plumiSimultaneous equations: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.02.4 Simultaneous equations, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 13 questions on Simultaneous equations, as a list
- June 2025, Paper 1, Q5 (8 marks): Scientists are comparing h, the average height of a child in cm, with t, the age of the child in years. They suggest the model h at + for t b 2 , where a and b
- June 2025, Paper 2, Q5 (8 marks): In this question you must show detailed reasoning. A circle has diameter PQ where P is ( 5 1 , ) and Q is (5, 1). The line x 2 y 12 meets the circle - + = at A
- June 2025, AS Paper 2, Q8 (6 marks): x y x 2 y 8 The curves e 2 e = and 2 1 e 3 e 4 1 intersect at the point P. - + = 2 + y y (a) Show that the y-coordinate of P satisfies the equation 3 e 4 e 39 0
- June 2024, Paper 1, Q7 (10 marks): The point A has coordinates (1, 7), and the point B has coordinates (h, 10). (a) You are given that the gradient of the line AB is 2. Find the value of h. [2] (
- June 2024, AS Paper 1, Q6 (7 marks): A curve has the following properties: d y • The gradient of the curve is given by d 2 x . =- x • The curve passes through the point ( , 4 13 ) . - Determine the
- June 2023, Paper 2, Q6 (10 marks): A circle has centre C which lies on the x-axis, as shown in the diagram. The line y = meets the x circle at A and B. The midpoint of AB is M. y y =x B M A C x 2
- June 2022, Paper 1, Q3 (7 marks): (a) In this question you must show detailed reasoning. 2 Find the coordinates of the points of intersection of the curves with equations y x 2 x + 1 = - 2 and y
- November 2021, Paper 1, Q2 (4 marks): Alex is comparing the cost of mobile phone contracts. Contract A has a set-up cost of £40 and then costs 4p per minute. Contract B has no set-up cost, does not
- November 2021, AS Paper 1, Q9 (6 marks): In this question you must show detailed reasoning. Find the equation of the straight line with positive gradient that passes through (0, 2) and is a 2 tangent t
- November 2020, Paper 3, Q6 (11 marks): In this question you must show detailed reasoning. y P x O Q 2 2 The diagram shows the curve with equation 4 xy 2 ( x 4 y ) 9 x . = + - y x y d = 4 4 - . 9 - (a
- November 2020, AS Paper 1, Q7 (5 marks): 7 Determine the points of intersection of the curve xy 3 x 14 0 and the line x 2 y 4 . [5] + + = + =
- June 2019, AS Paper 1, Q6 (6 marks): B xcm 60° A ycm C The diagram shows triangle ABC, with AB = x cm, AC = y cm and angle BAC = 60°. It is given that ^ h 3cm2 the area of the triangle is x y . + (
- June 2018, AS Paper 2, Q5 (5 marks): In this question you must show detailed reasoning. 2 - The line x 5 y k is a tangent to the curve x 4 y 10 . Find the value of the constant k. [5] + = =
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