Practice questions for the OCR GCSE Mathematics (J560), Higher tier specification, for teaching in England. Every answer is explained, so you can see why the right option is right.
About this practice. Revision Robin is built and maintained by Bloor Engineering Ltd, a UK-registered company. Our GCSE Mathematics Higher (OCR) questions are written and reviewed in-house to match the current syllabus, each with a plain-English worked explanation. They are original practice material, not the official exam questions and not affiliated with or endorsed by OCR. Always confirm current test rules, fees and content with the official provider. See our Terms and Privacy.
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Q1. Solve 3x² + 10x - 4 = 0. Give your solutions correct to 2 decimal places.
A. x = -0.46 and x = -2.87
B. x = 0.46 and x = -3.79
C. x = -0.36 and x = 3.69
D. x = 0.36 and x = -3.69
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✓ Answer: D. x = 0.36 and x = -3.69
Use the quadratic formula x = [-b ± √(b²-4ac)] / 2a, with a=3, b=10, c=-4. This gives x = [-10 ± √(100 - 4(3)(-4))] / 6 = [-10 ± √148] / 6. Calculating the two possible values for x gives the answer.
Q2. Calculate (7.2 × 10⁵) + (4 × 10⁴). Give your answer in standard form.
A. 7.6 × 10⁵
B. 7.6 × 10⁹
C. 11.2 × 10⁵
D. 4.72 × 10⁵
Show answer & explanation
✓ Answer: A. 7.6 × 10⁵
To add numbers in standard form, the powers of 10 must be the same. Convert 7.2 × 10⁵ to 72 × 10⁴. Then (72 × 10⁴) + (4 × 10⁴) = 76 × 10⁴. In standard form, this is 7.6 × 10⁵.
Q3. A, B and C are points on a circle. The line DE is a tangent to the circle at point B. Angle CBD is 68°. What is the size of angle BAC?
A. 22°
B. 112°
C. 68°
D. 34°
Show answer & explanation
✓ Answer: C. 68°
The Alternate Segment Theorem states that the angle between a tangent and a chord through the point of contact (∠CBD) is equal to the angle in the alternate segment (∠BAC). Therefore, angle BAC is 68°.
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Who has to sit the GCSE Mathematics Higher (OCR)
Who needs a GCSE Mathematics Higher (OCR)?
Legally compulsory in England for all students until they achieve a grade 4 or reach age 18. Resits are required if a grade 4 is not achieved by Year 11 and they continue further education.
The real GCSE Mathematics Higher (OCR): format
How many questions are in the GCSE Mathematics Higher (OCR)?
The real GCSE Mathematics Higher (OCR) has 3 questions and lasts 270 minutes. Our mock uses 40 questions in 60 minutes.
What it costs, and what a resit costs
How much does the GCSE Mathematics Higher (OCR) cost?
Rebooking after a fail: Autumn (November) or summer exam series.
How hard is it
What is the GCSE Mathematics Higher (OCR) pass rate?
Real exam first-time pass rate: 59.4% (OCR, Grade 4+ in June 2026). Difficulty: Higher tier covers advanced topics, emphasizing algebra, geometry, reasoning, and problem-solving. It requires connecting ideas and interpreting problems.
Figures for the real exam from vertexaisearch.cloud.google.com, checked October 2026. Fees and rules change, so confirm with the test provider before you book.
GCSE Mathematics Higher (OCR): common questions
Frequently asked
What is the pass mark for the GCSE Mathematics Higher (OCR)?
You need 24 out of 40 correct to pass, which is about 60%. Our mocks mark you against this exact threshold.
How long do you get?
The test is timed at 60 minutes. Our full mock runs on the same clock so you can practise your pacing.
Are these the real exam questions?
No. Our questions are original and written to match the current syllabus, so they give realistic practice without copying the official paper. Every answer comes with a plain-English explanation. Always confirm current rules and content with OCR.