C 不正确;D 中,|AB ⃗⃗⃗⃗⃗ ·AA 1⃗⃗⃗⃗⃗⃗⃗ ·AD ⃗⃗⃗⃗⃗ |=0,故D 也不正确.12.若曲线C 上存在点M ,使M 到平面内两点A (-5,0),B (5,0)距离之差的绝对值为8,则称曲线C 为“好曲线”.以下曲线是“好曲线”的是( ) A.x+y=5 B.x 2+y 2=9 C.x 225+y 29=1D.x 2=16y:点M 轨迹是以A ,B 为焦点的双曲线.则a=4,c=5,∴b 2=c 2-a 2=9,∴M 的轨迹方程为x 216−y 29=1.直线x+y=5过点(5,0),故直线与M 的轨迹有交点,是“好曲线”,A 正确;x 2+y 2=9是以(0,0)为圆心,3为半径的圆,与M 的轨迹没有交点,不是“好曲线”,B 错误;x 225+y 29=1的右顶点为(5,0),故椭圆与M 的轨迹有交点,是“好曲线”,C 正确;把x 2=16y 代入双曲线方程,可得y 2-9y+9=0,此时Δ>0,故抛物线与M 的轨迹有交点,是“好曲线”,D 正确.三、填空题:本题共4小题,每小题5分,共20分. 13.已知圆C :x 2+y 2-2x-1=0,以点12,1为中点的弦所在的直线l 的方程是 .(x-1)2+y 2=2,可知圆心为C (1,0).设A12,1,则以A 为中点的弦所在的直线l 即为经过点A 且垂直于AC 的直线.又知k AC =0-11-12=-2,所以k l =12,所以直线l 的方程为y-1=12x-12,即2x-4y+3=0.x-4y+3=014.在四棱锥P-ABCD 中,设向量AB ⃗⃗⃗⃗⃗ =(4,-2,3),AD ⃗⃗⃗⃗⃗ =(-4,1,0),AP ⃗⃗⃗⃗⃗ =(-6,2,-8),则顶点P 到底面ABCD 的距离为 .ABCD 的法向量n =(x ,y ,z ),则{AB⃗⃗⃗⃗⃗ ·n =4x -2y +3z =0,AD ⃗⃗⃗⃗⃗ ·n =-4x +y =0, 令x=3,则y=12,z=4,∴n =(3,12,4). ∴点P 到底面ABCD 的距离d=|AP ⃗⃗⃗⃗⃗ ·n ||n |=√9+144+16=2.15.(2019全国Ⅲ,理15)设F 1,F 2为椭圆C :x 236+y 220=1的两个焦点,M 为C 上一点且在第一象限.若△MF 1F 2为等腰三角形,则M 的坐标为 .a 2=36,b 2=20,∴c 2=a 2-b 2=16,∴c=4.由题意得,|MF 1|=|F 1F 2|=2c=8. ∵|MF 1|+|MF 2|=2a=12,∴|MF 2|=4. 设点M 的坐标为(x 0,y 0)(x 0>0,y 0>0), 则S △MF 1F 2=12×|F 1F 2|×y 0=4y 0. 又S △MF 1F 2=12×4×√82-22=4√15, ∴4y 0=4√15,解得y 0=√15. 又点M 在椭圆C 上,∴x 0236+(√15)220=1,解得x 0=3或x 0=-3(舍去). ∴点M 的坐标为(3,√15).√15)16.正方体ABCD-A 1B 1C 1D 1的棱长为2,M ,N ,E ,F 分别是A 1B 1,AD ,B 1C 1,C 1D 1的中点,则过EF 且与MN 平行的平面截正方体所得截面的面积为 ,CE 和该截面所成角的正弦值为 .A 1D 1的中点G ,BC 的中点P ,CD 的中点H ,连接GM ,GN ,MN ,PE ,PH ,PF ,HF ,∵MG ∥EF ,NG ∥EP ,MG ∩NG=G ,EF ∩EP=E ,∴平面MNG ∥平面PEFH , ∴过EF 且与MN 平行的平面截正方体所得截面为PEFH ,∵PE=2,EF=√12+12=√2,四边形PEFH 是矩形,∴过EF 且与MN 平行的平面截正方体所得截面PEFH 的面积为S=2√2.以D 1为原点,D 1A 1为x 轴,D 1C 1为y 轴,D 1D 为z 轴,建立空间直角坐标系, E (1,2,0),F (0,1,0),H (0,1,2),C (0,2,2),EC ⃗⃗⃗⃗⃗ =(-1,0,2),EF ⃗⃗⃗⃗⃗ =(-1,-1,0),EH ⃗⃗⃗⃗⃗⃗ =(-1,-1,2),设平面PEFH 的法向量n =(x ,y ,z ), 则{n ·EF ⃗⃗⃗⃗⃗ =-x -y =0,n ·EH ⃗⃗⃗⃗⃗⃗ =-x -y +2z =0,取x=1,得n =(1,-1,0),设CE 和该截面所成角为θ, 则sin θ=|EC ⃗⃗⃗⃗⃗ ·n ||EC ⃗⃗⃗⃗⃗||n |=√5·√2=√1010, ∴CE 和该截面所成角的正弦值为√1010.√2√1010四、解答题:本题共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.(10分)一座抛物线拱桥在某时刻水面的宽度为52米,拱顶距离水面6.5米. (1)建立如图所示的平面直角坐标系xOy ,试求拱桥所在抛物线的方程; (2)若一竹排上有一个4米宽、6米高的大木箱,问此木排能否安全通过此桥?由题意在平面直角坐标系xOy 中,设抛物线方程为y=ax 2(a<0).由条件得点(26,-6.5)在抛物线上,∴-6.5=262a ,解得a=-1104,∴抛物线方程为y=-1104x 2,即x 2=-104y.(2)由(1)可得抛物线的方程为x 2=-104y , 当x=2时,解得y=-126,∵6.5-6=0.5>126,∴木排可安全通过此桥. 18.(12分)如图,已知以点A (-1,2)为圆心的圆与直线l 1:x+2y+7=0相切.过点B (-2,0)的动直线l 与圆A 相交于M ,N 两点,Q 是MN 的中点,直线l 与l 1相交于点P. (1)求圆A 的方程;(2)当|MN|=2√19时,求直线l 的方程.由于圆A 与直线l 1:x+2y+7=0相切,∴R=√5=2√5,∴圆A 的方程为(x+1)2+(y-2)2=20.(2)①当直线l 与x 轴垂直时,易知x=-2与题意相符,使|MN|=2√19.②当直线l 与x 轴不垂直时,设直线l 的方程为y=k (x+2),即kx-y+2k=0,连接AQ , 则AQ ⊥MN ,∵|MN|=2√19,∴|AQ|=1,由|AQ|=√k 2+1=1,得k=34.∴直线l :3x-4y+6=0,故直线l 的方程为x=-2或3x-4y+6=0. 19.(12分)(2020山东,20)如图,四棱锥P-ABCD 的底面为正方形,PD ⊥底面ABCD.设平面PAD 与平面PBC 的交线为l. (1)证明:l ⊥平面PDC ;(2)已知PD=AD=1,Q 为l 上的点,求PB 与平面QCD 所成角的正弦值的最大值.PD ⊥底面ABCD ,所以PD ⊥AD.又底面ABCD 为正方形,所以AD ⊥DC. 所以AD ⊥平面PDC.因为AD ∥BC ,AD 不在平面PBC 中,所以AD ∥平面PBC ,又因为AD ⊂平面PAD ,平面PAD ∩平面PBC=l ,所以l ∥AD.所以l ⊥平面PDC. (2)D 为坐标原点,分别以DA ⃗⃗⃗⃗⃗ ,DC ⃗⃗⃗⃗⃗ ,DP ⃗⃗⃗⃗⃗ 的方向为x 轴,y 轴,z 轴的正方向,建立如图所示的空间直角坐标系Dxyz.由PD=AD=1,得D (0,0,0),C (0,1,0),B (1,1,0),P (0,0,1),则DC ⃗⃗⃗⃗⃗ =(0,1,0),PB ⃗⃗⃗⃗⃗ =(1,1,-1). 由(1)可设Q (a ,0,1),则DQ⃗⃗⃗⃗⃗⃗ =(a ,0,1). 设n =(x ,y ,z )是平面QCD 的法向量,则{n ·DQ⃗⃗⃗⃗⃗⃗ =0,n ·DC ⃗⃗⃗⃗⃗ =0,即{ax +z =0,y =0.可取n =(-1,0,a ).所以cos <n ,PB⃗⃗⃗⃗⃗ >=n ·PB⃗⃗⃗⃗⃗ |n ||PB⃗⃗⃗⃗⃗ |=√3√1+a 2.设PB 与平面QCD 所成角为θ,则sin θ=√33×√1+a 2=√33√1+2a a 2+1.因为√33√1+2a a 2+1≤√63,当且仅当a=1时,等号成立,所以PB 与平面QCD 所成角的正弦值的最大值为√63. 20.(12分)已知抛物线x 2=2py (p>0)的焦点到直线l :x-y-2=0的距离为3√22. (1)求抛物线的标准方程;(2)设点C 是抛物线上的动点,若以点C 为圆心的圆在x 轴上截得的弦长均为4,求证:圆C 恒过定点.x 2=2py 的焦点坐标为(0,p2),由点到直线的距离公式可得(|-p2-2|)√2=3√22, 解得p=2(负值舍去),所以抛物线的标准方程是x 2=4y.C 的坐标为(x 0,x 024),半径为r ,又圆C 在x 轴上截得的弦长为4, 所以r 2=4+(x 024)2,所以圆C 的标准方程为(x-x 0)2+(y -x 024)2=4+(x 024)2,化简得(1-y2)x 02-2xx 0+(x 2+y 2-4)=0,对于任意的x 0∈R ,上述方程均成立,故有{1-y2=0,-2x =0,x 2+y 2=4,解得x=0,y=2,所以圆C 恒过定点(0,2).21.