: Edexcel past-paper questions pack
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Parametric equations

Past-paper questions pack

Name
Class
Date set
Date due
Score/ 47

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 · 14 parts, 47 marks · mark schemes follow the questions · www.mathsaleveltutor.com · Questions and mark schemes © Pearson Education Ltd

1. June 2025 · Paper 2 · Q5(a) · 2 marks
5. The curve C has parametric equations O 31 t 4 t ∈ ℝ x 2 y = 5(t + 2) The point P with x coordinate –3 lies on C. (a) Find the y coordinate of P. (2)
2. June 2025 · Paper 2 · Q5(b) · 2 marks
(b) Find a Cartesian equation for C, giving the answer in the form y = f (x) (2)
3. June 2024 · Paper 2 · Q10(b) · 1 marks
The curve C is used to model the profile of a slide at a water park. Units are in metres, with y being the height of the slide above water level. (b) Find, according to the model, the greatest height of the slide above water level. (1)
4. June 2023 · Paper 2 · Q9(a) · 3 marks
9. 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 are integers to be found. (3)
5. June 2022 · Paper 1 · Q16(a) · 5 marks
16. y C R x Figure 6 Figure 6 shows a sketch of the curve C with parametric equations x = 8 sin2 t y = 2 sin 2t + 3 sin t 0 t pi The region R, shown shaded in Figure 6, is bounded by C, the x-axis and the line with equation x = 4 (a) Show that the area of R is given by a ∫ ( ) - cos t + sin t cos t d t where a is a constant to be found. (5)
6. June 2022 · Paper 2 · Q16(b) · 2 marks
(b) Show that all points on C satisfy the equation y = 1 2 + 5 2 (x - 1) (2)
7. June 2022 · Paper 2 · Q16(c) · 5 marks
The straight line with equation y = - 1 2 x + k where k is a constant intersects C at two distinct points. (c) Find the range of possible values for k. (5)
8. Oct 2021 · Paper 1 · Q13 · 3 marks
13. A curve C has parametric equations x = t + t y = t ∈ t + t + Show that all points on C satisfy (x - 3) 2 + y2 = 4 (3)
9. Oct 2020 · Paper 2 · Q12(a)(i) · 3 marks
12. y R x Figure 3 The curve shown in Figure 3 has parametric equations pi x = 6 sin t y = 5 sin 2t 0 t 2 The region R, shown shaded in Figure 3, is bounded by the curve and the x-axis. pi ∫ (a) (i) Show that the area of R is given by 60sin cos t t t d (3)
10. Oct 2020 · Paper 2 · Q12(b) · 5 marks
y M N 4.2 x Figure 4 Part of the curve is used to model the profile of a small dam, shown shaded in Figure 4. Using the model and given that ● x and y are in metres ● the vertical wall of the dam is 4.2 metres high ● there is a horizontal walkway of width MN along the top of the dam (b) calculate the width of the walkway. (5)
11. June 2019 · Paper 2 · Q4 · 6 marks
4. y C2 C1 x S Figure 2 The curve C1 with parametric equations 2sin t , 0 - t : 2ʌ x = 10௘cos t , y = 4 meets the circle C2 with equation x2 + y2 = 66 at four distinct points as shown in Figure 2. Given that one of these points, S, lies in the 4th quadrant, find the Cartesian coordinates of S. (6)
12. June 2018 · Paper 1 · Q14(a) · 2 marks
14. A curve C has parametric equations x = 3 + 2 sin t, y = 4 + 2 cos 2t, 0 t < 2 pi (a) Show that all points on C satisfy y = 6 - (x - 3)2 (2)
13. June 2018 · Paper 1 · Q14(b) · 3 marks
(b) (i) Sketch the curve C. (ii) Explain briefly why C does not include all points of y = 6 - (x - 3)2, x ∈ ℝ (3)
14. June 2018 · Paper 1 · Q14(c) · 5 marks
The line with equation x + y = k, where k is a constant, intersects C at two distinct points. (c) State the range of values of k, writing your answer in set notation. (5)

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(b)
June 2024 · Paper 2 · Q10
Mark scheme June 2024 Paper 2 Q10(b)
June 2023 · Paper 2 · Q9
Mark scheme June 2023 Paper 2 Q9(a)
June 2022 · Paper 1 · Q16
Mark scheme June 2022 Paper 1 Q16(a)
June 2022 · Paper 2 · Q16
Mark scheme June 2022 Paper 2 Q16(c)
Oct 2021 · Paper 1 · Q13
Mark scheme Oct 2021 Paper 1 Q13
Oct 2020 · Paper 2 · Q12
Mark scheme Oct 2020 Paper 2 Q12(b)
June 2019 · Paper 2 · Q4
Mark scheme June 2019 Paper 2 Q4
June 2018 · Paper 1 · Q14
Mark scheme June 2018 Paper 1 Q14(c)