F4 Maths - Ans.fyi 參考答案

F4 Maths

2012-07-18 9:51 pm

1)In an experiment , it is discovered that the temperature difference ( in 。C) between a glass of hot water and the room decrease by 4% every minute, Suppose the original temperature of the glass of hot water is 100。C and the room temperature is 20。C, Let D be the temperature difference between the glass of hot water and the room after t minutes.
(A)Express D in terms of t
(B)Find the temperature of the glass of the hot water after 15 minutes correct to the nearest 。C
(C)(i) Make t the subject of the equations in (A)
(ii)Find the time required for the temperature of the hot water to decrease to 30。C . Given the answer correct to the nearest minute

2)
Factorize X² -3xy +2y² and X³ -8y³. Hence find the L.C.M of the two
expressions.

3)
The H.C.F and L.C,M of two polynomials f(x) and g(x) are (x+1) (x-3) and (x+1) (x-3)²(x-4) respectively. Suppose f(x) =(x+1) (x-3)²
a)find g(x)
b)if A/f(x) + B/g(x) ≡ 2/(x-3)² (x+4) ,find the value of A and B

回答 (1)

用戶2053

2012-07-21 4:26 am

✔ 最佳答案

1A)
D = (100 - 20) (1 - 4%)ᵗ
D = 80 (0.96)ᵗ
B)
80 (0.96)¹⁵ + 20
= 43.3669... + 20
= 63°C
Ci)
D = 80 (0.96)ᵗ
D/80 = 0.96ᵗ
log(D/80) = t log 0.96
t = log(D/80) / log 0.96 = (logD - log80) / log 0.96
ii)
t = (log(30 - 20) - log 80) / log 0.96 = 50.939... = 51 minutes. 2)x² -3xy +2y²
= x² - xy - 2xy + 2y²
= x(x - y) - 2y(x - y)
= (x - y) (x - 2y)x³ - 8y³
= x³ - (2y)³
= (x - 2y) (x² + 2xy + 4y²)∴ L.C.M. = (x - y) (x - 2y) (x² + 2xy + 4y²)

3a)[H.C.F of f(x) and g(x)] * [L.C.M. of f(x) and g(x)] = f(x) * g(x)
(x+1) (x-3) * (x+1) (x-3)² (x-4) = (x+1) (x-3)² * g(x)
g(x) = (x+1) (x-3) (x-4)
b)A / [(x+1) (x-3)²] + B / [(x+1) (x-3) (x-4)] ≡ 2 / [(x-3)² (x-4)]
(x+1) (x-3)² (x-4) {A / [(x+1) (x-3)²] + B / [(x+1) (x-3) (x-4)]}
≡ (x+1) (x-3)² (x-4) 2 / [(x-3)² (x-4)]
(x-4)A + (x-3)B ≡ 2(x+1)
(A+B)x + (- 4A - 3B) ≡ 2x + 2
Comparing coefficients , A+B = 2 ..... (1)
{
- 4A - 3B = 2 ..... (2)
(1) * 4 + (2) :4B - 3B = 2*4 + 2B = 10
A = - 8

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