Last updated on Oct 23, 2026

Parametric Equations - Sketching Graphs (AQA A-Level Mathematics): Quizzes

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Parametric Equations - Sketching Graphs

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What do parametric equations define $x$ and $y$ as?

Functions of a parameter $t$

As parameter $t$ varies, what does the pair $(x(t), y(t))$ do?

Traces a curve in the $xy$ -plane

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 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 $x = \cos t$ , $y = \sin t$ ( $t \in [0, 2\pi]$ ), what is the radius of the circle formed?

$1$

What direction does the circle $x = \cos t$ , $y = \sin t$ trace as $t$ increases?

Counter clockwise

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

$4$

Why are parametric equations useful?

They provide a flexible way to describe curves

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Parametric Equations - Sketching Graphs (AQA A-Level Mathematics): Quizzes

Practise the questions

What do parametric equations define xxx and yyy as?

As parameter ttt varies, what does the pair (x(t),y(t))(x(t), y(t))(x(t),y(t)) do?

What is a typical range for ttt when using trigonometric functions?

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

How should you indicate direction of increasing ttt on a parametric curve?

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

For x=cos⁡tx = \cos tx=cost, y=sin⁡ty = \sin ty=sint (t∈[0,2π]t \in [0, 2\pi]t∈[0,2π]), what is the radius of the circle formed?

What direction does the circle x=cos⁡tx = \cos tx=cost, y=sin⁡ty = \sin ty=sint trace as ttt increases?

For x=2cos⁡tx = 2\cos tx=2cost, y=sin⁡ty = \sin ty=sint, what is the horizontal axis length of the ellipse?

Why are parametric equations useful?

Explore AQA A-Level Mathematics Revision Notes by Topics

Parametric Equations

Further Parametric Equations

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Parametric Equations

Further Parametric Equations

Explore AQA A-Level Mathematics Flashcards by Topics

Parametric Equations

Further Parametric Equations

Explore AQA A-Level Mathematics Exam Questions by Topics

Parametric Equations

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Join 100,000+ A-Level students studying Quizzes with us.

What do parametric equations define $x$ and $y$ as?

As parameter $t$ varies, what does the pair $(x(t), y(t))$ do?

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

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

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

For $x = \cos t$ , $y = \sin t$ ( $t \in [0, 2\pi]$ ), what is the radius of the circle formed?

What direction does the circle $x = \cos t$ , $y = \sin t$ trace as $t$ increases?

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