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CE45=25CE+3.CE=5CE=-8().RtACG,AG=CG2-AC2=(45)2-(3+5)2=4.GAGB=GDGC,4(AB+4)=2545.AB=6.RtABC,BC=AB2+AC2=62+(3+5)2=10.14.A(x1,0)B(x2,0),,x1x2ax2+bx+c=0.abc,x1+x2=-ba0,x1x2=ca0.ax2+bx+c=0,x10,x20.=b2-4ac0.b2ac.|OA|=|x1|1,|OB|=|x2|1,,-1x10,-1x20.,ca=x1x21,ca.a,,x=-1,0,a-b+c0,a+cb.abc,a+cb+12ac+1.,a+c2ac+1.(a-c)21,a-c1,ac+12.,a4,a5.b2ac251=25,b5.,a=5,b=5,c=1,y=5x2+5x+1.,a+b+c11.()2006:()(),.(6,36)1.(i)()A={a2+8|aN},B={b2+29|bN}.AB=P,P().(A)0(B)1(C)2(D)3(ii)(),n.n().(A)4,6,8(B)4,6,7(C)4,5,7,8(D)4,6,7,82.(i)()12,15,20,().(A)(B)(C)(D)(ii)(),x,3x-4y=12.().(A)y2=-12x(B)y2=12x(C)y2=-16x(D)y2=16x3.(i)()f(x)=1+x1-x,f1(x)=f(x).fn+1(x)=f(fn(x)),f2006(x)=().(A)x(B)-1x(C)1+x1-x(D)x-1x+1(ii)()P-ABCDABCD(ABCD82),PB,PB=3,APD=.sin=().(A)22(B)33(C)55(D)664.a=sin+tan,b=cos+cot,().(A)sin=ab-1b+1(B)cos=1-aba+1(C)tan+cot=(a+b+1)2+1-2ab(a+1)(b+1)(D)tan-cot=(a-b)(a+b+2)(a+1)(b+1)5.10032006().(A)1(B)3(C)7(D)96.abcR+,ab+bc+ca=108.abc+bca+cab().(A)6(B)12(C)18(D)36(9,54)7.(i)()M={1,2,,100},AM,A.A.(ii)(),().,23,13.().8.(i)()A(1,0),G(2,0).BC.(ii)()1S.S.9.(i)()sin+cos=252.tan-cot=.(ii)()f(x)=1sin2x+2cos2x0x2.10.y=|x2-3|y=2x+k,k.11.{an},nSn=12an+1an.an=.12.,9n.,,,n=.(20,60)13.(i)(){an}:an=4n-1(nN+)35,{bn}.b2006.(ii)()P:x2+y2=2xS:y2=4x,Pl,ABCD.ABBCCD,l.114.1,ABCD,PAB,PEAD,PFBC,PGCD,MPGEF.:ME=MF.15.mnkmn=k2+1,:abcdN,m=a2+b2,n=c2+d2,k=ac+bd.1.(i)C.9220075a2+8=b2+29,a2-b2=21,(a-b)(a+b)=21.a-b=1,a+b=21,a=11,b=10.a-b=3,a+b=7,a=5,b=2.P={129,33},2.(ii)D.4;,6;7;8(8).2.(i)B.112115120=543..(ii)D.3x-4y=12x,(4,0).y2=2px.p2=4,p=8.3.(i)B.f4n+1(x)=1+x1-x,f4n+2(x)=-1x,f4n+3(x)=x-1x+1,f4n+4(x)=x.,f2006(x)=-1x.(ii)C.PA=12+(3)2=2,PD=BD2+PB2=2+3=5.PAAD,sin=ADPD=15=55.4.B.sincos=acos-sin,sincos=bsin-cos,acos-sin=bsin-cos.,(b+1)sin=(a+1)cos,tan=a+1b+1,cot=b+1a+1.tan+cot=a+1b+1+b+1a+1=(a+b+1)2+1-2ab(a+1)(b+1),tan-cot=a+1b+1-b+1a+1=(a-b)(a+b+2)(a+1)(b+1).,(C)(D).tan=a+1b+1sin=a-tan=a-a+1b+1=ab-1b+1,(A).cot=b+1a+1cos=b-cot=ab-1a+1,(B)ab-1=0,cos=0,,tan.5.D.,1003n3n,34k,34k+1,34k+2,34k+31,3,9,7,20064n+2.6.C.S=(ab)2+(bc)2+(ca)2abcabbc+bcca+caababc=a+b+c=(a+b+c)23(ab+bc+ca)=324=18.7.