lesson
Halving needs ordered data
1 · Learn
Binary search compares a target with a middle item in an ordered list, then discards the half that cannot contain the target. Repeating this can use fewer comparisons than checking every item, especially for long lists.
The ordering precondition is essential. On an unsorted list, discarding a half can discard the target. Count the cost of preparing or maintaining order when comparing complete solutions, not only the search step.
2 · Worked example
For sorted [2,5,8,11,14,17,20], the middle is 11. To find 17, keep the upper part; its middle is 17, found on the second comparison in this trace.
3 · Your turn
Why is binary search unsafe as described on [8,2,17,5,11]?
Check your answer
The list is not sorted, so a middle comparison does not identify a half guaranteed to exclude or contain the target.
4 · Apply your learning
Trace present and absent targets on a sorted list and record the interval remaining after each comparison.
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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