plumiSimultaneous equations: OCR GCSE Maths questions
Every OCR GCSE Maths exam question on A19 Simultaneous equations, 2017–2025, with its mark scheme and examiner’s report.
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All 19 questions on Simultaneous equations, as a list
- June 2025, Paper 4, Q11 (5 marks): Function A and function B are shown below. Function A: Input - 5 # a Output Function B: Input + b # 3 Output When the input for both machines is 11, the output
- June 2025, Paper 5, Q7 (6 marks): The graph of the line x y 3 is shown on this grid. + = y 5 4 3 2 1 x 0 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 (a) By drawing a suitable line on the grid, solve
- June 2025, Paper 6, Q21 (5 marks): The graph of y x intersects the graph of x y 70 at two points. + = Work out the exact coordinates of the two points. You must show your working. ( , ) and ( , )
- June 2024, Paper 5, Q21 (6 marks): Work out the coordinates of the intersection of the graphs of y 5 2 x and y 3 x . = - = You must show your working. ( , ) and ( , )
- November 2023, Paper 4, Q6 (5 marks): 2 kg of carrots and 5 kg of potatoes cost £6.36. 3 kg of carrots and 2 kg of potatoes cost £5.25. Find the cost of 1 kg of carrots and the cost of 1 kg of potat
- November 2023, Paper 5, Q24 (3 marks): The x-coordinates of the intersections of the graphs of y x ax 7 and y 3 x b are the = + + = + 2 + solutions to the equation x 8 x 13 0 . + = Find the value of
- June 2023, Paper 5, Q10 (6 marks): A student draws two different regular polygons. The exterior angle of one polygon is p°. The exterior angle of the other polygon is q°. The sum of p and q is 11
- June 2023, Paper 6, Q18 (9 marks): (a) Describe fully the graph of x 20 . y + = 2 2 (b) The graph of y 3 10 intersects the graph of x 20 at two points. x y = + + = Use an algebraic method to work
- November 2022, Paper 4, Q22 (5 marks): Solve algebraically. 2 2 18 x y + = y x 6 = - x = y =
- November 2021, Paper 4, Q20 (5 marks): Solve algebraically. y x 3 = + 2 2 ( 3 ) 50 x y - + = You must show your working. x = y = x = y =
- November 2020, Paper 4, Q20 (6 marks): Solve. 2 2 x y 34 + = y x 2 = + Show your working. x = y = x = y =
- November 2019, Paper 4, Q8 (5 marks): The diagrams show the price paid by two groups of people visiting a funfair. 5 adults £ 3 adults £ 4 children £ 6 children £ Total £ 78 Total £ 63 Assume each a
- November 2018, Paper 4, Q5 (5 marks): Marcin buys 7 rulers and 15 crayons for £7. A ruler costs 12p more than a crayon. Find the cost of one crayon. cost of one crayon = p
- November 2018, Paper 6, Q17 (5 marks): Find the exact coordinates of the two intersections of the line y 2 and the circle x 2 2 30 . x y = + = y y = 2x x2 + y2 = 30 Not to scale x O ( , ) and ( , )
- June 2018, Paper 4, Q9 (6 marks): The dimensions, in centimetres, of this rectangle are shown as algebraic expressions. Not to scale 5x – y – 8 3x + y – 4 2x – 6y – 3 3x + 5y + 4 Work out the le
- June 2018, Paper 5, Q18 (9 marks): (a) A straight line passes through the point (0, 6) and is perpendicular to y 4 x 5 . = - Find the equation of this line, giving your answer in the form y mx c
- November 2017, Paper 4, Q5 (12 marks): (a) Complete this table for y x x 4 . = + - -4 -3 -2 -1 0 1 2 3 x -4 -4 y 2 2 2 for -4 (b) Draw the graph of y 4 3 . x x x = + - G G y 10 9 8 7 6 5 4 3 2 1 -4 -
- November 2017, Paper 5, Q19 (6 marks): Solve these simultaneous equations algebraically. 2 y 2 x 7 x 4 = - + y 4 x 1 = - x = y = x = y =
- June 2017, Paper 4, Q9 (6 marks): Each week Dan drives two routes, route X and route Y. One week he drives route X three times and route Y twice. He drives a total of 134 miles that week. Anothe
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