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## GCSE Maths (Higher)

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**GCSE Maths(Higher)**Indirect Proportion**Types of proportion**• Direct Proportion • percentage • Conversions • Ratio • Fractions • Similar shapes • Arc & sectors • How many more can you think of? More Less 70 60 mph Time (min) ? 90 Less More Less More Inverse Proportion Any question where increasing one number has the effect of reducing the other 8 50 km miles 5 ? Less More**What is number?Can you think of any more?**Number Time Ratio Fractions Lengths Number Weights Money Percentages Standard Index Form**Below is a good rule of thumb for questions on proportion.**Number Number Area (squarenumber) Area (square number) Volume (cube number) Volume (cube number)**Relationships that don’t fit**No Number Number No Area (squarenumber) Area (square number) Volume (cube number) Volume (cube number) No**But what do you do when you are given a questions that**don’t seem to fit? Number Number Area (squarenumber) Area (square number) Volume (cube number) Volume (cube number)**A gift shop sells small candles that are 8cm high and cost**£3.20. It sells similar candles that are 14cm high. Number No Volume (cube number) What price are the large candles, if the cost of thecandleis proportional to its volume?**Strategy – extract information onto 3 lines**3.20 ? Cost 8 14 Height cm 512 2744 Height cm3 Large candles cost £17.15 in the gift shop A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high. What price are the large candles, if the cost of thecandleis proportional to its volume (not its height)?**No**Number Area (square number) A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high. It takes 144cm2 of plastic film to wrap the small candle. How much does the large candle need?**Strategy extract information onto 3 lines**144 ? area 8 14 Height cm 64 196 Height cm2 Large candles need 441cm2 of wrap A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high. It takes 144cm2 of plastic film to wrap the small candle. How much does the large candle need?**Extract information from question onto lines.**Question A simple pendulum of length L cm, takes T seconds to swing from A to B. T is proportional to square root of L. When T = 34 sec, L = 72.25cm • Express T in terms of L • Find T when L = 400 • Find L when T = 60 Calculation – to get method marks. a) Answer – make sure it is in context with the question a) T in terms of L is: T= 4 Strategy for Indirect proportion 72.25 L Lcm √72.25 √L √L 34 T T = sec**Extract information from question onto lines.**Question A simple pendulum of length L cm, takes T seconds to swing from A to B. t is proportional to square root of L. When T = 34 sec, L = 72.25cm • Express T in terms of L • Find T when L = 400 • Find L when T = 60 Calculation – to get method marks. b) From a) Answer – make sure it is in context with the question a) T in terms of L is: T= 4 b) T=80 Strategy for Indirect proportion 72.25 L Lcm √72.25 √L √l 34 T T = sec**Extract information from question onto lines.**Question A simple pendulum of length L cm, takes T seconds to swing from A to B. T is proportional to square root of L. When T = 34 sec, L = 72.25cm • Express T in terms of L • Find T when L = 400 • Find L when T = 60 Calculation – to get method marks. c) Answer – make sure it is in context with the question a) T in terms of L is: T= 4 b) T=80 when L = 400 c) L = 225 when T=60 Strategy for Indirect proportion 72.25 L Lcm √72.25 √L √l 34 T T = sec**Extract information from question onto lines.**Question Calculation – to get method marks. Answer – make sure it is in context with the question Strategy for Indirect proportion