PPR Maths nbk

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VARIATIONS Guided Practice:

A Direct Variation

1.

Given that E varies directly as J. Express E in terms of J when E = 6 and J = 12. Solution: E α J E = kJ Substitute the given values of E and J to find the value of k. 6 = k (12)

k=126

k = 21

Hence, E = J21

3.

Given that p varies directly as square root of q. Express p in terms of q when p = 10 and q = 25. Solution: p α q p = k q

2.

Given that R varies directly as the square of Q and R = 48 when Q = 4, express R in terms of Q. Solution: R α Q2

4.

The table shows the values of x and y. Given that x varies directly as y3, calculate the value of m. Solution:

x 32 m y 4 2

k is a constant

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B Inverse Variation

1.

Given that W varies inversely as X. Express W in terms of X when W = 8 and X = 2. Solution:

W α X1

W = kX1

W = Xk

8 = 2k

8(2) = k k = 16

Hence, W = X16

2.

Given that g varies inversely as h. Express g in terms of h when g = 25 and h = 0.6. Solution:

g α h1

g = hk

3.

Given that M varies inversely as the square of T and M = 8 when T = 2, express M in terms of T.

4.

The table shows the values of F and y. Given that F varies inversely as y2, calculate the value of e.

F 2 e y 4 8

5. The table shows the values of p and t. Given that p varies inversely as the square root t, calculate the value of a.

p 5 a t 16 4

6. The table shows the values of X and t. Given that X varies inversely as the square of t, calculate the value of a.

X 21 a

t 4 2

k is a constant

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C Joint Variation

1.

Given that m varies directly as n2 and p. Express m in terms of n and p when m = 270, p = 6 and n = 3.

2.

Given that h varies inversely as n3 and

m and h = 2 when n = 2 and m = 121. Express h in terms of n and m.

3.

Given that J varies directly as r3 and inversely as m2 and J = 144 when r = 4 and m = 2. a. Express J in terms of r and m. b. Find the value of i. J when r = 1 and m = 6, ii. m when J = 4.5 and r = 2.

4.

Given that D varies inversely as e2 and f. Complete the table.

D 61 10

e 2 31 3

f 81 51

5.

If p varies directly as q and p = 71 when q = 25, find

a. p when q = 9, b. q when p = 355.

6.

Given F varies directly as n and inversely as d. Complete the table.

F 10 20 n 40 60 90 d 20 45

7.

Given that m is directly proportional to n2 and m = 64 when n = 4, express m in terms of n.

(SPM 2003) A m = n2 C m = 16n2 B m = 4n2 D m = 64n2

8.

It is given that y varies directly as the square root of x and y = 24 when x = 9. Calculate the value of x when y = 40.

(SPM 2005)

A 5 C 25 B 18 D 36

PPR Maths nbk

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VARIATIONS (ANSWERS) Guided Practice:

A Direct Variation

1.

Given that E varies directly as J. Express E in terms of J when E = 6 and J = 12. Solution: E α J E = kJ Substitute the given values of E and J to find the value of k. 6 = k (12)

k=126

k = 21

Hence, E = J21

3.

Given that p varies directly as square root of q. Express p in terms of q when p = 10 and q = 25. Solution: p α q p = k q 10 = k 25

k=5

10

k = 2 Hence, p = 2 q

2.

Given that R varies directly as the square of Q and R = 48 when Q = 4, express R in terms of Q. Solution: R α Q2 R = kQ2 48 = k (4)2

k=1648

k = 3 Hence, R = 3Q2

4.

The table shows the values of x and y. Given that x varies directly as y3, calculate the value of m. Solution: x α y3 x = ky3 32 = k (4)3

k=6432

k = 21 , Hence, x = 3

21 y

x 32 m y 4 2

k is a constant

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B Inverse Variation

1.

Given that W varies inversely as X. Express W in terms of X when W = 8 and X = 2. Solution:

W α X1

W = kX1

W = Xk

8 = 2k

8(2) = k k = 16

Hence, W = X16

2.

Given that g varies inversely as h. Express g in terms of h when g = 25 and h = 0.6. Solution:

g α h1

g = hk

25 = 6.0

k

k = 15

Hence, g = h

15

3.

Given that M varies inversely as the square of T and M = 8 when T = 2, express M in terms of T.

Answer: 232T

M =

4.

The table shows the values of F and y. Given that F varies inversely as y2, calculate the value of e.

Answer: 21

F 2 e y 4 8

5.

The table shows the values of p and t. Given that p varies inversely as the square root t, calculate the value of a.

Answer: 10

p 5 A t 16 4

6.

The table shows the values of X and t. Given that X varies inversely as the square of t, calculate the value of a.

Answer: 2

X 21 a

t 4 2

k is a constant

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C Joint Variation

1.

Given that m varies directly as n2 and p. Express m in terms of n and p when m = 270, p = 6 and n = 3.

Answer: m = 5pn2

2.

Given that h varies inversely as n3 and

m and h = 2 when n = 2 and m = 121. Express h in terms of n and m.

Answer: h = mn3

176

3.

Given that J varies directly as r3 and inversely as m2 and J = 144 when r = 4 and m = 2. a. Express J in terms of r and m. b. Find the value of i. J when r = 1 and m = 6, ii. m when J = 4.5 and r = 2.

Answer: a. J = 2

39mr

b.i. 41

ii. 4

4.

Given that D varies inversely as e2 and f. Complete the table.

Answer: D= 2

18fe

D = 2 and f = 27

D 61 10

e 2 31 3

f 81 51

5.

If p varies directly as q and p = 71 when q = 25, find

c. p when q = 9, d. q when p = 355.

Answer: p = 42.6q = 625

6.

Given F varies directly as n and inversely as d. Complete the table.

Answer: dnF 5

=

F = 10 and d = 15

F 10 20 n 40 60 90 d 20 45

7.

Given that m is directly proportional to n2 and m = 64 when n = 4, express m in terms of n.

(SPM 2003) A m = n2 C m = 16n2 B m = 4n2 D m = 64n2

8.

It is given that y varies directly as the square root of x and y = 24 when x = 9. Calculate the value of x when y = 40.

(SPM 2005)

A 5 C 25 B 18 D 36

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