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AQA · GCSE · Mathematics

Free AQA GCSE Mathematics
Practice Paper

8 mixed-difficulty practice questions in the style of real AQA GCSE papers — answers, mark-scheme-style explanations, and the official exam structure all on one page.

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What the real AQA GCSE Mathematics paper looks like

Paper 1
Approximately 1 hour 30 minutes, ~70-100 marks. Covers Topics 1-4 of the specification.
Paper 2
Approximately 1 hour 30 minutes, ~70-100 marks. Covers Topics 5-8 of the specification.
Paper 3
Where applicable — e.g. Combined Science, Languages. Includes synoptic and applied questions.
Total exam time: ~3 hours across two or three papers.
Grading: Grades: 9 (highest) to 1 (lowest), with U (ungraded). A grade of 4 is a standard pass; 5 is a strong pass.

Mini practice paper: 8 questions

Mixed-difficulty questions from across the Mathematics syllabus. Tap "Show answer" after each to check yourself.

Q1 · Difficulty 1/3

If g(x) = x², find g(4).

  1. 4
  2. 16
  3. 8
  4. 12
Show answer & explanation
✓ Answer: B — 16
4² = 16.
Q2 · Difficulty 1/3

y is inversely proportional to x. When x = 5, y = 8. Which equation correctly represents this relationship?

  1. y = 5x/8
  2. y = 40/x
  3. y = x/40
  4. y = 8x/5
Show answer & explanation
✓ Answer: B — y = 40/x
Inverse proportion gives y = k/x where k = xy = 5 × 8 = 40. Therefore y = 40/x. Option D and A confuse direct and inverse proportion, and option C inverts the relationship incorrectly.
Q3 · Difficulty 1/3

A circle has a radius of 8 cm. Calculate its area. Give your answer in terms of π.

  1. 32π cm²
  2. 16π cm²
  3. 64π cm²
  4. 8π cm²
Show answer & explanation
✓ Answer: C — 64π cm²
Area = πr² = π × 8² = 64π cm². A common mistake is to use A = πd², which would give 256π, or to forget to square the radius and write 8π.
Q4 · Difficulty 1/3

Make x the subject of y = 2x.

  1. x = y − 2
  2. x = 2/y
  3. x = y/2
  4. x = 2y
Show answer & explanation
✓ Answer: C — x = y/2
Divide both sides by 2: x = y/2.
Q5 · Difficulty 1/3

If 2x + y = 7 and x = 2, find y.

  1. 5
  2. 2
  3. 4
  4. 3
Show answer & explanation
✓ Answer: D — 3
Substitute x = 2: 4 + y = 7, so y = 3.
Q6 · Difficulty 1/3

Simplify 2x × 3y.

  1. 6x + y
  2. 6x
  3. 6xy
  4. 5xy
Show answer & explanation
✓ Answer: C — 6xy
Multiply coefficients 2 × 3 = 6 and combine variables: 6xy.
Q7 · Difficulty 1/3

Which method is most commonly used to solve a pair of simultaneous equations where one is linear and one is quadratic?

  1. Graphing only, without algebraic working
  2. Multiplying both equations by the same constant
  3. Elimination by adding the two equations
  4. Substitution of the linear equation into the quadratic
Show answer & explanation
✓ Answer: D — Substitution of the linear equation into the quadratic
When one equation is linear and one is quadratic, substitution is the standard method. The linear equation is rearranged for one variable and substituted into the quadratic, producing a quadratic equation in one unknown. Elimination by adding is used for two linear equations, not this type.
Q8 · Difficulty 1/3

Solve x + y = 5 and x − y = 1.

  1. x = 3, y = 2
  2. x = 2, y = 3
  3. x = 4, y = 1
  4. x = 3, y = 1
Show answer & explanation
✓ Answer: A — x = 3, y = 2
Adding: 2x = 6, so x = 3 and y = 2.
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AQA GCSE Mathematics FAQ

What does the AQA GCSE Mathematics exam look like?
The AQA GCSE Mathematics exam is structured across 3 components. Paper 1: Approximately 1 hour 30 minutes, ~70-100 marks. Covers Topics 1-4 of the specification. Paper 2: Approximately 1 hour 30 minutes, ~70-100 marks. Covers Topics 5-8 of the specification. Paper 3: Where applicable — e.g. Combined Science, Languages. Includes synoptic and applied questions. Total exam time: ~3 hours across two or three papers.
Can I download a free AQA GCSE Mathematics past paper?
Real AQA past papers are published directly by AQA on their official website. Kramizo doesn't redistribute copyrighted past papers, but we do generate free AI-written practice papers in the exact same style — same command words, same difficulty tier, same mark conventions. Use this practice paper as warm-up, then time yourself on official past papers before exam day.
How is AQA GCSE Mathematics graded?
Grades: 9 (highest) to 1 (lowest), with U (ungraded). A grade of 4 is a standard pass; 5 is a strong pass. Kramizo's practice questions are tagged with difficulty 1-3 mapping roughly to the lower, middle, and top grade boundaries you'll encounter in the real exam.