National 5

Mathematics · National 5

National 5 Mathematics is three units in one exam — expressions and formulae, relationships, and applications — with no coursework at all. Your entire grade comes from two papers, one of which you sit without a calculator.

Where it leads

What it offers you

Mathematics is the entry requirement for a huge range of degrees — engineering, physics, economics, computing and more — and the reasoning it builds is valued in every technical career.

The exam, decoded

What National 5 actually asks of you

01

Paper 1 — non-calculator

Shorter paper testing core fluency: surds, indices, factorising, fractions, straight line, quadratics and trigonometry. No calculator, so the technique has to be solid.

02

Paper 2 — calculator

Longer paper with the same content in richer contexts: trigonometry in triangles, vectors, statistics, percentages and reasoned multi-step problems.

No coursework

This course is graded entirely on the question papers — there is no assignment or project to submit.

Exact timings and mark allocations are printed on the front cover of each paper below.

What's assessed

Topics that come up

Surds, indices and algebraic fractionsFactorising and completing the squareStraight line and simultaneous equationsQuadratics and their graphsFunctions and trigonometric graphsTriangle trigonometry and the sine/cosine rulesVectorsPercentages, fractions and statisticsArcs, sectors and the equation of a circle

The archive

Papers & marking schemes

2022–2026

2026

4 files

2025

4 files

2024

4 files

2023

4 files

Marking instructions

2022

4 files

SQA publishes the most recent five years of papers. Older papers and specimen papers live on their site — open Mathematics National 5 on sqa.org.uk.

All Mathematics levels