Qualifications Scotland (SQA) National 5 Mathematics Past Papers 2026

Non-calculator

Duration: 1 hour

Calculator-allowed

Duration: 1 hour 30 minutes

Basic algebraic skills — rearranging, factorising, simplifying, and indices

The single piece of advice that appears in all three course reports, for both question papers, is to maintain and practise basic algebraic skills. Candidates who could not demonstrate these skills missed marks across many questions — not just the dedicated algebra questions.

Question Paper 1, Question Paper 2

Discriminant — calculating correctly and giving a complete description of the nature of the roots

Errors in sign when evaluating the discriminant (for example treating b² − 4ac when c is negative) and giving incomplete descriptions such as 'no distinct real roots' instead of 'no real roots' were flagged in the 2023 and 2025 reports. The full three-word description is required for the mark.

Question Paper 1

Completing the square and linking it to the turning point of a quadratic graph

The 2024 report noted that many candidates did not link completing the square (part a) to finding the turning point (part b). Candidates who treated the two parts as unconnected — or who did not know that y = (x + a)² + b gives turning point (−a, b) — consistently lost the second mark.

Question Paper 1, Question Paper 2

Trigonometric identities — proof structure and use of sin²x + cos²x = 1

Trigonometric identity questions proved the hardest question in Paper 2 across all three years, with very few candidates achieving any marks in 2024. The core failure was not recognising that the identity sin²x + cos²x = 1 (and its rearrangements) is the key substitution, and not laying out the proof as a structured sequence of equal expressions.

Question Paper 2

Comparing statistical data sets — the required language for median and IQR comments

Across all three years, candidates lost marks by: omitting 'on average' from the median statement; including 'on average' in the IQR statement; not naming the groups being compared; or simply stating that one value was higher without a comparative sentence.

Question Paper 1, Question Paper 2

Vectors — 2D vector pathways involving fractional vectors and drawing resultant vectors

In 2024, many candidates could not deal with like terms involving fractional scalar multiples. In 2025, most candidates did not gain any marks on a directed-line-segment resultant vector question because they did not include fractional vectors in their pathway. Vector questions have appeared in a variety of formats not always covered by recent past papers.

Question Paper 1, Question Paper 2

Algebraic fractions — sign errors when subtracting, and incorrect further simplification

Both the 2023 and 2025 reports flagged that candidates regularly produced the wrong sign in the numerator when expanding a subtracted bracket, and then attempted further simplification incorrectly — for example cancelling a term rather than a factor — losing the final mark.

Question Paper 1, Question Paper 2

Equations with fractional coefficients — eliminating denominators

In 2025, most candidates could not correctly eliminate the denominators in an equation with fractional coefficients. This skill is required in both Paper 1 (inequations) and Paper 2 (trigonometric equations). Candidates who could eliminate denominators generally went on to score 3 or 4 marks; those who could not achieved 0 or 1.

Question Paper 1, Question Paper 2