: Edexcel past-paper questions pack
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Implicit and parametric differentiation

Past-paper questions pack

Name
Class
Date set
Date due
Score/ 65

Questions are numbered; the mark schemes (the answer key) follow on separate pages so the question pages can be handed out alone. www.mathsaleveltutor.com

Edexcel AS and A-level Maths past-paper questions since June 2018 · 17 parts, 65 marks · mark schemes follow the questions · www.mathsaleveltutor.com · Questions and mark schemes © Pearson Education Ltd

1. June 2025 · Paper 2 · Q5(c) · 3 marks
(c) Hence, or otherwise, find the gradient of C at the point P. (3)
2. June 2024 · Paper 2 · Q10(a) · 5 marks
10. y C x Figure 4 Figure 4 shows a sketch of the curve C with parametric equations / x t y O 3 t t The point P with coordinates (4, 2) lies on C. (a) Using parametric differentiation, show that the tangent to C at P has equation x y (5)
3. June 2024 · Paper 2 · Q15(a) · 5 marks
15. The curve C has equation x y x y ( ) (a) Find an expression for d y x in terms of x and y. d (5)
4. June 2024 · Paper 2 · Q15(b) · 2 marks
The point P(1, 0) lies on C. (b) Show that the normal to C at P has equation y x O 3 (2)
5. June 2023 · Paper 2 · Q7(a) · 4 marks
7. 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 = 47 (a) Find d y x in terms of x and y d (4)
6. June 2023 · Paper 2 · Q7(b) · 3 marks
The point P(–2, 5) lies on the curve. (b) Find the equation of the normal to the curve at P, giving your answer in the form ax + by + c = 0 , where a, b and c are integers to be found. (3)
7. June 2023 · Paper 2 · Q9(b) · 4 marks
The curve C cuts the y-axis at the point P (b) Show that the equation of the tangent to C at P can be written in the form ax + by = c ln 5 where a, b and c are integers to be found. (4)
8. June 2022 · Paper 2 · Q16(a) · 5 marks
16. y C P l x Figure 6 Figure 6 shows a sketch of the curve C with parametric equations pi t 3 pi x = 2 tan t + 1 y = 2 sec 2 t + 3 - 4 pi The line l is the normal to C at the point P where t = 4 (a) Using parametric differentiation, show that an equation for l is y = - 1 2 x + 17 (5)
9. Oct 2021 · Paper 2 · Q8(a) · 4 marks
8. The curve C has equation px3 + qxy + 3y2 = 26 where p and q are constants. (a) Show that y apx bqy d x qx cy d where a, b and c are integers to be found. (4)
10. Oct 2021 · Paper 2 · Q8(b) · 5 marks
Given that • the point P (–1, – 4) lies on C • the normal to C at P has equation 19x + 26y + 123 = 0 (b) find the value of p and the value of q. (5)
11. Oct 2021 · Paper 2 · Q13(a) · 3 marks
13. The curve C has parametric equations x = sin 2 theta y = cosec3 theta 0 < theta < pi (a) Find an expression for d y x in terms of theta d (3)
12. Oct 2021 · Paper 2 · Q13(b) · 3 marks
(b) Hence find the exact value of the gradient of the tangent to C at the point where y = 8 (3)
13. Oct 2020 · Paper 1 · Q15(a) · 4 marks
15. The curve C has equation pi x2 tan y = 9 0 < y < 2 (a) Show that d y x = - x d x + (4)
14. June 2019 · Paper 2 · Q11(a) · 5 marks
11. y C x 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 point of C. (Solutions based entirely on graphical or numerical methods are not acceptable.) (5)
15. June 2018 · Paper 1 · Q9(a) · 4 marks
9. North y Q East x P Figure 4 Figure 4 shows a sketch of the curve with equation x2 - 2xy + 3y2 = 50 (a) Show that d y y x - = d x y x - (4)
16. June 2018 · Paper 1 · Q9(b) · 5 marks
The curve is used to model the shape of a cycle track with both x and y measured in km. The points P and Q represent points that are furthest west and furthest east of the origin O, as shown in Figure 4. Using part (a), (b) find the exact coordinates of the point P. (5)
17. June 2018 · Paper 1 · Q9(c) · 1 marks
(c) Explain briefly how to find the coordinates of the point that is furthest north of the origin O. (You do not need to carry out this calculation). (1)

Mark schemes

Each mark scheme shows the whole question; the parts on this topic are the ones listed above.

June 2025 · Paper 2 · Q5
Mark scheme June 2025 Paper 2 Q5(c)
June 2024 · Paper 2 · Q10
Mark scheme June 2024 Paper 2 Q10(a)
June 2024 · Paper 2 · Q15
Mark scheme June 2024 Paper 2 Q15(b)
June 2023 · Paper 2 · Q7
Mark scheme June 2023 Paper 2 Q7(b)
June 2023 · Paper 2 · Q9
Mark scheme June 2023 Paper 2 Q9(b)
June 2022 · Paper 2 · Q16
Mark scheme June 2022 Paper 2 Q16(a)
Oct 2021 · Paper 2 · Q8
Mark scheme Oct 2021 Paper 2 Q8(b)
Oct 2021 · Paper 2 · Q13
Mark scheme Oct 2021 Paper 2 Q13(b)
Oct 2020 · Paper 1 · Q15
Mark scheme Oct 2020 Paper 1 Q15(a)
June 2019 · Paper 2 · Q11
Mark scheme June 2019 Paper 2 Q11(a)
June 2018 · Paper 1 · Q9
Mark scheme June 2018 Paper 1 Q9(c)