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Tasksheet 2 : Variations Name : ___________________________ Class : ____________ Example : (a) Varies Directly

Given that A is directly proportional to B and A = 15 when B = 5, express A in terms of B.

Answer : A ∝B A = kB 15 = k(5)

k = 5

15

= 3 Hence, A = 3B

(b) Varies Inversely Given that C varies inversely as D and

C = 2 when D = 9, express C in terms of D.

Answer :

C ∝D1

C = kD1

2 = k(91 )

k = 2 )19(

k = 18

Hence, C = D18

Answer all questions. 1. Given that G is directly proportional to s and G = 20 when s = 3, express G in terms of s. 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

3. The table shows the values of x and y. Given that x varies directly as the square of y, calculate the value of m.

x 44 m y 4 2

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4. The table shows the values of P and Q. Given that P varies directly as the square of Q, calculate the value of i.

P 200 72 Q 10 i

5. The table shows the values of u and v. Given that u varies inversely as the square of v, calculate the value of w.

u 16 w v 2 6

6. The table shows the values of E and F.

Given that E varies inversely as F, find the value of g.

E 2 g F 3 12

7. Given that S varies inversely as T and S = 7 when T = 5, express S in terms of T.

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8. The table shows the values of P and Q. Given that P varies inversely as the square of Q, calculate the value of R

P 31

3

Q 5 R

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

10. The table shows the values of d, e and f.

Given that d varies directly as square of e and inversely as square root of f , find the value of x and y.

d e f 4 1 4

10 x 16

51

31

y

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Answers for Tasksheet 2 : Variations Name : ___________________________ Class : ____________ Answer all questions. 1. Given that G is directly proportional to s and G = 20 when s = 3, express G in terms of s. Answer : G ∝ s G = ks 20 = k(3)

k = 320

Hence, G = 320 s

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

Answer : N ∝R N = kR 5 = k(30)

k = 305

= 61

Hence, N = 61 R

a = 61 (12)

= 2.

3. The table shows the values of x and y. Given that x varies directly as the square of y, calculate the value of m.

x 44 m y 4 2

Answer : x ∝ 2y x = k 2y 44 = k(4) 2

k = 1644

= 4

11

Hence, x = 4

11 2y

m = 4

11 (2) 2

= 11 4. The table shows the values of P and Q. Given that P varies directly as the square of Q, calculate the value of i.

K 200 72 L 10 i

Answer : P ∝ 2Q P = k 2Q 200 = k(10) 2

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k =

100200

= 2 Hence, P = 2 2Q 72 = 2(i) 2

i = 2

72

= 6 5. The table shows the values of u and v. Given that u varies inversely as the square of v, calculate the value of w.

u 16 w v 2 6

Answer :

u ∝ 2

1v

u = k 2

1v

16 = k( 221 )

k = 64

Hence, u = 2

64v

w = 2664

= 9

16

6. The table shows the values of E and F.

Given that E varies inversely as F, find the value of g.

E 2 g F 3 12

Answer :

E ∝F1

E = kF1

2 = k(31 )

k = 6

7. Given that S varies inversely as T and S = 7 when T = 5, express S in terms of T. Answer :

S ∝T1

S = kT1

7 = k(51 )

k = 35

Hence, S = T35

8. The table shows the values of P and Q. Given that P varies inversely as the square of Q, calculate the value of R

P 31

3

Q 5 R

Answer :

P ∝ 2

1Q

P = k 2

1Q

31 = k( 25

1 )

k = 325

Hence, P = )(3

252Q

3 = )(3

252R

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Hence, E = F6

g = 126

= 21

R = )3(3

25

= 35

= 321

9. The table shows the values of P, Q and R.

Given that J varies directly as Q and inversely as L , find the value of m and n.

P Q L 2 3 4

10 m 12 20 60 n

Answer :

P ∝RQ

P = k )(RQ

2 = k(43 )

k = 2(34 )

= 38

Hence, P = 38 )(

RQ

10 = 38 )

12( m

m = 10 )29(

= 45.

Hence, P = 38 )(

LK

20 = 38 )60(

n

10. The table shows the values of d, e and f.

Given that d varies directly as square of e and inversely as square root of f , find the value of x and y.

d e f 4 1 4

10 x 16

51

31

y

Answer :

d ∝f

e2

d = k(f

e2

)

4 = k(4

12

)

k = 4(12 )

= 8

Hence, d = 8(f

e2

)

10 = 8 )16

(2x

x = 2

10

= 5 .

Hence, d = 8(f

e2

)

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n = 20

160

= 8.

51 = 8

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⎠

⎞

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⎝

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y

2

31

y = 2

598

⎟⎠⎞

⎜⎝⎛ ×

= 81

1600

= 19.75 (2 d.p.)