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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

Simplify 3a + 5a.

  1. 8a
  2. 8a²
  3. 15a
  4. 2a
Show answer & explanation
✓ Answer: A — 8a
Add the like terms: 3a + 5a = 8a.
Q2 · Difficulty 1/3

What is the next term in the sequence 3, 7, 11, 15, ...?

  1. 19
  2. 18
  3. 20
  4. 17
Show answer & explanation
✓ Answer: A — 19
The common difference is 4, so 15 + 4 = 19.
Q3 · Difficulty 1/3

Solve (x − 3)(x + 2) = 0.

  1. x = 3 or x = −2
  2. x = −3 or x = 2
  3. x = 3 or x = 2
  4. x = −3 or x = −2
Show answer & explanation
✓ Answer: A — x = 3 or x = −2
Set each bracket to zero: x − 3 = 0 gives x = 3; x + 2 = 0 gives x = −2.
Q4 · Difficulty 1/3

What is the result of rationalising the denominator of 1/√5?

  1. √5/5
  2. 1/5
  3. 5/√5
  4. √5
Show answer & explanation
✓ Answer: A — √5/5
Multiply numerator and denominator by √5: (1 × √5)/(√5 × √5) = √5/5. Option B forgets to keep √5 in the numerator. Option D incorrectly removes the denominator entirely.
Q5 · Difficulty 1/3

What is the formula for the circumference of a circle with diameter d?

  1. C = πr²
  2. C = 2πr²
  3. C = πd
  4. C = πd²
Show answer & explanation
✓ Answer: C — C = πd
The circumference of a circle is found using C = πd, where d is the diameter. Alternatively, since d = 2r, this can be written as C = 2πr. The formula C = πr² gives the area, not the circumference.
Q6 · Difficulty 1/3

A tree diagram is drawn for two events A and B. Which expression correctly gives P(A and B)?

  1. A) P(A) + P(B)
  2. B) P(A) × P(B | A)
  3. C) P(B) × P(A | B) + P(A)
  4. D) P(A) + P(B) − P(A or B)
Show answer & explanation
✓ Answer: B — B) P(A) × P(B | A)
The multiplication rule states P(A and B) = P(A) × P(B | A), which is equivalent to multiplying along the branches of a tree diagram. Option A is the addition rule for mutually exclusive events and does not give the intersection.
Q7 · Difficulty 1/3

If t = 5, find 100 − 10t.

  1. 50
  2. 60
  3. 40
  4. 90
Show answer & explanation
✓ Answer: A — 50
100 − 10 × 5 = 100 − 50 = 50.
Q8 · Difficulty 1/3

What is the common ratio of 3, 6, 12, 24, ...?

  1. 2
  2. 3
  3. 6
  4. 0.5
Show answer & explanation
✓ Answer: A — 2
Each term is multiplied by 2: 6 ÷ 3 = 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.