(12分)在矩形ABCD 中,AB=3,AD=2,E 是线段CD 上靠近点D 的一个三等分点,F 是线段AD 上的一个动点,且DF ⃗⃗⃗⃗⃗ =λDA ⃗⃗⃗⃗⃗ (0≤λ≤1).如图,将△BCE 沿BE 折起至△BEG ,使得平面BEG ⊥平面ABED. (1)当λ=12时,求证:EF ⊥BG. (2)是否存在λ,使得FG 与平面DEG 所成的角的正弦值为13?若存在,求出λ的值;若不存在,请说明理由.当λ=12时,F 是AD 的中点,∴DF=12AD=1,DE=13CD=1.∵∠ADC=90°,∴∠DEF=45°.∵CE=23CD=2,BC=2,∠BCD=90°,∴∠BEC=45°.∴BE ⊥EF.又平面GBE ⊥平面ABED ,平面GBE ∩平面ABED=BE ,EF ⊂平面ABED , ∴EF ⊥平面BEG.∵BG ⊂平面BEG ,∴EF ⊥BG.(2)存在.以C 为原点,CD ⃗⃗⃗⃗⃗ ,CB ⃗⃗⃗⃗⃗ 的方向为x 轴,y 轴的正方向建立如图所示的空间直角坐标系. 则E (2,0,0),D (3,0,0),F (3,2λ,0).取BE 的中点O , ∵GE=BG=2,∴GO ⊥BE ,∴易证得OG ⊥平面BCE ,∵BE=2√2, ∴OG=√2,∴G (1,1,√2).∴FG ⃗⃗⃗⃗⃗ =(-2,1-2λ,√2),EG ⃗⃗⃗⃗⃗ =(-1,1,√2),DG ⃗⃗⃗⃗⃗ =(-2,1,√2). 设平面DEG 的一个法向量为n =(x ,y ,z ), 则{n ·DG⃗⃗⃗⃗⃗ =-2x +y +√2z =0,n ·EG ⃗⃗⃗⃗⃗ =-x +y +√2z =0,令z=√2,则n =(0,-2,√2).设FG 与平面DEG 所成的角为θ,则sin θ=|cos <FG ⃗⃗⃗⃗⃗ ,n >|=√6×√6+(1-2λ)=13,解得λ=12或λ=-710(舍去), ∴存在实数λ,使得FG 与平面DEG 所成的角的正弦值为13,此时λ=12. 22.(12分)(2020山东,22)已知椭圆C :x 2a2+y 2b 2=1(a>b>0)的离心率为√22,且过点A (2,1).(1)求C 的方程;(2)点M ,N 在C 上,且AM ⊥AN ,AD ⊥MN ,D 为垂足,证明:存在定点Q ,使得|DQ|为定值. 由题设得4a 2+1b 2=1,a 2-b 2a 2=12,11 解得a 2=6,b 2=3,所以C 的方程为x 26+y 23=1.M (x 1,y 1),N (x 2,y 2).若直线MN 与x 轴不垂直,设直线MN 的方程为y=kx+m ,代入x 26+y 23=1得(1+2k 2)x 2+4kmx+2m 2-6=0.于是x 1+x 2=-4km 1+2k 2,x 1x 2=2m 2-61+2k 2.由AM ⊥AN 知AM ⃗⃗⃗⃗⃗⃗ ·AN ⃗⃗⃗⃗⃗⃗ =0,故(x 1-2)(x 2-2)+(y 1-1)(y 2-1)=0,可得(k 2+1)x 1x 2+(km-k-2)(x 1+x 2)+(m-1)2+4=0.整理得(2k+3m+1)(2k+m-1)=0.因为A (2,1)不在直线MN 上,所以2k+m-1≠0,故2k+3m+1=0,k ≠1. 于是MN 的方程为y=k (x -23)−13(k ≠1).所以直线MN 过点P (23,-13).若直线MN 与x 轴垂直,可得N (x 1,-y 1).由AM ⃗⃗⃗⃗⃗⃗ ·AN ⃗⃗⃗⃗⃗⃗ =0得(x 1-2)(x 1-2)+(y 1-1)(-y 1-1)=0.又x 126+y 123=1,可得3x 12-8x 1+4=0.解得x 1=2(舍去)或x 1=23.此时直线MN 过点P (23,-13).令Q 为AP 的中点,即Q (43,13).若D 与P 不重合,则由题设知AP 是Rt △ADP 的斜边,故|DQ|=12|AP|=2√23.若D 与P 重合,则|DQ|=12|AP|.综上,存在点Q (43,13),使得|DQ|为定值.。
unit 1 理解·课文精研读Ⅰ.单词拼写1. The success of this experiment is crucial(关键性的) to the project as a whole.2.These people are short of all understanding of scientific(科学的) principles.3.At that time, I insisted(坚决要求) that they should wait for our return.4.The coach tried to analyse(分析) the cause of our defeat.5.The report concluded(得出结论) that no big changes were necessary.6.To their sadness, they failed to carry out all their objectives(目标).7.The plan might work better with more favourable circumstances(环境).8.It is distinct(清晰的) that smoking is harmful to health.9.She decided to go on her study after obtaining(获得) her first degree.10.He acknowledged(承认) that the accident was due to his carelessness.Ⅱ.阅读ABorn on April 4, 1928, Maya Angelou had a hard childhood.Her parents got divorced when she was very young.She was a single mother and being a single mother was very hard on her.It was finally in 1949 that she started to find her place in the world when she changed her name to show her Calypso dance performances at the night club where she worked.It was there that she won a scholarship and trained in African dance and modern dance.She formed a group and they traveled all over Europe with an opera production.As she traveled, she studied different languages and became excellent in several of them.During this time, she made her first album, Miss Calypso, and it was a success.In the 1950s, she moved to New York and started to work more on her writing.She heard Dr.Martin Luther King speak in 1960 and began organizing different benefits for Civil Rights.In 1961, she began to play a large role in the Civil Rights Movement and is remembered for her work around the country.She later moved to Ghana with her son and worked in the University of Ghana's School of Music and Drama.It was there that she became close friends with Malcolm X.She returned to the US in 1964 to help Malcolm X with a new Civil Rightsmovement.Shortly after she returned to the US, Malcolm X and Dr.King were both assassinated (暗杀).To deal with the deaths of her friends, she wrote her first book, I Kno w Why the Caged Bird Sings, which finally made her famous around the world.The 1970s were some of her most productive years as a writer, poet, as well as a singer.【语篇解读】作者向我们介绍了Maya Angelou 的生平故事,讲述了她艰难的一面,也讲述了她的成就。
