plumiImplicit and parametric differentiation: Edexcel A‑Level Maths questions
Edexcel A-Level Maths past-paper questions on 7.8 Implicit and parametric differentiation, 2010–2025, 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 Implicit and parametric differentiation, as a list
- June 2024, Pure 2, Q10 (6 marks): O C x y Figure 4 Figure 4 shows a sketch of the curve C with parametric equations x t y t t 3 1 2 1 2 3 The point P with coordinates (4, 2) lies on C. (a
- June 2024, Pure 2, Q15 (12 marks): The curve C has equation ( ) x y x y 3 2 3 3 2 (a) Find an expression for d d y x in terms of x and y. (5) The point P(1, 0) lies on C. (b) Show that the normal
- June 2023, Pure 2, Q7 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. A curve has equation x 3 + 2xy + 3y 2
- June 2023, Pure 2, Q9 (7 marks): The curve C has parametric equations x = t 2 + 6t – 16 y = 6 ln(t + 3) t > –3 (a) Show that a Cartesian equation for C is y = A ln (x + B) x > –B where A and B
- June 2022, Pure 2, Q16 (12 marks): y l P C O x Figure 6 Figure 6 shows a sketch of the curve C with parametric equations x = 2 tan t + 1 y = 2 sec 2 t + 3 − 4 π t 3 π The line l is the normal
- November 2021, Pure 2, Q8 (9 marks): The curve C has equation px3 + qxy + 3y2 = 26 where p and q are constants. (a) Show that d d y x apx bqy qx cy 2 where a, b and c are integers to be found. (4)
- November 2021, Pure 2, Q13 (6 marks): The curve C has parametric equations x = sin 2θ y = cosec3 θ 0 < θ < π 2 (a) Find an expression for d d y x in terms of θ (3) (b) Hence find the exact value of
- November 2020, Pure 1, Q15 (7 marks): The curve C has equation x2 tan y = 9 0 < y < 2 π (a) Show that d d y x = − + 18 81 4 x x (4) (b) Prove that C has a point of inflection at x = 27 4 (3)
- June 2019, Pure 2, Q11 (11 marks): y x C O Figure 8 Figure 8 shows a sketch of the curve C with equation y = x x , x 0 (a) Find, by firstly taking logarithms, the x coordinate of the turning poin
- June 2018, Pure 1, Q9 (10 marks): y Q O P East North x Figure 4 Figure 4 shows a sketch of the curve with equation x2 − 2xy + 3y2 = 50 (a) Show that d d y x y x y x = − − 3 (4) The curve is used
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