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Maths Gcse Edexcel Foundation

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  1. Scatter-Graphs-And-Correlation Edexcel Foundation
    2 主题
  2. Statistical-Diagrams Edexcel Foundation
    8 主题
  3. Statistics-Toolkit Edexcel Foundation
    7 主题
  4. Tree-Diagrams-And-Combined-Probability Edexcel Foundation
    2 主题
  5. Simple-Probability-Diagrams Edexcel Foundation
    4 主题
  6. Probability-Toolkit Edexcel Foundation
    3 主题
  7. Transformations Edexcel Foundation
    4 主题
  8. Vectors Edexcel Foundation
    3 主题
  9. Volume-And-Surface-Area Edexcel Foundation
    3 主题
  10. Circles-Arcs-And-Sectors Edexcel Foundation
    3 主题
  11. Area-And-Perimeter Edexcel Foundation
    4 主题
  12. Pythagoras-And-Trigonometry Edexcel Foundation
    5 主题
  13. Congruence-Similarity-And-Geometrical-Proof Edexcel Foundation
    5 主题
  14. Bearings-Scale-Drawing-Constructions-And-Loci Edexcel Foundation
    5 主题
  15. 2D-And-3D-Shapes Edexcel Foundation
    4 主题
  16. Angles-In-Polygons-And-Parallel-Lines Edexcel Foundation
    5 主题
  17. Geometry-Toolkit Edexcel Foundation
    4 主题
  18. Exchange-Rates-And-Best-Buys Edexcel Foundation
    2 主题
  19. Standard-And-Compound-Units Edexcel Foundation
    5 主题
  20. Direct-And-Inverse-Proportion Edexcel Foundation
    1 主题
  21. Ratio-Problem-Solving Edexcel Foundation
    2 主题
  22. Ratio-Toolkit Edexcel Foundation
    3 主题
  23. Sequences Edexcel Foundation
    4 主题
  24. Solving-Inequalities Edexcel Foundation
    3 主题
  25. Real-Life-Graphs Edexcel Foundation
    4 主题
  26. Graphs-Of-Functions Edexcel Foundation
    3 主题
  27. Linear-Graphs Edexcel Foundation
    3 主题
  28. Coordinate-Geometry Edexcel Foundation
    3 主题
  29. Functions Edexcel Foundation
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  30. Forming-And-Solving-Equations Edexcel Foundation
    2 主题
  31. Simultaneous-Equations Edexcel Foundation
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  32. Solving-Quadratic-Equations Edexcel Foundation
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  33. Linear-Equations Edexcel Foundation
    3 主题
  34. Algebraic-Reasoning Edexcel Foundation
    1 主题
  35. Rearranging-Formulas Edexcel Foundation
    1 主题
  36. Factorising Edexcel Foundation
    3 主题
  37. Expanding-Brackets Edexcel Foundation
    2 主题
  38. Algebraic-Roots-And-Indices Edexcel Foundation
    1 主题
  39. Algebra-Toolkit Edexcel Foundation
    4 主题
  40. Using-A-Calculator Edexcel Foundation
    1 主题
  41. Exact-Values Edexcel Foundation
    1 主题
  42. Rounding-Estimation-And-Error-Intervals Edexcel Foundation
    4 主题
  43. Fractions-Decimals-And-Percentages Edexcel Foundation
    2 主题
  44. Simple-And-Compound-Interest-Growth-And-Decay Edexcel Foundation
    4 主题
  45. Percentages Edexcel Foundation
    5 主题
  46. Fractions Edexcel Foundation
    6 主题
  47. Powers-Roots-And-Standard-Form Edexcel Foundation
    4 主题
  48. Types-Of-Number-Prime-Factors-Hcf-And-Lcm Edexcel Foundation
    6 主题
  49. Number-Toolkit Edexcel Foundation
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Exam code:1MA1

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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