Is OCR GCSE Maths 2026 Predicted Practice Paper — Paper 4 Higher an official exam paper?

No. It is an original StudyVector predicted-practice paper for revision. It is not official, leaked or guaranteed, and students should still revise the full specification.

How many marks and questions are in this predicted paper?

This paper has 100 marks across 21 questions and is designed for a 90-minute practice session.

Published 8 March 2026Updated 22 April 2026By Lizzie D., founderPrivacy Policy

Use official specifications and past papers as the source of truth: AQA, Pearson Edexcel and OCR. StudyVector is independent and is not affiliated with any exam board.

Predicted paper

OCR GCSE Maths 2026 Predicted Practice Paper — Paper 4 Higher

GCSE Mathematics · OCR-style · 90 minutes · 100 marks

Modelled component: J560/04 · Tier: Higher · Calculator permitted

Models OCR J560 Higher Paper 4: 1 hour 30 minutes, 100 marks, calculator permitted.

Prediction type: predicted_paper · Evidence mode: historical · Full-length original practice paper modelled on OCR J560's public GCSE Maths Higher structure. It is not official, leaked or guaranteed.

Evidence basis: official public assessment structure, full-paper mark total, board-specific calculator rules, GCSE Maths topic weighting, higher-tier problem-solving mix.

Predicted difficulty score (practice signal)

0–100 model (higher = more demanding)

Candidate focus topics (not guarantees)

Calculator trigonometry
Compound interest
Bounds
Iteration
Similarity
Histograms

I completed a StudyVector GCSE Mathematics derived predicted-practice paper (2026) and scored 0/100. This is practice-only and not an official paper:

Section A

Answer all questions. A calculator is permitted for this OCR Higher Paper 4 style paper.

Question A1 (2 marks)
Work out 3.7^2 - 2.4^2.
Question A2 (2 marks)
A car travels 156 miles in 2.5 hours. Work out its average speed in miles per hour.
Question A3 (3 marks)
Increase 84 by 17.5%.
Question A4 (3 marks)
GBP450 is invested for 4 years at 3% compound interest per year. Work out the final value.
Question A5 (3 marks)
Work out (6.4 x 10^5) x (3 x 10^-2). Give your answer in standard form.
Question A6 (4 marks)
In a right-angled triangle, the hypotenuse is 12 cm and an angle is 35 degrees. Work out the length of the side opposite the 35 degree angle.
Question A7 (4 marks)
The probability that a biased coin lands on heads is 0.62. The coin is tossed twice. Work out the probability of exactly one head.

Section B

Answer all questions. Give reasons or working where required.

Question B1 (4 marks)
An object has mass 780 g and volume 250 cm^3. Work out its density.
Question B2 (4 marks)
Solve the simultaneous equations 3x + 2y = 31 and x - y = 3.
Question B3 (4 marks)
Rearrange v^2 = u^2 + 2as to make s the subject. Then find s when v = 18, u = 6 and a = 3.
Question B4 (5 marks)
f(x) = 3x - 5. Find f^-1(x) and then find f^-1(16).
Question B5 (5 marks)
A sector has radius 8 cm and angle 110 degrees. Work out its area.
Question B6 (5 marks)
x = 12.4 correct to the nearest 0.1 and y = 5.8 correct to the nearest 0.1. Work out the lower bound for x/y.
Question B7 (6 marks)
A cumulative frequency table gives: up to 10: 4, up to 20: 12, up to 30: 27, up to 40: 40. Estimate the interquartile range.
Question B8 (6 marks)
OA = 2i + 3j and OB = 10i - 5j. P divides AB in the ratio 3 : 1 from A to B. Find the position vector of P.

Section C

Answer all questions. These questions assess linked reasoning and problem solving.

