高三总复习单元滚动测试卷·数学（五）第五单元三角函数时间：120分钟满分：150分第1一4单元30%+本单元70%6,我国负时期宝么数学客河酒考点：三角函数的图象与性质、三角恒等变换。箱之欢细，所失序少镇之又天矣”，也靠是角用圆物内接多形号第I卷（选择题共60分）积如图，圆0的半径为1，開一、选择题（本题共12小题，每小题5分，共60分。在每小题给出的四个选项中，只有一个选项似为者我们运用医木的是是符合题目要求的。)以此估计，圆0的面彩近似为A.36-21.已知a∈(0，r),若cosa=-，则tana的值为1(B307.已知xC(0,),函数m=2B.C.√3D.-√33A.存在工∈0，含准2.已知a∈R,则sne-”是2a号的C.对任意x∈0，分有A.充分不必要条件B.必要不充分条件:期面，=o荐了8.海水受日月的引力，在一定下，船在涨潮时驶进航道，C.充要条件留蓝自则的。袋定D.既不充分也不必要条件到水面的距离)为4m安3.黄金三角形有两种，其中底与腰之比为黄金分割比的黄金三角形被认表给出了某港口在某季气为是最美的三角形，它是一个顶角为36°的等腰三角形（另一种是顶角港口的水深与时间的函！为108°的等腰三角形).如图所示的五角星是由五个黄金三角形与一时刻个正五边形组皮，在其中一个黄金△AC中，C5己，根据这些0:003:006:00信息，可得sin126°=A.1-2⑤B3+6A.f(x)=2.5cos(648C.该货船在2：00至4C.1+5高可了想的地D.4+5C0发2米9.已知函数y=Asin(w84计端并基有实耐接断错误的是4.要得到函数y=sin(2x+)的图象，可以将函数y=cos(2x看)的图象年（能）A.该函数的解析式为A.向右平移器个单位长度B.向左平移个单位长度B.该函数图象的对称宽日位单C.向右平移石个单位长度式D.向左平移个单位长度C.该函数的单调递！5.对于函数f(x),若存在区间A=[m,n],使得{yy=f(x),x∈A}=A,则称函数f(x)为“同D.把函数y=2sin域函数”，区间A为函数f(x)一个“同域区间”.给出下列四个函数：数图象假纸限①f)=cos5x②f(x)=x2-1;质#前过10.设函数f(x)③f(x)=x2-1;④f(x)=log2（x-1).5p[0,3]内恒有四存在“同域区间”的“同域函数”的是A.2A.①②③B.①②C.②③D.①②④【S3【S3·高三单元滚动卷·数学卷五（文科·理科）等第5一1页（共6页）】

19.(12分)20.(12分)如图，在△ABC中，AB=BC=2,∠ABC=120°，AD=入AC,Ae(0,1),将△ABD沿BD折起，使点A到点P的位置，得到三棱锥P-BCD,E为PC的中点，G为△BCD的重心已知椭圆导·卡=1(a>6>0)的左焦点为P,右顶点为D(3.0),过F的直线1交装圆于A,8两(1)求证：EG不平行于平面PBD;点，C为线段AB的中点，线段AB的垂直平分线交x轴于点E,当直线1的斜率为1时，E和原点(2)若入-}，平面PBD1平面BCD,求二面角B-PC-D的正弦值0重合且1cE1-(1)求椭圆的标准方程；(2)若直线DA,DB分别交直线x=-33于点M,N,求证：以MN为直径的圆恒过点F.金考卷理科数学领航卷（八）全国卷第5页（共8页）理科数学领航卷（八）全国卷第6页（共8页）

所以T,=X21-2X022=(a-10×21+21-2已知数列{an}为等差数列，{bn}为等比数列，{bn)的前n项和为Sn,且a1=b1=1,a2=a3一b3,a3=S3十b2(1)求数列{an},{bn}的通项公式；(2)设cn=anbn,Tm为数列{cn}的前n项和，求Tm解：(1)设等差数列{am}的公差为d,等比数列{bn}的公比为q,因为a2=a3-b3,a3=S3+b2,所以1+d=2d+1-q2,2d+1=1+q+g2+q,解得=4或日=0（含去，q=2、9=0所以am=4n-3,bm=2m-1(2)因为cm=anbm=(4n-3)·2m-1,所以Tm=1×1+2×5+22×9+…+2m-2。(4n-7)+2m-1·(4n-3)①，①×2得，2Tn=2×1+22×5+23×9+…+2m-1·(4n-7)+2m。(4n-3)②，①一②得，-Tm=1+4(2+22十23+…+2m-1)-2·(4n-3)=1+4.21-2）-2.(4m-3)1-2=-2m。(4n-7)-7,故Tm=2m·（4n-7)+7.

