2023年4月27日 星期四

112年桃園市高中教甄聯招 (待續)

桃園市立高級中等學校112學年度教師聯合甄選筆試試題

第壹部份: 填充題 (共十二題,占84分)

解答|z|=aRa(3z+2i)=2(iz6)z=122ai3a2i|z|2=a2144+4a29a2+4=a29a4=144a4=16|z|=a=2
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解答{ar,a3+a4a2a1=8ar2+ar3ara=ar2(r+1)a(r+1)=8a(r1)(r+1)2=8a=8(r1)(r+1)2a5+a6+a7+a8=ar4(1+r+r2+r3)=8r4(1+r+r2+r3)(r1)(r+1)2=8r4(r41)(r1)2(r+1)2=8r4(r41)(r21)2f(r)f(r)=32r3(r41)+32r7(r21)232r5(r41)(r21)3=(32r3(r41)+32r7)(r21)32r5(r41)(r21)3=32r3(r21)(r41+r4r2(r2+1))(r21)3=32r3(r21)(r4r21)(r21)3f(r)=0r4r21=0r2=1+52r4=3+52f(r)=8r4(r41)(r21)2=83+521+52(512)2=2(8+45)352=(8+45)(3+5)=44+205
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解答{a=21b=20c=13s=(a+b+c)/2=27=s(sa)(sb)(sb)=276714=126=abc4=2020134126=656
解答a{A(a,0)B(0,0)C(0,a)P{(x+a)2+y2=1x2+y2=144x2+(ya)2=289{2ax+a2=1144=1432ay+a2=289143=145{2ax=a21432ay=a2145(2ax)2+(2ay)2=(a2143)2+(a2145)24a2(x2+y2)=2a44a2+1432+14524a2144=2a44a2+41474a4290a2+20737=0=a2=290+11522=145+122
解答,C74;,,1;2,H43;C74H43=35×20=700
解答{x+y+z=7H37=361+x+y+z=6H36=280199936+28=642005,2014,2023,202367,77
解答,n=abcd,da=2n=2004,2002,2{a=1d=0abcd005001400230032004100500029003800470056006500740083009200890098016{a=1d=218,{a=1d=416,{a=1d=616,{a=1d=818,{a=0d=015,{a=0d=217,{a=0d=417,{a=0d=616,{a=0d=817,2+16+18+16+16+18+15+17+17+16+17=168

第貳部份: 計算與證明題 (共一題,占16分)

解答7abcdefg,{a+c+e+g=mb+d+f=nmn=0±11m+n=1++7=28m,nmn=0m=n=28÷2=14n=1+6+7,2+5+7,3+4+7,3+5+6,,4×3!×4!=576


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解題僅供參考,其他教甄試題及詳解


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