DIRECT AND INDIRECT PROPORTION

1. Given that y is directly proportional to the positive square root of x, and y = 6 when x = 4,

(a) find the equation relating x and y, (b) find the value of y when x = 16,(c)find the value of x when y = 15.

Ans:(a)_________________[2]

(b)_________________[1]

(c) _________________[1]

2.The following table shows some corresponding values of x and y.

x0.30.822.4

y120451815

(i)Determine if x and y are in direct or inverse proportion.[2]

(ii)State the value of the constant, k. [1]

(iii)Hence write down an equation connecting x and y.[1]

(iv)Find the value of x when y = 22.5.[1]

3. It is given that y is inversely proportional to .

(a) Given that y = 2 when x = 4, express y in terms of x.

(b) Hence find the values of x when y = 8.

Ans: (a) _______________ [2]

(b) x = _____or _____ [2]

4.Given that y is inversely proportional to and that y = 5 when x = 9, find y when x is 484.

[3]

5.(a)Given that y is directly proportional to (2x + 1)2. The value of y when x = 1.5 is 48.

(i)Express y in terms of x.[2]

(ii)Hence find the value of y when x = 7.[1]

(b)Given that y is inversely proportional to square of x and that y = 5 when x = 2, find the positive value of x when y = 0.8.

[3]

(c)It takes 6 men 8 days to paint 20 halls. Assuming that all the men work at the same rate, how long will it take 3 men to paint 15 such halls? [2]

6. 45 men takes 29 days to complete painting a house. Assuming that the workers work at the same rate, how many more men must be hired, to complete the job 14 days earlier?

Answer ...................................................

[3]

7.When water is poured into a container, the depth of the water, d, is inversely proportional to the square of the base radius, r, of the container. When the radius is 3 cm, the depth of water is 24 cm. (a) Form an equation relating d and r. (b) Find the depth of the water when the radius is 4 cm.

Answer (a) ....... [2]

(b) .. cm [1]8.A ball is dropped from a height of 112 m. It reaches the ground in 4 s.Given that the vertical falling distance is directly proportional to the square of the falling time, find:(a) the equation connecting the vertical distance and the falling time,(b) the falling time, if the ball is dropped from a height of 1008 m.

Ans: (a)___________________ [2]

(b) __________________s [2]

9.Given p is inversely proportional to , and p = 2.5 when . Find the value of q when p = 4.[3]

10. If 2 soldiers take 3 hours to dig 2 trenches, find the time needed for 8 soldiers to dig 12 trenches.

_______________ hours [3]

11.

It is given that D is inversely proportional to . When , find the value of D when [4]

12. It is given that y is inversely proportional to the square of (x 3) and that y = 30 when x = 5.(a)Write down an equation connecting y and x.(b)Find the values of x if y = 4.

13.Given that , where k is a constant, and that y = 2 when x = 3, find

(a)the value of y when x = 48,

(b)the values of x when y = 1800.

Ans:(a)[2]

(b)[2]

14.12 men can build a house in 20 days. If 4 more men are employed, how many days would it take to build a similar house, assuming they work at the same rate?[2]

15.Two quantities, q and p, are in direct proportion. The sum of the values of q when p = 6 and when p = 11 is 51.

(a) Find an equation connecting q and p.

(b) Find then value of p when q = 72Ans :(a)____________________ [3]

(b)p = _________________ [1]

16.If 10 men take 16 hours to complete a renovation work in a day.

(a)How long will it take 4 men, working an 8-hour day?

(b) If they are paid $8.50 per hour each, find the labour cost of the work.

(c) Assuming that renovation work has to be completed within 4 days, how many hours will 3 men have to work a day to complete the job in time?

Ans :(a)_______________ days [2]

(b)$__________________ [2]

(c)_______________ hours [2]

17.John is a manager of a factory that builds machines. If it takes 8 workers to complete a machine in 30 days, find i.the number of workers John needs to deploy if the customer wants a machine in 16 days. [1]ii.the number of workers John needs to deploy to deliver 6 machines in 16 days. [1]

18.It takes 20 workers to complete a painting job of a housing estate in 30 days. (a) If only 15 workers are available, how long will they take to complete the job? (b) The contractor decided to speed up and complete the job within 10 days. How many workers would be required?

19(a).Given that h is inversely proportional to (x + 3) and h = 4 when x = 3. Find the value of h when x = 8. [3] (b).The period P of oscillation of a simple pendulum is directly proportional to the square root of its length L of the pendulum. When the length of the pendulum is 64 cm, the period is 3.2 seconds.Find(i)an equation connecting P and L, [2](ii)the period when the length is 144 cm, [1](iii)the length when the period is 6 seconds.[2]

20.y is directly proportional to x2. It is known that y = 10 for a particular value of x. Find the value of y when this value of x is halved.

Answer :[3]

21.The kinetic energy of a particle is directly proportional to the square of its speed. When the speed is 20 metres per second, the energy is E.

(a) When the speed is increased by 50%, find an expression for the energy of the particle in terms of E.

(b) When the energy is decrease by 36%, find the speed of the particle.

Answer (a)...............................[2]

(b)...............................[2]