Edexcel GCSE Maths 2027 Predicted Practice Paper — Paper 3 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 — non-calculator skills. Answer ALL questions.

• 1

  Question SECTION-A1 (4 marks)

  Work out the exact value of (3 + sqrt(5))(2 - sqrt(5)). Write your answer in the form a + b*sqrt(5), where a and b are integers.

  (Total for Question SECTION-A1 is 4 marks)
• 2

  Question SECTION-A2 (3 marks)

  Write 0.2(7) as a fraction in its simplest form, where the 7 is a single recurring digit (so the number is 0.27777...).

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

  Question SECTION-A3 (3 marks)

  Solve the equation x^2 - 7x + 10 = 0 by factorising.

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

  Question SECTION-A4 (3 marks)

  Simplify fully (12*a^5*b^3) / (18*a^2*b^7). Give your answer with positive indices where possible.

  (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 taking a red counter at random is 0.35 and the probability of taking a blue counter is 0.28. Work out the probability of taking a green counter.

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

  Question SECTION-A6 (3 marks)

  Make r the subject of the formula A = pi*r^2 + 5, where r is positive.

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

  Question SECTION-A7 (3 marks)

  The first four terms of a sequence are 5, 8, 11, 14. Find an expression, in terms of n, for the nth term of this sequence.

  (Total for Question SECTION-A7 is 3 marks)
• 8

  Question SECTION-A8 (3 marks)

  Without a calculator, work out 2 and 1/3 - 3/4. Give your answer as a mixed number in its simplest form.

  (Total for Question SECTION-A8 is 3 marks)

Section B

Standard questions — procedural and reasoning. Answer ALL questions.

• 1

  Question SECTION-B1 (5 marks)

  Priya invests GBP 2500 in a savings account that pays 3.2% compound interest per year. Work out the total value of her investment at the end of 4 years. Give your answer to the nearest penny.

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

  Question SECTION-B2 (5 marks)

  A right-angled triangle ABC has the right angle at B. The side AB = 6.5 cm and the angle BAC = 40 degrees. Work out the length of the side BC. Give your answer to 3 significant figures.

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

  Question SECTION-B3 (5 marks)

  The price of a laptop is reduced by 30% in a sale. The sale price is GBP 84. Work out the original price of the laptop before the sale.

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

  Question SECTION-B4 (5 marks)

  A car travels 210 km in 2 hours 30 minutes. Work out the average speed of the car in kilometres per hour, and then convert this speed into metres per second. Give the metres per second value to 1 decimal place.

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

  Question SECTION-B5 (5 marks)

  OABC is a parallelogram. The vector OA = a and the vector OC = c. The point M is the midpoint of the diagonal AC. Express the vector OM in terms of a and c, and hence show that M is also the midpoint of the diagonal OB.

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

  Question SECTION-B6 (5 marks)

  A solid metal block has a mass of 1335 grams and is made from a metal of density 8.9 g/cm^3. The block is melted down and recast into a cube. Work out the length of one edge of the cube. Give your answer to 3 significant figures.

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

  Question SECTION-B7 (5 marks)

  The number of bacteria in a culture is modelled by N = 12000 * (0.85)^t, where t is the time in hours after the start of an experiment. Work out the number of bacteria after 3 hours, and work out the percentage decrease in the number of bacteria over these first 3 hours. Give the percentage to 1 decimal place.

  (Total for Question SECTION-B7 is 5 marks)

Section C

Multi-step and problem-solving questions. Answer ALL questions.

• 1

  Question SECTION-C1 (5 marks)

  A cylindrical water tank has a radius of 40 cm and a height of 90 cm. Water flows into the empty tank at a constant rate of 15 litres per minute. Work out the time, in minutes, it takes to fill the tank completely. Use 1 litre = 1000 cm^3 and give your answer to the nearest minute. (Take pi = 3.142.)

  (Total for Question SECTION-C1 is 5 marks)
• 2

  Question SECTION-C2 (5 marks)

  A ship sails from port P on a bearing of 060 degrees for 80 km to reach point Q. It then sails on a bearing of 150 degrees for 60 km to reach point R. Show that angle PQR is 90 degrees, and hence work out the direct distance PR. Give your answer to 3 significant figures.

  (Total for Question SECTION-C2 is 5 marks)
• 3

  Question SECTION-C3 (5 marks)

  Two similar solid cones, cone A and cone B, are made of the same material. Cone A has a height of 8 cm and cone B has a height of 12 cm. The mass of cone A is 200 grams. Work out the mass of cone B.

  (Total for Question SECTION-C3 is 5 marks)
• 4

  Question SECTION-C4 (5 marks)

  The line L1 has equation y = 2x - 3. A second line L2 is perpendicular to L1 and passes through the point (4, 7). Find the equation of L2 in the form y = mx + c, and work out the coordinates of the point where L1 and L2 intersect.

  (Total for Question SECTION-C4 is 5 marks)