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Higher MathematicsArchive sourceFree practiceAutomatically indexed

2018 · Question 8

Wave-function form · Stationary points and optimisation

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7 marks

Viewer page 6 · check every required subpart

Question-type rarity

Common

Wave-function form

Found in 5 of 5 exam years · 5 indexed questions. Rarer does not mean harder.

  • 20221 matching questions
  • 20231 matching questions
  • 20241 matching questions
  • 20251 matching questions
  • 20261 matching questions
How this rating is calculated

We count the exam years containing this skill heading in the same subject and qualification, across the latest five available sittings (2022–2026). Several matching questions in one year still count as one year. This is a question-type match, not a claim that identical wording repeats.

Common
5/5 years
Uncommon
4/5 years
Rare
3/5 years
Epic
2/5 years
Legendary
1/5 years
Mythic
0/5 years

Automatic topic matching is provisional and can miss or misclassify questions. A question with several skills uses its first indexed skill for this meter. A question without a classification is not rated. A source gap is unknown, not a zero. Mythic means no indexed match in a complete five-year source window; it does not mean impossible. This is historical evidence, not an exam prediction or a reason to skip a topic. Index checked 2026-10-23.

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Original wording · Question 8

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Marking & methods.

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Published marking instructions and accepted methods

Match question 8 in the correct paper component. Use the official points, alternative methods, follow-through rules and any continuation pages. An answer key does not necessarily contain a complete worked explanation.

2018 marking · Paper 2 Calculator (PDF, new tab)

Question-table match starts at viewer page 17. Check the label and read any continuation pages.

Method guide · plan your approach

Original ScotSpark strategy guidance, not an official model answer or a question-specific worked solution. Skill matching is provisional; use only the advice relevant to the actual question.

  1. Identify what is being asked and choose the relevant relationship or algebraic strategy before substituting values.
  2. Set out each transformation or calculation. Keep exact values and intermediate precision until the final answer.
  3. Check the domain, units, rounding and whether every solution in the stated interval has been included.
  • Wave-function form

    Combine sine and cosine terms into a single wave expression.

  • Stationary points and optimisation

    Find critical values and justify their nature or practical relevance.

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