(i)2100-296(15296).M4,13233343;M2100,,296,2100-296.(ii)1781.3130,,.,:.5135;41C1513423;32C25133232.,1781.8.(i)52,3252,-32.03D.|AG|=2|GD|,D52,0.BC,BDAD.B52,32C52,-32.(ii)12.,.,S34;,1,S12,12().9.(i)-8623.sin+cos=251+2sincos=225.,sincos=-2350,(sin-cos)2=1-2sincos=4825.,,sin-cos=435.tan-cot=sincos-cossin=sin2-cos2sincos=(sin+cos)(sin-cos)sincos=-8623.(ii)3+22.f(x)=cot2x+1+2tan2x+2=3+(2tan2x+cot2x)3+22.2tan2x=cot2x,cotx=42,.10.4,23.(1)y=2x+ky=-(x2-3)P(),2x+k=3-x2,x2+2x+k-3=00.,22=4(k-3).k=4.(2)y=2x+kQ(-3,0),0=-23+k.,k=23.11.n-n-1.a1=S1=12a1+1a1,a1=1a1.a10,a1=1,S1=1.n1,Sn=12an+1an,Sn-1+an=12an+1an,Sn-1=12-an+1an.+Sn+Sn-1=1an.Sn-Sn-1=an,S2n-S2n-1=1.{S2n},1.,S2n=n.,Sn=n.n1,an=Sn-Sn-1=n-n-1.n=1,.12.12.99.,,,,36.,,,,n=363=12,12.12,:(1,2,3),(4,5,6),(7,8,9);(1,4,7),(2,5,8),(3,6,9);(1,5,9),(2,6,7),(3,4,8);(1,6,8),(2,4,9),(3,5,7).13.(i)an+15-an=60,an35an+1535.60:(0,+)=(0,60](60,120](120,180].{an}15,3,7,11,15,19,23,27,31,35,39,43,47,51,55,59,,{bn}8:b1=7,b2=11,b3=19,b4=23,b5=31,b6=43,b7=47,b8=59.,15{an},8{bn},b8k+r-br=60k(kN,1r8).2006=8250+6,b6=43,,b2006=60250+b6=60250+43=15043.1320075(ii)P(x-1)2+y2=1,|BC|=2,P(1,0).l:ky=x-1,x=ky+1,y2=4ky+4.A(x1,y1)D(x2,y2),y1+y2=4k,y1y2=-4.(y1-y2)2=(y1+y2)2-4y1y2.|AD|2=(y1-y2)2+(x1-x2)2=(y1-y2)2+y21-y2242=(y1-y2)21+y1+y242=16(k2+1)2.,|AD|=4(k2+1).2|BC|=|AB|+|CD|=|AD|-|BC|,,|AD|=3|BC|=6,4(k2+1)=6.k=22.lx=22y+1x=-22y+1.214.2,AF1BC,BE1AD(E1F1).PE1=12AB=PF1.PGE1F1=K.ABF1E1,CF1E1=A=-C.E1F1CD,PKE1F1.PE1F1,,KE1F1.PEKFABF1E1,,PEKF.ME=MF.15.mn.k.k=1,mn=2,m=1,n=2.,m=02+12,n=12+12,k=01+11,.kr(r2).k=r,mn=r2+1,nr+1,m=r2+1nr2+1r+1r2+rr+1=r.n=r+s,m=r-t(stN+).(r-t)(r+s)=r2+1,rs-ts-tr=1.t2(r-t)(s-t)=t2+1.r-t=m0,s-t0,tr.,a1b1c1d1N,r-t=a21+b21,s-t=c21+d21,t=a1c1+b1d1,m=r-t=a21+b21,n=r+s=(r-t)+(s-t)+2t=(a1+c1)2+(b1+d1)2,r=(r-t)+t=a1(a1+c1)+b1(b1+d1).a=a1,b=b1,c=a1+c1,d=b1+d1,m=a2+b2,n=c2+d2,k=r=ac+bd(abcdN),k=r,.,.()1.2006(88)a0a0.2.2007(3);(8)1(B);2006()7(5).3.2007(95)5abcd,.,,.23