(一)1试题)
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21.AR+AD=AC.证明：因为∠DCE=∠BC=∠A=90P,所以∠AC)+∠ACE=909=∠E+∠AC.所以∠AC)=∠∠A=∠EBC,在△ACD和△BEC中，{∠ACD=∠E,DC=CE.听以△ACD≌△BEC(AAS).所以AD=BC.所以AB+AD=AB+BC=AC22.(1)因为∠A+∠ABC+∠C+∠1DC=360°，∠A=∠C=90P.所以∠ABG+∠ADC=360°-90°-90°=180°.因为BE,DF分别分∠ABC和∠ADC,所以∠ABC=2∠1，∠ADG=2∠2.所以2∠1+2∠2=180°.所以21+∠2=号×180°=909(2)设多边形的边数为n,则(n-2)×180°=2×360°+360解得n=8.所以(8-2)×180°÷8=135°，即这个多边形的每个内角都是135°23.（1)因为ADLBC,BD=ED,所以AB=AE.所以∠D1E=2∠BME=20°，∠AED=90°-∠DAE=70°.因为EF垂H分AC,所以AE=CE.所以∠EAC=∠C,且∠AED=∠EAC+∠C=2∠C=70°.所以∠C=35.(2)因为△ABC的周长为18cm,AC=6em,听以AB+BG=18-6=12(cm).因为AE=CE.所以△ABB的周长=AB+B+AE=AH+BE EC=AB+BC=12(cm).24.（1)因为△ABC为等边三角形，所以∠ABG=60°.因为D为AC的中点，所以DB分∠ABC所以∠DC=30因为∠PDQ=120°，所以∠P=180°-120°-30°=30所以∠DBC=∠P.所以DB=DP(2)过点D作DBC交AB于点I.因为△ABC是等边三角形，AC=8,D是AC的中点，所以AD=CD=4,∠B=∠C=∠A=60°，BC=AC=8.因为DI∥BC,所以∠ADH=∠C=60°，∠AHD=∠B=60P.所以∠ADH=∠AHD=∠A=60所以△A)/是等边三角形，所以AD=HD=AH=4.所以IID=CD=BI=4.因为∠Q0P=∠H1DG=120P,所以∠QDH=∠PDC∠(OHDH=∠PDC,在△QDI和△PD中，HD=CD,∠(01110=∠C所以△ODH≌△PDC(ASA).所以HQ=CP:所以BQ+BP=BH+HQ+BP=4+BP+CP=1225.（1)选择方法证明如下因为AD分∠BAC,所以∠BAD=∠CMD,AB=AE.在△BAD和△EAD中，∠BAD=∠EAD,AD=AD.所以△BAD≌△AD(SAS).
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基础题与中考新考法·七年级·上·数学1.5有理数的乘方为122500.1.5.1乘方12.9【解析】由题意可得a-2=0,b+3=0,所第1课时有理数的乘方以a=2,b=-3,所以b=(-3)2=91.A13.解：原式=-2023×2023+3×202320234-2023×202342.1(3)【解析】根据乘方的概念可知-（-2023+3)×20234(1-2023)×20234)的3次幂应写成（一子(--2020-2022易错点拔1010负数的乘方，在书写时一定要把整1011个负数用小括号括起来，(-a)”与-a”是14.解：(1)<，<，>，>，>；不相同的，(-a)”表示(-a)·（-a)·…【解法提示】因为12=1,2=2，所以12<2；(-a),-a”表示-(a·a·…·a)因为23=8,32=9，所以23<32；因为34=81，同步课43=64,所以34>43；因为45=1024,54=625，2.22,4,-(2×2×2×2)所以45>54；因为56=15625,65=7776，所以3.D4.B分56>6.5.1-15.2-15.3-1;-1;1;-1练(2)当n≤2时，n<(n+1)";6.解：(1)216；(2)0；(3)0.25；(4)256；当n≥3时，n>(n+l)";第(56(6号(3)因为2023>3，章7.D所以20232024>202420238.解：第一次转发后接收到短信的人数为所以-20232024<-20242023」2个，15.解：(1)：【解法提示】由题图可得，部分①第二次转发后接收到短信的人数为22个，第三次转发后接收到短信的人数为21.11的面积是4，部分②的面积是4×416？个，…所以当转发完4次后，接收到这条短信的人部分③的面积是↓×1-1y.,阴影部分的面16464数为2+22+23+24=30（人）19.B【解析】m个3相乘可记为3m,n个2相积=部分③的面积=64加可记为2n,所以原式=3m+2n(2)333，,311+…十10.C【解析】A.(-2)3=-8,（-3)2=9,不符4T166449s1、11-4+(416)+合题意；B.(-2)3=-8,2=8,不符合题意；11、C.(-2)3=-8,-23=-8,符合题意；D.(-2)4=16,-24=-16,不符合题意16.C【解析】由题意可知，7×7×7×7×7×711.122500【解析】由表中数据可得，底数的=76小数点向左（右）移动一位，方数小数点第2课时有理数的混合运算向左（右）移动两位，所以3502的值1.D2.C3.A14万唯七年级QQ交流群：688570199
y/2sin6x+孕y=h0:y=t118.(1)如图所示：作AB中点O,连接OC,OA,B:AA=AB,∠BAA=60°，DABA是等边三角形，∴AB⊥OA又：C4=4,AB=25,CB=27,满足CA2+AB2=CB2,即有A,B,⊥AC,而AB∥AB,所以AB⊥AC,OA∩AC=A,OA,ACc面AOC,.:AB⊥面A,OC,而OCc面AOC,所以AB⊥OC,又因为O是AB中点，所以CA=CB(2)若CA=4,则0C=√4-52=3，易知04=3，以点O为原点，分别以OA,OA方向为x,y轴，以过点O竖直向上的直线为z轴建立空间直角坐标系，如图所示：
1试题)
