Page 21 - PBD Plus Matematik T5 (EG)

Matematik Tingkatan 5 Bab 1 Ubahan
18. Selesaikan. TP 3
Solve.
Contoh
Diberi bahawa P = 5 apabila Q = 9. Ungkapkan P dalam sebutan Q jika
Given that P = 5 when Q = 9. Express P in terms of Q if
(i) P berubah secara songsang dengan Q,
P varies inversely as Q,
(ii) P berubah secara songsang dengan punca kuasa dua Q.
P varies inversely as the square root of Q.
1 1
(i) P ∝ (ii) P ∝
Penerbitan Pelangi Sdn. Bhd.
Q √Q
k k
P = P =
Q √Q
k k
5 = 5 =
9 √9
k = 45 k = 15
45 15
P = P =
Q √Q

(a) Diberi bahawa m = 3 apabila n = 8. Ungkapkan m dalam sebutan n jika
Given that m = 3 when n = 8. Express m in terms of n if
(i) m berubah secara songsang dengan n,
m varies inversely as n,
(ii) m berubah secara songsang dengan punca kuasa tiga n.
m varies inversely as the cube root of n.

1 1
(i) m ∝ (ii) m ∝
n 3 √n
k k
m = m =
n 3 √n
k k
3 = 3 = 3
8 √8
k = 24 k = 6
24 6
m = m =
n 3 √n

(b) Diberi bahawa y = 5 apabila x = 2. Ungkapkan y dalam sebutan x jika
Given that y = 5 when x = 2. Express y in terms of x if
(i) y berubah secara songsang dengan x ,
2
2
y varies inversely as x ,
(ii) y berubah secara songsang dengan 3x – 1.
y varies inversely as 3x – 1.
1 1
(i) y ∝ (ii) y ∝
x 2 3x – 1
k k
y = y =
x 2 3x – 1
k k
5 = 5 =
2 2 3(2) – 1
k = 20 5 = k
20 5
y =
x 2 k = 25
25
y =
3x – 1

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