National 5 Maths 2027: the exam, grade boundaries and practice questions

The National 5 Maths exam in 2027

The times are from the 2027 exam timetable and match the course specification, which set these paper lengths and marks in May 2023. The course tests numerical, algebraic, geometric, trigonometric, statistical and reasoning skills, and your grade is based on your total across both papers.

National 5 Maths grade boundaries

Figures are from the 2026 course report, covering 33,858 candidates. Boundaries move each year to allow for how hard the papers were.

National 5 Maths practice questions

We wrote these questions for this guide. Try each one before you read the answer, and show your working.

Algebra

Question 1: expand and simplify (x + 4)(2x − 3). Answer: 2x² − 3x + 8x − 12 = 2x² + 5x − 12.

Question 2: factorise x² − 9x + 20. Answer: find two numbers that multiply to 20 and add to −9: −4 and −5. So it is (x − 4)(x − 5).

Question 3: solve 2x + y = 11 and x − y = 1. Answer: add the equations to remove y: 3x = 12, so x = 4. Then 4 − y = 1, so y = 3. Solve a pair yourself from our Algebra course and press Mark.

Straight lines

Question 4: a line passes through (1, 3) and (3, 11). Find its equation. Answer: gradient = (11 − 3) ÷ (3 − 1) = 4. Using y − b = m(x − a) with (1, 3): y − 3 = 4(x − 1), so y = 4x − 1. Check with the Linear Graph tool.

Trigonometry

Question 5: a triangle has sides of 7 cm and 9 cm with an angle of 40° between them. Find its area. Answer: area = ½ab sin C = ½ × 7 × 9 × sin 40° = 20.2 cm² to 3 significant figures. The angle must be the one between the two sides you use.

Percentages and volume

Question 6: a car worth £15,000 loses 12% of its value each year. What is it worth after 3 years? Answer: each year it keeps 88%, so the value is 15,000 × 0.88³ = £10,222.08. Taking 36% off once gives the wrong answer, because each year's loss is worked out on a smaller value.

Question 7: find the volume of a sphere with radius 6 cm. Answer: V = 4/3 πr³ = 4/3 × π × 216 = 905 cm³ to 3 significant figures.

Common National 5 Maths mistakes

• Sign errors when expanding or factorising. Check by expanding your answer.
• Simple instead of compound percentages. Multiply by the multiplier for each year.
• The wrong angle in the area formula.
• Rounding too early in multi-step calculations on Paper 2.
• Missing working. Marks are given for method, so a bare answer is risky.

Use a daily paper as a short timed prelim

Sit today's National 5 Maths paper as a short timed prelim. If you are aiming for Higher next year, try the Higher Maths: Algebra and Functions paper too. For prelim dates and how prelims are used, see the prelims guide.

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