plumiGraphs of functions and curve sketching: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.02.7 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 14 questions on Graphs of functions and curve sketching, as a list
- June 2025, Paper 1, Q2 (4 marks): y x O The diagram shows the curve y ax x ( b ) , where a and b are constants and b 0 . = - 2 (a) Given that the curve has a stationary point at x = , state the
- June 2024, Paper 1, Q2 (6 marks): You are given that y is inversely proportional to x6 and z is directly proportional to the cube root 2 of y. (a) (i) Find an equation for z in terms of x and k,
- June 2024, Paper 2, Q3 (6 marks): 2 3 The function f is defined by ( ) f x x x 5 x - . 3 = - - (a) Show that ( x 3 ) is a factor of ( ) f x . [1] - (b) Factorise ( ) f x completely. [2] Three st
- June 2022, AS Paper 1, Q3 (7 marks): 3 The diagram in the Printed Answer Booklet shows part of the graph of y x 4 x + . 3 = - 2 - (a) It is required to solve the equation x 3 x 1 0 graphically by d
- June 2022, AS Paper 2, Q5 (7 marks): y x O 1 ( , 1 ) - 2 The diagram shows a curve C for which y is inversely proportional to x. The curve passes through a k. 1 the point ,1 - 2 (a) (i) Determine t
- November 2021, Paper 1, Q3 (4 marks): It is given that x is proportional to the product of the square of y and the positive square root of z. When y 2 and z 9 , x 30 . = = = (a) Write an equation fo
- November 2021, Paper 3, Q4 (5 marks): (a) Sketch, on a single diagram, the following graphs. • y x 1 = - k • y , where k is a negative constant [2] = x (b) Hence explain why the equation x x 1 k has
- November 2021, AS Paper 1, Q3 (6 marks): The diagram shows the curve y f ( ) x , where ( )x f is a cubic polynomial in x. = This diagram is repeated in the Printed Answer Booklet. y 2 1 x 0 –3 –2 –1 1
- November 2021, AS Paper 1, Q6 (3 marks): The power output, P watts, of a certain wind turbine is proportional to the cube of the wind speed - . 1 v ms When v = 3.6, P = 50. Determine the wind speed tha
- November 2020, AS Paper 1, Q5 (8 marks): The function f is defined by ( ) f x ( x a x )( 3 a x )( b ) where a and b are positive integers. = + + - (a) On the axes in the Printed Answer Booklet, sketch
- November 2020, AS Paper 2, Q2 (5 marks): k 2 Two curves have equations y ln x and y , where k is a positive constant. = = x (a) Sketch the curves on a single diagram. [3] (b) Explain how your diagram s
- June 2019, AS Paper 1, Q4 (6 marks): 2 4 (a) Find the coordinates of the stationary points on the curve y x 6 x 9 x . [4] = - + 3 2 (b) The equation x 6 x 9 x k 0 has exactly one real root. - + + =
- June 2019, AS Paper 2, Q3 (5 marks): 3 (a) Sketch the curve y . [1] =- 2 x 1 (b) The curve y is translated by 2 units in the positive x-direction. =- 2 x State the equation of the curve after it ha
- June 2018, AS Paper 1, Q6 (7 marks): Sketch the following curves. 2 (i) y [2] = x 3 2 (ii) y x 6 x 9 x [5] = - +
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