25[A Math CD]

1 © Penerbitan Pelangi Sdn. Bhd.

Paper 1

1. y ∝ x y = kx 6 = k(2)

k = 6—2

= 3Hence, y = 3x

Answer: A

2. y ∝ x y = kx 10 = k(5)

k = 10–––5

= 2Hence, y = 2x

Answer: C

3. p ∝ t p = kt 4 = k(1) k = 4Hence, p = 4t

When t = 2, p = 4(2) p = 8Answer: D

4. y ∝ 1—x y = k—x

2 = k—3

k = 2 × 3 = 6

Hence, y = 6—x

Answer: B

5. Q ∝ 1—x Q = k—x

9 = k—4

k = 4 × 9 = 36

Hence, Q = 36–––x

Answer: D

6. w ∝ 1—v w = k—v

3 = k—4

k = 3 × 4 = 12

Hence, w = 12–––v

When v = 2, w = 12–––2

= 6

Answer: D

7. y ∝ x—t

y = kx–––t

15 = k × 6–––––4

k = 15 × 4––––––6

= 10

Hence, y = 10x––––t

Answer: B

CHAPTER

25 VariationsCHAPTER

2

Mathematics SPM Chapter 25

© Penerbitan Pelangi Sdn. Bhd.

8. P ∝ Q

–––R

P = kQ–––R

4 = k × 24––––––3

k = 3 × 4–––––24

= 1—2

Hence, P = Q

–––2R

Answer: C

9. T ∝ x—y

T = kx–––y

7 = k × 14––––––12

k = 7 × 12––––––14

= 6

Hence, T = 6x–––y

n = 6 × 16––––––8

= 12Answer: B

Paper 1

1. H ∝ 1x2

H = kx2

12

= k42

k = 12

× 42

= 8

Hence, H = 8x2

When H = 32, 32 = 8x2

x2 = 832

= 14

x = 14

= 12

Answer: C

2. Q ∝ H2

Q ∝ 1––––3 R

Hence, Q ∝ H2––––

3 RAnswer: B

3. H ∝ F2–––G

H = kF2–––G

12 = k × 62––––––

16

k = 12 × 16–––––––62

= 16–––3

Hence, H = 16F2––––3G

15 = 16F2––––––3 × 20

F2 = 15 × 3 × 20––––––––––16

= 225––––4

F = 225––––4

= 15–––2

Answer: D

4. T ∝ x3

T ∝ 1–––y

Hence, T ∝ x 3–––

y

x3 T ∝ ––– y

1—2

Compare with T ∝ x m

y n

Hence, m = 3, n = 12

Answer: C

5. E ∝ 1–––t

Answer: A

3



6. e ∝ 1––––f g

e = k––––f g

3 = k––––4 9

k = 3 × 4 9 = 36Hence, e = 36––––

f g

9—2 = 36––––

2 n

9—2 = 18–––

n

n = 2 × 18––––––9

= 4 n = 42

= 16

Answer: D

7. p ∝ q3

p = kq3

12 = k × 23

k = 12–––8

= 3––2

Hence, p = 3—2 q3

r = 3—2 (4)3

= 96

Answer: C

8. P ∝ 1x

P = kx

3 = k4

k = 12

Hence, P = 12x

Answer: A

9. P ∝ 1x2

P = k 1x2

6 = k 132

k = 54

Hence, P = 54 1x2

When x = 4, P = 54 142

= 278

Answer: A

10. y ∝ t

y = k t

2 = k 162 = 4k

k = 12

Hence, y = 12

t

When t = 25, y = 12

25

= 52

Answer: D

11. H ∝ xy

H = kxy

8 = k163

k = 3 ×84

= 6

Hence, H = 6xy

When x = 36 and y = 4

H = 6364

= 9Answer: B

12. MN 2 = k

M = k 1–––N 2

Hence, M ∝ 1–––N 2

Answer: B

4



13. R ∝ 1X3

R = k1 1X3 2

32

= k1 123 2

k = 12

Hence, R = 12X 3

m = 1243

= 316

Answer: A

14. y ∝ x3

y = kx3

6 = k × 23

k = 6–––23

= 3—4

Hence, y = 3—4

x3

When y = 48, 48 = 3—4

x3

x3 = 48 × 4––––––3

x = 3 64 = 4

Answer: C

15. w ∝ 1–––x2

w = k–––x2

6 = k–––32

k = 6 × 32

= 54

Hence, w = 54–––x2

When x = 6, w = 54–––62

= 3—2

Answer: A

16. y ∝ rt2

y = krt2

54 = k × 4 × 32

k = 54–––––4 × 9

= 3—2

Hence, y = 3—2

rt2

45 = 3—2

× h × 52

h = 2 × 45––––––3 × 52

= 1.2

Answer: A

Paper 1

1. y ∝ x y = kx 10 = k × 2

k = 10–––2

= 5Hence, y = 5x

When x = 4, y = 5 × 4 = 20

Answer: C

2. n ∝ p n = kp 12 = k × 3

k = 12–––3

= 4Hence, n = 4p

Answer: D

5



3. y ∝ t2

y = kt 2 36 = k × 32

k = 36–––9

= 4Hence, y = 4t2

When y = 100, 100 = 4t2

t2 = 100––––4

= 25 t = 25 = 5

Answer: B

4. T ∝ q2

T = kq2

24 = k × 42

k = 24–––16

= 3—2

Hence, T = 3—2

q2

Answer: A

5. H ∝ G3

H = kG3