SectionⅢGrammar一、将下列直接引语变为间接引语1.“I will take it home with me,” she said.She said that it home with her.答案:she would take2.“I will meet you tomorrow,” Mr Black said to me.Mr Black me that he meet me . 答案:told;would;the next/following day3.“You must come here before five,” he said.He said that I to go before five.答案:had;there4.“I am reading now,” my friend said.My friend said that he .答案:was reading then5.“Who will clean the room tomorrow morning?” she said.She clean theroom .答案:asked who would;the next/following morning6.He said,“You can sit here,Jim.”He Jim that he sit there.答案:told;could7.The young man asked,“How do you make it,Mother?”The young man asked his mother made it.答案:how she8.“Where are you these days?” the girl asked.The girl asked me days.答案:where I was those9.“I never eat beef,” the little girl said.The little girl said that never beef.答案:she;ate10.“Are you interested in this?” my uncle said to me.My uncle me I interested in . 答案:asked;whether/if;was;that二、将下列间接引语变为直接引语1.Mary asked Ann why she wanted to do that.答案:Mary asked Ann,“Why do you want to do this?”2.Jim said to me that he would visit the Summer Palace the next week.答案:Jim said to me,“I will visit the Summer Palace next week.”3.She said she had lost a pen the day before.答案:She said,“I lost a pen yesterday.”4.The teacher told us light travels faster than sound.答案:The teacher said to us,“Light travels faster than sound.”5.He asked her if she was interested in English.答案:He said to her,“Are you interested in English?”6.Kate said she was watching TV then.答案:Kate said,“I am watching TV now.”7.Lily told me that I could play with her the next Sunday.答案:Lily said,“You can play with me next Sunday.”8.Linda asked me what I was doing there.答案:Linda asked me,“What are you doing here?”9.Jack asked John where he was going when he met him in the street.答案:Jack asked John,“Where were you going when I met you in the street?”10.Peter told me that I had better go there that day.答案:Peter said to me,“You had better come here today.”三、单句改错1.He said those books are his.答案:are→were2.My mother asked me whether I have finished the homework.答案:have→had3.John said that he is going to London with his father.答案:is→was4.She said that their bus will arrive in five minutes.答案:will→would5.The teacher told me that the moon moved around the earth.答案:moved→moves6.She asked me if I came there to read newspapers.答案:came→went7.He told me that he had been born in 1973.答案:had been→was8.He told me that he had taught English since he had went there.答案:去掉第二个had9.Mum told me that I had to clean my bedroom by yourself.答案:yourself→myself10.Susan asked her husband how much they have spent on petrol that year. 答案:have→had四、完形填空Everyone needs friends.There is an old saying:friends are God’s way of taking care of us.But 1 do you find real friendship and keep it?TheCareandKeepingofFriends 2 the American author Sally Seamans tells young students some smart ways to find friends.Sally says finding friendship is just like a tree 3 .You plant the seed and take care of it to 4 it grow.First,you should choose a friend.What 5 a good friend?It is not 6 a person has money or good looks.A good friend should be 7 and patient.For example, 8 you have a bad day,a good friend should listen to your complaints and