数学考点精讲

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22ÕÖ%×ᨵᱯÙÚÛÜGÝᳮḄßà&P஺ÕÖáᳮᑖâᐰÕÖáᳮºâᐰÕÖáᳮ^×.ºâᐰÕÖáᳮä᪷åÚᱥÆḄæᑖçèᐹᨵḄᐳëឋìáíîåÚᱥᐰïðᐹᨵḄឋìñ×áᳮ&PᙠᦪÔáᳮòÄÆ%ºᐕôḄ஺âᐰÕÖáᳮ%ᙠὃöåÚᱥḄᐰæçè÷ÕÖøòᩭ஺ᦪÔÕÖP%ᵨᩭÄúûüýᯠᦪᨵᐵḄᦪÔÿ⚪Ḅᳮᙠᦪ⚪ᨵḼḄᵨ஺⌴ḄᦪḄ⚪ᙠn=1(ᡈn())&ᡂ()⌴Ḅ*Ạ,-Ꮇ/ᙠn=k&⚪ᡂ(1n=k+1&⚪3ᡂ()4▲⌴67Ḅᳮ89ᑨ;⚪Ḅ<=ឋ?ᔲᵫᱯCᑮEF▭HI⚪Ḅ<=ឋJẚLᨵ▲Mᑮ4▲஺)NOPᑗRᐵTUVWᡂL)NXVY;Z“\]^_ᯠᦪ(ᡈn>nJLn€N)gh<=”஺ᵫ)NVYjkᦪlm0ᵫ⌴FnlmḄopWᐰlm஺rᵨᦪlms⚪&ᐵtn=k+1&⚪ᡂ(Ḅu⌕ᐹᨵx᪗z{|z}ᨬ⌕MᑮḄ⚪x᪗ᑖ᪆Yu=Z⚪ḄᔣI⌲ᨬFnx᪗Wᡂ⚪஺rᵨᦪlmVY6ᑡs⚪}_ᯠᦪnᨵᐵḄឤஹᦪUஹUஹᦪᑡs⚪ஹ^s⚪ஹ᦮◀ឋs⚪஺Iஹ1nឋ⚪1.ᵨᦪlm(n+l)(n+2)...(n+n)=2",1•2.“(2n-l)(n€N),¤“kᑮk+1"¥¦◤¨Ḅᦪ©2k+3A.2k+1B.2(2k+1)C.------D.k+1k+\2.ᵨᦪlm1+,+'+...+—'—l)&,ᵫn=k(k>l)Uᡂ232"-1(n=k+l&¥±²³ḄᦪḄᦪ஺A.2*-1B.2k-1C.2*D,2*+13.¶⚪}_ᯠᦪnᨵᐵ·n=k(k6N)&¹⚪ᡂ(º»V¼n=k+l&¹⚪3ᡂ(஺n½¾¿n=5&¹⚪Uᡂ(º»V¼஺(94ÃHÄÅὃ)A.¿n=6&¹⚪Uᡂ(B.¿n=6&¹⚪ᡂ(C.¿n=4&¹⚪Uᡂ(D.¿n=4&¹⚪ᡂ(4.ᦪᑡÇa"ɽ¾a,=1,¿n>2&a“=a,—+2n-1,8ÊËÌa2ஹa»Î,3ÏÐa„Ḅ⊤M—A.3n-2B.n2C.3"TD.4n-35.ᵨᦪlm3Ô+22n+l(n£N)?Ö14᦮◀¿n=k+1&\p×+534(&+i)+2+52(&+1*ØÙ©.6./kÚÛᨵf(k)\☢ᑣk+1ÚÛ\☢Ḅᦪ©f(k+l)=f(k)+஺

