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2021年3月2日 星期二

107年中科實中教甄-數學詳解

 國立中科實驗高級中學107學年度國中部數學科教師甄選

一、填充題

解答:{z=3sinθ+i(3cosθ+2)Γ:x2+(y2)2=(3)2z1=33iP(z1)=(3,3)z2=3+iQ(z2)=(3,1)L(PQ):y=1+33+3x(0,2)L=2(3+3)16+248=2(3+3)23+2=3=ΓL|zz1|+|zz2|=|z1z2|=¯PQ=(3+3)2+(1+3)2=2+23
解答:xyx+y=520xy520(x+y)=0(x520)(y520)=5202=52×26×132(2+1)×(6+1)×(2+1)=6363(x,y)
解答::Cn0+Cn1+Cn2+Cn3=1+C202+C202+C203=1+20+190+1140=1351
解答:α,β,γ,δx4+x3+1=04{α+β+γ+δ=1αβ+βγ+γδ+δα+αγ+βδ=0αβγδ=1|α1111β1111γ1111δ|=α|β111γ111δ||1111γ111δ|+|1β111111δ||1β111γ111|=α(βγδ+2βγδ)(γδ+1γδ)+(δ+ββδ1)(1+βγβγ)=αβγδ(αβ+βγ+γδ+δα+αγ+βδ)+2(α+β+γ+δ)3=1023=4
解答:{a=340+1113b=3401113{a3+b3=80ab=316001573=3(a+b)3=a3+b3+3ab(a+b)k3=80+9kk39k80=0k=(a+b)(k5)(k2+5k+16)=0k=5
解答:{A(0,0,4)B(1,2,3)C(3,1,2)D(3,5,1)R(13,36,9){L1:x1=y2=z41L2:x36=y+16=z23{P(s,2s,s+4)Q(2t+3,2t1,t+2);PQRRPRQ=ks+132t+16=2s362t37=s+13t+11=k{(2s36)+2(s+13)(2t37)+2(t+11)=23=k(s+13)+(2s36)(2t+16)+(2t37)=3s2321=k3s2321=23s=3t=4{P(3,6,1)Q(11,9,6)¯PQ=82+152+52=314
解答:y=f(x)=x3+ax2+1f(x)=3x2+2ax(k,k3+ak2+1)y=(3k2+2ak)(xk)+k3+ak2+10=(3k2+2ak)(k)+k3+ak2+1g(k)=2k3+ak21=0g(k)=06k2+2ak=02k(3k+a)=0k=0,a/3;g(k)=0g(0)g(a/3)<0(1)(2a3/27+a3/91)<0a3271>0a>3
解答:limx19+29++x910x10=limnnk=1k910n10=limnnk=11101n(kn)9=10110x9dx=1100
解答:
DEF¯CMPQ¯CP=¯PQ=¯QA=a{QMD=PMDQDM=MPD()MQDMDP¯MQ¯MD=¯MD¯MP¯MD2=¯MPׯMQ=2a2(1)¯CF2=¯CPׯCQ=2a2¯CE=¯CF¯CE=¯CF=¯MD=b(2)(2)(1)b2=2a2b=2a:¯CA2+¯CB2=2(¯CM2+¯AM2)(5+2b)2+52=2(9a2+52)(5+22a)2+25=18a2+5010a2202a=0a=22b=4ABC{¯AB=10¯BC=5¯AC=5+2b=13ABC=s(s10)(s5)(s13)=14491=614s=(10+5+13)÷2=14

解答:
¯AB=¯AC=a¯BC=2a{ABD:¯BD=a24AGC:¯GC=a236BCF:¯CF=2a264;¯BD=¯FGa24=a236+2a264a440a2=0a2(a240)=0a2=40ABC=12a2=20
解答:{a+b+c=0abc=100{b+c=abc=100a>0,:b+c2bca2100aa24100aa3400a3400=202/3a202/3

解答:aB{A(0,a)B(0,0)C(a,0)D(a,a)P(x,y){¯PA=7¯PB=3¯PC=5{x2+(ya)2=49x2+y22ay+a2=49(1)x2+y2=9(2)(xa)2+y2=25x2+y22ax+a2=25(3)(2)(1)(3){2ay=40a2(4)2ax=16a2(5)(4)2+(5)24a2(x2+y2)=(a240)2+(a216)236a2=2a4112a2+1856a474a2+928=0(a216)(a258)=0=a2=58(a=4¯AC=42<¯PA,)

解答:ωx2+x+1=0,ω2+ω+1=0(ω1)(ω2+ω+1)=ω31=0ω3=1(1+x)107=107k=0C107kxkf(x)=x2(1+x)107=107k=0C107kxk+2{f(1)=2107=107k=0C107kf(ω)=ω2(1+ω)107=ω2(ω2)107=ω216=1=107k=0C107kωk+2f(ω2)=ω4(1+ω2)107=ω4(ω)107=ω111=1=107k=0C107kω2k+4f(1)+f(ω)+f(ω2)=21072=107k=0akC107k,ak={1+ω3s+2+ω6s+4=1+ω2+ω=0if k=3s1+ω3s+3+ω6s+6=1+1+1=3if k=3s+11+ω3s+4+ω6s+8=1+ω+ω2=0if k=3s+2,s=0,1,3(C20171+C20174+C20177++C2017106)=21072=Xlog(21072)log2107107×0.301=32.207X33m=33;2.07<0.301=log211n=1;2m:2,4,8,6,2,4,8,6,4107=4×26+3210782107282=6k=6(m,n,k)=(33,1,6)

解答:42=2×3×7=(1+1)(2+1)(6+1)X=p3+2p2+p=a×b2×c6,a,b,c使Xc=2,b=2X=p(p+1)2=a×32×26=a×(3×23)2p+1=3×23=24p=23

解答:



{x2+y2=1(x3)2+y2=9x:(x3)2+(1x2)=9x=16{x=11/6(1x2)πdx=325648πx=1/60(9(x3)2)πdx=53648π=7π12
解答:x+19100++x+911009119+1=73kk+1,kN546÷737.5k=7m773m87m+8(73m)=546m=38{38x+56100=739x+57100=87.44>x7.43100x=743
解答:

{AEB=αCFB=βAPC=α+βEPF=α+βBEPF=360=90+2(α+β)α+β=135{tanCFB=tanβ=64=32(1)tanAEB=tan(135β)=tan135tanβ1+tan135tanβ=1tanβ1tanβ=a+42(2)(1)(2)13/213/2=a+42a=6=(6+4)×(2+4)=60

解答:ORO1,O2,O310OO1O2O3O1O2O2,OO1O2,OO2O3,OO1O3GO1O2O3OGO1{¯GO=10¯GO1=20×32×23=2033¯OO1=R10¯OO12=¯GO12+¯OG2(R10)2=(2033)2+102=7003R10=1073R=10(1+73)



解答:(1+1n+1)n+1(1+1n)n+1=(n(n+2)(n+1)2)n+1=(11(n+1)2)n+1>1n+1(n+1)2=nn+1=11+1n(1+1n+1)n+1(1+1n)n+1>11+1n(1+1n+1)n+1>(1+1n)n:(1+x)n>1+nx,x>1,n1




1 則留言:

  1. 第11題,依你的解法 a>0-> b, c<0怎麼用算幾?題目並沒說 a>0, b>0, c>0

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