Discrete Mathematics — OCR GCSE Further Mathematics
In summary: Discrete Mathematics is a key topic in OCR GCSE Further Mathematics. Key exam tip: Always check if the order of items matters before choosing between permutations and combinations
Exam Tips for Discrete Mathematics
- Always check if the order of items matters before choosing between permutations and combinations
- For arrangement problems with restrictions, consider the 'gap method' or 'subtraction method' (total arrangements minus forbidden arrangements)
- When using the inclusion-exclusion principle, clearly define the sets involved
- Show clear working for counting problems to allow for method marks even if the final calculation is incorrect
- Use the notation nPr and nCr correctly as specified in the formulae booklet
- When asked to show two graphs are isomorphic, provide a clear mapping of vertices.
- Always check if a graph is simple before applying theorems like Ore's theorem.
- Use colouring arguments to test for bipartiteness.
Common Mistakes
- Confusing permutations (order matters) with combinations (order does not matter)
- Incorrectly applying the inclusion-exclusion principle by failing to subtract the intersection
- Misinterpreting constraints in arrangement problems (e.g., items that cannot be next to each other)
- Failing to account for identical items when calculating arrangements
- Misapplying the pigeonhole principle by not correctly identifying the 'pigeons' and 'holes'
- Confusing the definitions of walk, trail, path, and cycle.
Marking Points
- Correct classification of problems into existence, construction, enumeration, or optimisation
- Accurate use of set notation and partition counting
- Correct application of the pigeonhole principle
- Accurate use of the multiplicative principle for arrangements
- Correct calculation of permutations (nPr) and combinations (nCr)
- Correct handling of constraints in arrangement and selection problems
- Accurate application of the inclusion-exclusion principle for two sets
- Correct use of terminology: vertex (node), arc (edge), degree, adjacent, tree, simple, connected, simply connected.
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