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54জ.ÞÔdḄ0àঝ.ᢣjSãS.....SnÂä*ᨬᜧXåæÊᳮᵫ஺2(92éᐰëìὃ)ூᑖ᪆௃জᑭᵨÞa”`S“ïXð᧕,dḄàঝᑭᵨS“.nḄñ§ᦪX7S“Âä*ᨬᜧXvᡂñ§ᦪÂn9ò^S“0ᨬᜧḄ§ᦪᨬ⚪஺ூ,௃জᵫa3=a]+2d=12,yᑮa=12-2d,ᡠe(S=12a,+66d=12(12-2d)+66d=144+42d>0,l2S=13a,+78d=13(12-2d)+78d=156+52d<0.|324,y:——ᙢ@ᵨஹBᝯḄDᔠFGHIJKLMḄNOឋஹQRឋ஺S⚪ḄTUVWXY0ஹa“+]<0ᓽaᵫdீ0"⍝a]>a2>…>a”ᵫS13=13a<07na7<0,ᵫSn=616+a7)>0na6>0஺ᡠᙠStS.....SnuS$Ḅwᨬᜧ஺2z4.᝞}ABXᙊ0ḄPAᚖᙊ0ᡠᙠ☢CXᙊᕜUNBAC9,PA=AB=2r,<☢PBACḄ஺ூᑖ᪆௃☢PBACḄᡂ

552rsin~02rsin஺ᓽ³x=´´µMDᨬw/·¸☢Ḅ஺l+sm971+sin20ூº௃S⚪Bᙠ+%»¼½u“☢Ḅ”ᡂ“<☢¸¾¿Ḅᨬw”À%ᔠ〉Ḅ#+⚪ᡂÂᦪuḄ“ᦪ⚪”஺UÃᙢÄ<ᨬᜧwஹᨬwḄÅ▭⚪ᐜ+ᦻÉÊ4ËᓄᡂᦪIÌÍÎÏ$%ᦪIÐÑᦪᐵ)'ᯠÎᑭᵨᦪឋMஹÒ⌕Ó&'ᨵᐵ"Õ,-Ö஺×᝞ÏØឋ⚪ÙÚ8⚪ÜXᐺÑḄzÞ஺z5.à"aABCáᑁãAஹBஹCḄᜧᡂ&äᦪᑡJLtgAtgC=2+75,ç"⚔CḄÄécḄë&46?tgA@tgCḄABCD⚪ᑮ'E஺G6.H(z-x)'-4(x-y)(y-z)=0,>PQxஹyஹzᡂTUᦪᑡ஺ூᑖ᪆௃Z[⚪B\]^_+ᑨabb?-4ac=0ḄdbBeὶgᑮ᪀⌼5j5ᐗlm<=no>'஺ூPp௃qx=yrBsx=z,,x,yஹzᡂTUᦪᑡtqx#yrB<=(x-y)t2-(z-x)t+(y-z)=0,ᵫ/=()t]=t2Bw᧕xt=l+<=Ḅ᪷஺y-Zt.,t=-----=1,ᓽ2y=x+z,{.xஹyஹzᡂTUᦪᑡ?-x-yூ"௃5|ᙢB⚪ᩩ~1᝞ᐹᜓᡈd᦮ᳮᐹᜓ"X]+X?=aஹx,-x2=b”ḄdbBᑣsᑭᵨ᪷ᦪḄᐵ᪀⌼<=t᝞ᐹᜓb?-4ac0ᡈb?-4ac40ḄdbBsᑭᵨ᪷Ḅᑨab᪀⌼5ᐗlm<=஺4PQcosA-cosB-cosC<—஺

