PROPORTION
TIP: When doing these sort of problems, remember:
a) A test
to see if two quantities are directly proportional: Firstly if one quantity
= 0 does the other quantity = 0? Secondly if one quantity is doubled, is the
other quantity doubled?
If the answer to both of these questions is yes, then the two quantities are
directly proportional to each other.
b) The symbol a means "is proportional to".
c) If a a b then a = kb (where k is a constant). Most questions revolve around you having to find k, then using k to solve a related problem.
d) Inverse proportion is where a a 1/b. Other types of proportion seen are square and cubic where a a b2 and a a b3.
e) Direct proportionality appears on a graph as a straight line which passes through the origin.
Solve the following:
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1. The cost of Chanel T'Unnel perfume is directly proportional to the amount of perfume in the bottle. A bottle containing 50ml of perfume costs £20.00 a) Find a rule which connects the price and the volume of perfume. b) Work out the cost of a 100ml bottle of perfume.
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2. The extension E of a spring is directly proportional to the force F pulling the spring. If a force of 15N is applied to the spring the extension is measured as 4cm. What is the extension when the force is 12N ? |
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3. The distance d travelled by a car is directly proportional to the square of the time t taken for the journey. a) Deduce a formula for d in terms of t. When t = 10 seconds d = 200 metres. b) Calculate: i) The distance travelled in 1 minute. ii) The time taken when d = 3,000 metres.
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4. The time taken to build a house is inversely proportional to the number of builders working on it. If 2 builders are working on the house it will take a two months to complete. How long will it take to complete the house if 5 builders are working on it? |
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5. The variables m and n are related in such a way that n is directly proportional to the cube of m. Complete the table of values below:
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6. q is directly proportional to the square root of p.
a) Work out a formula involving p and q. b) What is the value of q when p = 36?
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7. A football kicked into the air to height h is directly proportional to square of the speed v at which it was kicked. If the ball is kicked at 20 metres per second, it will reach a height of 20 metres. a) How high does the ball reach if it is kicked at 18 m/s ? b) How high does the ball reach if it is kicked at 25 m/s ?
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8. A lorry travels 350km in 2 hours 40 minutes. The distance it travels is directly proportional to the time taken. How far will the lorry travel in 4 hours?
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