plumiPoints of inflection, concave and convex: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.07.7 Points of inflection, concave and convex, 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 8 questions on Points of inflection, concave and convex, as a list
- June 2025, Paper 2, Q6 (7 marks): 3 2 6 A curve has equation y 3 x 4 x 6 x 12 x . = - - + d . y (a) (i) Find x [2] d (ii) Use your answer to part (a)(i) to find the x-coordinates of the stationa
- June 2024, Paper 3, Q5 (13 marks): y x O M ^ h 3 2 y x x x The diagram shows the curve with equation 2 ln . The curve has a point of inflection = - at the point M. (a) (i) Show that the x-coordin
- June 2023, Paper 1, Q6 (9 marks): + . ex 2 3 x 6 A curve has equation y = (a) Determine the x-coordinates of any stationary points on the curve. [4] (b) Show that the curve is convex for all val
- June 2022, Paper 2, Q5 (4 marks): In this question you must show detailed reasoning. 3 2 A curve has equation y x 3 x 4 x . = - + (a) Show that the curve has no stationary points. [2] (b) Show 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, Q8 (11 marks): y L R P M O x 2 x The diagram shows the curve M with equation y xe - . = (a) Show that M has a point of inflection at the point P where x = . 1 [5] The line L p
- November 2020, Paper 3, Q4 (11 marks): 4 A curve has equation y 2 ln ( k 3 x ) x 3 x , where k is a positive constant. = - + - (a) Given that the curve has a point of inflection where x = 1, show tha
- June 2019, Paper 1, Q12 (12 marks): a x 3 2 12 A curve has equation y , where a is a constant greater than 1. = y d 3 2 x (a) Show that 6 xa ln a . [3] = x d 3 passes through the point ( 2 1 , 0).
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