216 = k × 33

k = 216––––33

= 8Hence, H = 8G3

Answer: B

6. e ∝ f 3 e = kf 3 36 = k × 33

k = 36–––27

= 4—3

Hence, e = 4—3

f 3

x = 4—3

× 63

= 288

Answer: C

7. L ∝ m L = k m 3 = k 144 3 = k(12)

k = 3–––12

= 1—4

Hence, L = 1—4

m

Answer: D

8. P ∝ h P = k h

15 = k 9–––16

15 = k × 3—4

k = 4 × 15––––––3

= 20

Hence, P = 20 h 60 = 20 w

w = 60–––20

= 3 w = 32

= 9

Answer: C

9. y ∝ m y = km y = k(5h − 3) 14 = k(5 × 2 − 3) 14 = 7k

k = 14–––7

= 2Hence, y = 2(5h − 3)

When y = 44, 44 = 2(5h − 3) = 10h − 6 44 + 6 = 10h

h = 50–––10

= 5

Answer: A

6



10. P—Q

= 2—1

= 3–––3—2

= 4—2

= 2

Hence, P—Q

= 2

P = 2Q

Answer: B

11. F–––e2 = 4–––

12 = 16–––22 = 36–––

32 = 4

Hence, F–––e2 = 4

F = 4e2

Answer: A

12. y ∝ n y = kn

y = k––––––8x – 5

5 = k–––––––8(1) – 5

5 = k—3

k = 3 × 5 = 15

Hence, y = 15––––––8x – 5

When x = 5, y = 15–––––––8(5) – 5

= 15–––35

= 3—7

Answer: C

13. J ∝ 1—e

J = k—e

8 = k—5

k = 5 × 8 = 40

Hence, J = 40–––e

When J = 10, 10 = 40–––e e = 40–––

10 = 4

Answer: D

14. m ∝ 1—t

m = k—t

8 = k—2

k = 2 × 8 = 16

Hence, m = 16–––t

Answer: A

15. Q ∝ 1–––x2

Q = k–––x2

10 = k––––– 1—

2

2

k = 1—2

2 × 10

= 5—2

Hence, Q = 5––––2x2

Answer: C

16. g ∝ 1–––r2

g = k–––r2

32 = k–––12

k = 32

Hence, g = 32–––r2

128 = 32–––h2

h2 = 32––––128

= 1—4

h = 1—4

= 1—2

Answer: D

7



17. G ∝ 1–––y3

G = k–––y3

2 = k–––43

k = 2 × 43 = 128

Hence, G = 128––––y3

Answer: D

18. h ∝ 1–––g3

h = k–––g3

3 = k–––23

k = 23 × 3 = 24

Hence, h = 24–––g3

1––9

= 24–––x3

x3 = 24 × 9 x = 3 216 = 6

Answer: D

19. y ∝ 1–––q

y = k–––q

1—6

= k––––81

k = 81

––––6

= 9—6

= 3—2

Hence, y = 3––––2 q

Answer: A

20. P ∝ 1–––y

P = k–––y

2 = k –––––121

k = 2 × 121 = 22

Hence, P = 22–––

y

When y = 16, P = 22––––16

= 22–––4

= 11–––2

Answer: B

21. R ∝ x–––p3

R = kx–––p3

3 = k(4)––––23

k = 23 × 3––––––4

= 6

Hence, R = 6x–––p3

2 = 6x–––33

x = 2 × 33––––––

6 = 9

Answer: C

22. D ∝ H 2–––E

D = kH 2––––E

10 = k × 52––––––

20

k = 20 × 10–––––––52

= 8

Hence, D = 8H 2––––E

18 = 8 × 62––––––

E E = 8 × 62

––––––18

= 16

Answer: C

8



23. F ∝ 1LM

F = kLM

45 = k12

× 6

45 = k3

k = 3 × 45 = 135

Hence, F = 135LM

27 = 13513

x

13

x = 13527

x = 135 × 327

= 15

Answer: C

24. f ∝ m2–––

n

f = km2

––––n

16 = k × 42––––––

9

k = 16 9–––––42

= 3

Hence, f = 3m2––––

n

Answer: B

25. p ∝ x y p = kx y 6 = k(6) 4 = 12k

k = 612

= 12

Hence, p = 12

x y

9 = 12

(2) a

9 = a a = 92

= 81

Answer: D

26. Q ∝ x3

Q ∝ 1y

Hence, Q ∝ x3

y

Q ∝ x3 y− 1—2

Compare with Q ∝ xmyn

Hence, m = 3 and n = − 12

.

Answer: C

27. Let d = density of the iron cube m = mass of the iron cube and x = lenght of the side of the iron cube

d ∝ mx3

d = k mx3

7.85 = k 7 850103 7.85 kg = 7 850 g

k = 1

Hence, d = mx3

When x = 6 cm,

7.85 = m63

m = 1695.6 g = 1.6956 kg

Answer: A

28. Let E = kinetic energy m = mass of the object and v = speed of the object

E ∝ mv2

E = kmv2

640 = k(5)(16)2 k = 0.5Hence, E = 0.5 mv2

When m = 5, E = 1000 1000 = 0.5(5)v 2 v2 = 400 v = 20 m s–1

Answer: B

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25[A Math CD]