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100+ Free GCSE Mathematics Practice Questions

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A car cost £15 000. Its value depreciates by 18% in the first year. What is its value after one year?

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Key Facts: GCSE Mathematics Exam

9-1

Grading scale

Ofqual

May-June

Exam series

AQA, Edexcel, OCR timetable

3 boards

Specifications available

AQA, Edexcel, OCR

100

Free practice questions here

OpenExamPrep

AQA, Edexcel, OCR GCSE Mathematics is assessed through linear end-of-course exam papers (Key Stage 4). Coverage spans number, algebra, ratio proportion and rates of change, and grading uses the 9-1 scale on 2026 specifications.

Sample GCSE Mathematics Practice Questions

Try these sample questions to test your GCSE Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Write 0.000 045 6 in standard form.
A.4.56 x 10^-5
B.4.56 x 10^-4
C.4.56 x 10^-6
D.45.6 x 10^-6
Explanation: To write in standard form A x 10^n, move the decimal point so 1 <= A < 10. 0.0000456 becomes 4.56, and the decimal moved 5 places to the right, so n = -5. Answer: 4.56 x 10^-5.
2Work out 3/4 + 2/5.
A.5/9
B.1 3/20
C.23/20
D.6/20
Explanation: Use a common denominator of 20: 3/4 = 15/20 and 2/5 = 8/20. Adding gives 15/20 + 8/20 = 23/20. As a mixed number this is 1 3/20, but the improper form 23/20 is option C.
3Find the highest common factor (HCF) of 36 and 84.
A.6
B.12
C.18
D.252
Explanation: Prime factorise: 36 = 2^2 x 3^2 and 84 = 2^2 x 3 x 7. Take the lowest power of each shared prime: 2^2 x 3 = 12. So HCF(36, 84) = 12.
4Simplify sqrt(50) + sqrt(8).
A.sqrt(58)
B.7 sqrt(2)
C.2 sqrt(58)
D.10 sqrt(2)
Explanation: sqrt(50) = sqrt(25 x 2) = 5 sqrt(2), and sqrt(8) = sqrt(4 x 2) = 2 sqrt(2). Adding like surds: 5 sqrt(2) + 2 sqrt(2) = 7 sqrt(2).
5Calculate 2^5 x 2^3 / 2^4.
A.2^2
B.2^4
C.2^6
D.2^12
Explanation: Use the index laws: multiplying adds exponents (5 + 3 = 8), dividing subtracts (8 - 4 = 4). So 2^5 x 2^3 / 2^4 = 2^4 = 16.
6A length is given as 12.5 cm to the nearest 0.1 cm. What is the lower bound?
A.12.4 cm
B.12.45 cm
C.12.5 cm
D.12.55 cm
Explanation: The nearest 0.1 cm means rounding within ±0.05 cm. The lower bound is 12.5 − 0.05 = 12.45 cm, and the upper bound is 12.55 cm (which would round up).
7Increase £240 by 15%.
A.£255
B.£276
C.£260
D.£36
Explanation: Multiplier for a 15% increase is 1.15. £240 x 1.15 = £276. Alternatively, 15% of 240 = 36, then 240 + 36 = £276.
8Write 84 as a product of its prime factors.
A.2^2 x 3 x 7
B.2 x 3 x 14
C.4 x 21
D.2 x 3 x 7
Explanation: 84 = 2 x 42 = 2 x 2 x 21 = 2 x 2 x 3 x 7 = 2^2 x 3 x 7. All factors must themselves be prime.
9Convert the recurring decimal 0.4444... (with the 4 recurring) to a fraction in its simplest form.
A.4/9
B.4/10
C.44/99
D.2/5
Explanation: Let x = 0.444.... Then 10x = 4.444.... Subtracting: 10x − x = 4, so 9x = 4 and x = 4/9. This is already in simplest form because gcd(4, 9) = 1.
10Estimate the value of (498 x 21) / 0.49 by rounding each number to 1 significant figure.
A.20
B.200
C.20 000
D.2 000 000
Explanation: Round to 1 s.f.: 498 -> 500, 21 -> 20, 0.49 -> 0.5. Then (500 x 20) / 0.5 = 10 000 / 0.5 = 20 000.

About the GCSE Mathematics Exam

GCSE Mathematics is offered by AQA, Edexcel, OCR as part of the UK General Certificate of Secondary Education qualification framework. The course covers number, algebra, ratio proportion and rates of change, geometry and measures and is assessed primarily through written exam papers at the end of the two-year course.

Questions

100 scored questions

Time Limit

3-5 hours total across multiple papers

Passing Score

Grade 4 is the standard pass, Grade 5 is the strong pass (1-9 scale)

Exam Fee

£40-£80 per subject (school-set entry fee) (AQA, Edexcel, OCR)

GCSE Mathematics Exam Content Outline

Core

Number

Fractions, decimals, percentages, indices, standard form, surds, factors, primes

Core

Algebra

Manipulation, equations, inequalities, sequences, functions, graphs

Core

Ratio, Proportion & Rates of Change

Ratio sharing, proportion, growth/decay, compound measures

Core

Geometry & Measures

Angles, polygons, transformations, congruence, Pythagoras, trigonometry, circle theorems

Core

Probability

Theoretical and experimental probability, tree diagrams, Venn diagrams, conditional probability

Core

Statistics

Averages, range, frequency tables, cumulative frequency, box plots, scatter graphs

How to Pass the GCSE Mathematics Exam

What You Need to Know

  • Passing score: Grade 4 is the standard pass, Grade 5 is the strong pass (1-9 scale)
  • Exam length: 100 questions
  • Time limit: 3-5 hours total across multiple papers
  • Exam fee: £40-£80 per subject (school-set entry fee)

Keys to Passing

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

GCSE Mathematics Study Tips from Top Performers

1Use past papers from your specific exam board — questions follow the same style year on year
2Time yourself on full papers to build pacing for the long extended-response questions
3Build a clear understanding of mark schemes — examiners reward specific assessment objectives
4Review examiner reports each summer; common errors repeat

Frequently Asked Questions

What exam boards offer GCSE Mathematics?

GCSE Mathematics is offered by AQA, Edexcel, OCR. All boards follow Ofqual subject content but vary in the choice of set texts, optional topics, and paper structure.

When is the GCSE Mathematics exam taken?

Exams are written in the May-June series at the end of the two-year Key Stage 4 course. Most students sit the papers in Year 11.

How is GCSE Mathematics graded?

GCSEs are graded on the 9-1 scale, where 9 is the highest grade. A grade 4 is a standard pass, and grade 5 is a strong pass. Grade 7 is broadly equivalent to the old A grade.

How many papers does GCSE Mathematics have?

Most GCSE subjects have 2-3 written papers. The exact number, timing, and weighting depend on the chosen exam board. Some subjects also include a non-examined assessment (NEA) coursework component.