AQA GCSE Maths 2027 Predicted Practice Paper — Paper 2 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 using a calculator, work out (2/3) + (3/5) x (5/9). Give your answer as a single fraction (or whole number) in its simplest form.

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

  Question SECTION-A2 (3 marks)

  Simplify fully sqrt(72) + sqrt(50) - sqrt(8). Give your answer in the form k*sqrt(2).

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

  Question SECTION-A3 (2 marks)

  Write 0.0000408 in standard form.

  (Total for Question SECTION-A3 is 2 marks)
• 4

  Question SECTION-A4 (3 marks)

  n is an integer. Prove that the sum of any three consecutive integers is always a multiple of 3.

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

  Question SECTION-A5 (3 marks)

  Solve the simultaneous equations 3x + 2y = 16 and 5x - 2y = 8 without using a calculator.

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

  Question SECTION-A6 (3 marks)

  Expand and simplify (2x - 5)(x + 3).

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

  Question SECTION-A7 (3 marks)

  Work out (2^5 x 2^(-3)) / 2^(-2), giving your answer as a single power of 2 and then as an ordinary number.

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

  Question SECTION-A8 (5 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 0.2. There are 9 green counters. (a) Work out the total number of counters in the bag. (b) Work out how many red counters are in the bag.

  (Total for Question SECTION-A8 is 5 marks)

Section B

Standard questions — procedural and reasoning. Answer ALL questions.

• 1

  Question SECTION-B1 (5 marks)

  A car is bought for GBP 18500. In the first year its value falls by 22%. In each following year its value falls by 15% of its value at the start of that year. Work out the value of the car at the end of 3 years. Give your answer to the nearest GBP.

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

  Question SECTION-B2 (5 marks)

  Make r the subject of the formula A = pi*r^2 + 2*pi*r*h. [Hint: treat it as a quadratic in r and use the quadratic formula, giving r in terms of A, h and pi.]

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

  Question SECTION-B3 (6 marks)

  Solve the equation (2/(x+1)) + (3/(x-2)) = 1. Give your answers to 2 decimal places.

  (Total for Question SECTION-B3 is 6 marks)
• 4

  Question SECTION-B4 (4 marks)

  Two solid cones are mathematically similar. The smaller cone has height 6 cm and volume 90 cm^3. The larger cone has height 9 cm. Work out the volume of the larger cone.

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

  Question SECTION-B5 (4 marks)

  The mean of a set of 8 numbers is 14. When one further number is added to the set, the mean of all 9 numbers becomes 15. Work out the value of the number that was added.

  (Total for Question SECTION-B5 is 4 marks)
• 6

  Question SECTION-B6 (6 marks)

  A firm surveyed the time, t minutes, that 80 customers spent in its shop. A histogram of the results has bars with frequency densities: 0 < t <= 5 has frequency density 3.0; 5 < t <= 10 has frequency density 6.0; 10 < t <= 20 has frequency density 2.5; 20 < t <= 40 has frequency density 0.5. Show that these frequencies account for all 80 customers, and estimate the number of customers who spent more than 15 minutes in the shop.

  (Total for Question SECTION-B6 is 6 marks)
• 7

  Question SECTION-B7 (5 marks)

  The nth term of a quadratic sequence is given by a*n^2 + b*n + c. The first three terms of the sequence are 5, 14 and 27. Work out the values of a, b and c, and hence find the 10th term.

  (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)

  In triangle ABC, angle ABC = 90 degrees, AB = 8 cm and BC = 15 cm. M is the midpoint of AC. Work out the length of BM, giving your answer as an exact value or to 1 decimal place, and explain why BM is equal to half of AC.

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

  Question SECTION-C2 (5 marks)

  OACB is a parallelogram. Vector OA = a and vector OB = b. The point P lies on the diagonal AB such that AP : PB = 1 : 3. Express the vector OP in terms of a and b, fully simplified.

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

  Question SECTION-C3 (5 marks)

  A cylindrical water tank has radius 40 cm and height 90 cm. Water flows into the empty tank at a constant rate of 12 litres per minute. Work out how long, in minutes and seconds, it takes to fill the tank completely. Use pi = 3.142 and give the seconds to the nearest second. (1 litre = 1000 cm^3.)

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

  Question SECTION-C4 (5 marks)

  A shop sells two sizes of a product. A pack of 6 pens costs GBP 4.20 and a pack of 10 of the same pens costs GBP 6.50. A customer needs at least 62 pens and wants to spend as little as possible, buying only whole packs. Work out the minimum cost and state how many of each pack the customer should buy.

  (Total for Question SECTION-C4 is 5 marks)