1.Which of the following companies rates highest?A.Allied.B.American Van Lines.C.International Van Lines.D.North American Moving Services.2.What is the advantage of American Van Lines?A.It gives pricing information online.B.It is experienced in packing expensive items.C.It has moving containers for interstate moves.D.It guarantees the lowest price of the same service.3.What do the four companies have in common according to the text?A.They feature highly skilled movers.B.They have over 80 years of experience.C.They can provide moving services nationwideD.They can offer services for customized packing.BIn 2014,Mahoney performed an act of kindness as part of a Facebook challenge.She picked a79-year-old senior named Wagner,who regularly gave back to the community.Mahoney wanted toknow Wagner better,so they spent a day together,picking up groceries and getting their nails done."It was the first time in years that someone had made a day about her,"says Mahoney.Their shared experience got Mahoney thinking.How many other seniors might benefit fromdedicated attention?She came up with a plan:find local seniors with long-time dreams and work tofulfill their wishes.She named the new charity:We Are Young,or WAY for short.Seniors can nominate (themselves or be nominated by someone else;wishes are thenassessed by a community committee that looks at factors such as age-related physical barriers,socialisolation and financial need.Melanie nominated her husband,78-year-old Victor,to go rockhounding,a hobby he'd given upwhen it became too physically difficult to access the bay where he hunted for geodes ()Theteam at WAY hired a boat for him and his son so they could reach the bay and search out geodes onthe beach."Now,Victor has regained his self-confidence and is willing to take on new challenges.Wewant to show that anything is possible with the support of others,"says Mahoney.Up to now,WAY has delivered on 41 dreams,ranging from a helicopter trip over a childhoodblueberry-picking spot to travelling to Toronto to watch a Blue Jays game.While her charity operatesonly in Nova Scotia,Mahoney has her own dream.Each WAY wish is recorded on video,and shewants people watching to be inspired to fulfill a wish for a senior in their own community."We wantto create a national movement that shifts how we as a society view,value and support seniors,"saysMahoney."That is the impact we're trying to create."英语试题第3页共10页
