Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
P1 Variation Modul 2
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Tasksheet 2 : Variations
Name : ___________________________
Class : ____________
Example :
(a) Varies Directly (b) Varies Inversely
Given that A is directly proportional to B Given that C varies inversely as D and
and A = 15 when B = 5, express A in C = 2 when D = 9, express C in terms of
terms of B. D.
Answer : Answer :
A ∝B 1
A = kB C∝
D
15 = k(5) 1
15 C =k
k = D
5 1
= 3 2 = k( )
9
9
Hence, A = 3B k =2 ( )
1
k = 18
18
Hence, C =
D
Answer all questions.
1. Given that G is directly proportional to s and 3. The table shows the values of x and y.
G = 20 when s = 3, express G in terms of s. Given that x varies directly as the square of
y, calculate the value of m.
x 44 m
y 4 2
2. The table shows the values of N and R.
Given that N varies directly as R,
find the value of a.
N 5 a
R 30 12
1
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4. The table shows the values of P and Q. 6. The table shows the values of E and F.
Given that P varies directly as the square Given that E varies inversely as F,
of Q, calculate the value of i. find the value of g.
P 200 72 E 2 g
Q 10 i F 3 12
5. The table shows the values of u and v. 7. Given that S varies inversely as T and
Given that u varies inversely as the square S = 7 when T = 5, express S in terms of T.
of v, calculate the value of w.
u 16 w
v 2 6
2
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8. The table shows the values of P and Q. 10. The table shows the values of d, e and f.
Given that P varies inversely as the square Given that d varies directly as square of e
of Q, calculate the value of R and inversely as square root of f , find the
value of x and y.
P 1 3
3 d e f
Q 5 R 4 1 4
10 x 16
1 1 y
5 3
9. The table shows the values of P, Q and R.
Given that P varies directly as Q and
inversely as R, find the value of m and n.
P Q R
2 3 4
10 m 12
20 60 n
3
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Answers for Tasksheet 2 : Variations
Name : ___________________________
Class : ____________
Answer all questions.
1. Given that G is directly proportional to s and 3. The table shows the values of x and y.
G = 20 when s = 3, express G in terms of s. Given that x varies directly as the square of
y, calculate the value of m.
Answer :
G ∝s x 44 m
G = ks y 4 2
20 = k(3)
20 Answer :
k =
3 x ∝ y2
x = k y2
20
Hence, G = s 44 = k(4) 2
3 44
k =
16
2. The table shows the values of N and R. 11
=
Given that N varies directly as R, 4
find the value of a. 11 2
Hence, x = y
4
N 5 a 11
R 30 12 m = (2) 2
4
= 11
Answer :
N ∝R
N = kR 4. The table shows the values of P and Q.
5 = k(30) Given that P varies directly as the square
5 of Q, calculate the value of i.
k =
30
1 K 200 72
=
6 L 10 i
1 Answer :
Hence, N = R P ∝ Q2
6
1 P = k Q2
a = (12)
6 200 = k(10) 2
= 2.
4
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200
k =
100
=2
Hence, P = 2 Q 2
72 = 2(i) 2
72
i =
2
= 6
5. The table shows the values of u and v. 7. Given that S varies inversely as T and
Given that u varies inversely as the square S = 7 when T = 5, express S in terms of T.
of v, calculate the value of w.
Answer :
u 16 w 1
S∝
v 2 6 T
1
Answer : S =k
T
1
u∝ 1
7 = k( )
v2 5
1 k = 35
u =k 2
v
1 35
16 = k( ) Hence, S =
22 T
k = 64
64 8. The table shows the values of P and Q.
Hence, u =
v2 Given that P varies inversely as the square
64 of Q, calculate the value of R
w= 2
6
P 1 3
16 3
= Q 5 R
9
Answer :
6. The table shows the values of E and F. 1
P∝
Given that E varies inversely as F, Q2
find the value of g. 1
P =k 2
Q
E 2 g
F 3 12 1 1
= k( 2 )
3 5
Answer : 25
k =
1 3
E ∝
F
1 25
E =k Hence, P =
F 3(Q 2 )
1 25
2 = k( ) 3=
3 3( R 2 )
k =6
5
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6 25
Hence, E = R =
F 3(3)
6
g = 5
12 =
3
2
1 = 1
= 3
2
9. The table shows the values of P, Q and R. 10. The table shows the values of d, e and f.
Given that J varies directly as Q and Given that d varies directly as square of e
inversely as L , find the value of m and n. and inversely as square root of f , find the
value of x and y.
P Q L
2 3 4 d e f
10 m 12 4 1 4
20 60 n 10 x 16
1 1 y
Answer : 5 3
Q
P∝
R
Answer :
Q
P = k( ) e2
R d∝
3 f
2 = k( )
4 e2
d = k( )
4 f
k = 2( )
3 12
8 4 = k( )
= 4
3
2
k = 4( )
8 Q 1
Hence, P = ( ) =8
3 R
8 m e2
10 = ( ) Hence, d = 8( )
3 12 f
9 x2
m = 10 ( ) 10 = 8 ( )
2 16
= 45. 10
x =
2
8 K
Hence, P = ( ) = 5.
3 L
8 60 e2
20 = ( ) Hence, d = 8( )
3 n f
6
