Higher Mathematics develops algebraic, trigonometric, and calculus skills essential for STEM subjects and university entry. The course covers functions, calculus, trigonometry, vectors, and statistics, assessed through an SQA examination and coursework.

Functions, notation, domain/range, quadratic functions, composite and inverse functions, graph transformations, and polynomial algebra.

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Trigonometric functions, identities, equations, addition formulae, wave functions, and geometric applications.

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Differentiation and integration of polynomial, trigonometric, and exponential functions, applications to rates of change and areas.

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Vector components, scalar product, angle between vectors, vector geometry, and matrix operations.

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Probability distributions, statistical analysis, data interpretation, and hypothesis testing.

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Focus on understanding function notation early, as it underpins calculus and trigonometry topics. Practice graph sketching regularly. SQA exams frequently test integration of multiple topic areas in single questions.

These notes are aligned with the official SQA syllabus and cover Higher and Advanced Higher material. Each topic includes worked examples, common pitfalls, and practice problems to reinforce understanding.

The examination commonly consists of a written paper testing knowledge, understanding, and problem-solving across all topics. Coursework or project components may also contribute to the final grade, depending on the subject and level.

1. Start with the topic you find most challenging and work through systematically
2. Complete all worked examples before moving on. They reinforce key concepts
3. Review the Common Pitfalls section in each topic to avoid frequent mistakes
4. Use the Summary section as a quick reference for last-minute revision
5. Attempt practice problems under timed conditions to build exam confidence