学方法报湘教七年级B国内统一连续出版物号：CN14-0706/(F)数学周刊参考答案第5期2023年11月07日第13期参考答案第1课时数据的收集与抽样第5章数据的收集与统计图(5.1~5.2)同步诊断自主学：抽样调查一、选择题课堂探究：例140%例2C1.C2.D3.B4.B5.C6.C即学即练：1.D2.C3.D4.D5.B6.D二、填空题7.全面调查7.折线8.全面调查9.样本选取不合理8.解：总体是该市七年级学生的视力状况；个体是该市每10.A酒店营业额逐月稳定上升名七年级学生的视力状况：样本是抽取的1000名七年级学生11.80012.30的视力状况：样本容量是1000.三、解答题9.(1)抽样调查.(2)抽样调查.(3)全面调查.13.解：(1)采用的是抽样调查.第2课时统计图(2)总体：七年级400名学生的视力情况；自主学：折线扇形条形条形扇形折线样本：抽取的80名学生的视力情况；课堂探究：(1)抽查的样本总人数为14÷28%=50，等级B的个体：该校七年级每一名学生的视力情况：人数为50×40%=20，补全条形统计图略样本容量：80.(2)等级D所在扇形的圆心角的度数为360°×4=28.8°14.(1)抽样调查300即学即练：1.B2.A3.D4.D5.A6.60°(2)喜欢收听易中天《品三国》的学生最多，7.乙3620甲15.解：(1)选择交通监督的人数是12+15+13+14=54（人）.8.解：(1)调查的总人数为20÷40%=50，则b=50×8%=4,a=选择交通监督的人数占调查人数的百分比是，54××100%=20050-20-16-4=10.27%.2360×072扇形统计图中交通监督所在扇形的圆心角度数是360°×答：表示“比较熟练”的扇形部分的圆心角的度数为72°、27%=97.2°.9.解：(1)国庆期间物华超市4日的营业额最高，蓝天超市(2)D班选择环境保护的学生人数是200×30%-15-14-16=1日的营业额最低15(人).补全折线统计图如图所示：(2)蓝天超市3日、7日的营业额超过了物华超市，6日的营个人数（人）业额和物华超市最接近.16----·一环境保护15·交通监督14(3)蓝天超市国庆节期间的营业额整体呈现先升后降的1312趋势；物华超市国庆节期间的营业额整体呈现先升后降再升最后降的趋势0A BC D班级
g(x)=3x2-2x-1=(3x+10x-1,g0=3x+1x-1）=0,x=-l,…7分列表如下：1(1,2)233g(x)00+单调递增极大值单调递减极小值-1单调递增28(x)7…11分所以g(x)的值域为[-1,2].…12分19.(本题满分12分)解：(1)f(x)是R上的奇函数，.f(0)=0.1+k=0.k=-1,经检验k=一1符合题意。…3分0=a-a气即2a2-3a2=0.解得a舍，0=2.5分》2故a=2,k=-1.(2)3x∈使得f(2x2)<-f(1-mx),即f(2x2)
Part 3 /Using Language Assessing your ProgressCOLLECTIONS1.cross the whole country by railL.用括号内所给单词的适当形式填空。详情请参考2.take a boat ride out into the bay1.Astonished (astonish),I realized that the boys had also3.take a pleasant hike in a forest4.take a coach bound northrecognized what the gesture meant.5.the most awesome journey2.It was a misty (mist)morning,so I didn't drive to work.6.看到种类繁多的生物3.In that experiment,volunteers were asked for their案解析一7.向东南方驶去opinions about a series of advertisements(advertisement).8.持续…4.My father is one of the most famous9.继续下一段旅程photographers(photographer),and he has won many10.游览这个城市national prizes for his photos.11.take sb's breath away with its exceptional beauty5.Our language is filled with.idioms (idiom)whick may12.beautiful cobblestone streets③make no sense to you if you haven't learned them.13.古老的砖建筑14.蒙特利尔的红枫叶山根据汉语提示补全下列句子，每空一词。l5.be typical of.…1.Contrary to(与…相反)the16.a short distance awayexpectations of their parents,the children behaved17.a bunch of farmsbravely in the hiking18.in an urban area2.Lily sat down and proceededto详情请参考19.all in alltell(进而告诉)me about her skiing holiday20.have a few hours to kill3.In the TV interview,the coach owedthevictoryto_(把胜利归功于)the team spirit..4.Incontrastto(与…形成对比)案解析21.站在远处22.驶过23.有空做某事her elder brother,Mary is always considerate in her24.与…形成对比treatment of others.25.说英语有口音5.Many cars and trucks rolledby(驶过26.一个拥有绝妙风景和声音的城市gbut no one gave us a lift.