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2021年5月3日 星期一

110學年度四技二專統測--數學(B)詳解

110 學年度科技校院四年制與專科學校二年制
統一入學測驗-數學(B)


解答f(x)=(π4)x{f(0)=1π4<1xf(x)(D)
解答{{x+2y=3ax+6y=91a=26=39a=3{2x+y=54x+by=1024=1b=510b=22ab=62=4(B)
解答(A)×:(0,0)100x+2y100=1000(B)×:(1,1)2x+100y+100=2020(C)×:(2,1)2x+100y+100=2040(D):{(2,2)100x+2y100=960(2,2)2x+100y+100=960(D)
解答(A)9π5+2π=π5=36(B)36(C)π5=36(D)1116360×3=36(A)=(C)=(D)=36(B)
解答921(B)
解答{a=log2b=log3{10a=210b=3102a+b=(10a)210b=223=12(C)
解答x2+y28x+6y=0(x4)2+(y+3)2=42+32=52=5=10(C)
解答3×4×5=60(D)
解答=C53C83=1056=528=420×528+140×(1528)=112028=40(A)
解答(C)
解答h(x)=4g(x)7x+9h(x)=4g(x)7h(0)=4g(0)7=4×37=5(A)
解答L:2x+3y=1y=23x+13L=23=L1y=23x+bL(2,0)0=43+bb=43{m+b=23+43=23m×b=23×43=89(A)
解答


C1:x2+y22x+2y=0(x1)2+(y+1)2=(2)2O1(1,1),r1=2C2:x2+y24x+4y=0(x2)2+(y+2)2=22O2(2,2),r2=2{¯O1O2=2=r1dist(O1,L)=2=r1dist(O2,L)=0O2C1,LO2{LC1LC23(C)
解答tanθ=725{sinθ,cosθsinθ=7674cosθ=25674a=sinθcosθ=7×25674=175674<12(B)
解答{|2340a1062|=4a+12|0b2465031|=244b4a+12=244b4a+4b=12a+b=3(C)
解答{0<θ<π2sinθ=35cosθ=45sin(2θ)=2sinθcosθ=23545=2425cos(2θ)=725a=sin(4θ)=2sin(2θ)cos(2θ)=22425725=33662512<a<34(C)
解答:{F1(2,3)F2(4,3)2a=10{c=¯F1F2÷2=3a=5b=4=2b=8(D)
解答+600x+y6002x2y(A)
解答A(0,0)B(240,120)C(240+180,12040)=(60,80)¯AC=602+802=100(A)
解答n=1an=n=1n(n+1)2an=n(n+1)2{a1=1a2=3a3=6a4=10a5=155n=1an=35(A)
解答(11+12++17)+(21++27)++(71++77)(11+22++77)=(28×7÷2)+(48×7÷2)+(148×7÷2)11(1+2++7)=72(28+48+68++148)11×8×72=44×4911×28=1848(C)
解答36530C3653030P365301365P36530×136530(D)
解答10[2x+f(x)]dx+31f(x)dx+03f(x)dx=102xdx+10f(x)dx+31f(x)dx30f(x)dx=102xdx+30f(x)dx30f(x)dx=102xdx=x2|10=1(B)
解答f(x)=x2+bx+c=(x+1)2+(b2)x+(c1)f(x)(x+1)2(b2)x+(c1)x1b2+c1=0b+c=3;,f(x)=(x1)2+(b+2)x+(c1)(b+2)x+(c1)x+1b2+c1=0b+c=3{b+c=3b+c=3{c=3b=0(D)
解答
tan3734tan53=43{tan37=h/(a+31)=3/4tan53=h/a=4/3a=43h31=34h712h=31h=3727=53.1(B)

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