5生物体死亡后，它机体内原有的碳14合量P会按确定的比率衰藏（称9.已知A,B是抛物线C为衰减率)，P与死亡年数之间的函数关系式为P=(号》广（其中a为说法错误的是。了常数)，大约每经过5730年衰减为原来的一半，这个时间称为“半衰A.直线AB过焦点F期”，若2021年某遗址文物出士时碳14的残余量约占原始含量的B.直线AB过焦点】-2 BF5%,则可推断该文物属于个点零增(x)门商牌①(S)C.若AB中点M的参考数据：l0g20.75≈-0.4。参考时间轴：=义家@D.点A坐标(4,4)，宝交点为D,则直线平段草的公元2021年战国唐宋10.在三棱锥P-ABC围球A宋B.唐C.汉D.战国外接圆圆心分别为36.《红海行动》是一部现代海军题材影片，该片讲述了中国海军“蛟龙突击16π，设OA=a,(队”奉命执行撤侨任务的故事.撤侨过程中，海军舰长要求队员们依次A.√5B完成六项任务，并对任务的顺序提出了如下要求：重点任务A必须排11.蜂巢是由工蜂分在前三位，且任务E,F必须排在一起，则这六项任务的不同安排方案的中空柱状体连共有成，菱形的一个有A.240种B.188种C.156种D.120种7.函数f(x)=2sin(wx十p)(w>0且0

所以y=-)-a)=2 in-2nr+哥》雪慧进·高考总复习·单元濛动创新卷，数学理科第八单元三角恒等变换=2snor-2 2sin c号-2 in号(第七单元30%，第八单元70%)【案容】由y=2如m-号引的图泉关于直线x语对#，可得m侣-写引=士1，第I卷（选择题共60分）选择题：本题共12小题，每小题5分，共60分.在每小题给出的四个选项中，只有一项是符合题所以受-号=km+受，keZ,部得@w=号+2，keZ1,在平面直角坐标系中，已知点A(280,2sin809),B(2s20,2n20°，那么1AB:身目要求的.D.40>20又因为0>03【答案】A0察塔1【解析】AB|=√(2c0s20°-200s80y+(2sin20°-2sin80°每得-晋+≤号+keZ4+4-8os20o80+n20m80时-8-8m20-80可=8842，故即8()在[0，上的单调运增区间为0，司][侣可小（6分）得号到又由xe[0,π]，所以=0或k=1恶A.长四：(2)由已知得g)=2simx-引+】，令g()=0得a(-)+号=km,keZ，2.若sin37=a,则c0916°=0B1-223而，0=oE-C.2a√1-aD.a√2a-1<是5k如+-【答案】c即x=,keZ,因为g()在[5可上仅有一个零点，【解析】由sim37=a,37是第一象限角，则c0s37=V-m37=1-0,所以如74km+景-in37cos37°=2aV1-a,则c0s16°=sin74°=2a√-a,故选C.≤m已知锐角9的始边与x轴的非负半轴重合，终边与单位圆的交点的横，纵坐标之差为，则所以-+0-置k五an20的值为50奇-eDA.2+1)+知-1的->T-1sws66-26k-2>0-E+≤n【解折由题老可知一9-血0旦口为钙有，计实行得m0-25【答案B。2an0号，战选B8-合+m+110由于0>0，所以0>6k-86-8<2'月不3k-1≤6k-2,9,得2号，从面可得m20-万已知e(0,且9+2@则m2a、1<222m+]=+解得3

