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2024年8月20日 星期二

113年大直高中教甄-數學詳解

 臺北市立大直高級中學 113 學年度第一次專任教師甄選

一、填充題(48 分)

解答:2310=2×3×5×7×11,5,Case I 3a,2bc,C53=10Case II 2a,32b,C52C32=3010+30=40
解答:an=SnSn1=(Sn+Sn1)(SnSn1)=Sn+Sn1(Sn+Sn1)(SnSn11)=0Sn=Sn1+1bn=Sn,bn=bn1+1=bn2+2==b1+(n1)=nSn=n2S20S19+S18=202192+182=39+182=363
解答:an=|nn+10n+2n+1n+2n+20n+2|=|nn+1020n+2n+20n+2|=(n+1)(n+2)22(n+1)(n+2)=n(n+1)(n+1)1ak=1k(k+1)(k+2)=12(1k(k+1)1(k+1)(k+2))limnnk=11ak=limn12nk=1(1k(k+1)1(k+1)(k+2))=limn12(1216+16112+1(n+1)(n+2))=limn12(121(n+1)(n+2))=14
解答:{O(0,0)A(0,4)B(4,0)C(0,2)D=(4C+3B)/7=(127,87){L1=AD:y=53x+4L2=AB:x+y=4L3=OD:y=23x{E=L1x=(125,0)F=L2L3=(125,2415)SCEFSOAB=02112/50112/524/151041001401=962516=625
解答:
解答:

{A(0,20)B(0,0)C(5,0)P(5,a)L1=AP:y=a205x+20Q(10020a,0)SADP+SPQC=12(5(20a)+(10020a5)a)f(a)=5(20a)+(10020a5)af(a)=010+10020a+100a(20a)2=0a240a+200=0a=20102
解答:x29+y225=1{a=5b=3c=4(y)=2π40(9(1y225))2dy=2π[9y3y425]|40=141625π
解答:{A(1,3,2)B(3,3,4){AB=(4,0,2)P=¯AB=(1,3,3)PABEp:2x+z=5OL=EpEO(t,1052t,52t),tRR=¯OA=(t+1)2+(752t)2+(32t)2f(t)=(t+1)2+(752t)2+(32t)2f(t)=0t=2{R=14O(2,5,1):(x2)2+(y5)2+(z1)2=14

二、非選題(52 分)

解答:西:xy=((xz)+z)(z+(yz))(z(xz)+z(yz))2xyz(xz)+z(yz),
解答:


L:{3xz6=0y=0{A=Lxy=(23,0,0)B=Lz=(0,0,6){P(0,0,r),rQLABOPBQ(AAA)¯OA¯AB=¯PQ¯PB2343=r6rr=2P(0,0,2)
解答:n=7,:
解答:


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解題僅供參考,教甄歷年試題及詳解











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