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2022年2月8日 星期二

105年身心障礙學生四技二專甄試-數學(C)-詳解

105 學年度身心障礙學生升學大專校院甄試
甄試類(群)組別:四技二專組-數學(C)

單選題,共 20 題,每題 5 分

解答sin(870)=sin870=sin(360×2+150)=sin150=12(B)
解答(3x24x+5)(2x3+ax+b){x3=3a+10=7a=1x2=3b4a=1b=1a+b=2(A)
解答|1202212a3|=6+412a=2a=1a=3(A)
解答{3x+10y=1(1)5x+26y=1(2)5×(1)3×(2)28y=8y=2/7(1)3x+20/7=1x=9/7x+y=a+b=1(B)
解答bk=b1rk1=4096(12)k1=1821221k(1)k1=23213k(1)k1=23{13k=3k1k=16(D)
解答6!2!3!=72012=60(A)
解答y=3x2+2x+1=3(x2+23x+19)+23=3(x+13)2+23(13,23)(B)
解答2312+38932+{a1=2/3r=(1/2)÷(2/3)=3/4S=a11r=2/31+3/4=821(B)
解答ax+by+2=0(4,2)2/3{4a+2b+2=0(1)a/b=2/3(2)(2)2b=3a(1)4a3a+2=0a=22b=6b=3a+b=2+3=1(C)
解答{θsinθ=3/5cosθ=4/5sin(2θ)=2sinθcosθ=2(35)(45)=2425(D)
解答{a=(x,y)b=(1,2)c=(3,4){ab=0ac=2{x+2y=03x4y=2{x=2y=1x+y=3(B)
解答f(x)=ax3+bx2+x2=(x2x2)g(x)=(x2)(x+1)g(x){f(2)=8a+4b=0f(1)=a+b3=0{a=1b=2a+b=1(C)
解答1+2ia+bi=3+4i1+2i=(a+bi)(3+4i)=3a4b+(4a+3b)i{3a4b=14a+3b=2{a=11/25b=2/25a+b=13/25(D)
解答x2+3x6<2xx2+x6<0(x+3)(x2)<03<x<2(C)
解答(A)×:{log28=3log327=3log28log327(B)×:(A)(C)×:{log2(1/3)=log232<log2(1/3)<1log3(1/2)=log321<log3(1/2)<0log3(1/2)>log2(1/3)(D):(C)(D)
解答(1,67)2(2,57)3(3,47)4(4,57)3(5,67)2(6,7)12+3+4+3+2+1=1515C72=1521=57(A)
解答(2x4)38=(2x4)323=(2x42)((2x4)2+2(2x4)+22)=(2x6)(4x24x+12)lim
解答\cases{\int_0^1 3x^2+ ax+b\;dx=1 \\[1ex]\int_0^2 3x^2+ ax+b\;dx=4} \Rightarrow \cases{\left.\left[ x^3+ax^2/2+bx \right]\right|_0^1 =1\\[1ex] \left.\left[ x^3+ax^2/2+bx \right]\right|_0^2 =4} \Rightarrow \cases{1+a/2+ b=1\\ 8+2a+2b=4} \\ \Rightarrow \cases{a+2b=0\\ a+b=-2} \Rightarrow \cases{a=-4 \\b=2} \Rightarrow a+b=-2,故選\bbox[red,2pt]{(A)}
解答9^{x^2-2x+3} =27^x \Rightarrow 3^{2x^2-4x+6} =3^{3x} \Rightarrow 2x^2-4x+6=3x \Rightarrow 2x^2-7x+6=0\\ \Rightarrow 兩根之和= 7/2,故選\bbox[red,2pt]{(C)}
解答x+y=k \Rightarrow y=k-x代入圓C\Rightarrow x^2+(k-x)^2 = k \Rightarrow 2x^2-2kx+k^2-k=0\\ 圖形相切代表判別式=0 \Rightarrow 4k^2-8(k^2-k)=0 \Rightarrow k^2-2k^2+2k=0 \Rightarrow k^2-2k=0\\ \Rightarrow k(k-2)=0 \Rightarrow k=2,故選\bbox[red,2pt]{(C)}
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