P1 Variation Modul
- 1. PPR Maths nbk VARIATIONS Guided Practice: A Direct Variation 1. Given that E varies directly as J. 3. Given that p varies directly as square Express E in terms of J when E = 6 and root of q. Express p in terms of q when p J = 12. = 10 and q = 25. Solution: EαJ Solution: p α q E = kJ k is a constant p =k q Substitute the given values of E and J to find the value of k. 6 = k (12) 6 =k 12 1 k= 2 1 Hence, E= J 2 2. Given that R varies directly as the 4. x 32 m square of Q and R = 48 when Q = 4, y 4 2 express R in terms of Q. The table shows the values of x and y. Solution: Given that x varies directly as y3, R α Q2 calculate the value of m. Solution: 1
- 2. PPR Maths nbk B Inverse Variation 1. Given that W varies inversely as X. 2. Given that g varies inversely as h. Express W in terms of X when W = 8 Express g in terms of h when g = 25 and X = 2. and h = 0.6. Solution: 1 Solution: W α X 1 g α h 1 k is a constant W=k X k g = k h W = X k 8 = 2 8(2) = k k = 16 16 Hence, W= X 3. Given that M varies inversely as the 4. F 2 e square of T and M = 8 when T = 2, y 4 8 express M in terms of T. The table shows the values of F and y. Given that F varies inversely as y2, calculate the value of e. 5. 6. p 5 a 1 t 16 4 X a 2 t 4 2 The table shows the values of p and t. Given that p varies inversely as the The table shows the values of X and t. square root t, calculate the value of a. Given that X varies inversely as the square of t, calculate the value of a. 2
- 3. PPR Maths nbk C Joint Variation 1. Given that m varies directly as n2 and p. 2. Given that h varies inversely as n3 and Express m in terms of n and p when m m and h = 2 when n = 2 and m = 121. = 270, p = 6 and n = 3. Express h in terms of n and m. 3. Given that J varies directly as r3 and 4. 1 inversely as m2 and J = 144 when r = 4 D 10 6 and m = 2. 1 a. Express J in terms of r and m. e 2 3 b. Find the value of 3 i. J when r = 1 and m = 6, 1 f 81 ii. m when J = 4.5 and r = 2. 5 Given that D varies inversely as e2 and f. Complete the table. 5. If p varies directly as q and p = 71 6. when q = 25, find F 10 20 a. p when q = 9, n 40 60 90 b. q when p = 355. d 20 45 Given F varies directly as n and inversely as d. Complete the table. 7. Given that m is directly proportional to 8. It is given that y varies directly as the 2 n and m = 64 when n = 4, express m in square root of x and y = 24 when x = 9. terms of n. Calculate the value of x when y = 40. (SPM 2003) (SPM 2005) A m = n2 C m = 16n2 A 5 C 25 B m = 4n2 D m = 64n2 B 18 D 36 3
- 4. PPR Maths nbk VARIATIONS (ANSWERS) Guided Practice: A Direct Variation 1. Given that E varies directly as J. 3. Given that p varies directly as square Express E in terms of J when E = 6 and root of q. Express p in terms of q when p J = 12. = 10 and q = 25. Solution: EαJ Solution: p α q E = kJ k is a constant p =k q Substitute the given values of E and J to find the value of k. 6 = k (12) 10 = k 25 6 10 =k =k 12 5 1 k=2 k= 2 Hence, p =2 q 1 Hence, E= J 2 2. Given that R varies directly as the 4. x 32 m square of Q and R = 48 when Q = 4, y 4 2 express R in terms of Q. The table shows the values of x and y. Solution: Given that x varies directly as y3, R α Q2 calculate the value of m. Solution: R = kQ2 x α y3 48 = k (4)2 x = ky3 48 32 = k (4)3 =k 16 32 =k k=3 64 Hence, R = 3Q2 1 1 3 k= , Hence, x= y 2 2 4
- 5. PPR Maths nbk B Inverse Variation 1. Given that W varies inversely as X. 2. Given that g varies inversely as h. Express W in terms of X when W = 8 Express g in terms of h when g = 25 and X = 2. and h = 0.6. Solution: 1 Solution: W α X 1 g α h 1 k is a constant W=k X k g = k h W = X k 25 = k 0.6 8 = 2 k = 15 8(2) = k 15 Hence, g= k = 16 h 16 Hence, W= X 3. Given that M varies inversely as the 4. F 2 e square of T and M = 8 when T = 2, y 4 8 express M in terms of T. The table shows the values of F and y. Given that F varies inversely as y2, calculate the value of e. 1 Answer: 2 Answer: M = 32 T2 1 5. p 5 A 6. X a 2 t 16 4 t 4 2 The table shows the values of p and t. The table shows the values of X and t. Given that p varies inversely as the Given that X varies inversely as the square root t, calculate the value of a. square of t, calculate the value of a. Answer: 10 Answer: 2 5
- 6. PPR Maths nbk C Joint Variation 1. Given that m varies directly as n2 and p. 2. Given that h varies inversely as n3 and Express m in terms of n and p when m m and h = 2 when n = 2 and m = 121. = 270, p = 6 and n = 3. Express h in terms of n and m. Answer: m = 5pn2 Answer: h = 176 n3 m 3. Given that J varies directly as r3 and 4. 1 D 10 inversely as m2 and J = 144 when r = 4 6 and m = 2. 1 a. Express J in terms of r and m. e 2 3 3 b. Find the value of 1 i. J when r = 1 and m = 6, f 81 ii. m when J = 4.5 and r = 2. 5 Given that D varies inversely as e2 and f. 9r 3 Answer: a. J = 2 Complete the table. m 18 1 Answer: D= 2 b.i. fe 4 D = 2 and f = 27 ii. 4 5. If p varies directly as q and p = 71 6. F 10 20 when q = 25, find n 40 60 90 c. p when q = 9, d 20 45 d. q when p = 355. Given F varies directly as n and Answer: p = 42.6 inversely as d. Complete the table. q = 625 5n Answer: F = d F = 10 and d = 15 7. Given that m is directly proportional to 8. It is given that y varies directly as the 2 n and m = 64 when n = 4, express m in square root of x and y = 24 when x = 9. terms of n. Calculate the value of x when y = 40. (SPM 2003) (SPM 2005) A m = n2 C m = 16n2 A 5 C 25 B m = 4n2 D m = 64n2 B 18 D 36 6
- 7. PPR Maths nbk 7