A-level · Coordinate geometry

Parametric curvesExam-style questions

Defining a curve by parametric equations x = f(t), y = g(t), finding the coordinates of points on the curve, finding the parameter value at a given point, and reading off the range of x- and y-values from the domain of t.

Start practising Read the lesson

15 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3

1
A curve has parametric equations $x = 3t,\ y = t^2 + 1$ .
(a) Find the coordinates of the points where $t = 2$ and $t = -1$ .
(b) The curve passes through the point $(12, k)$ . Find the value of $t$ there and the value of $k$ .
Level 2 · 4 marksTry it
2
A curve has parametric equations $x = t - 2,\ y = t^2 + t$ . Find the coordinates of the points on the curve where $t = -2,\ 0,\ 1$ and $3$ .
Level 2 · 2 marksTry it
3
A curve has parametric equations $x = 2t - 1, \; y = t^{2} + 3$ .
(a) Find the coordinates of the point where $t = 2$ . (1 mark)
(b) Find the value of $y$ at the point where $x = 5$ . (2 marks)
Level 2 · 3 marksTry it
4
A curve has parametric equations $x = 2t,\ y = t^2 - 4t$ for $-1 \le t \le 5$ . Find the range of values of $x$ and the range of values of $y$ .
Level 3 · 3 marksTry it
5
A curve has parametric equations $x = t + 1,\ y = \dfrac{4}{t}$ , $t \ne 0$ .
(a) Find the coordinates of the point where $t = 2$ .
(b) Find the value of $t$ for which $x = 5$ , and the corresponding $y$ .
(c) Explain why the curve never meets the $x$ -axis.
Level 3 · 4 marksTry it

10 more questions on parametric curves

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free