National 5 Applications of Maths: the 2027 exam, 2026 grade boundaries and practice

The National 5 Applications of Maths exam in 2027

Both papers are set and marked by Qualifications Scotland (the new name for SQA). Most questions are set in a context, and Paper 2 includes case studies, so the 1 hour 40 minutes includes time to read and take in the information. The grade is based on the total mark across both papers (course specification, version 3.0; Exam Timetable 2027, version 02). Passing the course also gives you the Core Skill of Numeracy at SCQF level 5.

A formulae list is printed in both papers. It is short: see our National 5 Applications of Maths formula sheet for what is on it and what is not.

What National 5 Applications of Maths covers

The specification groups the skills the papers sample into six areas:

• Numeracy. Fractions, percentages including compound change, ratio and proportion, speed, distance and time, rounding, and perimeter, area and volume.
• Finance. Budgets, income and deductions such as National Insurance, income tax and pension contributions, best buys, currency conversion, and interest on savings and loans.
• Statistics. Mean, median, mode, range, interquartile range and standard deviation, box plots, scatter graphs with a line of best fit, and the link between probability and expected frequency.
• Measurement. Scale drawings, bearings and navigation, container packing, precedence tables, time zones and tolerance.
• Geometry. Gradient, composite shapes, the volume of composite solids and Pythagoras' theorem.
• Graphical data and probability. Reading tables and charts, and comparing data sets.

How it differs from National 5 Maths

Applications of Maths works with real situations and decisions, and justifying a decision with your results is part of the marks. National 5 Maths is more algebraic: it has the quadratic formula, trigonometry and the sine and cosine rules. The Higher Applications course follows on from either one. If you are weighing the two, read our National 5 Maths guide and Higher Applications of Maths guide.

National 5 Applications of Maths grade boundaries

In 2026, out of 90 marks, an A needed 65 (72%), a B 56, a C 48 and a D 39. Of 30,078 candidates, 31.9% got an A. Entries rose from 27,706 in 2025 (course report 2026). The boundary moves with the difficulty of the papers: in 2026 Paper 2 was less demanding than intended, and that was taken into account.

Qualifications Scotland aims for a C at about 50% and an A at about 70% of the marks, and adjusts the boundaries up or down for the year ( how National Courses are graded). Use the daily paper below to estimate where you are, and treat the result as a guide.

National 5 Applications of Maths practice questions

Every question below is our own, one from each of four skill areas.

1. Compound percentage

£3,000 is invested at 2.5% a year for 3 years. How much is it worth? Use the multiplier and a power, not a year-by-year table:

2. Probability and expected frequency

The probability of rain on any day in a holiday is 0.15. How many wet days should you expect in 40 days? 0.15 × 40 = 6 days.

3. Precedence table and critical path

Task A takes 3 hours. Task B takes 2 hours and Task C takes 4 hours, and both can start only after A. Task D takes 1 hour and can start only after B and C. B and C can run at the same time, so the shortest time is the longest route: A, C, D = 3 + 4 + 1 = 8 hours. Adding every time to get 10 hours is the common slip.

4. Tolerance

A shaft is made to be 25 mm with a tolerance of ±0.2 mm. The limits are 25 − 0.2 = 24.8 mm and 25 + 0.2 = 25.2 mm.

Check a set of numbers in the Standard Deviation Calculator, or practise statistics in the Probability course.

Where candidates lose marks

From the 2026 course report, these are the questions that went wrong:

• Units in a gradient. Most candidates did not give the height and the horizontal distance in the same units.
• Critical path. Some candidates simply added all the times.
• Commission. Many found 5% of the wrong value.
• Using a formula. Many did not change 1.5 minutes into seconds.
• Net pay. Many subtracted National Insurance before working out the pension contribution, and some forgot the 0% band in National Insurance.
• Percentage profit. Most divided by the wrong number.
• Comparing data sets. Few compared both the mean and the standard deviation, and the standard deviation comments were weaker.
• Direct proportion. Most did not use a valid strategy.

Use a daily paper as a short timed prelim

Many schools set a National 5 prelim in winter: see our prelims guide. Uni-Sine publishes a free daily paper for National 5 Maths, the closest track to Applications of Maths. It is a short timed paper of 8 questions worth 25 to 35 marks, not a full SQA paper and not written by SQA. Do the non-calculator ones without a calculator, and show every step.

Exam answers

The answers and a worked mark scheme come with today's paper once it is marked. Sit the paper as a timed mock, mark it, and the worked answers show where the marks were. We do not publish official or past paper answers.

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Scotland · National 5National 5 Applications of Maths formula sheetThe National 5 Applications of Maths formula sheet: circle, Pythagoras, gradient, volumes and standard deviation, what is not on it, and worked examples.