Theppy所以，不等式f()≤9的解集为（女-子≤x<号》.(2)由(1)x<-2时，J(x)>8,-2≤x≤2时，f(x)≥4x>2时，f(x)>4,中所以f(x)的最小值为M=4,则a+b=4.……-++“a]>s+严]-号当且仅当，名=“a卫且a+6=4即a=号0-9取等号，20.(12分)解，QD由fx)=x-号ar+1得f(x)-3x2-3ax,由于f(x)的单调递增，则∫(x)=3x2-3ax≥0，即x2-ax≥0恒成立，则4=a'≤0，故a=0,所以，a的值为0.(2)存在.方法1：由题，f(x)=3x2-3ax=3x(x-a),(1)当a≤0时，可知x>0时，f(x)>0,f(x)单调递增，则f(x)在(1,2)上不存在极值，此时不满足条件；(i)当a>0时，可知x<0时，f(x)>0,f(x)单调递增；0a时，f(x)>0,f(x)单调递增，所以x=0时，f(x)取得极大值；x=a时，f(x)取得极小值.………10分要使f(x)在区间(1,2)上存在极小值，则必有10,l12-6a>0,解得11时，∫(x)>0,f(x)单调递增，故x=1时，f(x)取得极小值f(1)=a一1，也即为最小值，第2套·理数参考答案第3页（共4页）

2.如图所示的复古时钟显示的时刻为10：10，将时针与分针视为两条线段，则该时刻的时针与分针所夹的钝角为A号23π6.96cn陪【答案】B【解析】时钟上有12个刻度，相邻两个刻度所对的圆心角为登看当时针招向10，分针指向2时，时针与分针央12.1的4X不-2但当分针指向2时，时针由10向1移动了百×6-,所以该时刻的时针与分针所夹钝角为2π元23π336=363.已知函数f(x)=sin(x十p)(aw>0)的图象与函数g(x)=cos(2z+)的图象关于y轴对称，则符合条件的m,9的对应值可以为A1,B1,8c2,D2,君【答案】D【解析】国为g(x)=cos(2x+)的图象与y=cos(-2x+)的图象关于y轴对称，所以f(x)=sin(ox十p)=cos(一2z+智+2kxe∈z,即cos[臣-(or+p]=cos(-2红+音+2kk∈Z,所以2-0x-g=-2x+弩+2kx,k∈Z,即(2-w)x-9=26x-，k∈Z,所以w=2,9=否-2张，∈Z,所以选预D符合.4.设函数f(z)=asin(z十1)+bsim(z十p:),则“f()=0”是f(x)为偶函数”的A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分也不必要条件【答案】C【解析】若f(x)为偶函数，则f(x)=f(-x),即asin(x+p1)+bsin(x+p2)=asin(-x+p1)+bsin(-x+,),整理得2 asin0s9:十2 bsin60s9:=0,即acos91十bcos:=0,所以f(）=asin(2+9）十bsin(受+9r）=acos91+:=0.若f(经）=0，则acos91+bcos9:=0,所以“f(）=0”是“f(x)为偶函数”的充要条件。4πsin a55.若tana=2tan5,则n(a)A.-5B.-3C.3D.5【答案】B【解析】因为tan。=2tan牙，所以sim(e-）;sinl(e-）sim-）·34·

coS x18.(12分)*已知函数f(x)=，则其图象可能是lg(W2+1+x)已知函数f(x)=1og(4-x)+1og(4+x).2-(1)求f(x)的定义域；(2)判断f(x)的奇偶性，并加以证明，婚·资(3)求f(√15)的值.只为燕货个到出的暖容。分共，伦色蓝点小术长“人不食程衣端大有挥。家要百营分苏质月二、填空题：本题共4小题，每小题5分，共20分。13.设函数f(x)=logx(a>0,且a≠1)，若f(x1x2…x221)=1010,则f(x)十f(x)十…十f(x021)=1.814.函数g(x)=log。(x十2+ab)(a>0,且a≠1)为奇函数，则2-4a的最小值为15.若函数f(x)=1og(-x2+4x十5)在区间(3m一2，m十2)内单调递增，则实数iSadl--8.m的取值范围为16.已知函数f)=z+1.≤0若方程3m[Fx)]-(2m+3)f(x)+2=0Ig x,>0,有6个不同的实数解，则实数m的取值范围是三、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)(1)求值：lg52+号lg8十lg5X1g20十(1g2)2；司(2)设2：-3-72，求2+2的值x y理数·周测卷（四）第3页（共8页）理数·周测卷（四）第4页（共8页）

