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.

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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