OCR GCSE Maths 2027 Predicted Practice Paper — Paper 6 Higher

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

Section A

Short questions — fluency and direct application. Answer ALL the questions.

• 1

  Question SECTION-A1 (3 marks)

  Work out 3/4 + 2/5, giving your answer as a fraction in its simplest form.

  (Total for Question SECTION-A1 is 3 marks)
• 2

  Question SECTION-A2 (3 marks)

  A car travels 150 km in 2 hours 30 minutes. Work out the average speed of the car in km/h.

  (Total for Question SECTION-A2 is 3 marks)
• 3

  Question SECTION-A3 (3 marks)

  Simplify fully (12 x^5 y^3) / (3 x^2 y).

  (Total for Question SECTION-A3 is 3 marks)
• 4

  Question SECTION-A4 (3 marks)

  The nth term of a sequence is given by 5n - 2. Work out the 20th term, and determine whether 250 is a term in this sequence.

  (Total for Question SECTION-A4 is 3 marks)
• 5

  Question SECTION-A5 (3 marks)

  A bag contains only red, blue and green counters. The probability of picking a red counter is 0.35 and the probability of picking a blue counter is 0.28. (a) Work out the probability of picking a green counter. (b) Work out the probability of picking a counter that is NOT green.

  (Total for Question SECTION-A5 is 3 marks)
• 6

  Question SECTION-A6 (3 marks)

  (a) Expand and simplify (x + 6)(x - 4). (b) Hence solve (x + 6)(x - 4) = 0.

  (Total for Question SECTION-A6 is 3 marks)
• 7

  Question SECTION-A7 (3 marks)

  (a) Write 0.000 065 in standard form. (b) Write 4.2 x 10^3 as an ordinary number.

  (Total for Question SECTION-A7 is 3 marks)

Section B

Standard questions — reasoning and linked methods. Answer ALL the questions.

• 1

  Question SECTION-B1 (5 marks)

  Solve the simultaneous equations: 3x + 2y = 16 and 5x - 2y = 8.

  (Total for Question SECTION-B1 is 5 marks)
• 2

  Question SECTION-B2 (5 marks)

  A right-angled triangle has a hypotenuse of length 13 cm and one shorter side of length 5 cm. Work out the length of the third side, and then find the size of the smallest angle in the triangle. Give the angle to 1 decimal place.

  (Total for Question SECTION-B2 is 5 marks)
• 3

  Question SECTION-B3 (5 marks)

  A jacket is reduced by 20% in a sale. In a further clearance, the sale price is then reduced by an additional 15%. The final clearance price is GBP 68. Work out the original price of the jacket before any reductions.

  (Total for Question SECTION-B3 is 5 marks)
• 4

  Question SECTION-B4 (4 marks)

  The mean of five numbers is 14. When a sixth number is added, the mean of all six numbers becomes 16. Work out the value of the sixth number.

  (Total for Question SECTION-B4 is 4 marks)
• 5

  Question SECTION-B5 (5 marks)

  Make r the subject of the formula V = (1/3) pi r^2 h.

  (Total for Question SECTION-B5 is 5 marks)
• 6

  Question SECTION-B6 (5 marks)

  In a class of 30 students, 18 study French, 14 study Spanish, and 6 study both languages. Using a Venn diagram or otherwise, work out the probability that a randomly chosen student studies neither French nor Spanish.

  (Total for Question SECTION-B6 is 5 marks)
• 7

  Question SECTION-B7 (5 marks)

  A sum of GBP 4000 is invested in an account paying 3.5% compound interest per year. Work out the total value of the investment after 4 years. Give your answer to the nearest penny.

  (Total for Question SECTION-B7 is 5 marks)
• 8

  Question SECTION-B8 (5 marks)

  The ratio of adults to children at a swimming pool is 5 : 3. There are 24 children at the pool. Each adult ticket costs GBP 6 and each child ticket costs GBP 4. (a) Work out the total number of people at the pool. (b) Work out the total ticket income from everyone at the pool.

  (Total for Question SECTION-B8 is 5 marks)

Section C

Extended problem-solving questions. Answer ALL the questions.

• 1

  Question SECTION-C1 (7 marks)

  The curve y = x^2 - 6x + 5 is drawn. (a) Write y = x^2 - 6x + 5 in the completed-square form (x - a)^2 + b. (b) Hence state the coordinates of the turning point of the curve. (c) Find the coordinates of the two points where the curve crosses the x-axis.

  (Total for Question SECTION-C1 is 7 marks)
• 2

  Question SECTION-C2 (7 marks)

  A cone has a base radius of 6 cm and a slant height of 10 cm. (a) Work out the vertical height of the cone. (b) Work out the volume of the cone, giving your answer in terms of pi. (c) A solid sphere is melted down and recast to have exactly the same volume as this cone. Work out the radius of the sphere, giving your answer to 2 significant figures. [Volume of a sphere = (4/3) pi r^3; volume of a cone = (1/3) pi r^2 h.]

  (Total for Question SECTION-C2 is 7 marks)
• 3

  Question SECTION-C3 (7 marks)

  Two bags each contain coloured discs. Bag A contains 3 white and 2 black discs. Bag B contains 4 white and 1 black disc. One disc is taken at random from Bag A and one disc is taken at random from Bag B. (a) Draw or describe a probability tree for this situation. (b) Work out the probability that both discs are the same colour. (c) Work out the probability that at least one disc is black.

  (Total for Question SECTION-C3 is 7 marks)
• 4

  Question SECTION-C4 (7 marks)

  OABC is a parallelogram. The vector OA = a and the vector OC = c. The point M is the midpoint of AB, and the point N lies on the diagonal OB such that ON : NB = 3 : 1. (a) Write the vector OB in terms of a and c. (b) Write the vector OM in terms of a and c. (c) Show that the vector MN can be written as k a + m c, and find the values of k and m.

  (Total for Question SECTION-C4 is 7 marks)
• 5

  Question SECTION-C5 (6 marks)

  A field is being cleared of an invasive weed. At the start of a treatment programme the weed covers an area of 800 m^2. Each week the treated area of weed is reduced to 65% of its area at the start of that week. (a) Work out the area covered by the weed after 3 weeks, to the nearest m^2. (b) The programme is judged successful once the weed covers less than 50 m^2. Determine the first whole week by which the programme becomes successful, showing your reasoning.

  (Total for Question SECTION-C5 is 6 marks)
• 6

  Question SECTION-C6 (6 marks)

  A drinks company sells cordial in two sizes of geometrically similar bottles. The small bottle is 18 cm tall and holds 250 ml. The large bottle is 27 cm tall. (a) Work out the volume of the large bottle, giving your answer to the nearest ml. (b) The small bottle costs GBP 1.80 and the large bottle costs GBP 5.40. Determine, with clear reasoning, which bottle is better value for money.

  (Total for Question SECTION-C6 is 6 marks)