plumiGraphs of functions and curve sketching: OCR MEI A‑Level Maths questions
OCR MEI A-Level Maths past-paper questions on 2.7 Graphs of functions and curve sketching, 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 10 questions on Graphs of functions and curve sketching, as a list
- June 2025, Paper 2, Q4 (5 marks): 2 4 (a) Use the factor theorem to show that ( x 3 ) is a factor of x 4 8 x 11 x - . 3 [1] - - - 3 2 2 (b) Hence show that 4 x 8 x 11 x 3 ( x 3 )( ax b ) , where
- June 2025, Paper 3, Q12 (7 marks): 3 a x - 12 (a) Show that for the point on the curve where x , 0 as given in line 10. [1] H = a x + (b) Use the equation of the curve given in line 8 to show tha
- June 2023, AS Paper 2, Q4 (3 marks): k 4 The equation of a curve is y , where k is a constant. = 2 x The curve passes through the point (2, 1). (a) Find the value of k. [1] (b) Sketch the curve. [2
- June 2022, Paper 3, Q1 (2 marks): A curve for which y is inversely proportional to x is shown below. y 4 3 2 1 x –4 –3 –2 –1 1 2 3 4 5 6 0 –1 –2 –3 Find the equation of the curve. [2]
- June 2022, AS Paper 1, Q6 (8 marks): d y 2 6 x x The curve passes through the The gradient of a curve is given by the equation 6 20 6 . = - + d x point (2, 6). (a) Find the equation of the curve. [
- June 2022, AS Paper 2, Q7 (7 marks): (a) On the pair of axes in the Printed Answer Booklet, sketch the graphs of • y 2 x 4 = + 2 • y [2] = x (b) Determine the x-coordinates of the points of interse
- November 2021, Paper 3, Q8 (3 marks): a 8 For a particular value of a, the curve y passes through the point (3, 1). = 2 x Find the coordinates of all the other points on the curve where both the x-c
- November 2021, AS Paper 1, Q9 (9 marks): (a) Sketch both of the following on the axes provided in the Printed Answer Booklet. 12 (i) The curve y , stating the coordinates of at least one point on the c
- June 2019, AS Paper 1, Q7 (11 marks): In this question you must show detailed reasoning. 3 - (a) Nigel is asked to determine whether ( x 7 ) is a factor of x 37 x 84 . He substitutes x 7 + + = 3 and
- June 2019, AS Paper 1, Q11 (11 marks): David puts a block of ice into a cool-box. He wishes to model the mass m kg of the remaining block of ice at time t hours later. He finds that when t = 5, m = 2
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