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OCR · GCSE · Mathematics

Free OCR GCSE Mathematics
Practice Paper

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

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What the real OCR 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

Vertically opposite angles are always:

  1. right angles
  2. equal
  3. supplementary
  4. complementary
Show answer & explanation
✓ Answer: B — equal
Vertically opposite angles are equal.
Q2 · Difficulty 1/3

Calculate the hypotenuse of a right triangle with legs 5cm and 12cm.

  1. 17 cm
  2. 13 cm
  3. 7 cm
  4. 169 cm
Show answer & explanation
✓ Answer: B — 13 cm
c² = 5² + 12² = 25 + 144 = 169. c = √169 = 13 cm.
Q3 · Difficulty 1/3

The area of a triangle with base 8 cm and height 5 cm is:

  1. 40 cm²
  2. 13 cm²
  3. 80 cm²
  4. 20 cm²
Show answer & explanation
✓ Answer: D — 20 cm²
Area = ½ × 8 × 5 = 20 cm².
Q4 · Difficulty 1/3

7² equals:

  1. 14
  2. 49
  3. 42
  4. 21
Show answer & explanation
✓ Answer: B — 49
49.
Q5 · Difficulty 1/3

An ogive is best described as a graph of:

  1. Frequency against class boundaries
  2. Cumulative frequency against upper class boundaries
  3. Relative frequency against midpoints
  4. Frequency density against class width
Show answer & explanation
✓ Answer: B — Cumulative frequency against upper class boundaries
An ogive (cumulative frequency curve) is constructed by plotting cumulative frequency on the vertical axis against the upper class boundaries on the horizontal axis. Plotting against midpoints or using frequency density are features of other statistical graphs such as frequency polygons or histograms.
Q6 · Difficulty 1/3

What is a bearing of 045°?

  1. South-East
  2. North-East
  3. North-West
  4. South-West
Show answer & explanation
✓ Answer: B — North-East
Bearings are measured clockwise from North. 045° = North-East direction.
Q7 · Difficulty 1/3

The probability it rains tomorrow is 0.3. What is the probability it does not rain?

  1. 0.3
  2. 1.3
  3. 0.5
  4. 0.7
Show answer & explanation
✓ Answer: D — 0.7
Complement: 1 − 0.3 = 0.7.
Q8 · Difficulty 1/3

A bag has 3 red and 5 blue counters. What is the probability of drawing a red?

  1. 5/8
  2. 1/3
  3. 3/8
  4. 3/5
Show answer & explanation
✓ Answer: C — 3/8
3 red out of 8 counters.
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OCR GCSE Mathematics FAQ

What does the OCR GCSE Mathematics exam look like?
The OCR 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 OCR GCSE Mathematics past paper?
Real OCR past papers are published directly by OCR 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 OCR 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.