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2021年5月9日 星期日

110年新北市立高中教甄聯招-數學詳解

新北市立高級中等學校 110 學年度教師聯合甄選

一、填充題: 

解答{f(x,y)=x2+y2g(x,y)=11x216xy+11y21依 Lagrange 算子{fx=λgxfy=λgyg=0{2x=λ(22x16y)(1)2y=λ(16x+22y)(2)11x216xy+11y2=1(3),(1)(2)λ=x11x8y=y8x+11y8x2+11xy=11xy8y28(x2y2)=0{x=yx=y(3){x2=1/6x2=1/38x2+y2=16+16=13
解答{O(0,0,0)A(1,1,2)B(0,3,0)Q(3,4,4){OA=(1,1,2)OB=(0,3,0)n=OA×OB=(6,0,3)E:2xz=0P(t,y,2t)¯PQ=(t3)2+(y4)2+(2t+4)2=5(t+1)2+20+(y4)2{t=1y=4¯PQP(1,4,2)
解答(3,0)(2,0)f(3)()f(x)=(ax+b)(x3)2f(0)=29b=2b=29f(x)=(ax29)(x3)2f(x)=a(x3)2+2(ax29)(x3)(0,2),(2,0)1f(0)=19a+129=1a=127f(x)=(127x29)(x3)2
解答{3cosA+5sinB=6(1)3sinA+5cosB=1(2)(1)2+(2)234+30sinBcosA+30sinAcosB=37sin(A+B)=110sin(πC)=110sinC=110
解答log2log4xlog4log2x=log2(12log2x)log2(log2x)1/2=log212logxx(log2x)1/2=1212logxx(log2x)1/2=21/214(log2x)2log2x=2(log2x)28log2x=0log2x=8x=256
解答X=1:292C82X=2:392C72X=3:492C62X=4:592C52X=5:692C42X=6:792C32X=7:892C22EX=(C82+2C72+3C62+4C52+5C42+6C32+7C22)÷C93=21084=52
解答

ABC+DEF=2×2=4;ACDF=62×22=24=4+24=28
解答

:{|z1|=|z2|=|z3|=|z4|=1z1+z2+z3+z4=0z1,z2,z3,z4f(z)=(zz1)(zz2)(zz3)(zz4)f(z)=0z1,z2,z3,z4f(z)=z4+az3+bz2+cz+d,a=(z1+z2+z3+z4)=0,c=(z1z2z3+z1z2z4+z2z3z4+z1z3z4)z1+z2+z3+z4=0ˉz1+ˉz2+ˉz3+ˉz4=01z1+1z2+1z3+1z4=0z2z3z4+z1z3z4+z1z2z4+z1z2z3=0c=0f(z)=z4+bz2+d(0)f(z)=0±α,±β,α,βC{z1z2z3=z1z4=z2{z1+z3=0z2+z4=0|z1z3|2=(z1z3)(ˉz1ˉz3)=z1ˉz1z1ˉz3z3ˉz1+z3ˉz3=1(z3)ˉz3(z1)ˉz1+1=4|z1z3|=2z1,z2,z3,z4{z1=a+biz2=a+biz3=abiz4=abiz21+z22+z23+z24=(a+bi)2+(a+bi)2+(abi)2+(abi)2=4(a2b2)=1a2b2=14a2+b2=1{a=522b=322=2a×2b=52×32=152
解答
ABCP{APBB60BDCAPCC60AFBBPCC60AECAECDBF=ABC2{PAF3PBD4PCE5PBF,PAE,PCD3,4,5AECDBF=34(32+42+52)+3×123×4=2523+18ABC=12(2523+18)=2543+9
解答01:35=24321:C5233=27041:C543=15243+270+15=528

二、計算題: 

主辦單位公布的解答





主辦單位公布的解答








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解題僅供參考,其它教甄試題及詳解


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