Processing math: 100%

2022年5月20日 星期五

111年新北樟樹高中教甄-數學詳解

新北市立樟樹國際實創高級中等學校 111 學年度教師甄選筆試

【數學科專業能力】試題

解答1n(x+y)n+12022(x+y)20232022=220232;220=576mod1000240=776mod1000280=176mod10002160=976mod10002320=576mod1000=422023=21280264028022023=1767761765768mod1000=608mod1000220232=606mod1000
解答an=nk=13kn4+4k2n2=nk=11n3kn2+4k2=nk=11n3k/n1+4(k/n)2limnan=103x1+4x2dx=[341+4x2]|10=34(51)
解答x=2022:120212C20212;x=2021:120202C20202;x=3:122C22;=2021k=2(k+1)Ck2/C20223=1C202232021k=2(k+1)k(k1)2=12C202232021k=2(k3k)=3202220212020(20212202224202120222)=32021202242020322020=320211011322020=60694
解答
OAOB:BOC:COD:DOE:EOF:FOA=5:5:7:7:5:7{AOB=BOC=EOF=50COD=DOE=FOA=70BAF=120cosBAF=cos120=52+72¯BF2257=12¯BF2=109ABCDEF=BDF+3×ABF=34¯BF2+3257sin120=10943+10543=10723
解答A=[3113]=2[3/21/21/23/2]=2[cos30sin30sin30cos30]A99=(2)99[cos2970sin2970sin2970cos2970]=(2)99[cos90sin90sin90cos90]=(2)99[0110]=[02992990]=[abcd]{a=d=0b=299c=299log4adbca+bcd=log421982100=log4298=log4449=49
解答{L1:xy=0L2:xy=8L3:3x+y=0L3:3x+y=kd(L1,L2)=d(L3,L4)82=|k|10=|k|=85k=85(){A=L1L3=(0,0)B=L2L3=(2,6)a=¯AB=210ka=85210=22
解答
(1){A(1,2,0)B(4,2,3)C(1,8,3)H(a,b,c){AB=(3,0,3)AC=(0,6,3)AH=(a1,b2,c)n=AB×AC=(18,9,18)AH=23AB13AC+2(AB×AC)(a1,b2,c)=(2,0,2)(0,2,1)+(36,18,36)=(38,20,33)=16303063382033=14586=243(2)AH=(a1,b2,c)=(38,20,33){a=39b=18c=33H(39,18,33)E:18(x1)9(y2)+18z)=02xy+2z=0H(d,e,f){HH=(39d,18e,33f)nH=¯HH=((39+d)/2,(18+e)/2,(33+f)/2))E{39d:18e:33f=2:1:2(1)39+d(18+e)/2+33+f=0(2)(1){d=392te=t18f=332t(2)t=36{d=33e=18f=39H=(33,18,39)(3)H=(H+H)/2=(3,0,3)AH=(2,2,3)=αAB+βAC=(3α,6β,3α+3β){α=2/3β=1/3;1/3<0
解答


(1)D(x)=S(x)x210+270=x220+3x+45320x2+3x225=0x2+20x1500=0(x30)(x+50)=0x=30D(30)=S(30)=180=(30,180)(2)=300180S(x)dx=54003150=2250 

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解題僅供參考,其他教甄試題及詳解


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