Qualifications Scotland (SQA) Higher Mathematics Past Papers 2026

Non-calculator

Duration: 1 hour 15 minutes

Calculator-allowed

Duration: 1 hour 30 minutes

Calculus — differentiation using the chain rule

The 2024 report notes that 'many candidates did not complete their application of the chain rule' (Q3, Paper 1). The 2025 report records errors from candidates who 'did not differentiate +3 correctly or did not apply the chain rule correctly' (Q12(b), Paper 2). Partial differentiation — finding the outer derivative without multiplying by the inner derivative — is the most common error.

Question Paper 1, Question Paper 2

Integration — indefinite integrals, constant of integration, and definite integral evaluation

Omitting the constant of integration and failing to integrate every term in the integrand were flagged in all three years. The 2023 report notes that some candidates 'were unable to process the exact values to evaluate the definite integral.' The 2025 report flags omission of 'dx' in the integral statement as a recurring mark loss.

Question Paper 1, Question Paper 2

Trigonometric equations — double-angle formulae, addition formulae, and the wave function

The wave function question in 2024 produced very few correct answers (Paper 1, Q11(b)). The 2025 report notes that 'only a few candidates dealt with the phase change accurately' for the wave function and that candidates 'incorrectly stated that sin 2q = 2 sin q'. The double-angle formula was misapplied in 2023 and 2024 as well.

Question Paper 1, Question Paper 2

Vectors in 3D — pathways, dot products, and collinearity proofs

The 2025 report records that 'many candidates did not gain any marks' for the vector pathway question (Q8, Paper 2) and that 'few candidates communicated their conclusions unambiguously' for the collinearity question. Errors include stating incorrect pathways, attempting to find 'the gradient of a vector', and drawing incorrect conclusions about parallelism.

Question Paper 2

Recurrence relations — limit of a sequence and applying the condition for a limit to exist

Recurrence relation questions appeared across multiple years; the 2025 report notes that 'a few candidates did not make reference to m' when finding the limit. Candidates who failed to state or check the condition −1 < a < 1 (where u_{n+1} = au_n + b) lost marks in the justification step.

Question Paper 1

Polynomials and synthetic division — non-unitary quadratics and communicating the remainder

The 2023 report notes that 'many candidates were unable to deal with the irreducible quadratic appropriately' and that 'a few candidates did not communicate that the remainder was 0'. The 2024 and 2025 reports flag errors where candidates wrote inconsistent lines of working when factorising non-unitary quadratic expressions.

Question Paper 1

Logarithms and exponentials — converting between forms and applying log laws

Converting from exponential to logarithmic form was flagged in 2023, 2024, and 2025. The 2023 report records that 'some were unable to convert from logarithmic form into exponential form'. The 2025 report also notes that 'many candidates did not evaluate the final logarithmic expression correctly' (Q4, Paper 1).

Question Paper 1, Question Paper 2

Graph transformations — applying multiple transformations in the correct order

Transformation questions were a persistent weakness. The 2023 report notes that 'many candidates were unable to carry out the two transformations required.' The 2025 report states that common issues included 'not considering the shape of the transformed graph, only applying a single transformation, and applying a reflection in the x-axis'. Candidates who treated x-coordinates and y-coordinates separately for each transformation scored better.

Question Paper 1, Question Paper 2