do his or her 9 to help.To make a friend,you cannot be too shy.You 10 make each other happy and share your lives.But things cannot always be 11 .Even the best friends have fights.What should you do when you have a 12 with your friend?You have to talk to him or her.When there is no one around,have an honest talk.If he or she doesn’t want to 13 ,you could write a letter.Sally says there are three steps to being 14 again:tell him or her 15 you are feeling;say what your friend has done wrong,and 16 why you did this or that.The 17 also has advice on some small but important things like celebrating your friends’18 . 19 you haven’t had a real friend before,you will start to think of having one if you20 this book.Because the book tells that friendship is the most important thing in your life. 1.A.how B.why C.where D.when答案:A解析:从下文我们可以看出,作者要告诉我们如何发现并保持真正的友谊。
新课程高中数学训练题组《必修1》《必修1》第一章(上)集合[ 基础训练A组]一、选择题1.下列各项中,不可以组成集合的是()A.所有的正数B.等于2的数C.接近于0的数D.不等于0 的偶数2.下列四个集合中,是空集的是()A.{ x | x 3 3} B.{( x,y)| y2 x2,x, y R} C .{ x | x2 0} D.{ x| x2 x 1 0,x R}3.下列表示图形中的阴影部分的是()A.(A C) (B C) B.(A B) (A C) C.(A B)(B C) D.(A B) CA B 4.下面有四个命题,其中正确命题的个数为()(1)集合N 中最小的数是1;(2)若 a 不属于N ,则a 属于N ;2的解可表示为1,1;C (3)若a N,b N,则a b的最小值为2;(4)x 1 2x第3 题图A.0个B.1个C.2个D.3个5.若集合M a,b,c 中的元素是△ABC 的三边长,则△ABC 一定不是()A.锐角三角形B.直角三角形C.钝角三角形D.等腰三角形6.若全集U 0,1,2,3 且C A 2 ,则集合A的真子集共有()UA.3个B.5个C.7 个D.8个二、填空题1.用符号“”或“”填空1 ,___ Q ,e C Q(1)0 __ N , 5 ___ N , 16 ___ N (2)___ Q___ ( e 是无理数)R2(3) 2 3 2 3 ________ x|x a 6b, a Q,b Q2. 若集合A x|x 6,x N ,B { x|x是非质数} ,C A B,则C的非空子集的个数为3.若集合A x|3x 7 ,B x | 2 x 10 ,则A B _____________4.设集合A {x 3 x 2}, B {x2k 1 x 2k 1}, 且A B,则实数k 的取值范围是5.已知 2 2 1 , 2 1A y y x xB y y x ,则A B _________三、解答题81.已知集合NA x N| ,试用列举法表示集合A。
2010年上海高考英语阅读理解新题型13文来高中Section DDirections:Read the following passage and complete the sentences or answer the questions according to the information given in the passage you have just read.Writing being largely a self-taught occupation, texts on how to get about it —though great in number— seldom are of much use.You try, and fail. Then try again, and perhaps fail not quite so grievously. Until at last, if you have some gift for it, the failures become less frequent, or at any rate less noticeable.It is this ability to conceal one’s defects(瑕疵)that passes, finally, for accomplishment.Along the way there are the discouragements of unkind criticism, outright rejection, nagging insecurity and irregular inability to meet debts.It is uncommon, therefore, to come across a book containing advice of much practical value for anyone toying with the dangerous idea of staring on a writing life.A friend recently loaned me such a book, however —one I wish I’d had the luck to read years ago, and which I would commend to any young person bent on making a career of words. It is the autobiography of the English novelist Anthony Trollope, first published in 1883, the year after his death.Needing some means to support himself, Trollope at age 19 signed on as a junior clerk in the British postal service. He was at his desk at 5:30 each morning to write for three hours. And he remained in the mail service 33 years, long after reputation and prosperity had come to him.Now, what of his advice?1. For safety’s sake, arm yourself with some other skills, some other line of work to fall back on. That way, failure at writing, though the disappointment may be keen, will not mean utter ruin.2. Do not depend overly much on inspiration. Writing is a craft, which Trollope compared to the craft of shoemaking. The shoemaker who has just turned out one pair of his work sets to work immediately on the next pair.3. Have a story to tell, but, more important than that, people it with