National 5 exam guide
National 5 Mathematics
Course code C847 75 · Specification Version 3.0, May 2023 · valid from 2023–24
Your 2027 exam
- Paper 1 (non-calculator)
- – BST
- Paper 2
- – BST
Published national times, in UK local time. Confirm your personal timetable, room and any assessment arrangements with your school or college. Coursework deadlines are set by your centre.
- Results day
- National contingency day
Qualifications Scotland timetable · Version 02, August 2026 · checked .
How the exam is marked
90 course marks after scaling
Paper 1 (non-calculator)
40 marks
44% of the course result
1 hour
Short-answer and extended-response questions without a calculator.
Paper 2
50 marks
56% of the course result
1 hour 30 minutes
Short-answer and extended-response questions. A calculator may be used.
Course areas and revision checklist
Use this summary alongside the full official specification. ScotSpark practice covers selected skills, not every item below; your teacher can help you fill the gaps.
Numerical skills
- Surds: simplifying and rationalising denominators
- Laws of indices, including negative and fractional indices
- Scientific notation
- Rounding to significant figures
- Reverse percentages
- Appreciation, compound interest and depreciation
- Operations on fractions and mixed numbers
Algebraic skills
- Expanding brackets
- Factorising: common factor, difference of squares, trinomials
- Completing the square
- Simplifying and combining algebraic fractions
- Equation of a straight line and function notation
- Linear equations and inequations
- Simultaneous equations (from text, graphically, algebraically)
- Changing the subject of a formula
- Quadratic graphs: equation, sketching, turning point, axis of symmetry
- Solving quadratics, including the quadratic formula
- The discriminant and nature of roots
Geometric skills
- Gradient of a straight line
- Arc length and sector area
- Volume of a sphere, cone and pyramid
- Pythagoras, including converse and 3D
- Angles in shapes and circles
- Similarity: length, area and volume scale factors
- 2D and 3D vectors, components and magnitude
- 3D coordinates
Trigonometric skills
- Trig graphs: amplitude, period, phase, vertical translation
- Trig values 0° to 360°, related angles, basic equations
- Identities sin²x + cos²x = 1 and tan x = sin x / cos x
- Area of a triangle (½ab sin C)
- Sine and cosine rules
- Bearings with trigonometry
Statistical skills
- Comparing data sets using interquartile range and standard deviation
- Line of best fit on a scattergraph
Reasoning skills
- Interpreting a situation and choosing a strategy
- Explaining a solution in context
Exam technique
- Paper 1 is 40 of the 90 marks, so practise arithmetic, fractions and surds without a calculator.
- Reasoning marks can be attached to any topic: always state your answer in context.
- Use the language "two real and distinct roots", "one repeated root" or "no real roots" for the discriminant.
Version 3.0, May 2023 · checked . Qualifications Scotland replaced SQA in February 2026; official documents may still use the SQA name. Check for later updates and confirm arrangements with your teacher.