Answer the following
1. If y ∝ x and y = 123 when x = 7.1, find:
a) y when x = 13.2
b) x when y = 391
2. The speed of a falling object is directly proportional to the time it falls. The speed after 5 seconds is 49 m/s.
a What will be the speed of a falling object after 8 seconds?
b How long will it take a falling object to reach a speed of 100 m/s?
3. T is directly proportional to d2 and T = 100 when d = 2. Find:
a T when d = 3
b d when T = 200
4. M is directly proportional to the cube of x and when x = 2, M = 24. Find:
a the value of M when x = 3
4. M is directly proportional to the cube of x and when x = 2, M = 24. Find:
a the value of M when x = 3
b the value of x when M = 120
5. When a stone falls freely, the time taken to hit the ground varies in direct proportion to the square root of the distance fallen. If it takes a stone 4 seconds to fall 78.4 m, find how long it would take for a stone to fall 500 m down a mine shaft.
6. If M is inversely proportional to t and M = 200 when t = 3, find:
a M when t = 5
b t when M = 746 (to 2 d.p.)
7. The velocity V of a body travelling a fixed distance is inversely proportional to the time taken t to complete the journey. When the velocity is 40 cm/s, the time taken is 280 seconds.
Find the time when the velocity is 50 cm/s.
8. P varies inversely to the square root of g. When g = 9, P = 20:
a Find P when g = 4.
b Find g when P = 50
9. The time taken to complete a certain job varies inversely to the number of workers doing the task. If 20 workers could do the job in 6 days, find how long it would take 15 workers to do the job.
10. The resistance, R ohms, to the flow of electricity in a wire varies inversely to the area of the cross-section of the wire. When the area is 0.15 cm2, the resistance is 0.24 ohms. Find:
a the resistance when the area is 0.06 cm2
b the area when the resistance is 0.45 ohms.
Answers for IGCSE Maths Variation -Direct & Inverse
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5. When a stone falls freely, the time taken to hit the ground varies in direct proportion to the square root of the distance fallen. If it takes a stone 4 seconds to fall 78.4 m, find how long it would take for a stone to fall 500 m down a mine shaft.
6. If M is inversely proportional to t and M = 200 when t = 3, find:
a M when t = 5
b t when M = 746 (to 2 d.p.)
7. The velocity V of a body travelling a fixed distance is inversely proportional to the time taken t to complete the journey. When the velocity is 40 cm/s, the time taken is 280 seconds.
Find the time when the velocity is 50 cm/s.
8. P varies inversely to the square root of g. When g = 9, P = 20:
a Find P when g = 4.
b Find g when P = 50
9. The time taken to complete a certain job varies inversely to the number of workers doing the task. If 20 workers could do the job in 6 days, find how long it would take 15 workers to do the job.
10. The resistance, R ohms, to the flow of electricity in a wire varies inversely to the area of the cross-section of the wire. When the area is 0.15 cm2, the resistance is 0.24 ohms. Find:
a the resistance when the area is 0.06 cm2
b the area when the resistance is 0.45 ohms.
Answers for IGCSE Maths Variation -Direct & Inverse
Downloaded from http://qusaistuition.blogspot.com
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