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Maths Gcse Aqa Foundation

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  1. Scatter-Graphs-And-Correlation Aqa Foundation
    2 主题
  2. Statistical-Diagrams Aqa Foundation
    6 主题
  3. Averages-Ranges-And-Data Aqa Foundation
    7 主题
  4. Tree-Diagrams-And-Combined-Probability Aqa Foundation
    2 主题
  5. Simple-Probability-Diagrams Aqa Foundation
    4 主题
  6. Transformations Aqa Foundation
    4 主题
  7. Vectors Aqa Foundation
    3 主题
  8. Pythagoras-And-Trigonometry Aqa Foundation
    5 主题
  9. Congruence-Similarity-And-Geometrical-Proof Aqa Foundation
    5 主题
  10. Volume-And-Surface-Area Aqa Foundation
    3 主题
  11. Circles-Arcs-And-Sectors Aqa Foundation
    3 主题
  12. Area-And-Perimeter Aqa Foundation
    4 主题
  13. Bearings-Scale-Drawing-Constructions-And-Loci Aqa Foundation
    5 主题
  14. 2D-And-3D-Shapes Aqa Foundation
    4 主题
  15. Angles-In-Polygons-And-Parallel-Lines Aqa Foundation
    5 主题
  16. Symmetry-And-Shapes Aqa Foundation
    4 主题
  17. Exchange-Rates-And-Best-Buys Aqa Foundation
    2 主题
  18. Standard-And-Compound-Units Aqa Foundation
    5 主题
  19. Direct-And-Inverse-Proportion Aqa Foundation
    1 主题
  20. Ratio-Problem-Solving Aqa Foundation
    2 主题
  21. Sequences Aqa Foundation
    4 主题
  22. Solving-Inequalities Aqa Foundation
    3 主题
  23. Real-Life-Graphs Aqa Foundation
    4 主题
  24. Graphs-Of-Functions Aqa Foundation
    3 主题
  25. Linear-Graphs Aqa Foundation
    3 主题
  26. Coordinate-Geometry Aqa Foundation
    3 主题
  27. Functions Aqa Foundation
    1 主题
  28. Forming-And-Solving-Equations Aqa Foundation
    2 主题
  29. Simultaneous-Equations Aqa Foundation
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  30. Solving-Quadratic-Equations Aqa Foundation
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  31. Linear-Equations Aqa Foundation
    3 主题
  32. Algebraic-Reasoning Aqa Foundation
    1 主题
  33. Rearranging-Formulas Aqa Foundation
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  34. Introduction Aqa Foundation
    10 主题
  35. Factorising Aqa Foundation
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  36. Expanding-Brackets Aqa Foundation
    2 主题
  37. Algebraic-Roots-And-Indices Aqa Foundation
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  38. Using-A-Calculator Aqa Foundation
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  39. Exact-Values Aqa Foundation
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  40. Rounding-Estimation-And-Error-Intervals Aqa Foundation
    4 主题
  41. Fractions-Decimals-And-Percentages Aqa Foundation
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  42. Simple-And-Compound-Interest-Growth-And-Decay Aqa Foundation
    4 主题
  43. Percentages Aqa Foundation
    5 主题
  44. Fractions Aqa Foundation
    6 主题
  45. Powers-Roots-And-Standard-Form Aqa Foundation
    4 主题
  46. Types-Of-Number-Prime-Factors-Hcf-And-Lcm Aqa Foundation
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  47. Number-Operations Aqa Foundation
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Exam code:8300

Systematic lists

What are systematic listing strategies?

  • Systematic listing strategies are a way of writing out all possible combinations or arrangements of items in an organised way, without missing any

  • A strategy can be used to make sure that no options are missed out by choosing one item as the first possible option, then arranging the rest using a similar technique

  • For example, to list all the ways arrange the letters A, B and C

    • Begin by fixing the letter A and arranging the others
      A B C or A C B

    • Then fix the letter B and arrange the others
      B A C or B C A

    • Then fix the letter C and arrange the others
      C A B or C B A

    • So the six arrangements are ABC, ACB, BAC, BCA, CAB and CBA

    • This idea can be applied to arrangements of more items and longer lists

Examiner Tips and Tricks

  • Using systematic listing techniques can be particularly helpful in probability.

    • Practice finding methods that will ensure you do not miss out any options.

Worked Example

List all the possible combinations of one filling, one side and one sauce from the sandwich menu below.

Filling

Side

Sauce

Steak

Lettuce

Ketchup

Chicken

Tomato

Mayo

Veggie Patty

Mushroom

Apple

 
Simplify the problem by assigning a letter to each of the items.

Filling

Side

Sauce

Steak S

Lettuce L

Ketchup K

Chicken C

Tomato T

Mayo Y (M is taken, use a different letter)

Veggie Patty V

Mushroom M

Apple A

‘Fix’ the letter S and the letter L and arrange the other possibilities.

S L K
S L Y
S L A

‘Fix’ the letter S and the letter T and arrange the other possibilities.

S T K
S T Y
S T A

‘Fix’ the letter S and the letter M and arrange the other possibilities.

S M K
S M Y
S M A

Repeat the process by fixing the letter C in the first position.

C L K

C T K

C M K

C L Y

C T Y

C M Y

C L A

C T A

C M A

Repeat the process again by fixing the letter V in the first position.

V L K

V T K

V M K

V L Y

V T Y

V M Y

V L A

V T A

V M A

So there are 27 different ways of choosing one item from each of the options on the sandwich menu, and they can be listed as follows:

S L K, S L Y, S L A

S T K, S T Y, S T A

S M K, S M Y, S M A

C L K, C L Y, C L A

C T K, C T Y, C T A

C M K, C M Y, C M A

V L K, V L Y, V L A

V T K, V T Y, V T A

V M K, V M Y, V M A

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