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2022年2月11日 星期五

104年身障生升大學-數學甲詳解

104 學年度身心障礙學生升學大專校院甄試
甄試類(群)組別:大學組數學甲

單選題,共 20 題,每題 5 分

解答
rθ1:rθ2=5:1θ1:θ2=5:1θ2=BAC=16×360=60=¯AD=rcos(θ2/2)=8cos30=43(B)
解答{O(0,0)A(2,3)P(x,y){OA=(2,3)OP=(x,y)OPOA=52x+3y=5m=2/31m<0(B)
解答[abcdef][142536]=[1212]{a+2b+3c=1(1)4a+5b+6c=2(2)d+2e+3f=1(3)4d+5e+6f=2(4){(2)(1)3a+3b+3c=1(4)(3)3d+3e+3f=3{a+b+c=1/3(5)d+e+f=1(6)(5)+(6)a+b+c+d+e+f=1/3+1=4/3(D)
解答{f(x)=(x22x+1)p(x)+x+2=(x1)2p(x)+x+2g(x)=(x22x+1)q(x)+x+3=(x1)2q(x)+x+3f(x)g(x)=(x1)4p(x)q(x)+(x1)2((x+2)q(x)+(x+3)p(x))+(x+2)(x+3)f(1)g(1)=34=12(A)
解答
{y=x2=3xx=0,3y=x2=23xx=0,23{P(3,3)Q(23,12)O(0,0){¯OQ=239d(P,y=23x)=3/13OPQ=12239313=33(A)
解答{{272=729282=78427<777<28{93=729103=10009<3777<10|k|=10,11,,27k=±10,±11,,±2736(D)
解答
{h=¯ABa=¯AD{tanθ1=h/(a+100)=0.3tanθ2=h/a=0.4h=0.3(a+100)=0.4a0.1a=30a=300h=0.4a=120(D)
解答7θcosθ=52+6272256=15sinθ=265:2R=7sinθ=3526=3521.4141.7327.15(C)
解答{u=(1,1,1)v=(2,3,4)au+bv=(a+2b,a+3b,a+4b)(A){a=0b=0au+bv=(0,0,0)(B){a=5b=1au+bv=(7,8,9)(C)au+bv=(8,7,9){a+2b=8(1)a+3b=7(2)a+4b=9(3){(1)(2){a=10b=1(2)(3){a=1b=2(D){a=11b=1au+bv=(9,8,7)(C)
解答O(1,2){d1=d(O,L1)=13/5d2=d(O,L2)=8/5d3=d(O,L3)=42/13d3>d1>d2d1<r<d313/5r<42/13L1,L2L3(C)
解答(11%)(1+0%)(1+c%)>(1+10%)30.99(1+c%)>1.131+c%>1.13/0.99=1.344c>34(C)
解答x2+x=1.23×1018x2+x1.23×1018=0a=1+1+4×1.23×10182=1+1+4.92×101821+4.92×101821+2.2×1092=1.1×1090.5109a<5×109(B)
解答{A=L1L2=(0,8)B=L2L3=(8,10)C=L3L1=(4,0){P¯ABP=(4t,t+8),t(0,2)Q¯BCQ=(2t+4,5t),t(0,2)R¯ACR=(t+4,2t),t(4,0){t=1Pt=1Qt=3,2,1RABC8(A)
解答{p+0.8q+0.6r=8200.8p+0.6q+r=7700.6p+q+0.8r=810[145358204535177035145810][100350010400001250]{p=350q=400r=250q>p>r(C)
解答cotx>0kπ<x<2k+12π,kZ{0<1,2<π/2π/2<3,4,,9<ππ<10<3π/2{cot1,cot2,cot10(B)
解答{P(A)=0.28P(B)=0.4P(AB)=0.4P(AB)P(B)=0.4P(AB)=0.4×0.4=0.16P(AB)=P(AB)P(B)=P(A)P(AB)1P(B)=0.280.1610.4=0.2(A)
解答P(X=4)=1/6=4/6P(X=5)=1/6=5/6P(X=6)=1/6=6/6P(X=1)=1/6{P(X=1)=(1+1)/36P(X=2)=(1+2)/36P(X=6)=(1+6)/36=(2+3+7)/36=27/36P(X=2)=1/6{P(X=1)=(2+1)/36P(X=2)=(2+2)/36P(X=6)=(2+6)/36=(3+4+8)/36=33/36P(X=3)=1/6{P(X=1)=(3+1)/36P(X=2)=(3+2)/36P(X=6)=(3+6)/36=(4+5+9)/36=39/36=(4+5+6)/6+(27+33+39)/36=189/36=21/4(D)
解答(A)20x<30{4<log2x<52x/10<3(B)30x<40{5log2x<63x/10<4(C)40x<50{5<log2x<64x/10<5(D)50x<60{5log2x<65x/10<6(D)
解答P(X6=2)=(C62+C64)/26=30/64(D)
解答

z=3+i=2(cosπ6+isinπ6)zn=2n(cosnπ6+isinnπ6),nN{Pn=(2ncosnπ6,2nsinnπ6)O(1,1)dn=¯OPn{P1(3,1)P2(2,23)P3(0,8)P4(8,83){d1=423<9d2=1443<9d3=50<9d4=92+(831)2>93(C)
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