Senior Phase

Advanced Higher Mathematics

The most advanced mathematics course we offer. Matrices, complex numbers, sequences, vectors and further calculus — the standard preparation for a mathematics, physics or engineering degree.

SCQF Level 7 Updated for the 2026 session PDF downloads

Course Outline - Past Papers and Revision for assessment Everything for Advanced Higher Mathematics in three sections: outline, past papers and practice assessments. Open resources

Course outline

What is taught, how it is assessed, and what pupils should be able to do by the end.

Advanced Higher Mathematics is a serious, university-level introduction to pure mathematics. Pupils work with abstraction and proof rather than procedure alone. The leap from Higher is the biggest in the mathematics curriculum, and we recommend pupils begin the bridging work in the summer before S6.

Topics covered

MatricesMatrix algebra, determinants, inverses and transformations.
Complex numbersArgand diagrams, modulus-argument form, and De Moivre's theorem.
Sequences and seriesArithmetic and geometric progressions, summation notation and limits.
Further calculusDifferentiation of products and quotients, integration by substitution and parts.
Vectors and geometryThe vector product, lines and planes in three dimensions.
Proof and reasoningProof by induction and contradiction, and careful mathematical argument.

How this course is assessed

Question paper 1 — non-calculator, 1 hour, 30 marks.
Question paper 2 — calculator, 2 hours 30 minutes, 90 marks.
Both papers are externally marked by the SQA.
Prelim-style assessment in January/February.

Downloads

Course outlines are reviewed each August. If a topic differs from what your child is being taught, speak to their teacher — the class plan always takes precedence.

Past papers

Real papers and official marking instructions, ordered newest first.

Past papers are the most effective revision tool there is — but only when they are marked honestly. Print the paper, work it in one sitting under timed conditions, then mark it against the scheme and write down every question type that cost marks. Bring that list to your teacher.

Past papers and marking instructions are produced by the Scottish Qualifications Authority and reproduced here for pupils at Madras High School. Always check the SQA website for the current specification.

Practice assessments

Written by our own teachers for the assessment your child is about to sit.

These are not random worksheets. Each practice assessment mirrors the format, length and mark distribution of the forthcoming classroom assessment, so pupils know exactly what to expect — including the questions that are designed to be difficult.

Answer booklets are included for every practice assessment. Attempt the paper first — the value is in the attempt, not the answer sheet.

Key dates for this course

Assessments, prelims and parents' evenings. Provisional — confirmed by the school.

Aug 2026Bridging work due and course begins
Dec 2026Senior Phase parents' evening
Jan 2027Prelim-style assessment
Mar 2027Final revision block begins
May 2027SQA examination diet