plumiImplicit and parametric differentiation: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.07.8 Implicit and parametric differentiation, 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 9 questions on Implicit and parametric differentiation, as a list
- June 2025, Paper 1, Q7 (9 marks): In this question you must show detailed reasoning. 3 2 2 A curve has parametric equations x t t , y t t2 for all real values of t. = + = + The curve passes thro
- June 2024, Paper 3, Q7 (7 marks): y Q P x O 2 The diagram shows the curve x 5 2 xy 2 y k 0 , where k is a positive integer. - + - = At the points P and Q on the curve, the tangents to the curve
- June 2022, Paper 1, Q7 (8 marks): 2 7 A curve has equation x 2 6 xy 3 y 2 . + - = Show that there are no points on this curve where the tangent is parallel to y = . x [8]
- June 2022, Paper 1, Q12 (12 marks): c m. 1 1 2 12 A curve has parametric equations x t y , 2 t . The point P is ,p p = = 2 (a) Show that the equation of the tangent at P can be written as y 2 p x
- November 2021, Paper 1, Q9 (10 marks): A particle moves in the x-y plane so that at time t seconds, where t 0 , its coordinates are given by H - . 2 t t 3 t x e 4 e 3 , y 2 e = - + = (a) Explain why
- November 2020, Paper 3, Q5 (12 marks): y P R C x O 1 6 The diagram shows the curve C with parametric equations 3 - , where t 3 2 t x , y t e 2 0 . = = t The maximum point on C is denoted by P. (a) De
- 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
- June 2019, Paper 1, Q5 (8 marks): 2 2 5 A curve has equation x 3 x y y 1 0 . - + + = 2 y xy x d 6 3 - (a) Show that x . [4] = d 2 2 y 3 x - (b) Find the equation of the normal to the curve at th
- June 2019, Paper 2, Q3 (9 marks): (a) A circle is defined by the parametric equations x 3 2 cos , y 4 2 sin . = + =- + i i (i) Find a cartesian equation of the circle. [2] (ii) Write down the ce
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