F.2數學..........20marks－香港特色

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F.2數學..........20marks

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1.Expand the expressions by using identities.(a) x^2-(y-z)^2(b) [(-(4x/3)+2][(-(4x/3)-2](c) (x+y+z)(x+y-z)(d) [2x+(3y-2)][2x-(3y-2)]2.Write down a polynomial of degree 4 with each of the following:(a) four different factors of degree 1(b) two different factors of degree 2(c) one factor of degree 2... 顯示更多 1.Expand the expressions by using identities. (a) x^2-(y-z)^2 (b) [(-(4x/3)+2][(-(4x/3)-2] (c) (x+y+z)(x+y-z) (d) [2x+(3y-2)][2x-(3y-2)] 2.Write down a polynomial of degree 4 with each of the following: (a) four different factors of degree 1 (b) two different factors of degree 2 (c) one factor of degree 2 and two factors of degree 1 3. Solve the simultaneous equations. (x/4)+(y/3)=1 y=(3/4)x 4.Solve the simultaneous equations with three unknowns. a+b+c=4 2a-b+c=0 2a+b-3c=10 5. She can finish a job in six days while he can finish the same job in three days. If they do the job together, how many days will they take to finish? 6. If interest rate=4%, time(years)=18 months, amount=$3180, what is the principal and the simple interest?

最佳解答:

1.(a) x2-(y-z)2 = [x+(y-z)][x-(y-z)] = (x+y-z)(x-y+z) ===== 1.(b) [(-4x/3)+2][(-4x/3)-2] = (-4x/3)2-(2)2 = (16x2/9) - 4 [or = (16x2-36)/9] ===== 1.(c) (x+y+z)(x+y-z) = [(x+y)+z][(x+y)-z] = (x+y)2-z2 = (x2+2xy+y2)-z2 = x2+2xy+y2-z2 ===== 1.(d) [2x+(3y-2)][2x-(3y-2)] = (2x)2-(3y-2)2 = 4x2-[(3y)2-2(3y)(2)+(2)2] = 4x2-9y2+12y-4 ===== 2.(a) x4+2x3-2x2-2x = x(x+1)(x-1)(x+2) ===== 2.(b) x4+3x2+2 =(x2+1)(x2+2) ===== 2.(c) x4-x2 =x2(x+1)(x-1) ===== 3. (x/4)+(y/3)=1 3x+4y=12 ...... (*) y=(3/4)x 3x = 4y 3x-4y = 0 ...... (**) (*)+(**): 6x = 12 x = 2 (*)-(**): 8y = 12 y = 1.5 Hence, x = 2 and y = 1.5 ===== 4. a+b+c=4 ...... (1) 2a-b+c=0 ...... (2) 2a+b-3c=10 ...... (3) (1)+(2): 3a+2c = 4 ...... (4) (2)+(3): 4a-2c = 10 ...... (5) (4)+(5): 7a = 14 a = 2 Subst. a=2 into (4) 3(2)+2c=4 c = -1 Subst. a=2 and c=-1 into (1) (2)+b+(-1) = 4 b = 3 Ans: a = 2, b = 3, c = -1 ===== 5. She can finish (1/6) of the job in one day. He can finish (1/3) of the job in one day. When they work together, fraction of job finished in one day = (1/6)+(1/3) = 1/2 No. of days they will take to finish the job = 2 days ===== 6. Amount A = $3180 Interest rate R% = 4% (per annual) No. of years = 18/12 = 1.5 years Principal = ? A = P(1+nR%) 3180 = P(1+1.5x4%) 1.06P = 3180 P = 3000 Hence, principal = $3000 Simple interest = $(3180-3000) Simple interest = $180 =

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