Topic summary · Student revision
Algorithms Topic Review summary
Self-review on algorithmic thinking for Decision maths: sorting, packing, and analysing efficiency with bubble/quick ideas and bin packing.
Files: Topic-Review-Algorithms.pdf · Topic-Review-Algorithms-Answers.pdf · free public downloads · diagrams in the PDFs
Key learning points
- Follow an algorithm exactly as written — exam marks track each pass.
- Bubble sort: compare adjacent items; count comparisons and swaps.
- Bin packing: first-fit, first-fit decreasing, and full-bin methods.
- Order of an algorithm describes how run time grows with input size.
- Trace tables must show every update the mark scheme expects.
Worked example 1 — Bubble pass
Perform one bubble-sort pass on 4, 2, 5, 1 (ascending).
Working
Largest element bubbles toward the end.
Worked example 2 — Bin packing
First-fit items 6,5,3,2 into bins of capacity 8.
Working
Place each item in the first bin that fits.
Worked example 3 — Practice point 1
Apply this idea from the Topic Review: Follow an algorithm exactly as written — exam marks track each pass.
Working
Attempt without notes, then check the answers PDF.
Worked example 4 — Practice point 2
Apply this idea from the Topic Review: Bubble sort: compare adjacent items; count comparisons and swaps.
Working
Attempt without notes, then check the answers PDF.
Scaffolded Learning Sheet and answers (PDFs)
This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.