本期报纸其他版块参考答案1版详情请TOPIC READING4版①对于那些想要品尝这座城市最美味菜肴的人来说，蒙特利尔举世闻名的美食界将是一个巨大详情请参考答案解析完形填空1-5 BDCAB 6-10 ADCBD的吸引力。11-15ACDBC答案解析②即使你没有计划，仅仅在风景优美的鹅卵石街道上漫步也是值得的。阅读理解1-4 CBDALISTENING PRACTICE阅读填空1-5 BCABC6-10 ABABA1-5 DGCBF11-15 BABAC16-20 ACBCA摩豆2版MIND MAP1.from Vancouver to Toronto详情请参考答案解析2.the massive mountains and forests of Canada3.took their breath away with its exceptional beauty4.bound for Jasper5.spectacular mountain peaks and forests and manydifferent creatures6.Canada's huge oil and gas drilling industry7.many shopping malls8.they travelled through the night9.a land of forests and lakes10.Lake HuronINTO THE TEXTSAB详情请参1.enjoying1.proceeded2.an2.astonished3.to take3.which答案解析4.where4.had moved5.its5.with6.creatures6.talking7.stops7.were8.to8.an9.truly9.themselves10.that10.happily2
第二节（满分25分） 阅读下面材料，根据其内容和所给段落开头语续写两段，使 之构成一篇完整的短文。 Mr Dawson was an old grouch,and everyone in town knew it.Kids knew not to go into his yard to pick a delicious apple. Old Dawson,they said,would come after you with his gun. One Friday,12-year-old Janet was going to stay all night with her friend Amy.They had to walk by Dawson's house on the way to Amy's house,but as they got close,Janet saw him sitting on his front porch and suggested they cross over to the other side of the street.Like most of the children,Janet was scared of the old man. Amy said not to worry.Mr Dawson wouldn't hurt anyone.
【答案】 I have some good news for you,Simon.Some volunteer volunteers from all over the world are needing for the Olympic Winter needed Games in Beijing.The following is some requirements you are should meet.To be A Olympic volunteer,you must have a good an command of Chinese and English.Since you have been learning Chinese in America,you have an advantage over others in lan- guage.Beside you are enthusiastic,optimistic and active,that Besides which satisfies the demands for volunteers well.You will definitely de-
19.(12分)如图，四棱锥P-ABCD中，底面ABCD是行四边形，AB=1,BC=2,∠ABC=60,PC⊥CD,M为棱PA的中点.(1)证明：PA⊥CD;A0-09(2)若PA1AC,二面角P-CD-A的大小为60°，求直线MD与面PCD所成角的正弦值，(乃)y.120.(12分)已知在面直角坐标系x0y中，抛物线C:)2=2px(p>0)的焦点为F,过点P(0,3)的直线l与C交于A,B两点，且tan∠PF0=3.(1)求C的标准方程；(2)已知E为x轴上的点，直线EA与C的另一个交点为M,直线EB与C的另一个交点为N,当直线MN的斜率为1时，求点E的坐标。y=-3X+3X年719%4X99X-22121.(12分)已知函数f(x)=e-ax-lnx-1.(1)当a=e-1时，求f(x)的单调区间；心7mtXN≥2.(2)若f(x)存在零点，求实数a的取值范围。x:e=mx)x-(e-0'Inx100Xn汁e)哦Xexes mxe'x)mxexthx feInxr alnee'x+元0exalne"=x+mx +hx.22.(12分)现有甲、乙两个不透明盒子，盒子装有2个红球和2个白球，乙盒子装有4个白球，这些球的大小、形状、质地完全相同，在一次球交换过程中，从甲盒子与乙盒子中各随机选择1个球进行交换，重复几次这样的交换过程后，甲盒子里装有红球的个数为X(1)求X2的概率分布及数学期望；(2)求P(X.=1).PlXn+60ED用1甲堂材4奇(四@x烟+和动+数收x②包②甲冰X()
