Q1 · Difficulty 1/3
Work out √144 + √25.
- 17
- 13
- 19
- 169
Show answer & explanation
✓ Answer: A — 17
12 + 5 = 17.
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.
Take a Mini Mock →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.
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.
Q2 · Difficulty 1/3
Simplify the ratio 18 : 24.
- 6 : 8
- 9 : 12
- 3 : 4
- 2 : 3
Show answer & explanation
✓ Answer: C — 3 : 4
Divide both parts by the HCF 6.
Q3 · Difficulty 1/3
A fair six-sided die is rolled. What is the probability of scoring a 4?
- 1/6
- 1/4
- 4/6
- 1/2
Show answer & explanation
✓ Answer: A — 1/6
One favourable outcome out of six.
Q4 · Difficulty 2/3
Work out 3/4 + 1/6.
- 11/12
- 4/10
- 1
- 5/6
Show answer & explanation
✓ Answer: A — 11/12
Common denominator 12: 9/12 + 2/12 = 11/12.
Q5 · Difficulty 2/3
In a class of 30, 18 study French. What is the probability a random student studies French?
- 3/5
- 18/12
- 1/18
- 12/30
Show answer & explanation
✓ Answer: A — 3/5
18/30 = 3/5.
Q6 · Difficulty 2/3
A card is drawn from a standard 52-card pack. What is the probability it is a heart?
- 1/2
- 13/52 = 1/3
- 1/4
- 1/13
Show answer & explanation
✓ Answer: C — 1/4
13 hearts out of 52 = 1/4.
Q7 · Difficulty 1/3
The probability it rains tomorrow is 0.3. What is the probability it does not rain?
- 0.3
- 1.3
- 0.5
- 0.7
Show answer & explanation
✓ Answer: D — 0.7
Complement: 1 − 0.3 = 0.7.
Q8 · Difficulty 1/3
Find the range of 12, 5, 20, 8, 15.
- 12
- 25
- 15
- 20
Show answer & explanation
✓ Answer: C — 15
Range = 20 − 5 = 15.
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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.