characters who will speak and move as living creatures in the reader’s mind. Without memorable c haracters, story alone is nothing.4. Meet your deadlines. Life is endlessly “painful and troublesome” for writers who can’t finish their work on time.5. Do not be inflated by praise. And, above all, do not be crushed by criticism.6. Understand the risks of writing for a living. “The career, when successful, is pleasant enough certainly; but when unsuccessful, it is of all careers the most painful.”1. What is the passage mainly about?2. From the context, what does the phrase “pass for” in Paragraph 3 mean?3. According to the author, what is the definition of writing ?4. What is the author ’s most probable profession?Keys:1. The passage is mainly about sound advice provided in A. Trollope’s autobiography.2. It means “be regarded as”.3. Writing is basically a self-taught occupation and no instructions on how to deal with it are of any practical use.4. He is most probably a writer.Section DDirections:Read the following passage and complete the sentences or answer the questionsaccording to the information given in the passage you have just read.A long-awaited final report from the Food and Drug Administration (FDA) concludes that foodsfrom healthy cloned animals and their offspring are as safe as those from ordinary animals, effectively removing the last US regulatory barrier to the marketing of meat and milk from cloned cattle, pigs and goats.The 968-page "final risk assessment," not yet released but obtained by The Washington Post, finds no evidence to support people’s concerns that fo od from clones may have hidden risks.But, recognizing that a majority of consumers are wary of food from clones—and that cloning could damage the good image of American milk and meat—the report includes hundreds of pages of raw data so that others can see how it came to its conclusions.The report also acknowledges that human health concerns are not the only subject raised by the coming-out of cloned farm animals.“Moral, religious and ethical concerns have been raised,” the agency notes in a document acco mpanying the report. But the report is “exactly a science-based assessment.” It reports, because the agency is not authorized by law to consider those issues.In practice, it will be years before foods from clones make their way to store shelves in large quantities, in part because the clones themselves are too valuable to kill or milk. Instead, the expensive animals — replicas(复制品) of some of the finest farm animals ever born — will be used firstly as breeding stock to create what supporters say will be a new generation of superior farm animals.When food from those animals hits the market, the public may yet have its say. FDA officials have said they do not expect to require food from clones to be labeled as such, but they may allow foods from ordinary animals to be labeled as not from clones.1. What conclusion has FAD drawn after the public waited for a long time?2. Foods from clones won’t be available soon partly because __________________________.3. With the appearance of cloned farm animals, people care more about _________________________________________________________________ problems.4. How will foods from ordinary animals be labeled?Keys:1. FDA made the conclusion that foods from healthy cloned animals and their offspring are as safe as those from ordinary animals.2. the clones themselves are too valuable to kill or milk.3. human health, moral, religious and ethical4. They will be allowed to be labeled as not from clones.Section DDirections:Read the following passage and complete the sentences or answer the questions according to the information given in the passage you have just read.President Barack Obama met briefly with his half brother, Mark Okoth Obama Ndesandjo, who lives in China since 2002.The three chatted on Monday night, with Obama being introduced to Ndesandjo's wife, a native of Henan, China, whom he married a year ago.