【答案】1.of2.annoyed3.who/that 4.(should)be taught 5.which 6.Apparently 7.how 8.in 9.Whether 10.changing
less compared with migratory(迁移的)animals such as birds. "It's an insight into how they build up their picture of space, adds Richard Holland,a biologist at Bangor University who studies bird navigation. There were already indications that dogs-like many ani- mals,and maybe even humans-can sense Earth's magnetic field.In 2013,Hynek Burda,a sensory ecologist at the Czech U- niversity of Life Sciences Prague who has worked on magnetic re ception for 3 decades,and his colleagues showed dogs tend to o- rient themselves north-south while excreting ()Because this behavior is involved in marking and recognizing field,Burda reasoned the line-up helps dogs figure out the location relative e to other spots.But fixed line-up isn't the same thing as navigation.
答案：61.it62.easily63.to please64.a6 65.pushed 66.where 67.choice 68.pipes 69.at 70.was informed
【答案】56.on57.whose58.to use59.interesting 60.have learnt/learned 61.newly 62.Known 63.was invented 64.the 65.appreciation
答案：61.cools62.Unluckily63.to make64.named 65.keeping 66.was forced 67.which 68.himself 69.it 70.the
【答案】l.criminal2.with3.be converted4.frightening 5.trying 6.simplified 7.sounds 8.making 9.variety 10.since
will be rude later on. Once infected,we are more aggressive, less creative and worse at our jobs.The only way out is to make a conscious decision to do so.We must have the courage to call it out,face to face.We must say,"Just stop.For Winston,that would have meant approaching the woman,telling her that her conversation was frustrating other passengers and politely asking her to speak more quietly or make the call at another time. The anger we feel at the rude behavior of a stranger can drive us to do out-of-place things.Research discovered that the acts of revenge (people had taken ranged from the ridicu- lous to the disturbing.Winston did shine a spotlight on the woman's behavior-but in a way that shamed her. When we see rudeness occur in public places,we e must step
tower struck two when she arrived. (Text 3) W:Do you have something to write with?How am I supposed to sign my name?Can I use a pencil? M:No,we lost our electronic pen.It doesn't matter,though. You can use your finger to sign right on the screen. (Text 4) M:You look sad.What's the matter with you? W:I went hiking yesterday.The mountains and the weather re- minded me of my hometown. M:I'm sorry to hear that.Why not give your family a call? (Text 5) M:I didn't see you last night at the office.Are you OK?