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31.What is the text?and educator guide the childA.A book review.y and pproprie第二节（共5小题；每小题2.5分，满分12.5分）will improve their health and make them feel better.B.A news report.and their families can make a difference in the根据短文内容，从短文后的选项中选出能填A.Suggest activities that don't involve drinkingC.A diary entry.of children with mental disorders入空白处的最佳选项。选项中有两项为多余alcohol.D.A travel guide.Being mentally healthy during chilhod选项。B.If you love them,you definitely want toreaching developmental and emotionalIs someone you love drinking too much?36support them.DMental disorders among children are describedandleamning healthy social skills andRead on for some great ways to support your friendC.Encourage the person to find new hobbies andas serious changes in the way children typicallyheree poblems Menlly beaor family member and encourage them to continueinterests.learn,behave,or handle their emotions,whichhateive ty nf lie andown the path to sobriety(清醒).With your help,D.Part of the habit of drinking is having a drinkcause distress and problems getting through theat home,in school,and in their commuthey can make the changes they want in their life.in your hand.day.Many children occasionally experienceSuporting children'memtalTalk to the person while they're sober.E.That way,they'll have their favorite flavorattention-deficit/hyperactivity disorder,fears andindludle makingchlrenme deIf you want to raise the issue of alcohol,do itwithout the alcohol.worries or display disruptive behaviors.If symptomsmilestons,understanding what todohewhen they're not drinking to draw their attention.F.Look up local groups or treatment centers thatareroudpersiste erencrin poive n37 But you can't have this conversation whenmight help the person.they're currently under the influence.G.To this end,you can show them how theirschool,home,or play activities,the child may beand improving access to care.32.What does theunderined word“dipive。Point the person to helpful resources anddrinking is affecting others.diagnosed(诊断)with a mental disorder.Paragraph 1 probably mean?tools.第三部分语言运用（共两节，满分30分）Symptoms of mental disorders change over time38 A lot of times,someone makes theas a child grows.They often start in earlyA.Different.B.Constructive.decision to quit drinking but doesn't know where to第一节（共15小题：每小题1分，满分15分）childhood,although some disorders may developC.Ruinous.D.Indescribableturn for any help they might need.You can help阅读下面短文，从短文后各题所给的A、B、during the teenage years.The diagnosis is often33.What does Paragraph 3 mainly talk abou?your friend or family member by researching theC、D四个选项中，选出可以填人空白处的最佳made in the school years and sometimes earlier;A.Who is affected by mental disorders.issue and showing them websites they can check out选项。B.What effects mental disorders can bringWhen she was 21 years old,Laura Carstensenhowever,some children with a mental disorder mayor phone numbers they can call.went to a concert with some co-workers.After thenot be recognized or diagnosed as having one.C.How boys differ from girls in mental dison39show,they all 41 different cars for the rideChildhood mental disorders affect many childrenD.Why American children suffer from mentalSomeone who's quit drinking often needs toand families.Boys and girls of all ages and racialdisorders.keep busy.If your friend or family member washome.backgrounds and living in all regions of the United34.What is an effective way to treat mental disordsdrinking a lot,it probably also took up a lot of theirCarstensen ended up in a car driven by aA.Canceling outdoor activities.time.New hobbies and interests,especially thingsyoung man,and it soon became 42 that he wasStates experience mental disorders.It is estimatedthat keep them active,will help them feel likedrunk.The car weaved in and out of the 43 atthat in 2007,13%-20%of children living in theB.Providing more care and supportthey're too busy to drink.top speed.United States experienced a mental disorder in aC.Depending fully on doctors.D.Helping children gain academic success.Provide the person with plenty of non-"I was 44 him to slow down,which wasgiven year,costing individuals,families,andin vain,"Carstensen recalled."And then the nextsociety an estimated $247 billion per year.35.From which section of a magazine can youalcoholic drinks.Help the person stay hydrated(含水的）and thing I45 was that I was laying on the side ofChildhood mental disorders can be treated andthe text?resist the urge to drink alcohol.40 Your friend the road outside of the car."managed.To this end,parents and doctors shouldA.Sports and fitness.or family member will find it easier to resistThe driver had 46 direction suddenly,work closely with everyone involved in the child'sB.Children's mental health.temptation if they already have something to drink.and Carstensen had tumbled(翩滚)out of atreatment.Taking advantage of all the resourcesC.Coping with stress.You can also help them stay well-hydrated,which window.The good news was that she was near theavailable will help parents,health professionals,D.Mental health quiz.猜题金卷，英语（一）第6页（共8页）猜题金卷·英语（一）第5页（共8页）

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