Is OCR GCSE Maths 2027 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.

What is the GCSE Mathematics Paper 4 Higher format (J560/04)?

GCSE Mathematics Paper 4 Higher (J560/04) is 100 marks over 90 minutes. Models OCR J560 Higher Paper 4: 1 hour 30 minutes, 100 marks, calculator permitted.

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

Source note: use official specifications as the source of truth. StudyVector is an independent revision platform. AQA, Pearson Edexcel and OCR

Direct answer

This page hosts StudyVector’s independent 2027 GCSE Mathematics Paper 4 Higher predicted-practice paper modelled on J560/04,100 marks over 90 minutes. Predicted focus topics: surds-and-indices, quadratic-graphs-and-completing-the-square, vectors-and-geometric-proof, trigonometry-sine-and-cosine-rules, compound-growth-and-iteration. It is not an official paper, not a leaked paper and not a guarantee — students should still revise the full specification and verify against official past papers from OCR.

Qualification: GCSE Mathematics
Exam board model: OCR
Paper code: J560/04
Total marks: 100 marks
Time allowed: 90 minutes
Last reviewed: 16 May 2026

StudyVector is independent revision support, not affiliated with AQA, Edexcel, OCR, JCQ or any exam provider. Always verify topic coverage with your exam-board specification.

Predicted paper

OCR GCSE Maths 2027 Predicted Practice Paper — Paper 4 Higher

Q: What are the GCSE Mathematics Paper 4 Higher predictions for 2027?

StudyVector's 2027 GCSE Mathematics Paper 4 Higher predicted paper focuses on surds-and-indices, quadratic-graphs-and-completing-the-square, vectors-and-geometric-proof, trigonometry-sine-and-cosine-rules, compound-growth-and-iteration, histograms-and-cumulative-frequency. This is an independent, OCR-style predicted-practice paper modelled on the published specification — it is not a leaked paper and is not official.

Q: Which topics are likely to come up in GCSE Mathematics Paper 4 Higher 2027?

Based on the OCR-style structure and recent paper patterns, StudyVector's prediction prioritises: surds-and-indices; quadratic-graphs-and-completing-the-square; vectors-and-geometric-proof; trigonometry-sine-and-cosine-rules; compound-growth-and-iteration; histograms-and-cumulative-frequency. Students should still revise the full specification because exam boards rotate topics.

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.

AI-generated practice paper. Not an official OCR-style paper, not leaked exam content, and not an exam-board endorsement.

Predicted difficulty score (practice signal)

0–100 model (higher = more demanding)

Candidate focus topics (not guarantees)

surds-and-indices
quadratic-graphs-and-completing-the-square
vectors-and-geometric-proof
trigonometry-sine-and-cosine-rules
compound-growth-and-iteration
histograms-and-cumulative-frequency

Preview mode

0/21 questions attempted · score 0/100 (0%)

90:00Warm up with cards Play Daily

Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working.

Section A

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

Question A1 (3 marks)
Work out the value of 5^(-2) + 27^(2/3). Give your answer as an exact fraction or mixed number.
(Total for Question A1 is 3 marks)
Question A2 (3 marks)
A shop increases the price of a coat by 15%, then in a sale reduces the new price by 20%. The final sale price is GBP 82.80. Work out the original price of the coat before any change.
(Total for Question A2 is 3 marks)
Question A3 (3 marks)
Simplify fully sqrt(50) + sqrt(18) - sqrt(8). Give your answer in the form k*sqrt(2).
(Total for Question A3 is 3 marks)
Question A4 (3 marks)
The nth term of a sequence is given by 2n^2 - 3. Work out the first three terms and determine whether 195 is a term of the sequence, showing your reasoning.
(Total for Question A4 is 3 marks)
Question A5 (3 marks)
y is directly proportional to the square of x. When x = 4, y = 48. Work out the value of y when x = 7.
(Total for Question A5 is 3 marks)
Question A6 (3 marks)
Solve the inequality 4(x - 2) >= 2x + 5 and represent the solution set on a number line.
(Total for Question A6 is 3 marks)
Question A7 (3 marks)
A bag contains only red and blue counters in the ratio 5 : 3. There are 24 blue counters. Some red counters are removed so that the ratio becomes 3 : 2. Work out how many red counters were removed.
(Total for Question A7 is 3 marks)

Section B

Answer all questions. Give reasons or working where required.

