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Maths Gcse Aqa Higher

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  1. Scatter-Graphs-And-Correlation Aqa Higher
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  2. Cumulative-Frequency-And-Box-Plots Aqa Higher
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  3. Histograms Aqa Higher
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  4. Statistical-Diagrams Aqa Higher
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  5. Averages-Ranges-And-Data Aqa Higher
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  6. Combined-And-Conditional-Probability Aqa Higher
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  8. Simple-Probability-Diagrams Aqa Higher
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  9. Transformations Aqa Higher
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  10. Vectors Aqa Higher
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  11. 3D-Pythagoras-And-Trigonometry Aqa Higher
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  12. Sine-Cosine-Rule-And-Area-Of-Triangles Aqa Higher
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  13. Pythagoras-And-Trigonometry Aqa Higher
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  14. Area-And-Volume-Of-Similar-Shapes Aqa Higher
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  15. Congruence-Similarity-And-Geometrical-Proof Aqa Higher
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  16. Volume-And-Surface-Area Aqa Higher
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  17. Circles-Arcs-And-Sectors Aqa Higher
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  23. Exchange-Rates-And-Best-Buys Aqa Higher
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  24. Standard-And-Compound-Units Aqa Higher
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  25. Direct-And-Inverse-Proportion Aqa Higher
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  35. Functions Aqa Higher
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  36. Forming-And-Solving-Equations Aqa Higher
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  37. Graphs-Of-Functions Aqa Higher
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  38. Linear-Graphs Aqa Higher
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  44. Algebraic-Proof Aqa Higher
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  53. Rounding-Estimation-And-Bounds Aqa Higher
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  54. Fractions-Decimals-And-Percentages Aqa Higher
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  55. Introduction Aqa Higher
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Exam code:8300

Working with proportion

What is direct proportion?

  • Direct proportion

    • As one quantity increases/decreases by a certain rate (factor)

    • The other quantity will increase/decrease by the same rate 

  • The ratio of the two quantities is constant

    • E.g. 2 boxes of cereal is 800 g of cornflakes

    • Doubling the number of boxes of cereal (4 boxes) will double the amount of cornflakes (1600 g)

How do I solve direct proportion questions?

  • Read through wordy direct proportion questions carefully

    • Ensure that you understand the context of the question

    • Some questions may tell you the relationship between the two values as a ratio

  • Identify the two quantities involved

    • E.g. Hours worked and pay

  • Find the factor that you will be increasing/decreasing by

    • This may be given to you in the question, e.g. ‘the amount is tripled’

      • The quantity is multiplied by three

    • Alternatively, find the factor by dividing the ‘new’ quantity by the ‘old’ quantity

  • Multiply the other quantity by this factor to find the required quantity

    • E.g. If three times as many hours are worked, the pay will be three times more in total

  • Give your final answer in context

    • Round and give units where appropriate

Examiner Tips and Tricks

  • You may have to round an answer to a whole number, but think carefully about the context of the question!

    • Rounding to the nearest whole number is often appropriate

    • Sometimes you need to round up to the next whole number even if it is not the nearest

      • E.g. If you need 1.3 tins of paint, round the number of tins required up to 2 to ensure that you have enough paint

What is the unitary method?

  • The unitary method means finding one of something (1 unit of something)

    • This can be a useful strategy

  • For example, find the weight of 7 boxes, if 8 boxes weigh 60 kg

    • Find the weight of 1 box (1 unit) using division

      • 60 kg ÷ 8 boxes = 7.5 kg per box

    • Scale this unit up using multiplication

      • 7.5 kg per box × 7 boxes = 52.5 kg

Worked Example

The bonus received by an employee is directly proportional to the profit made by the company they work for.
Bonuses are paid at a rate of $250 per $3000 profit the company makes.

(i) Work out the bonus an employee receives if the company makes a profit of $18 000.

(ii) If the company makes less than $600 profit, no bonus is paid.

Find the lowest bonus an employee could receive.

(i) Identify the two quantities ‘profit’ and ‘bonus’

Find the factor (‘new’ ÷ ‘old’) from the profit

fraction numerator 18 space 000 over denominator 3000 end fraction equals 6

Multiply the bonus by the factor

250 cross times 6 equals 1500

Answer in context with units

An employee should receive a bonus of $1500 

(ii) We are still working with profit and bonus

The lowest bonus will be when the company makes exactly $600 profit

Find the factor using ‘new’ ÷ ‘old’

600 over 3000 equals 1 fifth

Find the amount of bonus by multiplying by the factor

250 cross times 1 fifth equals 50

Answer in context with units

The lowest amount of bonus an employee could receive is $50

What is inverse proportion?

  • Inverse proportion

    • As one quantity increases by a certain rate (factor)

    • The other quantity will decrease by the same rate

  • This relationship applies vice versa too, if one quantity decreases the other increases 

  • E.g. If 2 robots take 15 hours to build a car

    • Tripling the number of robots (6) would mean the time taken to build a car would be divided by 3 (5 hours)

How do I solve inverse proportion questions?

  • Read through wordy inverse proportion questions carefully

    • Ensure that you understand the context of the question

    • Some questions may tell you the relationship between the two values as a ratio

  • Identify the two quantities involved

  • Find the factor that you will be increasing/decreasing by

    • This may be given to you in the question, e.g. ‘the amount is tripled’

    • Alternatively, find this by dividing the ‘new’ quantity by the ‘old’ quantity

  • Divide the other quantity by this factor to find the required quantity

  • Give your final answer in context

    • Round and give units where appropriate

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