1、2024年衡水金卷先享题 分科综合卷[新教材]语文(一)1试题
名师导学·高考二轮总复·语文（学生用书）利于孩子形成规律稳定的睡眠周期，刺激人体分泌更也更加陡峭。为了安全着陆，嫦娥四号采取的是近乎多的生长激素，能更高效地帮助孩子长高。对于那些垂直的降落方式。睡得
2、2024年衡水金卷先享题 分科综合卷[新教材B]语文(一)1试题
13.(1)(窦宪)让（梁讽）先带上财物出使北单于，宣扬国亲自率领七八千骑兵迎战，包围梁懂。梁懂披甲奔驰出家的威德，有一万多人归附。(“赍”“宣”各1分，省略击，所攻之处敌人皆溃败，匈奴于是引兵回到虎
3、2024年衡水金卷先享题 分科综合卷[新教材]语文(一)1答案
村”。这一思想的主旨在于将现代工业文明的因子引入3.根据材料内容，下列各项中不属于费孝通学术贡献的传统乡村，在此基础上对传统乡村的各种因素进行重组、一项是整合，调动农民潜在的创造性和积极性，通过链式反
4、2024年衡水金卷先享题 分科综合卷[新教材]语文(一)1答案
村”。这一思想的主旨在于将现代工业文明的因子引入3.根据材料内容，下列各项中不属于费孝通学术贡献的传统乡村，在此基础上对传统乡村的各种因素进行重组、一项是整合，调动农民潜在的创造性和积极性，通过链式反
5、2024年衡水金卷先享题 分科综合卷[新教材B]语文学(一)1答案
译正确各1分，大意正确2分)【参考译文】夏季四月癸已日，后周昭义节度使李筠发兵起事。起初，皇帝刚刚登位，派遣使节升李筠任中书令。使节到达潞州李筠想要拒绝使节的任命，幕宾佐吏直言劝谏（不可违抗皇命)，他
1、2024届衡水金卷先享题 分科综合卷 全国乙卷 英语(一)1试题
2、2024年衡水金卷先享题 分科综合卷 全国甲卷 语文(一)2试题
1、2024年衡水金卷先享题 分科综合卷[B]语文(一)1试题
”分別描绘了鸟儿月夜悲啼和沙洲飞旋的画面。(3)《岳阳楼记》中“。”两句借描绘日、星、的情状，侧面描写洞庭湖的
3、2024年衡水金卷先享题 分科综合卷[新教材]英语(一)1答案
第40期参考答案A)在下列每小题内，你将听到一个或两个句子W:Hmm,I like oranges too.But I never eatIn the afternoon,he'll go to th
4、2024年衡水金卷先享题 分科综合卷[B]语文(一)1答案
(二)实用类文本阅读（本题共3小题，12分）阅读下面的文字，完成4一6题。险事实。目前，对于导致冰面低摩擦系数特征的机制科学界尚无定论。冰是水的固态形式，其最显著的特征就是表面异常的“滑”，即冰面摩擦
5、2024年衡水金卷分科综合卷 老高考英语三全国二卷
【答案与解析】 受跆拳道的启发，Grace创立了Kickin'Violence,教年轻人正 确认识暴力、对抗暴力，并在学校成立了俱乐部，帮助学生找到他 们的兴趣。 1.D7 根据第3段可知，刚开始的时
1、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
舍为第12期数列求和，数列的综合问题①高考链接1.C解析：数列{a。}为等差数列台an=am+b台Sn=差n(a+b+am+b）,S。11故2分n2m+2(+2b)为等差数列，所以甲是乙的充要条件故选
2、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
1、2024届全国高考分科调研模拟测试卷(二)2数学(XGK)试题考试试卷
口彩▣高一同步周测卷/数学4.第24届冬奥会于2022年02月04日~2022年02月20日在我国
3、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
1、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
2、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
舍为第12期
4、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
1、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
1、2024届全国高考分科调研模拟测试卷(二)2数学(XGK)试题考试试卷
口彩▣高一同
5、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
