lesson
Count work under stated assumptions
1 · Learn
Linear search may inspect every item until it finds a match or reaches the end. Binary search repeatedly halves a sorted search interval. Its advantage depends on sorted data and an appropriate way to access the middle item.
Comparing algorithms requires a stated input size and cost measure. A count of comparisons is not identical to elapsed time on every machine, and sorting beforehand has its own cost.
2 · Worked example
A linear search for an absent value in eight items can inspect all eight. A binary search can discard roughly half the remaining candidates after each comparison.
3 · Your turn
Why should binary search not be applied directly to an unsorted list?
Check your answer
Discarding one half relies on the ordering; without it, a possible match can be discarded incorrectly.
4 · Apply your learning
Trace both methods on a sorted list and record comparisons for a first, middle, last and absent value.
Adult guidance and safety
Use an approved sandbox with invented data. Never ask for real passwords, personal records or access to another person's system. These text examples need executable projects and assessed evidence in two languages; reading code alone is not practical mastery.
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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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