Qualifications Scotland (SQA) Higher Applications of Mathematics Past Papers 2026

Calculator-allowed

Duration: 2 hours 5 minutes

Researched investigation

Duration: Coursework (recommended 8 hours; externally assessed)

Regression line — stating equation in context and interpreting slope and intercept

In 2023, the majority of candidates failed to write the regression equation using variable names from the context, and most were unable to write appropriate comments for either the slope or intercept parameters. This area demands that candidates translate algebraic output into plain English using the specific units and variable names in the question.

Hypothesis testing — forming null/alternative hypotheses and concluding in context

In 2025, most candidates did not gain any marks for hypothesis formulation because they did not refer to the difference in the mean mass or answer in context. In 2024, candidates who ran the test correctly still lost the conclusion mark by not interpreting the result in the specific scenario. Both formulation and conclusion must name the actual variables and groups.

Relative purchasing power and reverse-percentage calculations

In 2023, most candidates were unable to make the link that as the prices rise the same amount of money will buy less, and most approached the calculation by subtracting a percentage rather than applying reverse-percentage or present-value logic. This topic links inflation, purchasing power, and percentage change in a multi-step calculation.

Describing a frequency distribution — skewness and appropriate measure of location

In 2025, most candidates did not describe the distribution correctly and many defaulted to 'normally distributed' or 'skewed to the left' without justification. Many also did not identify the appropriate measure of location given the distribution shape — for a skewed distribution, the median is preferred over the mean.

Project data validity and unbiasedness — providing a genuine explanation rather than a bare assertion

All three Course Reports flag this as a persistent weakness: candidates say 'the source is a government website so it is valid and unbiased' without explaining the sampling method, coverage, or how potential bias has been minimised. Marks 5 and 6 require a genuine explanation, not a statement of faith.

Project conclusion — integrating graphical, descriptive, and additional statistics into a connected summary

All three reports note that many candidates lost conclusion marks because they did not make appropriate connections or provide a summary between their graphical displays, descriptive statistics, or additional statistics in their conclusion. A valid conclusion must draw all three strands together and relate them to the original research question.

Type of mathematical model — distinguishing model type from data type

In 2023, some candidates seemed unsure of what was meant by 'mathematical model' and gave answers such as 'continuous', 'numerical', or referred to distribution of data. The question asks for the algebraic family of the model (linear, quadratic, exponential) — not a description of the data's measurement scale.

Effective interest rate calculation — using the compound formula rather than dividing by 12

In 2024, many candidates simply divided the interest rate by 12 to find the monthly effective rate, rather than applying the compound formula ((1 + annual rate)^(1/12) − 1). This systematic error then propagated into the spreadsheet loan model, losing marks across multiple parts.