1. GCSE Maths (Higher) Indirect Proportion

2. Types of proportion Time (min) mph 90 60 ? 70 MoreLess MoreLess ?5 MoreLess MoreLess 508 Direct Proportion percentage Conversions Ratio Fractions Similar shapes Arc & sectors How many more can you think of? km miles Inverse Proportion Any question where increasing one number has the effect of reducing the other

3. What is number? Can you think of any more? Number Ratio Percentage s Money Number Fractions Time Lengths Weights Standard Index Form

4. Below is a good rule of thumb for questions on proportion. Number Area (square number) Area (square number) Volume (cube number) Volume (cube number)

5. Relationships that don’t fit Number Area (square number) Area (square number) Volume (cube number) Volume (cube number) No

6. But what do you do when you are given a questions that don’t seem to fit? Number Area (square number) Area (square number) Volume (cube number) Volume (cube number)

7. 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. No What price are the large candles, if the cost of the candle is proportional to its volume?

8. Strategy – extract information onto 3 lines A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high. Cost Height cm Height cm 3 8 512 3.20? 14 2744 Large candles cost £17.15 in the gift shop What price are the large candles, if the cost of the candle is proportional to its volume (not its height)?

9. Number Area (square number) No A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high. It takes 144cm 2 of plastic film to wrap the small candle. How much does the large candle need?

10. Strategy extract information onto 3 lines A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high. It takes 144cm 2 of plastic film to wrap the small candle. How much does the large candle need? area Height cm Height cm 2 8 64 144? 14 196 Large candles need 441cm 2 of wrap

11. Strategy for Indirect proportion Answer – make sure it is in context with the question a) T in terms of L is: T= 4 Calculation – to get method marks. a) 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 a)Express T in terms of L b)Find T when L = 400 c)Find L when T = 60 Lcm √L T = sec 72.25 L √72.25√L 34 T

12. Strategy for Indirect proportion Answer – make sure it is in context with the question a) T in terms of L is: T= 4 b) T=80 Calculation – to get method marks. b) From a) 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 a)Express T in terms of L b)Find T when L = 400 c)Find L when T = 60 Lcm √l T = sec 72.25 L √72.25√L 34 T

13. Strategy for Indirect proportion 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 Calculation – to get method marks. c) 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 a)Express T in terms of L b)Find T when L = 400 c)Find L when T = 60 Lcm √l T = sec 72.25 L √72.25√L 34 T

14. Strategy for Indirect proportion Answer – make sure it is in context with the question Calculation – to get method marks. Extract information from question onto lines. Question