Senior Phase

Higher Mathematics

The course that opens doors. Higher Mathematics develops calculus, algebra, geometry and vectors, and is a stated entry requirement for many degree courses in engineering, science and business.

SCQF Level 6 Updated for the 2026 session PDF downloads

Course Outline - Past Papers and Revision for assessment Everything for 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.

Higher Mathematics is fast and cumulative. Each week's work depends on the week before, so pupils who fall behind rarely catch up without deliberate effort. The department runs a weekly supported study session from October, and the resources on this page are designed to be used throughout the year rather than only before the exam.

Topics covered

DifferentiationRules for differentiation, stationary points, optimisation and rates of change.
IntegrationIndefinite and definite integrals, areas under curves and differential equations.
Straight line and functionsGradients, perpendicularity, composite and inverse functions.
Quadratics and polynomialsThe discriminant, completing the square, and the factor theorem.
TrigonometryThe addition and double-angle formulae, and solving trigonometric equations.
Vectors and circlesVector pathways in 3D, the circle equation, and tangency conditions.

How this course is assessed

Paper 1 — non-calculator, 1 hour 30 minutes, 60 marks.
Paper 2 — calculator, 1 hour 30 minutes, 70 marks.
Both papers are externally marked by the SQA.
Prelim in January/February; unit assessments across the year.

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.

Oct 2026Weekly supported study begins
Nov 2026Unit assessments begin
Dec 2026Senior Phase parents' evening
Jan 2027Prelim examination
May 2027SQA examination diet