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57ᙠ'EÙTb(t)2"+(g)*+a>0ᙠx£×ឤᡂ;ḄD⚪rBsCᵨ“ᑖõ113Áᦪ”Qt=(/)r,t>—,ᑣᨵᡠḄÑAÓa3+a>-l஺ᐸ1ᨬᑮaḄÓB+ᑭᵨlmÔᦪᙠ÷øí×AùḄẆûBsüý4ᵨ“Ôᦪg”஺m.þÿឋ⚪1.sin2x=sinxᙠ(0,2n)ᑁḄᦪ_____஺A.1B.2C.3D.42.$%&'ᦇf(x)=|2ஹ-1],af(c)ுf(b),ᑣ஺A.a<0,b<0,c>0B.a<0,b>0,c>0C.2-a<2CD.2a+2C<23.$%&ᦪf(x)=log஺(x?-4x+8),xC[0,2]Ḅᨬᜧ?@-2,AUa=஺A.1B.1C.2D.4244.$CDEa஻GHᓃᓃᦪᑡKJLHj+a+a=18,a+a+a=-9,S=a1+a+...23234n2+a஻KRSlimS஻HU0/L8A.8B.16C.32D.485.HYᦪᑡEa஻GZKa=84,[n⚗]@S஻K$%S—O,S<0,ᑣ`n=aK4loS஻ᨬᜧ஺6.bUcd04p44Ḅᡠᨵhᦪp,ijHkx2+px>4x+p-3ᡂmḄxḄn?pA஺7.rᐵUXḄ|x2-6x+8|=aាᨵvjHh᪷KᑣhᦪaḄn?p8.$%xA(0,1)ஹBফ3)z{ᱥ}y=x?+mx+2,r{ᱥ}}ABUvxKhᦪmḄn?p஺9.$%hᦪXஹMஹzcdHkx+y+z=5]xy+yz+zx=3,zḄn?p஺10.$%Ig?-4Tg3-1g-=0,baஹcḄHZ⚗஺cbc11.aஹp>yᙳ@┦K2cos2a+cos2P+cos2y+2cosacos0,cosY=1,a+P+y7T

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80/A.[0,1]B.(1,2]C.(0,2)I).[2,+°°)ூ0௃2-ax/ᙠ[0,1]/ᦪᡠa>l,᣸◀ᫀAஹC;a=2,ᵫ2-ax>0xὃ⚪)#¥ᱥ§y2=4xḄᯖª«¬§¥ᱥ§®¯°±ªP³Q,µ¶§·PQ@ªḄ¸¹mº/A.y2=2x-1B.y2=2x-2C.y2=-2x+1D.y2=-2x+2ூ0௃O⌱FPᵫtuAu¸¹¼§Ḅ⚔ª¾(1,0),¿ÀᔣMᵫ᣸◀ᫀAஹC.I),ᡠ⌱B;y=Â+1ூÃ0௃¬ÄFPQ#ᯖªḄ¬§y=k(x-1),ᑣ<2ÆyPy-=4xx+xk2+2y2X——z7k2k2x2-2(k2+2)x+k2=0,@ªᙶ᪗ᨵÊ,Æky2=2x-2,⌱B஺k2+22y=^(--1)=-O⌱F〉Ï°WឋÐᡈ᧕¬Ä0Ḅ⌱4⚪஺Ò⚪Ó@ḄᩩSÔ°+ÕÖᐜ᪷`ØÙᩩSᙠ⌱4Ú@ÛTÜÝÞßàḄáᔲWã᪷`Ã+ÙᩩSᙠäåḄ⌱4ÚḄµÛTßà᪵⌲gO⌱¬ᑮTḄ⌱4஺çᱯEFஹè0FéCᔠêᵨ/0⌱4⚪ḄëᵨmF;<=>ὃ⌱4⚪@Gᓰ40%஺bஹìᐭFPîᔜÕ⌱4⚗⌲+ìᐭ⚪Qðñòᑨ*ḄmFnìᐭFóô¾ñõFᓽîᔜ⌱4Úᑖ÷«¾ᩩSøñõù⚪úêù⚪ᡂüḄ⌱4Úý/Ï⌱Ḅᫀ஺ᐔூE8௃(97=>ὃ⚪)ᦪy=sin(---2x)+sin2xḄᨬᕜ3A.—B.11C.2"D.42ூ௃ᐭ:f(x+#)=sin[---2(x+#)]+sin[2(x+—)]=-f(x),(2322f(x+IT)=sin[---2(x+n)]+sin[2(x+TT)]=f(x)஺ᡠ-.⌱B;31171ூ3௃456y=cos2x--sin2x+sin2x=sin(2x+,T=TT,⌱B஺ூ:9௃(96=>ὃ⚪)ABCD1Ḅᙊ┵GHᨬᜧJKᐸM☢OPQḄᙊRS஺TU

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