plumiQuadratic equations: AQA GCSE Maths questions
Every AQA GCSE Maths exam question on A18 Quadratic equations, 2017–2025, with its mark scheme and examiner’s report.
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All 35 questions on Quadratic equations, as a list
- June 2025, Paper 1H, Q10 (4 marks): The area of the rectangle is 120 cm2 Work out the value of x. Not drawn accurately x =
- June 2025, Paper 1H, Q25 (5 marks): There are n counters in a box. 6 of the counters are black. Two counters are chosen at random without replacement. The probability that both counters are black
- June 2025, Paper 2H, Q15 (2 marks): Solve 3x2 + 5x – 9 = 0 Give your solutions as decimals. Answer and
- November 2024, Paper 2H, Q16 (4 marks): Solve (x + 2)(x – 5) = 6x Answer
- June 2024, Paper 1H, Q24 (7 marks): (a) 9k + 7 and 2k2 + 3 are consecutive integers. 9k + 7 is the smaller integer. Work out the value of the next consecutive integer. Answer 24 (b) x is a square
- June 2024, Paper 2H, Q20 (4 marks): (x – 9) = 3 6 2 2 + − x x ) ( and x = d e f ± Work out one set of possible values for d, e and f. d = e = f =
- June 2024, Paper 3H, Q19 (6 marks): f(x) = x – 3 g(x) = 4x – 7 19 (a) Work out the value of fg Answer 19 (b) Solve (f(x))2 = g(x) Answer
- June 2024, Paper 3H, Q24 (3 marks): Write 2x2 – 12x + 7 in the form d(x + e)2 + f where d, e and f are integers. Answer
- November 2023, Paper 1H, Q9 (2 marks): Here is the graph of y = 0.5x2 – 6x + 12 Use the graph to estimate the solutions of 0.5x2 – 6x + 12 = 0 Answer
- November 2023, Paper 3H, Q20 (4 marks): Solve 2x(x + 10) = 5x – 18 Answer
- June 2023, Paper 1H, Q21 (2 marks): Express x2 – 6x – 15 in the form (x – a)2 – b where a and b are integers. Answer
- June 2023, Paper 3H, Q18 (6 marks): f(x) = x2 + 6x g(x) = 2x + 4 18 (a) Show that fg(x) = 4x2 + 28x + 40 18 (b) Solve fg(x) = –5 Answer
- November 2022, Paper 1H, Q20 (3 marks): The only solution to x2 + bx + c = 0 is x = –15 Work out the values of b and c. b = c =
- November 2022, Paper 2H, Q19 (2 marks): Using the quadratic formula, or otherwise, solve 3x2 + x – 5 = 0 Answer
- November 2022, Paper 2H, Q27 (4 marks): In a class there are n boys a total of 25 students. Two of the students are chosen at random. The probability that both students are boys is 20 7 Work out the v
- June 2022, Paper 2H, Q18 (2 marks): Solve x2 + 7x – 11 = 0 Give your solutions as decimals. Answer
- June 2022, Paper 3H, Q19 (5 marks): Here is the plan of the floor of an L-shaped room. All lengths are in metres. Not drawn accurately 19 (a) The area of the floor is 75 m2 Show that x2 + x – 90 =
- November 2021, Paper 2H, Q24 (5 marks): The flight of a plane was in two stages. The table shows information about the flight. Distance (miles) Speed (mph) Time (hours) 1st stage 731 x x 731 2nd stage
- November 2020, Paper 1H, Q13 (3 marks): (a) s and t are positive integers. (x + s)(x – t) is expanded and simplified. The answer is x2 + kx – 40 where k is a positive integer. Work out the smallest po
- November 2020, Paper 2H, Q29 (5 marks): Solve 1 4 5 + x = 3 2 2 + x x Give your solutions to 3 significant figures. You must show your working. Answer
- November 2019, Paper 2H, Q18 (4 marks): Kate has the following question for homework. 18 (a) Show that Kate can form the equation x2 + 5x – 1400 = 0 18 (b) Kate correctly factorises the equation to ge
- November 2019, Paper 3H, Q18 (1 mark): Work out the two roots of (7x + 1)(2x – 3) = 0 Circle both roots. – 1 7 1 7 – 2 3 2 3
- November 2019, Paper 3H, Q22 (2 marks): The only solution to x2 + bx + c = 0 is x = 5 Work out the values of b and c. b = c =
- June 2019, Paper 3H, Q4 (1 mark): Circle the two roots of (x – 5)(x + 3) = 0 –5 –3 3 5
- June 2019, Paper 3H, Q18 (3 marks): (a) Write x(3x – 9) = 4 in the form ax2 + bx + c = 0 where a, b and c are integers. Answer 18 (b) Solve x(3x – 9) = 4 Give your answers to 2 decimal places. Ans
- November 2018, Paper 1H, Q12 (3 marks): Solve x2 – x – 12 = 0 Answer
- June 2018, Paper 1H, Q27 (4 marks): (a) Jo wants to work out the solutions of x2 + 3x – 5 = 0 She says, ‘‘The solutions cannot be worked out because x2 + 3x – 5 does not factorise to (x + a)(x + b
- June 2018, Paper 2H, Q26 (4 marks): A curve has equation y = 4x2 + 5x + 3 A line has equation y = x + 2 Show that the curve and the line have exactly one point of intersection. Do not use a graphi
- November 2017, Paper 1H, Q18 (1 mark): Circle the two roots of (2x + 3)(5x – 2) = 0 – 2 3 – 5 2 5 2 2 3
- November 2017, Paper 2H, Q19 (3 marks): The length of a rectangle is five times the width. The area of the rectangle is 1620 cm2 Not drawn accurately Work out the width of the rectangle. Answer cm
- November 2017, Paper 2H, Q21 (4 marks): (a) Meera is using a graphical method to solve 2x2 – 3x = 0 She draws the graph of y = 2x2 and a straight line graph on the same grid. Here is the graph of y =
- November 2017, Paper 2H, Q27 (6 marks): Solve 4 x – 2 2 + x x = 1 Give your solutions to 2 decimal places. You must show your working. Answer
- June 2017, Paper 2H, Q21 (4 marks): Solve 5x2 = 10x + 4 Give your answers to 2 decimal places. Answer
- Specimen, Paper 2H, Q11 (1 mark): Circle the equation with roots 4 and 8 4x(x – 8) = 0 (x – 4)(x + 8) = 0 x2 – 32 = 0 (x + 4)(x – 8) = 0
- Specimen, Paper 2H, Q25 (6 marks): 2x2 6x + 5 can be written in the form a(x b)2 + c where a, b and c are positive numbers. 25 (a) Work out the values of a, b and c. a = b = c = 25 (b) Using
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