Free Practice Questions for National 5 Mathematics
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Key Facts: National 5 Mathematics Exam
90 marks
Total across Paper 1 and Paper 2
Qualifications Scotland N5 Maths Course Spec
C847 75
Course code
Qualifications Scotland (formerly SQA)
SCQF Level 5
Qualification level
Scottish Credit and Qualifications Framework
100
Free practice questions here
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Scotland's National 5 Mathematics (C847 75) is a SCQF Level 5 qualification, assessed by a 40-mark non-calculator Paper 1 (1h 15min) and a 50-mark calculator Paper 2 (1h 50min). Awarded by Qualifications Scotland (formerly SQA) with grades A-D, A-C is a pass.
Sample National 5 Mathematics Practice Questions
Try these sample questions to review concepts for the National 5 Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1Simplify sqrt(12) + sqrt(27).
2Rationalise the denominator: 10 / sqrt(5).
3Simplify sqrt(8) * sqrt(6).
4Simplify (2x^3)^4.
5Evaluate 16^(3/4).
6Simplify x^(-2) * x^5.
7Write 0.000043 in scientific notation.
8Calculate (3 x 10^4) x (2 x 10^6) and write the answer in scientific notation.
9Simplify (x^5 * x^2) / x^3.
10Express sqrt(45) - sqrt(20) in simplest surd form.
About the National 5 Mathematics Exam
National 5 Mathematics (course code C847 75) is the standard Scottish qualification at SCQF Level 5, sat by most candidates in S4. It is awarded by Qualifications Scotland (formerly SQA) and covers three subject areas: Expressions and Formulae, Relationships, and Applications. Assessment is by two written papers — Paper 1 (non-calculator, 40 marks) and Paper 2 (calculator allowed, 50 marks).
Exam sponsor: Qualifications Scotland (formerly SQA). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.
Questions
100 questions
Time Limit
Paper 1: 1h 15min; Paper 2: 1h 50min (3h 5min total)
Passing Score
Grade C (typically ~50% of marks); A and B are higher pass grades
Exam / Certification Fees
Free for school candidates; approximately £14.05 per subject for private candidates
Exam sponsor websiteFees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.
Our practice resources: topics covered
We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.
Expressions and Formulae
Surds, laws of indices, scientific notation, algebraic fractions, brackets and factorising, completing the square
Relationships
Linear equations and inequations, simultaneous equations, straight line equation, quadratic functions and equations, trigonometry in right-angled and non-right-angled triangles
Applications
Pythagoras in 2D and 3D, volume and surface area of solids, similar shapes, arcs and sectors, statistics (mean, standard deviation, quartiles), percentages, ratio and proportion
Non-Calculator Paper
40 marks, 1 hour 15 minutes. Mental arithmetic and pencil-and-paper algebra; no calculator permitted
Calculator Paper
50 marks, 1 hour 50 minutes. Scientific calculator allowed; longer multi-step problems and contextualised questions
Preparing for the National 5 Mathematics Exam
What You Need to Know
- Passing score: Grade C (typically ~50% of marks); A and B are higher pass grades
- Exam length: 100 questions
- Time limit: Paper 1: 1h 15min; Paper 2: 1h 50min (3h 5min total)
- Exam / certification fees: Free for school candidates; approximately £14.05 per subject for private candidates Official sources
Using Our Practice Resources
- Work through all 100 available questions
- Review every answer and explanation
- Track weak areas and revisit them
- Use our AI tutor for tough concepts
National 5 Mathematics: Suggested Study Strategy
Frequently Asked Questions
Who awards National 5 Mathematics?
National 5 qualifications are awarded by Qualifications Scotland (formerly the Scottish Qualifications Authority, SQA). The body was renamed Qualifications Scotland on 1 February 2026; the course content and structure are unchanged.
How is National 5 Mathematics assessed?
Assessment is by two written papers totalling 90 marks. Paper 1 is non-calculator (40 marks, 1h 15min) and Paper 2 allows a scientific calculator (50 marks, 1h 50min). Both papers test all three subject areas.
What grade do I need to pass National 5 Mathematics?
Grades A, B and C are passes. Grade C requires roughly 50% of the available marks, although grade boundaries are set each year and vary between papers. Grade D is a near-miss and No Award is below that.
When are National 5 Maths exams sat?
The written exams are sat in the May exam diet, alongside the rest of the SQA/Qualifications Scotland diet. Results are released in early August.
Can I use a formula sheet in National 5 Maths?
Yes. Both papers come with a printed formulae list including the sine and cosine rules, area = 1/2 ab sin C, the quadratic formula, volumes of cones/spheres/pyramids, and the standard deviation formula.