Question B1 (5 marks)
Solve the simultaneous equations 3x + 2y = 4 and 5x - 3y = 25. Give your answers as exact values.
(Total for Question B1 is 5 marks)
Question B2 (5 marks)
Expand and simplify (2x - 3)(x + 4)(x - 1).
(Total for Question B2 is 5 marks)
Question B3 (5 marks)
The equation of a circle is x^2 + y^2 = 25. The point P(3, 4) lies on the circle. Find the equation of the tangent to the circle at P. Give your answer in the form y = mx + c.
(Total for Question B3 is 5 marks)
Question B4 (5 marks)
A cylinder has a volume of 500 cm^3. Its height is equal to its radius. Work out the radius of the cylinder. Give your answer to 3 significant figures. Use pi = 3.14159.
(Total for Question B4 is 5 marks)
Question B5 (5 marks)
Prove that the sum of the squares of any two consecutive odd numbers is always even but never a multiple of 4.
(Total for Question B5 is 5 marks)
Question B6 (5 marks)
In triangle ABC, AB = 9 cm, BC = 12 cm and angle ABC = 110 degrees. Work out the length of AC and the area of triangle ABC. Give each answer to 3 significant figures.
(Total for Question B6 is 5 marks)
Question B7 (5 marks)
Rationalise the denominator and simplify (5 + sqrt(3)) / (2 - sqrt(3)). Give your answer in the form a + b*sqrt(3) where a and b are integers.
(Total for Question B7 is 5 marks)
Question B8 (4 marks)
A car depreciates in value by 12% each year. It was bought new for GBP 22,000. Work out its value after 4 years, and find, by trial or otherwise, the first whole year at the end of which its value first falls below GBP 10,000.
(Total for Question B8 is 4 marks)

Section C

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

Question C1 (7 marks)
A curve has equation y = x^2 - 6x + 11. (a) Write y in the form (x - a)^2 + b. (b) Hence state the coordinates of the turning point of the curve and explain whether it is a maximum or minimum. (c) Explain why the equation x^2 - 6x + 11 = 0 has no real solutions.
(Total for Question C1 is 7 marks)
Question C2 (7 marks)
OACB is a parallelogram. Vector OA = a and vector OB = b. M is the midpoint of AC. N is the point on OB such that ON : NB = 3 : 1. (a) Express vector OM and vector ON in terms of a and b. (b) Express vector MN in terms of a and b, simplifying your answer. (c) Determine whether MN is parallel to the vector (3a - 2b), justifying your answer by comparing coefficients of a and b.
(Total for Question C2 is 7 marks)
Question C3 (7 marks)
The table gives the times, t minutes, taken by 80 runners to finish a race. 30<=t<40: 8 runners; 40<=t<50: 20 runners; 50<=t<60: 30 runners; 60<=t<70: 15 runners; 70<=t<80: 7 runners. (a) Construct a cumulative frequency table and estimate the median time. (b) Estimate the interquartile range. (c) The organisers award a medal to the fastest 25% of runners. Estimate the qualifying time for a medal.
(Total for Question C3 is 7 marks)
Question C4 (7 marks)
A solid cone has base radius 6 cm and slant height 10 cm. (a) Show that the vertical height of the cone is 8 cm. (b) Work out the total surface area of the cone (including base), giving your answer as a multiple of pi. (c) The cone is melted down and recast as a sphere. Work out the radius of the sphere to 3 significant figures. Use volume of cone = (1/3)*pi*r^2*h and volume of sphere = (4/3)*pi*r^3.
(Total for Question C4 is 7 marks)
Question C5 (6 marks)
A spinner has sections coloured red, green and blue. P(red) = 0.5 and P(green) = 0.3. Priya spins the spinner twice. (a) Work out the probability that she gets blue on both spins. (b) Work out the probability that she gets exactly one red in the two spins. (c) Priya now spins it three times. Work out the probability that she gets at least one green.
(Total for Question C5 is 6 marks)
Question C6 (6 marks)
The graph of y = f(x) has a single vertex (turning point) at (2, -5). (a) Describe fully the single transformation that maps y = f(x) to y = f(x - 3), and state the coordinates of the new vertex. (b) Describe the transformation that maps y = f(x) to y = f(x) + 4, and state the new vertex. (c) The graph of y = f(x) also passes through (0, 3). State the coordinates of the point that (0, 3) maps to under the transformation y = -f(x).
(Total for Question C6 is 6 marks)

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Direct answer

Qualification

GCSE Mathematics

Exam board model

OCR

Paper code

J560/04

Total marks

100 marks

Time allowed

90 minutes

Last reviewed

16 May 2026

StudyVector is independent revision support, not affiliated with AQA, Edexcel, OCR, JCQ or any exam provider. Always verify topic coverage with your exam-board specification.

OCR GCSE Maths 2027 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 (3 marks)

Work out the value of 5^(-2) + 27^(2/3). Give your answer as an exact fraction or mixed number.

(Total for Question A1 is 3 marks)

Question A2 (3 marks)

A shop increases the price of a coat by 15%, then in a sale reduces the new price by 20%. The final sale price is GBP 82.80. Work out the original price of the coat before any change.

(Total for Question A2 is 3 marks)

Question A3 (3 marks)

Simplify fully sqrt(50) + sqrt(18) - sqrt(8). Give your answer in the form k*sqrt(2).

(Total for Question A3 is 3 marks)

Question A4 (3 marks)

The nth term of a sequence is given by 2n^2 - 3. Work out the first three terms and determine whether 195 is a term of the sequence, showing your reasoning.

(Total for Question A4 is 3 marks)

Question A5 (3 marks)

y is directly proportional to the square of x. When x = 4, y = 48. Work out the value of y when x = 7.