“I think he came directly off the plane, changed some clothes and then came down and saw us.” Ndesandjo said, "And he just gave me a big hug. And it was so intense. I'm still over the moon on it. And my wife is also on the top of the world. She is his biggest fan and I think she is still recovering."In the CNN interview, president Obama told CNN ,"I don't know him well. We did not grow up together. I met him for the first time a couple of years ago.” The president said he hadn't read his brother's book, "Nairobi to Shenzhen," which features a boy who is the son of a Jewish mother and an abusive father from Kenya. Ndesandjo recently wrote this novel about the abusive Kenyan father they share, Obama Senior. In his book, Mark wrote : “My father beat my mother and also beat me. ”Ndesandjo said it took a long time for him to become "proud to be an Obama."The president himself also wrote about his father, who abandoned him as a child, in his best-selling memoir , “Dreams From My Father”. “It's no secret that my father was a troubled person,” President Obama said. “he had an alcoholism problem. He didn't treat his families very well. Obviously it's a sad part of my history and my background.”Ndesandjo said he bought tickets months ago to fly from the southern boomtown of Shenzhen, where he has lived, to Beijing, in hopes of reconnecting with his brother. The two last met in Januarywhen Ndesandjo attended Obama's inauguration as a family guest.Ndesandjo , the 43-year-old businessman and musician , earns a living as a marketing consultant in Shenzhen, near Hongkong. He earned degrees in physics from Brown University and Stanford and an MBA from Emory University. As a classical and jazz pianist, Ndesandjo also volunteers as a piano teacher in an orphanage. His fluent spoken and written Chinese impress many Chinese. "Mark is very smart and multitalented," wrote one state news agency. However, for most of time he has maintained a low profile, having repeatedly turned down offers from Chinese companies to be a product spokesman.1. Do president Obama and his brother feel proud of their father? What was their father like?2. When and on what occasion did the two brothers meet before Obama’s vist to Beijing?3. Why is Nesandjo constantly invited by the Chinese companies to be a product spokesman?4. We can tell from the passage that President Obama’s half brother is a caring person from the factthatKeys:1.No, they don’t. He was a troubled person.2.They last met in January when Ndesandjo attended Obama's inauguration as a family guest.3.He is now a celebrity because of his connection with the president./ He’s now famous……4.he also volunteers as a piano teacher in an orphanage.Section DDirections:Read the following passage and complete the sentences or answer the questionsaccording to the information given in the passage you have just read.Chinese Premier Wen Jiabao will meet here Wednesday with US President Barack Obama, who is on his first state visit to China since his January inauguration(就职典礼).They will have a working lunch before Obama's sightseeing visit to the Great Wall in the north suburb of the Chinese capital, which will be another chance for the US head of state, who toured the Imperial Palace Tuesday, to learn more about the ancient Chinese civilization.Obama will conclude his fist visit to China and fly to the Republic of Korea, the last leg of