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2024年6月24日 星期一

113年警專43期數學科(甲組)詳解

臺灣警察專科學校113學年度專科警員班第43期
正期學生組新生入學考試-甲組數學科

解答:xy=2(D)
解答:log2×1034.5=34.5+log2=34.5+0.301=34.80135(B)
解答:10log20=1012log20=10log20=20=25(B)
解答:loga4=loga1r3=loga1+3logr=10+3log10=10+32(D)
解答:A(5,0)y=xA(0,5)¯PA+¯PB=¯AB=52+122=13(C)
解答:{10x=30010y=30{x=log300y=log30x2y=log3002log30=log300302=log13=log3(A)
解答:P(2,3)x=7=r=5P3x4y=k=|612k|5=56k=25k=19(B)
解答:x2+y28x+4y=0(x4)2+(y+2)2=20{O(4,2)r=25{¯OQ=r=25¯OP=62+22=210¯PQ2=¯OP2¯OQ2=4020=20¯PQ=25(B)
解答:{|a|=4|b|=6ab=0{(x1,y1)=(4,0)(x2,y2)=(0,6)x1y1x2y2=|x1y2x2y1|=|240|=24(D)
解答:cosθ=102+12210221012=144240=35(A)
解答:1064,20!10!6!4!(D)
解答:CBBCAAAACBBC=d(A,L)2d(B,L)2=644=16(D)
解答:A[103014]=[21x32y]A=[2132][xy]=A[34]=[21](A)
解答:{x23=y+32y+32=z118{x=3y52z=9y26x3y+2z=3y523y18y52=4y=135{x=7/5y=13/5(x,y,z)=(75,135,135)(B)
解答:an=an12=an24==a22(n2)=a12(n1)=92(n1)a27a37=9226(9236)=20(C)
解答:sin(90θ)+cos(90+θ)+cos(180θ)=cosθsinθcosθ=sinθ=35(A)
解答:a=k+b,kk0a2+10b2=(k+b)2+10b2=k2+2kb+11b2=20{k=011b2=20b=2011>1k=111b2+2b19=0b=1+21011>1k=211b2+4b16=0b=2+6511>1k=311b2+6b11=0b=3+13011<1k=411b2+8b4=0b=4+21511<1k=511b2+10b+5=0bk=ab=34(B)
解答:f(x)=(3x6)P(x)+12=2xQ(x)+4=x(x2)+ax+b{f(2)=12=2a+bf(0)=4=ba=b=4:4x+4(D)
解答:y=3x3x1y=f(x)=3(xh)3(xh)1yf(x)=f(x)3(xh)3(xh)1=3(xh)3(xh)16hxx=6xh+x2x(6h+1)=0h=16(B)
解答:|xa|=b0{x=a+bx=abab=1.2(C)
解答:{OA=(2,5,1)OB=(3,11,3)n=OA×OB=(4,3,7)E:4x3y+7z=0CE8+6+7k=0k=2(A)
解答:x2+y2+7x5y+4=0O(7/2,5/2)O=(A+B)÷2B=2OA=(7,5)(0,4)=(7,1)(C)
解答:{A(3)B(83+5)=(4(53))C(5)¯AB:¯BC=4553:35+43=15:3=5:3(B)
解答:

{A(6,0)B(3,1)C(4,0)=ABC=12×2×1=1(A)
解答:f(x)=(x1)3+(x1)2+2(x1)+1f(0.99)=0.013+0.0120.02+10.98(B)
解答:(x23)(x233)03x233x=±2,±3,±4,±5,8(B)
解答:f(x)=ax+b{f(1113)f(113)1000=a=12f(1)=a+b=1{a=1/2b=3/2f(1)=a+b=2(D)
解答:a+ar+ar2++ar7=a(1r8)1r=3(1256)3=255(A)
解答:E(X)=4(60+80)8=70E(X2)=184(602+802)=5000Var(X)=5000702=100σ=100=10(C)
解答:{A(2,3,5)B(3,p,2)C(5,2,q){AB=(5,p+3,3)AC=(3,5,q5)53=p+35=3q5{p=34/3q=34/5(p,q)=(343,345)(B)
解答:{X=2X0.1Y=Y+0.2{σ(X)=2σ(X)σ(Y)=σ(Y)Cov(X,Y)=2Cov(X,Y)0.3=Cov(X,Y)σ(X)σ(Y)Cov(X,Y)σ(X)σ(Y)=Cov(X,Y)σ(X)σ(Y)=0.3(C)
解答:{33:C73C43=14024:C72C44=21140+21=161(A)
解答:96=9×6=544×2+6×3+4k=54k=7(C)
解答:AOB=θBAθB=[cosθsinθsinθcosθ][34]=[3/54/54/53/5][34]=[7/524/5]B=(75,245)(A)
解答:ADB+BDC=180sinADB=sinBDC{7sinADB=2r17sinBDC=2r2r1=r2r1:r2=1:1(A)
解答:B=(2π2π4)÷2=34πcosB=12=8+9¯AC2122¯AC2=29¯AC=29(D)
解答:sin(x+π3)+cos(x+π6)=12sinx+32cosx+32cosx12sinx=3cosx3(C)
解答:

1,E(0,0),,{A(12,323)B(0,3)C(0,23)D(1,23){DE=(1,23)AB=(12,123)CD=(1,0)(1,23)=x(12,123)+y(1,0)(x,y)=(4,3)(D)
解答:O=¯BD¯CE,{O(0,0,0)B(3/2,3/2,0)D(3/2,3/2,0)A(0,0,46/2){AB=(3/2,3/2,46/2)AD=(3/2,3/2,46/2)ABAD=92+464=7(C)
解答:|2a+3bba2c+3ddc|=|5aba5cdc|=|5ab5cd|=5|abcd|=510=50(C)

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解題僅供參考,警專歷年試題及詳解



2 則留言:

  1. 第17題,當k=3 ,4的時候才是符合的,k=1,2是不行的,因b>1.

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