24.(8分)如图，四边形ABCD是行四边形，对角线AC、BD相交于点0，点E、F分别在AB、AD上，AE=AF,连接EF,且AC⊥EF.(1)求证：四边形ABCD是菱形：(2)连接OE,若点E是A
1、2024年衡水金卷先享题 分科综合卷 全国甲卷 语文(一)2试题
1、2024年衡水金卷先享题 分科综合卷[A]语文(一)1试题
C.郭元帅与足下有旧/闻足下军乏食/他敌欲来攻特遣吾相报能相从/即与俱往/否则移兵避之郭元帅与足下有旧闻/足下
2、2024年衡水金卷先享题 分科综合卷 全国甲卷 语文(一)2试题
1、2024年衡水金卷先享题 分科综合卷[新教材]语文(一)1试题
名师导学·高考二轮总复·语文（学生用书）利于孩子形成规律稳定的睡眠周期，刺激人体分泌更也更加陡峭。为了安
3、2024年衡水金卷先享题 分科综合卷[新教材A]语文学(一)1试题
中文化2021~2022学年度高三年级密卷考试材料三先秦时期，语文（二）成后与王子期比赛，可是何心尽力教他。王子期不惯(满分150分，考诚时间150分钟王子期所言指的是赵襄子调，而这一点恰是驾车最一、
4、2024年衡水金卷先享题 分科综合卷[无角标]语文(一)1答案
却有胸治性情的功效。心里印者美的意象，常受美的意象浸润，自然也可以少存些浊念。苏东坡诗说：“宁可食无肉、不可居无什：无肉令人瘦，无竹令人俗，”竹不过是美的形象之一种，一切头的事物都有不令人俗的功效」(
5、2024年衡水金卷先享题 分科综合卷[新教材A]语文学(一)1答案
录太常博士。母服阁御史中丞石豫荐之，召赴阙道除左司速。时方究蔡邸狱，正夫入对，微宗语及之，徐引淮南“尺布、斗栗”之谣以对。帝感动，解散其犹，待蔡王如初。他日，谓正夫曰：“兄弟之间，人所难言，卿独能及此
(一)1答案)
在一个不透明的口袋中装有大小、形状完全相同的9个小球，将它们分别编号为1,2,3，…，9，甲、乙、丙三人从口袋中依次各抽出3个小球.甲说：我抽到了8号和9号小球；乙说：我抽到了8号和9号小球；丙说：我抽到了2号小球，没有抽到8号小球.已知甲、乙、丙三人抽到的3个小球的编号之和都相等，且甲、乙、丙三人都只说对了一半.给出下列四各结论：①甲抽到的3个小球的编号之和一定为15；②乙有可能抽到了2号小球；③丙有可能抽到了8号小球；④3号、5号和7号小球一定被同一个人抽到其中，所有正确结论的序号是【答案】①②④【解析】编号为1,2,3，，9的小球所有编号之和为1十2+…十9=9X)十9》=45，因为甲、乙，丙三人抽到的32个小球的编号之和都相等，所以每人抽到的3个小球编号之和为15，故①正确，依题意，由甲和乙的表述可知，甲和乙一人抽到了编号为8的小球，一人抽到了编号为9的小球，则丙所述没有抽到8号小球是正确的，故乙没有抽到2号小球，若甲抽到了编号为9的小球，乙抽到了编号为8的小球，设甲抽到的另外两个小球的编号分别为a1,a2,乙抽到的另外两个小球的编号分别为b1,b2,则a1十a2=6,b1十b2=7,所以a1,a2的取值只有1和5,2和4两种情况，当甲抽到的编号为1和5的小球时，乙只能抽到编号为3和4的小球，此时丙只能抽到编号为2,6,7，与条件矛盾，所以甲抽到编号为2与4的小球，则乙抽到编号为1和6的小球，所以甲抽到编号为2,4，9的小球，乙抽到编号为1,6,8的小球，丙则抽到编号为3,5,7的小球.同理，也可以是甲抽到编号为1,6,8的小球，乙抽到编号为2,4,9的小球，而丙则抽到编号为3,5,7的小球，故②正确，③错误，④正确.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)已知之1=4，之2=4i,之3=一2十4i,之4=一4十3i,则以上四个复数对应的点是否在同一个圆上？(2)设w=-号-号i,求w2,w2,1+u十a2+w3+…十w2.解：(1)由题意，复数之1=4，之2=4i,之3=一2+4i,之4=一4十3i,根据复数的几何意义，可得复数对应的点分别为Z1(4,0),Z2(0,4),Z3(-2,4),Z4(一4,3)，设经过三，点Z1(4,0),Z2(0,4),Z3(-2,4)的圆的方程为x2十y2+Dx十Ey十F=0,16+4D十F=0,可得16+4E+F=0,解得D=2,E=2,F=一24，4+16-2D+4E+F=0,所以圆的方程为x2十y2+2x十2y一24=0，即(x+1)2+(y+1)2=26,其中点Z4(一4,3)不适合圆的方程，即点Z4不在圆上，所以四点Z1,Z2,Z3,Z4不共圆.i=-1+342+2i,w-ww-(+()=-1i,w6=1,…,13.13.可得w3+1十w3+2十w3+3=0,且w”是以一2一i,一2十？i,1为周期循环，以1十u十w2+u3+…+w2=1+0X7+u=1-号-2i=2-18.(12分)已知函数f(x)=log2(x十2)，a,b,c是互不相等的正数，且a,b,c成等比数列，试判断f(a)十f(c)与2f(b)的大小关系，并证明你的结论。解：取a=1,b=2,c=4,则f(a)+f(c)=f(1)+f(4)=log23+log26=log218,2f(b)=2f(2)=2log24=log216,·78·
