1. PPR Maths nbk
VARIATIONS
Guided Practice:
A Direct Variation
1. Given that E varies directly as J. 3. Given that p varies directly as square
Express E in terms of J when E = 6 and root of q. Express p in terms of q when p
J = 12. = 10 and q = 25.
Solution:
EαJ Solution:
p α q
E = kJ k is a constant
p =k q
Substitute the given values of E and J to
find the value of k.
6 = k (12)
6
=k
12
1
k=
2
1
Hence, E= J
2
2. Given that R varies directly as the 4. x 32 m
square of Q and R = 48 when Q = 4, y 4 2
express R in terms of Q.
The table shows the values of x and y.
Solution: Given that x varies directly as y3,
R α Q2 calculate the value of m.
Solution:
1
2. PPR Maths nbk
B Inverse Variation
1. Given that W varies inversely as X. 2. Given that g varies inversely as h.
Express W in terms of X when W = 8 Express g in terms of h when g = 25
and X = 2. and h = 0.6.
Solution:
1 Solution:
W α
X 1
g α
h
1 k is a constant
W=k
X k
g =
k h
W =
X
k
8 =
2
8(2) = k
k = 16
16
Hence, W=
X
3. Given that M varies inversely as the 4. F 2 e
square of T and M = 8 when T = 2, y 4 8
express M in terms of T.
The table shows the values of F and y.
Given that F varies inversely as y2,
calculate the value of e.
5. 6.
p 5 a 1
t 16 4 X a
2
t 4 2
The table shows the values of p and t.
Given that p varies inversely as the The table shows the values of X and t.
square root t, calculate the value of a. Given that X varies inversely as the
square of t, calculate the value of a.
2
3. PPR Maths nbk
C Joint Variation
1. Given that m varies directly as n2 and p. 2. Given that h varies inversely as n3 and
Express m in terms of n and p when m m and h = 2 when n = 2 and m = 121.
= 270, p = 6 and n = 3. Express h in terms of n and m.
3. Given that J varies directly as r3 and 4. 1
inversely as m2 and J = 144 when r = 4 D 10
6
and m = 2. 1
a. Express J in terms of r and m. e 2 3
b. Find the value of 3
i. J when r = 1 and m = 6, 1
f 81
ii. m when J = 4.5 and r = 2. 5
Given that D varies inversely as e2 and f.
Complete the table.
5. If p varies directly as q and p = 71 6.
when q = 25, find F 10 20
a. p when q = 9, n 40 60 90
b. q when p = 355. d 20 45
Given F varies directly as n and
inversely as d. Complete the table.
7. Given that m is directly proportional to 8. It is given that y varies directly as the
2
n and m = 64 when n = 4, express m in square root of x and y = 24 when x = 9.
terms of n. Calculate the value of x when y = 40.
(SPM 2003) (SPM 2005)
A m = n2 C m = 16n2 A 5 C 25
B m = 4n2 D m = 64n2 B 18 D 36
3
4. PPR Maths nbk
VARIATIONS (ANSWERS)
Guided Practice:
A Direct Variation
1. Given that E varies directly as J. 3. Given that p varies directly as square
Express E in terms of J when E = 6 and root of q. Express p in terms of q when p
J = 12. = 10 and q = 25.
Solution:
EαJ Solution:
p α q
E = kJ k is a constant
p =k q
Substitute the given values of E and J to
find the value of k.
6 = k (12) 10 = k 25
6 10
=k =k
12 5
1 k=2
k=
2
Hence, p =2 q
1
Hence, E= J
2
2. Given that R varies directly as the 4. x 32 m
square of Q and R = 48 when Q = 4, y 4 2
express R in terms of Q.
The table shows the values of x and y.
Solution: Given that x varies directly as y3,
R α Q2 calculate the value of m.
Solution:
R = kQ2 x α y3
48 = k (4)2 x = ky3
48 32 = k (4)3
=k
16
32
=k
k=3 64
Hence, R = 3Q2 1 1 3
k= , Hence, x= y
2 2
4
5. PPR Maths nbk
B Inverse Variation
1. Given that W varies inversely as X. 2. Given that g varies inversely as h.
Express W in terms of X when W = 8 Express g in terms of h when g = 25
and X = 2. and h = 0.6.
Solution:
1 Solution:
W α
X 1
g α
h
1 k is a constant
W=k
X k
g =
k h
W =
X
k
25 =
k 0.6
8 =
2
k = 15
8(2) = k
15
Hence, g=
k = 16 h
16
Hence, W=
X
3. Given that M varies inversely as the 4. F 2 e
square of T and M = 8 when T = 2, y 4 8
express M in terms of T. The table shows the values of F and y.
Given that F varies inversely as y2,
calculate the value of e.
1
Answer:
2
Answer: M = 32
T2
1
5. p 5 A 6. X a
2
t 16 4
t 4 2
The table shows the values of p and t. The table shows the values of X and t.
Given that p varies inversely as the Given that X varies inversely as the
square root t, calculate the value of a. square of t, calculate the value of a.
Answer: 10 Answer: 2
5
6. PPR Maths nbk
C Joint Variation
1. Given that m varies directly as n2 and p. 2. Given that h varies inversely as n3 and
Express m in terms of n and p when m m and h = 2 when n = 2 and m = 121.
= 270, p = 6 and n = 3. Express h in terms of n and m.
Answer: m = 5pn2
Answer: h = 176
n3 m
3. Given that J varies directly as r3 and 4. 1
D 10
inversely as m2 and J = 144 when r = 4 6
and m = 2. 1
a. Express J in terms of r and m. e 2 3
3
b. Find the value of 1
i. J when r = 1 and m = 6, f 81
ii. m when J = 4.5 and r = 2. 5
Given that D varies inversely as e2 and f.
9r 3
Answer: a. J = 2 Complete the table.
m 18
1 Answer: D= 2
b.i. fe
4
D = 2 and f = 27
ii. 4
5. If p varies directly as q and p = 71 6.
F 10 20
when q = 25, find n 40 60 90
c. p when q = 9, d 20 45
d. q when p = 355.
Given F varies directly as n and
Answer: p = 42.6
inversely as d. Complete the table.
q = 625
5n
Answer: F =
d
F = 10 and d = 15
7. Given that m is directly proportional to 8. It is given that y varies directly as the
2
n and m = 64 when n = 4, express m in square root of x and y = 24 when x = 9.
terms of n. Calculate the value of x when y = 40.
(SPM 2003) (SPM 2005)
A m = n2 C m = 16n2 A 5 C 25
B m = 4n2 D m = 64n2 B 18 D 36
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