his four-state Asian tour, in the afternoon.He arrived in China's economic hub Shanghai Sunday night to kick off this visit as guest of his Chinese counterpart Hu Jintao. Hu held talks with him in Beijing on Tuesday and they met international reporters for about 40 minutes after the talks, both pledging to further bilateral ties.Top Chinese legislator Wu Bangguo also met Obama on Tuesday, several hours before a state banquet in the Great Hall of the People in downtown Beijing.In a joint statement issued on Tuesday, the two sides spoke highly of the tremendous development achieved since the two countries established diplomatic relations 30 years ago and reached consensus on further bilateral ties.1. Why will Obama tour the Imperial Palace?_______________________________________________________________2. How many Asian countries will he plan to tour?_______________________________________________________________3. Which economic hub did he arrive in?________________________________________________________________4. In a joint statement issued on Tuesday, what did the two sides reach?________________________________________________________________。
广东省高考英语新题型之仿真模拟考试试题(十三)(本试卷共三大题,满分135分;考试用时1。
)Ⅰ语言知识及应用(共两节,满分45分)第一节完形填空(共15小题;每小题2分.满分30分)阅读下面短文,掌握其大意.然后从1—15各题所给的A、B、C和D项中,选出最佳选项,并在答题卡上将该项涂黑。
“Cheerfulness keeps up a kind of daylight in the mind, and fills it with a steady perpetual(永久的)serenity (平静).’’— Joseph Addison[Annually my husband’s family has a reunion.At one of the recent 1 ,the weather was cloudy, and more rain was 2 .The family members who arrived early were 3 about the possibility of rain and the effect it would have on attendance.It did rain,but as it started,a car 4 and out of the passenger side suddenly appeared Uncle Earl,5 by the family, who is 96 years old and has been blind for many years.Just the arrival of Uncle Earl immediately 6 the spirits of the group.Ever cheerful and optimistic,Uncle Earl 7 to amaze the family.One by one he 8 each member, held their hands,gave them a piece of candy and made them laugh.As I stood back,1 watched how his behavior and 9 brought a smile to everyone’s face He didn’t spend time telling everyone about his illness as others were doing.I 10 that it was his choice to be of good cheer and not focus on the 11 aspects of his life.By doing so, each family member had to respond in the same 12 .Just before we began to feast on the wonderful food,Earl stood up and spoke to the group for a few minutes.He asked everyone to take a lighthearted approach to 13 happened. He said he had prayed for us all to arrive and to return home safely,so we need not worry about the rain.Then he gave us all his blessing.I know I felt 14 to be with him.What is happening in your life 15 ?Are you taking a cheerful approach to your day? Be of good cheer! Like Uncle Earl!1.A.moments B.reunions C.meals D.discussions2.A.informed B.argued C.predicted D.demanded3.A.happy B.excited C.interested D.concerned4.A.pulled up B.drove off C.pushed in D.sped up5.A.told B.called C.known D.recognized6.A.changed B.reacted C.bothered D.showed7.A.continues B.refuses C.plans D.tends8.A.scratched B.admired C.scolded D.addressed9.A.cheerfulness B.thankfulness C.pessimism D.complaint10.A.realized B.explained C.decided D.urged11.A.violent B.positive C.meaningful D.negative12.A.order B.place C.manner D.direction13.A.whatever B.whichever C.however D.wherever14.A.beaten B.disappointed C.blessed D.surprised15.A.at times B.in time C.right now D.from now第二节语法填空(共10小题;每小题l 5分.满分l5分)阅读下面短文,按照句子结构的语法性和上下文连贯的要求,在空格处填入一个适当的词或使用括号中词语的正确形式填空,并将答案填写在答题卡标号为16—25的相应位置上。
匀变速直线运动的位移与时间的关系(满分100分,60分钟完成)班级_______姓名______ 目的要求:1.熟练掌握匀变速直线运动的基本规律;2.能用位移公式、速度公式及匀变速直线运动的平均速度公式解题。
