OCR GCSE Maths 2026 Predicted Practice Paper — Paper 4 Higher

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.

• 1

  Question A1 (2 marks)

  Work out 3.7^2 - 2.4^2.

  (Total for Question A1 is 2 marks)
• 2

  Question A2 (2 marks)

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

  (Total for Question A2 is 2 marks)
• 3

  Question A3 (3 marks)

  Increase 84 by 17.5%.

  (Total for Question A3 is 3 marks)
• 4

  Question A4 (3 marks)

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

  (Total for Question A4 is 3 marks)
• 5

  Question A5 (3 marks)

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

  (Total for Question A5 is 3 marks)
• 6

  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.

  (Total for Question A6 is 4 marks)
• 7

  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.

  (Total for Question A7 is 4 marks)

Section B

Answer all questions. Give reasons or working where required.

• 1

  Question B1 (4 marks)

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

  (Total for Question B1 is 4 marks)
• 2

  Question B2 (4 marks)

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

  (Total for Question B2 is 4 marks)
• 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.

  (Total for Question B3 is 4 marks)
• 4

  Question B4 (5 marks)

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

  (Total for Question B4 is 5 marks)
• 5

  Question B5 (5 marks)

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

  (Total for Question B5 is 5 marks)
• 6

  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.

  (Total for Question B6 is 5 marks)
• 7

  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.

  (Total for Question B7 is 6 marks)
• 8

  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.

  (Total for Question B8 is 6 marks)

Section C

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

• 1

  Question C1 (6 marks)

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

  (Total for Question C1 is 6 marks)
• 2

  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.

  (Total for Question C2 is 6 marks)
• 3

  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.

  (Total for Question C3 is 7 marks)
• 4

  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.

  (Total for Question C4 is 7 marks)
• 5

  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.

  (Total for Question C5 is 7 marks)
• 6

  Question C6 (7 marks)

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

  (Total for Question C6 is 7 marks)