AQA 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 (3 marks)

  Without a calculator, write sqrt(50) + sqrt(18) in the form k*sqrt(2), where k is an integer. Show your working.

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

  Question SECTION-A2 (2 marks)

  Without a calculator, evaluate (2^5 * 2^(-2)) / 2^4. Give your answer as an exact fraction in its simplest form.

  (Total for Question SECTION-A2 is 2 marks)
• 3

  Question SECTION-A3 (3 marks)

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

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

  Question SECTION-A4 (3 marks)

  Without a calculator, express the recurring decimal 0.272727... (with the 27 recurring) as a fraction in its simplest form. Show your method.

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

  Question SECTION-A5 (3 marks)

  Without a calculator, factorise fully x^2 - 5x - 14.

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

  Question SECTION-A6 (4 marks)

  A jacket is reduced in a sale. After a 20% reduction its sale price is GBP 96. Without a calculator, work out the original price of the jacket before the reduction. Show your reasoning.

  (Total for Question SECTION-A6 is 4 marks)
• 7

  Question SECTION-A7 (3 marks)

  96 is shared between Amir and Bea in the ratio 3 : 5. Without a calculator, work out how much more Bea receives than Amir.

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

  Question SECTION-A8 (4 marks)

  Without a calculator, work out (3 x 10^4) * (2 x 10^(-6)). Give your answer in standard form.

  (Total for Question SECTION-A8 is 4 marks)

Section B

Standard questions — procedural and reasoning. Answer ALL questions.

• 1

  Question SECTION-B1 (5 marks)

  Solve the simultaneous equations 3x + 2y = 16 5x - 2y = 8 Show your working and give the values of x and y.

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

  Question SECTION-B2 (5 marks)

  Solve x^2 - 6x + 7 = 0. Give your solutions in the form a +/- sqrt(b), where a and b are integers.

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

  Question SECTION-B3 (5 marks)

  Priya invests GBP 2400 in a savings account that pays 3.5% compound interest per year. Work out the total value of the investment at the end of 4 years. Give your answer to the nearest penny.

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

  Question SECTION-B4 (5 marks)

  In a right-angled triangle, the angle at A is 34 degrees and the side opposite A has length 9 cm. This side is not the hypotenuse. Work out the length of the hypotenuse. Give your answer to 2 decimal places.

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

  Question SECTION-B5 (5 marks)

  A solid cone has base radius 6 cm and vertical height 14 cm. Using the formula V = (1/3) * pi * r^2 * h, work out the volume of the cone. Give your answer to 1 decimal place.

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

  Question SECTION-B6 (5 marks)

  A bag contains 3 red counters and 5 blue counters. Two counters are taken from the bag at random, one after the other, without replacement. Work out the probability that exactly one of the two counters is red. Give your answer as a fraction in its simplest form.

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

  Question SECTION-B7 (5 marks)

  The nth term of a quadratic sequence is given by 2n^2 - n. (a) Work out the 5th term. (b) Work out the difference between the 6th term and the 5th term. Show your working.

  (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)

  Two solid statues are mathematically similar. The smaller statue has height 18 cm and the larger statue has height 30 cm. The total surface area of the smaller statue is 45 cm^2. Work out the total surface area of the larger statue. Show your reasoning clearly.

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

  Question SECTION-C2 (5 marks)

  A car travels a distance of 48 km, measured to the nearest kilometre, in a time of 1.5 hours, measured to the nearest 0.1 hour. Average speed = distance / time. Work out the upper bound for the average speed of the car, in km/h. Give your answer to 2 decimal places and explain which bounds you used.

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

  Question SECTION-C3 (5 marks)

  In triangle PQR, PQ = 8 cm, PR = 11 cm and the angle QPR between them is 67 degrees. Using the cosine rule, work out the length of QR. Give your answer to 2 decimal places.

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

  Question SECTION-C4 (5 marks)

  Tom sets up a savings plan. In month 1 he saves GBP 200. Each month after that he saves 5% more than the previous month, so month 2 is GBP 210, month 3 is GBP 220.50, and so on. Work out the total amount Tom saves over the first 12 months (months 1 to 12 inclusive). Give your answer to the nearest penny.

  (Total for Question SECTION-C4 is 5 marks)