Senior Phase

National 5 Mathematics

The qualification most pupils aim for. National 5 Mathematics develops algebra, geometry, trigonometry and the beginnings of calculus, assessed by two externally marked papers.

SCQF Level 5 Updated for the 2026 session PDF downloads

Course Outline - Past Papers and Revision for assessment Everything for National 5 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.

National 5 Mathematics is the standard entry requirement for many college courses and for Higher Mathematics. The course rewards fluency: pupils need to recall key facts, select a method without prompting and communicate a solution clearly. Both papers are externally marked by the SQA in May.

Topics covered

Expressions and formulaeSurds, indices, algebraic fractions, completing the square and the discriminant.
RelationshipsQuadratics, the straight line, functions, simultaneous equations and trigonometry in triangles.
ApplicationsVectors, percentages, arcs and sectors, the sine and cosine rules, and statistics.
Calculus (introduction)Differentiating powers of x and using calculus to find rates of change and gradients.
ReasoningMulti-mark questions requiring justification, proof and interpretation of a result.
Non-calculator fluencyPaper 1 rewards confident mental and written arithmetic; we practise it weekly.

How this course is assessed

Paper 1 — non-calculator, 1 hour 15 minutes, 55 marks.
Paper 2 — calculator, 1 hour 50 minutes, 60 marks.
Both papers are set and marked by the SQA, usually in May.
Prelim examination in January/February; unit assessments through 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.

Nov 2026Unit assessments begin
Dec 2026Senior Phase parents' evening
Jan 2027Prelim examination
Mar 2027Final revision block begins
May 2027SQA examination diet