Career upgrade: Learn practical AI skills for better jobs and higher pay.
Level up
PracticeVideosBlogFlashcardsEspañol
All Practice Exams

100+ Free National 5 Mathematics Practice Questions

Pass your National 5 Mathematics (Scotland) exam on the first try — instant access, no signup required.

✓ No registration✓ No credit card✓ No hidden fees✓ Start practicing immediately
100+ Questions
100% Free
1 / 100
Question 1
Score: 0/0

Two similar cuboids have lengths 4 cm and 12 cm. The smaller has volume 32 cm^3. Find the volume of the larger.

A
B
C
D
to track
Same family resources

Explore More Scottish Qualifications (National 5, Higher, Advanced Higher)

Continue into nearby exams from the same family. Each card keeps practice questions, study guides, flashcards, videos, and articles in one place.

Scottish Advanced Higher Biology

Practice Questions

Scottish Advanced Higher Chemistry

Practice Questions

Scottish Advanced Higher Computing Science

Practice Questions

Scottish Advanced Higher English

Practice Questions

Scottish Advanced Higher French

Practice Questions

Scottish Advanced Higher History

Practice Questions
2026 Statistics

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

OpenExamPrep

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 test your National 5 Mathematics exam readiness. 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).
A.5*sqrt(3)
B.sqrt(39)
C.6*sqrt(3)
D.5*sqrt(6)
Explanation: sqrt(12) = sqrt(4*3) = 2*sqrt(3) and sqrt(27) = sqrt(9*3) = 3*sqrt(3). Adding gives 2*sqrt(3) + 3*sqrt(3) = 5*sqrt(3).
2Rationalise the denominator: 10 / sqrt(5).
A.2*sqrt(5)
B.sqrt(50)
C.10*sqrt(5)/5
D.sqrt(2)
Explanation: Multiply top and bottom by sqrt(5): 10*sqrt(5) / 5 = 2*sqrt(5). The rationalised form is 2*sqrt(5).
3Simplify sqrt(8) * sqrt(6).
A.4*sqrt(3)
B.sqrt(48)
C.2*sqrt(12)
D.sqrt(14)
Explanation: sqrt(8)*sqrt(6) = sqrt(48) = sqrt(16*3) = 4*sqrt(3). Always reduce surds to simplest form.
4Simplify (2x^3)^4.
A.16x^12
B.8x^12
C.16x^7
D.2x^12
Explanation: Raise each factor to the power 4: 2^4 = 16 and (x^3)^4 = x^(3*4) = x^12. Result: 16x^12.
5Evaluate 16^(3/4).
A.8
B.12
C.4
D.64
Explanation: 16^(3/4) = (16^(1/4))^3 = 2^3 = 8. The denominator gives the root and the numerator gives the power.
6Simplify x^(-2) * x^5.
A.x^3
B.x^(-10)
C.x^7
D.1/x^3
Explanation: When multiplying powers with the same base, add the exponents: -2 + 5 = 3. So x^(-2) * x^5 = x^3.
7Write 0.000043 in scientific notation.
A.4.3 x 10^(-5)
B.4.3 x 10^(-4)
C.43 x 10^(-6)
D.4.3 x 10^5
Explanation: Move the decimal point 5 places to the right to get 4.3, giving 4.3 x 10^(-5). The number is less than 1 so the index is negative.
8Calculate (3 x 10^4) x (2 x 10^6) and write the answer in scientific notation.
A.6 x 10^10
B.6 x 10^24
C.5 x 10^10
D.6 x 10^11
Explanation: Multiply the numbers and add the indices: 3 x 2 = 6 and 10^4 x 10^6 = 10^(4+6) = 10^10. So the answer is 6 x 10^10.
9Simplify (x^5 * x^2) / x^3.
A.x^4
B.x^10/3
C.x^0
D.x^(10/3)
Explanation: Multiply: x^5 * x^2 = x^7. Divide by x^3: x^(7-3) = x^4. Add indices when multiplying and subtract when dividing.
10Express sqrt(45) - sqrt(20) in simplest surd form.
A.sqrt(5)
B.5*sqrt(5)
C.sqrt(25)
D.sqrt(5)/2
Explanation: sqrt(45) = 3*sqrt(5) and sqrt(20) = 2*sqrt(5). Subtracting: 3*sqrt(5) - 2*sqrt(5) = sqrt(5).

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).

Questions

100 scored 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 Fee

Free for school candidates; approximately £14.05 per subject for private candidates (Qualifications Scotland (formerly SQA))

National 5 Mathematics Exam Content Outline

~30%

Expressions and Formulae

Surds, laws of indices, scientific notation, algebraic fractions, brackets and factorising, completing the square

~40%

Relationships

Linear equations and inequations, simultaneous equations, straight line equation, quadratic functions and equations, trigonometry in right-angled and non-right-angled triangles

~30%

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

Paper 1

Non-Calculator Paper

40 marks, 1 hour 15 minutes. Mental arithmetic and pencil-and-paper algebra; no calculator permitted

Paper 2

Calculator Paper

50 marks, 1 hour 50 minutes. Scientific calculator allowed; longer multi-step problems and contextualised questions

How to Pass 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 fee: Free for school candidates; approximately £14.05 per subject for private candidates

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

National 5 Mathematics Study Tips from Top Performers

1Practise Paper 1 without a calculator — mental arithmetic and fraction handling are heavily tested
2Memorise the exact trig values for 0, 30, 45, 60 and 90 degrees; they are required for non-calculator marks
3Always show full working — even a wrong final answer earns method marks if working is clear
4Use the SQA formulae sheet under exam conditions so you know exactly what is and is not given
5Work through at least the past 5 years of past papers and the marker's commentary published each year

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.