Graph transformations: OCR A‑Level Maths questions

OCR A-Level Maths past-paper questions on 1.02.8 Graph transformations, 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.

All 18 questions on Graph transformations, as a list

June 2025, Paper 1, Q10 (12 marks): ex e x 2 1 10 The graph of y can be transformed to the graph of y - by a stretch parallel to the = = x-axis followed by a translation. (a) (i) State the scale f
June 2025, Paper 3, Q2 (4 marks): 2 (a) The curve y is translated by 4 units in the positive x-direction. = 3 x Write down the equation of the curve after it has been translated. [2] 5 2 (b) The
June 2025, AS Paper 2, Q6 (6 marks): (a) The curve y ln x is stretched by a scale factor 3 in the x-direction. = State the equation of the curve after it has been stretched. [2] 2 (b) Describe full
June 2024, AS Paper 2, Q4 (4 marks): - is stretched by a scale factor 1 4 (a) The curve y 2 x 1 4 parallel to the x-axis. = [2] Find the equation of the curve after it has been stretched. c m, and
June 2023, Paper 3, Q3 (8 marks): 3 The cubic polynomial ( ) f x is defined by ( )x f x px + , where p and q are constants. q = + (a) (i) Given that f 2 ( ) 13 , find the value of p. [2] l = (ii
June 2023, AS Paper 2, Q5 (5 marks): y 2 x 3 2 y + = 2 x 3 y = x O + . The graph of y 2 x 3 2 x 3 2 2 x 3 The diagram shows the graphs of y and y can be = = = 2 x 3 2 transformed to the graph of y
June 2022, Paper 1, Q5 (8 marks): 2x 2x 4 5 (a) The graph of y can be transformed to the graph of y + either by a translation or = = by a stretch. (i) Give full details of the translation. [2] (
June 2022, Paper 3, Q2 (5 marks): x3 2 (a) Give full details of the single transformation that transforms the graph of y to the graph = 3 of y x - . 8 [2] = 3 The function f is defined by ( ) f
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, Q5 (7 marks): (a) The graph of the function y f ( ) x passes through the point P with coordinates (2, 6), and = is a one-one function. State the coordinates of the point corr
November 2021, Paper 3, Q7 (8 marks): A curve C in the x-y plane has the property that the gradient of the tangent at the point P x y is ( , ) three times the gradient of the line joining the point
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 2020, Paper 3, Q2 (3 marks): + . ex e x 2 3 2 A sequence of transformations maps the curve y to the curve y = = Give details of these transformations. [3]
November 2020, AS Paper 2, Q5 (5 marks): 5 A curve has equation y a x ( b ) + , where a, b and c are constants. The curve has a stationary c = + point at ( 3 2 , ) . - (a) State the values of b and c.
June 2019, Paper 1, Q9 (11 marks): 9 (a) Express cos 3 3 x 7 sin 3 x in the form R cos ( 3 x ) , where R 2 0 and 0 1 1 r. [3] + - a a 2 (b) Give full details of a sequence of three transformation
June 2019, Paper 3, Q3 (7 marks): (a) In this question you must show detailed reasoning. Solve the inequality x 2 2 x 6 . [4] - G - (b) Give full details of a sequence of two transformations nee
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 2, Q2 (4 marks): 2 (i) The curve y + is translated by four units in the positive x-direction. State the equation of the = 3 x curve after it has been translated. [2] 2 5 (ii) De

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