lesson
A pass does not always finish the job
1 · Learn
A simple adjacent-swap sort compares neighbours and swaps them when they are out of order. Repeated passes move items towards their correct positions. A pass with no swaps can establish completion for this algorithm.
Keep comparisons and swaps distinct when analysing work. A list already in order may need no swaps but still needs comparisons to establish that fact under the algorithm.
2 · Worked example
One left-to-right pass on [4,1,3,2] gives [1,3,2,4]. The largest value reaches the end, but 3 and 2 are still out of order.
3 · Your turn
Is [1,3,2,4] fully sorted after that pass? What adjacent pair still needs attention?
Check your answer
No. The pair 3,2 is out of order.
4 · Apply your learning
Trace complete passes on four fictional values and count comparisons separately from swaps.
Adult guidance and safety
Use an approved private interpreter, simulator or authoring tool with fictional data. Trace and predict before running. Never execute unknown downloaded code, inspect real credentials or use other people's private data. Working examples still need saved-project and assessment integration before release.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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