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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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  19. Circle-Theorems Aqa Higher
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  20. Bearings-Scale-Drawing-Constructions-And-Loci Aqa Higher
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  22. Symmetry-And-Shapes 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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  26. Problem-Solving-With-Ratios Aqa Higher
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  27. Ratios Aqa Higher
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  28. Sequences Aqa Higher
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  29. Transformations-Of-Graphs Aqa Higher
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  30. Graphing-Inequalities Aqa Higher
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  32. Real-Life-Graphs Aqa Higher
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  33. Estimating-Gradients-And-Areas-Under-Graphs Aqa Higher
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  34. Equation-Of-A-Circle 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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  39. Coordinate-Geometry Aqa Higher
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  40. Iteration Aqa Higher
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  41. Simultaneous-Equations Aqa Higher
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  42. Quadratic-Equations Aqa Higher
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  43. Linear-Equations Aqa Higher
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  44. Algebraic-Proof Aqa Higher
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  45. Rearranging-Formulas Aqa Higher
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  46. Algebraic-Fractions Aqa Higher
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  48. Factorising Aqa Higher
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  52. Surds 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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  56. Simple-And-Compound-Interest-Growth-And-Decay Aqa Higher
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  57. Percentages Aqa Higher
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  58. Fractions Aqa Higher
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Exam code:8300

Ratios & FDP

How are ratios and fractions linked?

  • Fractions and ratios are closely linked and are used to compare a part of a whole

    • A fraction compares a part to the whole

    • A ratio compares one part to another part

  • For example, a pizza is sliced into 8 pieces, and shared between two people such that the first person receives 5 slices, and the second person receives 3 slices

    • As a fraction (of the whole)

      • The first person receives 5 over 8 of the pizza

      • The second person receives 3 over 8 of the pizza

  • The ratio of slices of the first person to the second person is 5 : 3

    • The 8 does not appear in the ratio but is obtained by adding the parts together (5 + 3 = 8)

  • Unlike ratios, fractions can be converted/expressed as percentages or decimals

How do I answer questions involving ratios along with fractions and/or percentages?

  • In harder ratio questions, the information you are given may also involve fractions and/or percentages

  • Remember that you can use multiplication to find fractions or percentages of something

    • E.g. Finding a fraction of a fraction 

      • Of the 3 over 40 of the people in the school who are members of staff, 2 over 3 of them wore Christmas jumpers on a particular day

      • That means 3 over 40 space cross times space 2 over 3 space equals space 6 over 120 space equals space 1 over 20 of the people in the school that day were members of staff wearing Christmas jumpers

    • E.g. Finding a percentage of a fraction

      • Of the 37 over 40 of the people in the school who are students, 88% of them wore Christmas jumpers on that same day

      • To find 88% of something, you can multiply it by 0.88

      • 37 over 40 space cross times space 0.88 space equals space 0.814, so this means 81.4% of the people in the school that day were students wearing Christmas jumpers

  • An alternative method is to ‘pick a number‘ for the total number of things in the question 

    • E.g. Assume there are a 1000 people in the school (this is not necessarily the actual total) 

    • You can calculate the percentages or fractions using real numbers

    • Remember to turn your final answer back into the correct form

Examiner Tips and Tricks

  • In these types of questions it is really important to read the question carefully, so that you are clear about which bits are referring to what!

  • Give your final answer in the form asked for by the question (fraction, ratio, or percentage).

Worked Example

A shop sells only two flavours of crisps – Stilton Surprise and Pickled Haggis. Packages of those two flavours of crisps only occur in two sizes – regular and jumbo.

The ratio of packages of Stilton Surprise crisps to packages of Pickled Haggis crisps in the shop is 7:3.

30% of the packages of Stilton Surprise crisps are regular sized.
2 over 5 of the packages of Pickled Haggis crisps are regular sized.

What percentage of all the packages of crisps in the shop are jumbo sized?

Method 1 (Pure fractions and percentages metho

Responses

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