(Total for Question A5 is 3 marks)

Question A6 (3 marks)

Solve the inequality 4(x - 2) >= 2x + 5 and represent the solution set on a number line.

(Total for Question A6 is 3 marks)

Question A7 (3 marks)

A bag contains only red and blue counters in the ratio 5 : 3. There are 24 blue counters. Some red counters are removed so that the ratio becomes 3 : 2. Work out how many red counters were removed.

(Total for Question A7 is 3 marks)

Section B

Answer all questions. Give reasons or working where required.

Question B1 (5 marks)

Solve the simultaneous equations 3x + 2y = 4 and 5x - 3y = 25. Give your answers as exact values.

(Total for Question B1 is 5 marks)

Question B2 (5 marks)

Expand and simplify (2x - 3)(x + 4)(x - 1).

(Total for Question B2 is 5 marks)

Question B3 (5 marks)

The equation of a circle is x^2 + y^2 = 25. The point P(3, 4) lies on the circle. Find the equation of the tangent to the circle at P. Give your answer in the form y = mx + c.

(Total for Question B3 is 5 marks)

Question B4 (5 marks)

A cylinder has a volume of 500 cm^3. Its height is equal to its radius. Work out the radius of the cylinder. Give your answer to 3 significant figures. Use pi = 3.14159.

(Total for Question B4 is 5 marks)

Question B5 (5 marks)

Prove that the sum of the squares of any two consecutive odd numbers is always even but never a multiple of 4.

(Total for Question B5 is 5 marks)

Question B6 (5 marks)

In triangle ABC, AB = 9 cm, BC = 12 cm and angle ABC = 110 degrees. Work out the length of AC and the area of triangle ABC. Give each answer to 3 significant figures.

(Total for Question B6 is 5 marks)

Question B7 (5 marks)

Rationalise the denominator and simplify (5 + sqrt(3)) / (2 - sqrt(3)). Give your answer in the form a + b*sqrt(3) where a and b are integers.

(Total for Question B7 is 5 marks)

Question B8 (4 marks)

A car depreciates in value by 12% each year. It was bought new for GBP 22,000. Work out its value after 4 years, and find, by trial or otherwise, the first whole year at the end of which its value first falls below GBP 10,000.

(Total for Question B8 is 4 marks)

Section C

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

Question C1 (7 marks)

A curve has equation y = x^2 - 6x + 11. (a) Write y in the form (x - a)^2 + b. (b) Hence state the coordinates of the turning point of the curve and explain whether it is a maximum or minimum. (c) Explain why the equation x^2 - 6x + 11 = 0 has no real solutions.

(Total for Question C1 is 7 marks)

Question C2 (7 marks)

OACB is a parallelogram. Vector OA = a and vector OB = b. M is the midpoint of AC. N is the point on OB such that ON : NB = 3 : 1. (a) Express vector OM and vector ON in terms of a and b. (b) Express vector MN in terms of a and b, simplifying your answer. (c) Determine whether MN is parallel to the vector (3a - 2b), justifying your answer by comparing coefficients of a and b.

(Total for Question C2 is 7 marks)

Question C3 (7 marks)

The table gives the times, t minutes, taken by 80 runners to finish a race. 30<=t<40: 8 runners; 40<=t<50: 20 runners; 50<=t<60: 30 runners; 60<=t<70: 15 runners; 70<=t<80: 7 runners. (a) Construct a cumulative frequency table and estimate the median time. (b) Estimate the interquartile range. (c) The organisers award a medal to the fastest 25% of runners. Estimate the qualifying time for a medal.

(Total for Question C3 is 7 marks)

Question C4 (7 marks)

A solid cone has base radius 6 cm and slant height 10 cm. (a) Show that the vertical height of the cone is 8 cm. (b) Work out the total surface area of the cone (including base), giving your answer as a multiple of pi. (c) The cone is melted down and recast as a sphere. Work out the radius of the sphere to 3 significant figures. Use volume of cone = (1/3)*pi*r^2*h and volume of sphere = (4/3)*pi*r^3.

(Total for Question C4 is 7 marks)

Question C5 (6 marks)

A spinner has sections coloured red, green and blue. P(red) = 0.5 and P(green) = 0.3. Priya spins the spinner twice. (a) Work out the probability that she gets blue on both spins. (b) Work out the probability that she gets exactly one red in the two spins. (c) Priya now spins it three times. Work out the probability that she gets at least one green.

(Total for Question C5 is 6 marks)

Question C6 (6 marks)

The graph of y = f(x) has a single vertex (turning point) at (2, -5). (a) Describe fully the single transformation that maps y = f(x) to y = f(x - 3), and state the coordinates of the new vertex. (b) Describe the transformation that maps y = f(x) to y = f(x) + 4, and state the new vertex. (c) The graph of y = f(x) also passes through (0, 3). State the coordinates of the point that (0, 3) maps to under the transformation y = -f(x).

(Total for Question C6 is 6 marks)