SQA Advanced Higher Maths specification (X847 77)
Understanding the exam specification is key to doing well in your SQA Advanced Higher Maths exam. It lays out exactly what you need to learn, how you'll be assessed, and what skills the examiners seek. Whether you're working through the course for the first time or revising for your final exams, the specification helps you stay focused and confident in your preparation.
We've included helpful revision tools to support you in putting the specification into practice. Wherever you're starting from, you'll find everything you need to feel prepared, from the official specification to high-quality resources designed to help you succeed.
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In the next section, you'll find a simplified summary of the official SQA Advanced Higher Maths specification, along with a breakdown of key topics, assessment structure, and useful study resources. We've also included links to topic-level guides and revision tools to help you put the specification into practice.
Contents
Disclaimer
This page includes a summary of the official SQA Advanced Higher Maths (X847 77) specification, provided to support your revision. While we've made every effort to ensure accuracy, Save My Exams is not affiliated with the awarding body.
For the most complete and up-to-date information, we strongly recommend consulting the official SQA specification PDF.
Specification overview
The Advanced Higher Mathematics course provides learners with an in-depth understanding of complex mathematical concepts and techniques. It aims to develop mathematical reasoning, logical thinking and problem-solving skills that are essential for higher education and many areas of employment. Learners are encouraged to explore advanced mathematical ideas, apply skills to abstract and real-world problems, and communicate solutions with clarity and rigour. The course also enhances understanding of how mathematics is used to model real-life situations, supporting learning across science, technology, engineering and beyond.Subject content breakdown
Calculus
- Differentiate exponential, logarithmic, trigonometric and inverse trigonometric functions
- Apply chain, product, quotient, implicit, logarithmic, and parametric differentiation
- Optimise and solve related rates problems
- Integrate using standard results, substitution, parts, partial fractions
- Apply integration to volumes, areas and contextual problems
- Solve first-order separable and linear differential equations using integrating factors
- Solve second-order linear differential equations with various types of roots
Algebra, proof and number theory
- Use partial fractions and sketch rational functions with asymptotes
- Investigate features of graphs: inflection, extrema, domain, symmetry
- Apply the binomial theorem and find specific terms
- Work with arithmetic and geometric series, including convergence
- Use summation formulas and Maclaurin expansions
- Disprove conjectures, use direct/indirect proof, proof by induction
- Apply Euclid’s algorithm and fundamental theorem of arithmetic
Matrices, vectors and complex numbers
- Use Gaussian elimination to solve 3×3 systems, identify inconsistency/redundancy
- Perform matrix operations and apply properties: inverse, transpose, identity
- Calculate determinants and find 2×2 and 3×3 matrix inverses
- Use 2×2 matrices for geometric transformations
- Apply vector products, scalar triple product, and work with lines and planes in 3D
- Solve vector intersection and angle problems
- Perform operations on complex numbers in Cartesian and polar form
- Use de Moivre’s theorem, find roots, interpret loci geometrically
Assessment structure
Paper 1 (Non-Calculator)
- 35 marks, 1 hour
- Short-answer and extended-response questions
- Tests numerical, algebraic, geometric, trigonometric, calculus and reasoning skills without a calculator
- Focus on assessing understanding of mathematical processes
Paper 2
- 80 marks, 2 hours 30 minutes
- Short-answer and extended-response questions
- Covers same skills as Paper 1, calculator allowed for complex reasoning and application
Overall Assessment
- Approximately 30–50% marks: Calculus
- Approximately 20–40% marks: Algebra, Proof and Number Theory
- Approximately 20–40% marks: Matrices, Vectors and Complex Numbers
- ~65% of marks test operational skills; ~35% assess reasoning
- Both papers are externally marked by SQA; final grade A–D is based on combined total of 115 marks
Key tips for success
Doing well in your SQA Advanced Higher Maths isn't just about how much you study, but how you study. Here are a few proven tips to help you stay on track
- Start with a clear plan: Break the subject into topics and create a revision schedule that allows enough time for each. Start early to avoid last-minute stress.
- Focus on understanding, not memorising: Use our revision notes to build a strong foundation in each topic, making sure you actually understand the material.
- Practise regularly: Attempt past papers to familiarise yourself with the exam format and timing. Mark your answers to see how close you are to full marks.
- Be strategic with your revision: Use exam questions by topic to focus on weaker areas, and flashcards to reinforce important facts and terminology.
- Learn from mistakes: Whether it's from mock exams or practice questions, spend time reviewing what went wrong and why. This helps prevent repeat mistakes in the real exam.
- Stay balanced: Don't forget to take regular breaks, eat well, and get enough sleep, a healthy routine makes revision much more effective.
With the right approach and consistent practice, you'll build confidence and improve your chances of exam success.
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