Qualifications Scotland (SQA) National 5 Applications of Mathematics Past Papers 2026

Non-calculator

Duration: 50 minutes

Calculator-allowed

Duration: 1 hour 40 minutes

Statistics interpretation — comparing data sets with appropriate numerical statements

Candidates consistently fail to include both numerical values and a comparative conclusion when comparing means, standard deviations, or interquartile ranges. Vague phrases like 'on average' or 'more varied' without numbers do not earn marks. Both Paper 1 and Paper 2 include at least one comparison question each year.

National Insurance and net pay calculations

The 0% lower earnings band is routinely ignored, and pension contributions are frequently calculated on the wrong base (after NI subtraction rather than on gross). These are multi-mark questions where each step carries marks, so structural errors compound.

Gradient — unit consistency and comparison with tolerance

Many candidates compute gradient using mixed units (e.g. rise in cm, run in m) and then compare the resulting ratio directly to a tolerance given as a decimal, without converting the gradient to a consistent decimal form first.

Probability — combined events and expected frequency

In 2023, many candidates calculated one-event probabilities but could not progress to combined probability using a sample space table or tree diagram. In 2025, many candidates did not use a valid strategy for expected frequency questions.

Direct vs inverse proportion

Candidates who confuse direct and inverse proportion apply the wrong method and arrive at an answer that is implausible in context (e.g. more workers → more time needed). The error appears most often in Paper 2 extended questions.

Perimeter and area of composite shapes involving circles

Candidates swap circumference and area formulas, use radius when diameter is needed (or vice versa), and fail to subtract internal edges or extra radii when constructing composite perimeters. These questions appear in both papers.

Scale drawings and three-figure bearings

Few candidates successfully complete multi-leg navigation diagrams — they often draw only part of the route. When asked for a return bearing, most candidates do not attempt it, and those who do omit the three-figure format (e.g. write 45° instead of 045°).

Volume of composite solids — applying correct formula and using correct units

Candidates fail to calculate volumes of spheres (wrong formula despite formulae list access), cuboids (basic arithmetic errors), and triangular prisms (not identified as the correct shape). Unit conversion from cm³ to litres is also missed.