A-level · Coordinate geometry

Modelling with parametric equationsExam-style questions

Using parametric equations to model real situations where x and y each depend on time — projectiles and rotating points — reading positions, maxima and ranges from the model, and finding the Cartesian equation of the path.

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

DifficultyAll Level 3 Level 4 Level 5

1
A ball is thrown so that, $t$ seconds after release, its position in metres is given by $x = 20t,\ y = 15t - 5t^2$ . Its path is shown below.(a) Find the position of the ball after $1$ second.
(b) Find the time at which the ball lands.
(c) Find the horizontal distance travelled before it lands.
Level 3 · 4 marksTry it
2
A ball is launched from ground level so that, $t$ seconds after launch, its position in metres is $x = 8t,\ y = 6t - 5t^2$ .
(a) Find the greatest height reached and the time at which it occurs.
(b) Find the horizontal range (the distance from launch to where it lands).
Level 3 · 5 marksTry it
3
A particle moves so that, at time $t$ , its position is $x = 10t,\ y = 10t - 5t^2$ . Find the Cartesian equation of the path of the particle.
Level 3 · 2 marksTry it
4
A particle moves so that, $t$ seconds after it starts ( $t \ge 0$ ), its position in metres is $x = 3t,\ y = 4t$ .
(a) Show that the path is a straight line through the origin, and find its gradient.
(b) Find the distance of the particle from the origin when $t = 2$ .
Level 3 · 4 marksTry it
5
A stone is thrown so that, $t$ seconds after release ( $t \ge 0$ ), its position in metres is $x = 2 + 3t,\ y = 1 + 4t - 5t^2$ .
(a) Write down the position from which the stone is thrown.
(b) Find the greatest height of the stone and the time at which it occurs.
(c) Find the Cartesian equation of the path.
Level 3 · 5 marksTry it

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