Last updated on Sep 21, 2026

Parametric Equations (Edexcel A-Level Mathematics): Quizzes

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Parametric Equations - Sketching Graphs

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In parametric equations, what are $x$ and $y$ expressed as?

Functions of parameter $t$

What is a typical range for $t$ when using trigonometric functions?

$t \in [0, 2\pi]$

Why is the order of plotting points important when sketching parametric curves?

It shows the direction of the curve

How should you indicate the direction of increasing $t$ on a parametric curve?

With an arrow on the curve

How do you find where a parametric curve crosses the $x$ -axis?

Set $y(t) = 0$ and solve for $t$

For $x = \cos t$ , $y = \sin t$ , what are the coordinates when $t = \frac{\pi}{2}$ ?

$(0, 1)$

What shape is traced by $x = \cos t$ , $y = \sin t$ for $t \in [0, 2\pi]$ ?

Circle with radius 1 at origin

In what direction is the circle $x = \cos t$ , $y = \sin t$ traced as $t$ increases?

Counter-clockwise

For $x = 2\cos t$ , $y = \sin t$ , what is the horizontal axis length of the ellipse?

Length 4 (from $-2$ to $2$ )

For $x = 2\cos t$ , $y = \sin t$ , what are the coordinates at $t = \pi$ ?

$(-2, 0)$

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