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2020年2月5日 星期三

104學年度臺北市聯合轉學考-高中升高二-數學科詳解


臺北市高級中等學校 104 學年度聯合轉學考招生考試
升高二數學科試題
一、單選題


{a=11+7b=4+2c=23+6{a2=18+277>18+272=18+122b2=18+82c2=18+122a2>c2>b2a>c>b(E)


11+3ia+bi=2+i(a+bi)(2+i)=11+3i2ab+(a+2b)i=11+3i{2ab=11a+2b=3{a=5b=1(D)



99999=9×41×271141=9×27199999=243999999=0.¯024392014=5×402+42014=4=3(C)


1222+3242+5262++492502=12+(3222)+(5242)++(492482)502=1+5+9++97502=(97+1)×252502=12252500=1275(C)



{tanθ<0sinθ<0{cosθ>0sinθ<0tan2θ=sin2θcos2θ=2sinθcosθ2cos2θ1<0(E)




x(xlog32)(xlog312)(xlog354)00xlog32log312xlog354xlog32+(log354log312)=log32+log35412=log3(2×5412)=log39=2(A)





log(127)100=100(log12log7)=100(2log2+log3log7)=100(2×0.301+0.47710.8451)=23.4K=23+1=24;log2<0.4<log3S=2(K,S)=(24,2)(D)


x1+x2+x3+x4+x5=8H58=C128=495(B)



50×C496=699190800(C)


(,,)=(0,0,5),(0,1,4),(0,2,3),(1,1,3),(1,2,2)3C50C50C55+3!×C50C51C44+3!×C50C52C33+3×C51C41C33+3×C51C42C22=243(=2,,)=2,0,3),(2,1,2),(2,2,1),(2,3,0)C52C30C33+C52C31C22+C52C32C11+C52C33C00=C52(C30C33+C31C22+C32C11+C33C00)=10(1+3+3+1)=8080243(B)



P(AB)=P(A)+P(B)P(AB)=P(A)+P(B)P(A)×P(B)0.7=0.4+P(B)0.4P(B)0.3=0.6P(B)P(B)=0.5(C)


(2+i)6=a+bi=C6020i6+C6121i5+C6222i4+C6323i3+C6424i2+C6525i1+C6626i0b=C6121C6323+C6525(B)


=0.3×250.4×13+0.3×15+0.3×25=1815020+9+18150=1847(B)





{1{¯X=40σX=552=EX2402EX2=16252{¯Y=70σY=10102=EY2702EY2=500012¯Z=nX¯X+nY¯YnX+nY=20×40+10×7020+10=50σZ=EZ2(EZ)2=1nX+nY(nXEX2+nYEY2)502=130(20×1625+10×5000)2500=250225<σZ<25615<σZ<16(D)

二、多重選擇題



(A)×:20k=15=5+5++5=5×20=100(B):20k=1k=21×20÷2=210(C):22k=3(k2)2=12+22++202=20k=1k2(D):20k=1k3=(21×202)2=2102=44100(E)×:14+24+34+204(1+2+4++20)4(BCD)


(A):b24ac<0f(x)xf(1)<0a<0(B)×:{f(1)=4f(3)=1{ab+c=4(1)9a+3b+c=1(2),(2)(1)8a+4b=3,a<0,b>0(C):xf(x)<0,for all xf(0)=c<0(D):(B)8a+4b=3b>0a+b/2>0a+b/2+b/2=a+b>0f(1)f(0)=a+b>0(E)×:(b2a,f(b2a))f(x){x>b2ax<b2a{f(4)>f(5)4>b2af(4)<f(5)5<b2a;(B)8a+4b=3b=342a(1)c=1343a<0a>131238a<9264(b2a)=4+38a1=3+38a<3926=6926>04>b2af(4)>f(5)(ACD)






(A)×:(B):1,1,1r=1b2>b1b2>b3(C)×:10,1,8d=9,a1+a2=11<0,a2+a3=7>0(D):{b1b2=b21rb2b3=b21r3,b1b2<0r<0r3<0b2b3<0(E)×:b1=4,r=32b1,b2,b3=4,6,946(BD)


(A):a0=1(0,1)(B)×:0.52=0.25<1(C):(k,ak)(D)×:y=(12)x,0(E):a100+a2002>a100×a200=a300=a150(ACE)


(ˉx,ˉy)=(65,70)(5,46)y=0.4x+44(A)×:0.4(B):(ˉx,ˉy)=(65,70)(C)×:y=0.4x+44σ(Y)=0.4σ(X)σ(Y)<σ(X)(D):(C)(E)×:(BD)




解題僅供參考

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