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2022年3月30日 星期三

111年身障升大學-數學A詳解

111 學年度身心障礙學生升學大專校院甄試

甄試類(群)組別:大學組-數學 A

單選題,共 20 題,每題 5

解答a15(a5)+30a+5(a+45)=50×5050a=2350a=47(A)
解答{:2C3233!:2!=22C32×3!×2=72(B)
解答f(x)=x3+ax2+bx5=(x1)(x2)(x3)+kk()5=6+kk=1f(x)=(x1)(x2)(x3)+1f(4)=321+1=7(D)
解答A=[abcd]{A[10]=[abcd][10]=[ac]=[10]A[32]=[abcd][32]=[3a+2b3c+2d]=[32]{a=1b=0c=0d=1A=[1001]A2[54]=[1001][54]=[54]{p=5q=4p+q=1(A)
解答log2(260×3%)=60+log23100=60+log3100log2=60+0.477120.301605.06=54.94(D)
解答{a=1(2ab)a(8ab)b{(2ab)a=0(8ab)b=0{2|a|2ab=0(1)8ab|b|2=0(2)(1)ab=2|a|2=2(2)16|b|2=0|b|=4(B)
解答{O(0,0,0)A(5,4,3)B(a,0,0){BO=(a,0,0)BA=(5a,4,3)cosOBA=BOBA|BO||BA|=cosπ4a25aa25+(5a)2=a525+(a5)2=224(a5)2=50+2(a5)2(a5)2=25a=10(0a>0)(C)
解答3+2cosθ<01cosθ<321cos2θ>3401cos2θ<140sin2θ<1412<sinθ<12(C)
解答¯OB=hL1L2A(h,h)L2A1L:y=(xh)+hB(2h,0)OAB=12¯OBh=122hh=h2=100h=10(C)
解答LE1(2t+1)+2t(t2)=33t=0t=0P(1,0,2)LE2(2t+1)+2t(t2)=93t=6t=2Q(5,4,0)¯PQ=42+42+22=36=6(C)
解答{A(2,0)B(1,3)¯ABC(3/2,3/2);LO(0,0)C(3/2,3/2)L:y=x/3P=(3,3){OP=(3,3)OA=(2,0)OB=(1,3)OP=OA+OB{r=1s=1r+s=2(C)
解答

CAPCAQ=¯PB¯QA=¯CPsinθ¯CAtanθ=sinθ2tanθ=12cosθ(B)
解答f(x)=3x3+ax+bf(x)=9x2+af(x)=18x=0x=0y=f(x)(0,f(0))=(0,b)=(x0,y0)(A)g(x)=3x3axbg(x)=18x=0x=0(0,b)=(x0,y0)(B)g(x)=x3+ax+bg(x)=9x=0x=0(0,b)=(x0,y0)(3x0,3y0)(C)g(x)=3x3+a(x+1)+bg(x)=18x=0x=0(0,a+b)(x0+1,y0)(D)g(x)=3x3a(x1)+bg(x)=18x=0x=0(0,a+b)(x01,y0)(A)
解答|abc130340|=5c=52c=12ω=(a,b,c)z=|c|=12(B)
解答{a1=1an+1=1/an+1,nan+1=1/(an1)+1,n{a2k1=ka2k=1+1/k,kN{a3=2a11=6a11a3=4(C)
解答(,)={(2,1),(4,2),(6,3),(8,4)},{(2,1),(4,2),(6,4),(8,3)},{(2,1),(4,3),(6,2),(8,4)},{(2,1),(4,3),(6,4),(8,2)},44!=16(B)
解答


(x,y)=(1,0),(1,1),(2,0),(2,1),(2,2),(3,1),(3,2),(3,3),(4,2),(4,3),(4,4),(5,3),(5,4)13(D)
解答A=(1,1){BAαC2Aβ{¯OA=¯OB=1¯OC=2A+B+C=0{A(1,1)B(1,1)C(0,2)α=90(D)
解答{a4=1.30321×105a7=8.93871739×108{loga4=log(1.30321×105)loga7=log(8.93871739×108){4loga=5+log(1.30321)7loga=8+log(8.93871739){loga=1.25+14log(1.30321)>1.25+14log1=1.25loga=87+17log(8.93871739)<87+17log9=87+270.4771=1.2791.25<loga<1.279(B)
解答(a,b,c)=(4,10,20):abc410202042010101042041020442041042010410=(20+10+4+4+4+10)÷3!=263(A)

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