1. ppr maths nbk
DIAGNOSTIC TEST
VARIATIONS
1. If p ∝ q2 and q = 3 when p = 36, the value of q when p = 64 is
A ½
B 3
C 4
D 6
2. If R varies directly as S and R = 10 when S = 25, find the value of R
when S = 9.
A 2
B 3
C 5
D 6
P
3. Given that M ∝ and M = 4 when P = 6 and T = 3, express M in terms of P
T2
and T.
6P
A M=
T2
3P
B M= 2
T
C M = 3PT2
PT 2
D M=
4
1 1
4. Given that E ∝ and E = when F = 12 and G = 16, find the value of G
F G 3
when E = 4 and F = 8.
1
A
4
1
B
2
C 2
D 4
5. It is given that y varies directly as the square root of x and y = 6 when x = 9.
Calculate the value of x when y = 10.
A 5
B 10
C 15
D 25

2. ppr maths nbk
6. P varies directly as the cube of q and inversely as r. The relationship between P, q
and r is
q3
A P∝
r
1
3
q
B P∝ 1
2
r
q3
C P∝
r
q3
D P∝ 2
r
7. Table 1 shows some values of variables m, n and h such that m varies directly as
the square root of n and inversely as h.
m 3 3
n 36 81
h 10 15
Table 1
Find the relationship between m, n and h.
5 n
A m=
h
n
B m=
h
3 n
C m=
h
2
D m = 3n
h
8. It is given that y varies directly as xm and y = 8 when x =1. Calculate the value of
m when y = 72 and x = 3.
A 1
B 2
C 3
D 4

3. ppr maths nbk
9. Table 2 shows the relationship between three variables w, t and h.
w t h
2 2 4
4 m 9
Table 2
Given that w ∝ t , calculate the value of m.
h
A 3
B 6
C 12
D 18
10.
p 1 2
q 12 3
Table 3
Based on Table 3, if q varies inversely as the square of p. Find the reaction
between q and p.
A q = 12p2
3
B q = p2
4
12
C q= 2
p
3
D q=
4 p2
Answer :
1. C
2. D
3. A
4. A
5. D
6. C
7. A
8. B
9. B
10. C