1、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
1、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
1、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
1、2024届全国高考
2、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
1、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
1、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
1、衡水金卷先享题20
3、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
舍为第12期数列求和，数列的综合问题①高考链接1.C解析：数列{a。}为等差数列台an=am+b台Sn=差n(a+b+am+b）,S。11故2分n2m+2(+2b)为等差数列，所以甲是乙的充要条件故选
4、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
5、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
1、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A
1、2024届全国高考分科调研模拟测试卷(二)2数学(XGK)试题考试试卷
口彩▣高一同
【解标】对于A,设P(x,y)(z<0),则-b(后-，国为A(-a,0),A:(a,0),直线PA1与PA:的斜率之yyy2 62积等于3，所以%·kp4,=。·’。=”a-=3,得离心率e√1+名=2，=2,故A错误；对于B,因为e=后=2，所以c=2a,而P为双南线左支上的一点，根据双由线的定义可得1PF,一PF=2a又周为PF,⊥PF,且SAeg,=3,所以SAe-号PF·PF=3,则PF·PF,=6,由PF,P+IPF,(2c)2,可得(PF1-|PF21)2+21PF1l·1PF21=4c2,即4a2+12-16a2,解得a=1,故B错误；对于C,如图，设PF,的中，点为O1,0为原点，则00，为△PFF,的中位线，所以00，=2PFl=2PF+2a)-2PF,十a,时以线授PF,为直径的国，园心为0，半径=2PF,以线段AA:为直径的圆，国心为0，1半径=a,所以00-PF,十a=7,+r,故两个国外切，故C正确；对于D,因为点P,到C的-条浙近线的距离为√5，所以b=√3，又由前面的推理可知=3，所以a=1,故C的实轴长为2a=2,故D错误.012.已知抛物线y2=16x,过点M(2,0)的直线交抛物线于A,B两点，F为抛物线的焦点，若|AF|=12,O为坐标原点，则四边形OAFB的面积是展个一出A.20√2B.10√2C.52D.5V22家】【答案】A【解析】抛物线y2=16x的准线方程为x=一4，设A(x1,y1),B(x2,y2),由抛物线的定义可知，x1十4=12，得x1=8,yi=16X8,由抛物线的对称性，不坊令y=8巨，设直线AB的方程为x=my十2，由区=m+2”得y2=16x,y-16my-32=0,6>0,则1-=-32，片以2=-2，E,四边形0AFB的面叔5=20F1·y,-yl=名×4×10区=20E*数学中有许多寓意美好的曲线，曲线C:(x2十y2)3=4x2y2被称为“四叶玫瑰线”（如1v单图所示)给出下列三个结论：出灰因①曲线C关于直线y=x对称；②曲线C上任意一点到原点的距离都不超过1；○③存在一个以原点为中心、边长为√2的正方形，使曲线C在此正方形区域内（含边界）】其中，正确结论的序号是A.①②B.②③c.①③D.①②③【答案】A【解析】对于①，用(y,x)替换方程中的(x,y),方程形式不变，所以曲线C关于直线y=x对称，故①正确；对于。95·
