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2021年5月30日 星期日

110年桃園高中教甄-數學詳解

 桃園高中 110 學年度第 1 次教師甄選

一、填充題:共二十題,每題全對得5分

解答{(52)1/x=1041/y=10{52=10x14=10y{x=log52=12log2y=log14=2log2xy=1(xy)3=x3y33xy(xy)1=x3y33xyy3x3+3xy=1

解答an=an11+2an11an=1+2an1an1=2+1an1bn=bn1+2,where bn=1anb1=1bn=bn1+2=bn2+2×2==b1+2×(n1)=1+2n2=2n1an=1bn=12n1
解答n+2n!+(n+1)!+(n+2)!=n+2n!(1+(n+1)+(n+1)(n+2))=n+2n!(n+2)2=1n!(n+2)=n+1(n+2)!=(n+2)1(n+2)!=1(n+1)!1(n+2)!Sn=(12!13!)+(13!14!)++(1(n+1)!1(n+2)!)=121(n+2)!
解答(x+1)n=Cn0+Cn1x+Cn2x2++Cnkxk++Cnnxn10(x+1)ndx=[Cn0x+12Cn1x2+13Cn2x3++1k+1Cnkxk+1+1n+1Cnnxn+1]|10[1n+1(x+1)n+1]|10=Cn0+12Cn1+13Cn2++1n+1Cnn=4095n+11n+12n+11n+1=4095n+12n+11=4095n=11
解答1203a,b,cabc147201415820131117201258201322172011316192021317201141720114n=1nk=1k=1214n=1n(n+1)=560560C203=5601140=2857
解答limx1x3f(1)f(x2)x1=limx1(x3f(1)f(x2))(x1)=limx1(3x2f(1)2xf(x2))=3a2b
解答(,)(A,B)(C,D)B=CA,B,C,D5×4×1×4=80BCA,B,C,D5×4×3×3=18080+180=260
解答45n277n1=37n=3029=45n277=1073281107328=1045
解答1A3B:44132C44×C41×2C44×C41×2P1041A3B4A:41321C41×211A3B24AC44×C41×2P104×1C41×2=1P104=15040
解答an+1n+1AB1:nABan2:n+1AC13:nBAan4:n+1CB15:nABanan+1=an+1+an+1+an=3an+2(p,k)=(3,2)
解答y=f(x)=x3+ax2+x+1P(t,f(t))f(t)=3t2+2at+1:y=(3t2+2at+1)(xt)+t3+at2+t+1(0,0)0=(3t2+2at+1)(t)+t3+at2+t+12t3+at21=0g(t)=2t3+at21g(t)=6t2+2at=0t(3t+a)=0t=0,a/3g(0)(g(a/3))<0227a3+19a31>0127a3>1a>3
解答

A{C1:x2+(y6)2=6C2:(x32)2+y2=18{C1(0,6),r1=6C2(32,0),r2=32{x2+y2=26yx2+y2=62x26y=62xy=3xAP:y=3xC1P(322,326)¯OP=184+544=18=32=r2APO2PO2A=60cosPO1A=6+618266=12PO1A=120{=O2APO2AP=16×18π34×18=3π923=O1PAO1PA=13×6π12×6×32=2π323=3π923+2π323=5π63
解答(z+z2+z4)(z3+z5+z6)=z(1+z+z3)z3(1+z2+z3)=z4(1+z+z2+z3+z4+z5+z6+2z3)=z4(0+2z3)=2z7=2(z+z2+z4)(z3+z5+z6)=2αβ=2(1)1+z+z2+z3+z4+z5+z6=0(z+z2+z4)+(z3+z5+z6)=1α+β=1(2)(1)(2)α,βx2+x+2=0α=z+z2+z4=1±7i2
解答{(1+3)n=an+bn3(13)n=anbn3((1+3)(13))n=(an+bn3)(anbn3)(2)n=a2n3b2n(anbn)2=(2)nb2n+3limnanbn=limn(2)nb2n+3=3
解答{f(x)=an1xn1,1n<x1n1f(x)=anxn,1n+1<x1nf(x)(0,1]an1(1n)n1=an(1n)nan=nan1=n(n1)an2==n(n1)2a1=n!
解答f(x)=2(x+2)32(x+2)+3f(1.99)=23.99323.99+3=127.0423987.98+3=132.022398
解答{an:nbn:n{a1=1b1=1c10=a10+b10{a1=1b1=1{a2=1b2=2{a3=2b3=3{a4=3b4=5{a5=5b5=8{a6=8b6=13{a7=13b7=21{a8=21b8=34{a9=34b9=55{a10=55b10=89c10=55+89=144
解答

AB909010!4!6!=37
解答180.8810.88810.8899(10.88)100100(0.88+9(10.88))=9008000.88
解答z1,z2,¯z1z2=622,cosz1Oz2=1+1(622)22=32z1Oz2=30|z1z2|<622z1Oz2<30;2020z1z2...z2020,36020203602020×n<30n168zi168zj(ij),168zj(ij),使|zizj|<622zi,2019zj(ij)168×2=336,3362019=112673
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解題僅供參考,其他教甄試題及詳解

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