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Maths Gcse Wjec-Eduqas Foundation

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  1. Scatter-Graphs-And-Correlation Wjec-Eduqas Foundation
    2 主题
  2. Statistical-Diagrams- Wjec-Eduqas Foundation
    7 主题
  3. Statistics-Toolkit Wjec-Eduqas Foundation
    8 主题
  4. Tree-Diagrams-And-Combined-Probability Wjec-Eduqas Foundation
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  5. Simple-Probability-Diagrams- Wjec-Eduqas Foundation
    4 主题
  6. Probability-Toolkit Wjec-Eduqas Foundation
    3 主题
  7. Transformations Wjec-Eduqas Foundation
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  8. Vectors Wjec-Eduqas Foundation
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  9. Pythagoras-And-Trigonometry Wjec-Eduqas Foundation
    5 主题
  10. Congruence-Similarity-And-Geometrical-Proof Wjec-Eduqas Foundation
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  11. Volume-And-Surface-Area- Wjec-Eduqas Foundation
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  12. Circles-Arcs-And-Sectors Wjec-Eduqas Foundation
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  13. Area-And-Perimeter Wjec-Eduqas Foundation
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  14. Bearings-Scale-Drawing-Constructions-And-Loci- Wjec-Eduqas Foundation
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  15. 2D-And-3D-Shapes Wjec-Eduqas Foundation
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  16. Angles-In-Polygons-And-Parallel-Lines Wjec-Eduqas Foundation
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  17. Geometry-Toolkit Wjec-Eduqas Foundation
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  18. Exchange-Rates-And-Best-Buys Wjec-Eduqas Foundation
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  19. Standard-And-Compound-Units- Wjec-Eduqas Foundation
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  20. Direct-And-Inverse-Proportion- Wjec-Eduqas Foundation
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  21. Ratio-Problem-Solving- Wjec-Eduqas Foundation
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  22. Ratio-Toolkit Wjec-Eduqas Foundation
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  23. Sequences Wjec-Eduqas Foundation
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  24. Solving-Inequalities- Wjec-Eduqas Foundation
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  25. Real-Life-Graphs Wjec-Eduqas Foundation
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  26. Graphs-Of-Functions Wjec-Eduqas Foundation
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  27. Linear-Graphs Wjec-Eduqas Foundation
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  28. Coordinate-Geometry Wjec-Eduqas Foundation
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  29. Functions Wjec-Eduqas Foundation
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  30. Forming-And-Solving-Equations Wjec-Eduqas Foundation
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  31. Simultaneous-Equations Wjec-Eduqas Foundation
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  32. Solving-Quadratic-Equations- Wjec-Eduqas Foundation
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  33. Linear-Equations Wjec-Eduqas Foundation
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  34. Algebraic-Reasoning Wjec-Eduqas Foundation
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  35. Rearranging-Formulae Wjec-Eduqas Foundation
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  36. Factorising Wjec-Eduqas Foundation
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  37. Expanding-Brackets Wjec-Eduqas Foundation
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  38. Algebraic-Roots-And-Indices Wjec-Eduqas Foundation
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  39. Algebra-Toolkit Wjec-Eduqas Foundation
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  40. Using-A-Calculator Wjec-Eduqas Foundation
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  41. Exact-Values Wjec-Eduqas Foundation
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  42. Rounding-Estimation-And-Error-Intervals Wjec-Eduqas Foundation
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  43. Fractions-Decimals-And-Percentages Wjec-Eduqas Foundation
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  44. Simple-And-Compound-Interest-Growth-And-Decay Wjec-Eduqas Foundation
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  45. Percentages Wjec-Eduqas Foundation
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  46. Fractions Wjec-Eduqas Foundation
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  47. Powers-Roots-And-Standard-Form Wjec-Eduqas Foundation
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  48. Types-Of-Number-Prime-Factors-Hcf-And-Lcm- Wjec-Eduqas Foundation
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  49. Number-Toolkit Wjec-Eduqas Foundation
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Exam code:C300

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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