Question C1 (6 marks)
Solve 2x^2 - 5x - 3 = 0.
Question C2 (6 marks)
The equation x^2 + x - 10 = 0 can be solved using x = sqrt(10 - x). Starting with x0 = 2.5, find x1, x2 and x3. Give x3 to 3 significant figures.
Question C3 (7 marks)
Two mathematically similar solids have a linear scale factor of 1.5 from the smaller solid to the larger solid. The smaller solid has volume 240 cm^3. Work out the volume of the larger solid.
Question C4 (7 marks)
In triangle ABC, AB = 8 cm, AC = 11 cm and angle BAC = 42 degrees. Work out BC and the area of triangle ABC.
Question C5 (7 marks)
A histogram has classes 0-10, 10-25 and 25-40. The frequencies are 8, 24 and 15. Work out the frequency density for each class and state which class has the tallest bar.
Question C6 (7 marks)
Prove that (n + 1)^2 - (n - 1)^2 is always divisible by 4 for integer n.

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OCR GCSE Maths 2026 Predicted Practice Paper — Paper 4 Higher

GCSE Mathematics · OCR-style · 90 minutes · 100 marks

Modelled component: J560/04 · Tier: Higher · Calculator permitted

Models OCR J560 Higher Paper 4: 1 hour 30 minutes, 100 marks, calculator permitted.

Evidence basis: official public assessment structure, full-paper mark total, board-specific calculator rules, GCSE Maths topic weighting, higher-tier problem-solving mix.

Section A

Answer all questions. A calculator is permitted for this OCR Higher Paper 4 style paper.

Question A1 (2 marks)

Work out 3.7^2 - 2.4^2.

Question A2 (2 marks)

A car travels 156 miles in 2.5 hours. Work out its average speed in miles per hour.

Question A3 (3 marks)

Increase 84 by 17.5%.

Question A4 (3 marks)

GBP450 is invested for 4 years at 3% compound interest per year. Work out the final value.

Question A5 (3 marks)

Work out (6.4 x 10^5) x (3 x 10^-2). Give your answer in standard form.

Question A6 (4 marks)

In a right-angled triangle, the hypotenuse is 12 cm and an angle is 35 degrees. Work out the length of the side opposite the 35 degree angle.

Question A7 (4 marks)

The probability that a biased coin lands on heads is 0.62. The coin is tossed twice. Work out the probability of exactly one head.

Section B

Answer all questions. Give reasons or working where required.

Question B1 (4 marks)

An object has mass 780 g and volume 250 cm^3. Work out its density.

Question B2 (4 marks)

Solve the simultaneous equations 3x + 2y = 31 and x - y = 3.

Question B3 (4 marks)

Rearrange v^2 = u^2 + 2as to make s the subject. Then find s when v = 18, u = 6 and a = 3.

Question B4 (5 marks)

f(x) = 3x - 5. Find f^-1(x) and then find f^-1(16).

Question B5 (5 marks)

A sector has radius 8 cm and angle 110 degrees. Work out its area.

Question B6 (5 marks)

x = 12.4 correct to the nearest 0.1 and y = 5.8 correct to the nearest 0.1. Work out the lower bound for x/y.

Question B7 (6 marks)

A cumulative frequency table gives: up to 10: 4, up to 20: 12, up to 30: 27, up to 40: 40. Estimate the interquartile range.

Question B8 (6 marks)

OA = 2i + 3j and OB = 10i - 5j. P divides AB in the ratio 3 : 1 from A to B. Find the position vector of P.

Section C

Answer all questions. These questions assess linked reasoning and problem solving.

Question C1 (6 marks)

Solve 2x^2 - 5x - 3 = 0.

Question C2 (6 marks)

The equation x^2 + x - 10 = 0 can be solved using x = sqrt(10 - x). Starting with x0 = 2.5, find x1, x2 and x3. Give x3 to 3 significant figures.

Question C3 (7 marks)

Two mathematically similar solids have a linear scale factor of 1.5 from the smaller solid to the larger solid. The smaller solid has volume 240 cm^3. Work out the volume of the larger solid.

Question C4 (7 marks)

In triangle ABC, AB = 8 cm, AC = 11 cm and angle BAC = 42 degrees. Work out BC and the area of triangle ABC.

Question C5 (7 marks)

A histogram has classes 0-10, 10-25 and 25-40. The frequencies are 8, 24 and 15. Work out the frequency density for each class and state which class has the tallest bar.

Question C6 (7 marks)

Prove that (n + 1)^2 - (n - 1)^2 is always divisible by 4 for integer n.