第Ⅰ卷(选择题共48分)一、选择题:本大题共6小题,每小题8分,共48分。
在每小题给出的四个选项中,至少有一个选项正确,选对的得8分,对而不全得4分。
选错或不选的得0分。
1.一物体的位移函数式是s=4t+2t2+5(m),那么它的初速度和加速度分别是()A.2m/s,0.4m/s2B.4m/s,2m/s2C.4m/s,4m/s2D.4m/s,1m/s22.甲、乙两物体在同一条直线上,甲以v=6m/s的速度作匀速直线运动,在某时刻乙以a=3m/s2的恒定加速度从静止开始运动,则()A.在2s内甲、乙位移一定相等B.在2s时甲、乙速率一定相等C.在2s时甲、乙速度一定相等 D.在2s内甲、乙位移大小一定相等3.物体从静止开始做匀加速运动,当加速度为a、时间为t时,位移为s。
若要使位移变为2s,则()A.时间为2t,其它不变B.加速度为2a,其它不变C.末速度变为原来的2倍,时间不变D.以上都不行4.甲、乙、丙三个物体做匀变速运动,通过A点时,物体甲的速度是6 m/s,加速度是1m/s2;物体乙的速度是2 m/s,加速度是6 m/s2;物体丙的速度是-4m/s,加速度是2m/s2。
则下列说法中正确的是(A.通过A点时,物体甲最快,乙最B.通过A点前1 sC.通过A点后1 s时,物体乙最快D.以上说法都5.汽车由静止开始匀加速前进,经过10 s速度达到5 m/s,则在这10s内()A.汽车的平均速度是0.5 m/sB.汽车的平均速度是2.5 m/sC.汽车的平均速度是5 m/sD.汽车的位移是50 m6.一物体由静止开始,沿斜面匀加速下滑,它通过斜面一半所用时间是它通过整个斜面所用时间的n 倍,则n 于 ( )A .12-B .2C D第Ⅱ卷(非选择题,共52分)二、填空、实验题:本大题共3小题,每小题8分,共24分。
把正确答案填写在题中横线上或按要求作答。
7.一辆以12m/s 的速度在水平路面上行驶的汽车,在刹车过程中以3m/s 2的加速度做匀减速运动,那么t =5s 后的位移是_________m 。
8.一个物体做匀变速直线运动,某时刻的速度是v =2m/s ,加速度是a =-0.5m/s 2,那么它在3s 前的速度是_____________m/s ,3s 后的速度是______________m/s ,这6s 内的位移是_________m 。
9.一个物体由静止开始做匀加速直线运动,在t 时间内通过的位移是s ,则物体在t 时刻的速度为___________,物体的加速度为___________,它在前13t 时间内的位移是___________,它通过前13s 所用的时间是___________。
三、计算题:本大题共2小题,计28分。
解答应写出必要的文字说明、方程式和重要演算步骤。
只写出最后答案的不能得分。
有数值计算的题,答案中必须明确写出数值和单位。
10.(12分)在平直公路上,一自行车与同方向行驶的汽车同时经过某点,它们的位移随时间变化关系是,自行车:s 1=6t ,汽车:s 2=10t -41t 2,可知: (1)经多长时间,自行车追上汽车? (2)自行车追上汽车时,汽车速度为多少? (3)自行车追上汽车前,二者间最大距离为多少?11.(16分)如图所示,直线MN 表示一条平直公路,甲、乙两辆汽车原来停在A 、B 两处,A 、B 间的距离为85m ,现甲车先开始向右做匀加速直线运动,加速度a 1=2.5m/s 2,甲车运动6.0s 时,乙车立即开始向右做匀加速直线运动,加速度a 2=5.0m/s 2,求两辆汽车相遇处距A 处的距离。
参考答案一、选择题:1.【答案】C【点拨】一物体的位移函数式是s =4t +2t 2+5(m ),与一般的匀变速运动的位移公式s =v 0t +212at 对比可知,初速度v 0=4m/s ,加速度a =4m/s 2。
后面的常数项表示t =0时物体不在坐标原点。
2.【答案】B【点拨】甲、乙两物体在同一条直线上,可以同向,也可以反向。
在2s 内甲的位移:s 甲=vt =12m ,乙的位移:s 乙=2162at m =。
在2s 时甲的速率:v 甲=t =6m/s ,乙的速率:v 乙=at =6m/s 。
可知在2s 时甲、乙速率一定相等,但方向不一定相同。
在2s 内的位移大小不等,方向也不一定相同。
3.【答案】BC 【点拨】根据s =212at 知,若时间为2t ,其它不变,则位移变为4s ,A 错误;加速度为2a ,其它不变,位移变为2s ,B 正确;因初速度为零,末速度变为原来的2倍时,平均速度变为原来的2倍,时间不变时,位移变为2s ,C 正确。
4.【答案】ABC【点拨】通过A 点时,甲的速度最大,乙的速度最小,甲运动最快、乙最慢;由v t =v 0+at 知,通过A 点后1s 时三物体的速度分别为:v 甲=7 m/s ,v 乙=8 m/s ,v 丙=-2 m/s ,故乙最快,丙最慢;由v t =v 0+at 得v 0=v t -at ,可求得通过A 点前1s 时三物体的速度分别为:v 甲′=5 m/s ,v 乙′=-4m/s ,v 丙′=-6 m/s ,故丙最快,乙最慢。
故选项A 、B 、C 正确。
5.【答案】B【点拨】对于匀变速直线运动,有 02t v v v +=,得:052v +=m/s =2.5m/s 。
位移s vt ==2.5×10m =25m 。
6.【答案】D【点拨】设通过斜面一半所用的时间为t 1,通过斜面全长所用的时间为t 2,由212s at =得:t =aLaL t =⨯=221,a L t 22= ,则2221==t t n 。
二、填空、实验题:7.【答案】24【点拨】本题不能直接套用公式。
一辆以12m/s 的速度在水平路面上行驶的汽车,在刹车过程中以3m/s 2的加速度做匀减速运动,可以算出经t 0=4s 汽车已经停止运动了,所以在计算t =5s 后的位移时,时间只能用实际用的时间t 0=4s 代入。
20001242s v t at =-=m 。
【思考】在这种类型中,当t >t 0,t <t 0 ,t =t 0的情况下,如何计算位移? 8.【答案】3.5;0.5;12【点拨】根据v t =v 0+at 知,设3s 前的速度是v 1,3s 后的速度是v 2,则有v =v 1+at ,v 2=v +at ,解得:v 1=3.5m/s ,v 2=0.5m/s ;这6s 内的位移s =122v v vt t +==12m 。
9.【答案】2st ;22st ;9s【点拨】由212s at =得:a =22s t ;物体在t 时刻的速度v =at =2s t ;在前13t 时间内的位移211()23t s a ==9s ;设通过前13s 所用的时间为t 1,有21132s at =,得t 1。
三、计算题:10.【答案】(1)16s ;(2)2m/s ;(3)16 m 【解析】方法一:(1)自行车追上汽车时,两者位移相等,s 1=s 2,即6t =10t -24t解得:t =16 s(2)此时汽车的速度 v 16=v 0+at =10 m/s -0.5×16 m/s =2 m/s 。
(3)由题意可知,自行车以6m/s 的速度作匀速直线运动,汽车以10m/s 的初速度、0.2m/s 2的加速度作匀减速运动。
起初汽车速度大于自行车的速度,两者间的距离不断增加,当汽车与自行车速度相等时,两者间的距离最大,即: 6=10-0.5t ′ 得t ′=8s 。
此时两者间距离Δs =s 2-s 1=(10×8-41×82)m -6×8 m=16 m 。
方法二:本题也可以用数学方法解决。
由题设给出的位移公式,求出两者间距离:Δs =s 2-s 1=10t -42t -6t =-42t -4tΔs 为 t 的二次函数,根据有关数学知识,可求出 t =8s 时,Δs 取最大值,即两者间距离最大,最大值为 16m.当Δs =0时,t '=16 s ,即此时两者相遇。
相遇时汽车的速度 v 16=v 0+at ′=10 m/s -0.5×16 m/s =2 m/s 。
11.【答案】125 m ;245m【解析】甲车运动6s 的位移为:20101452s a t m ==尚未追上乙车,设此后用时间t 与乙车相遇,则有:2210211()8522a t t a t m +=+ 将上式代入数据并展开整理得:212320t t -+=解得:t 1=4s ,t 2=8st 1、t 2、都有意义,t 1=4s 时,甲车追上乙车;t 2=8s 时,乙车追上甲车再次相遇。
第一次相遇地点距A 的距离为:211101()2s a t t =+=125m第二次相遇地点距A 的距离为:221201()2s a t t =+=245m 。