Last updated on Oct 23, 2026

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

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Parametric Equations - Sketching Graphs

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Parametric equations define $x$ & $y$ in terms of

A parameter $t$

General form of parametric equations

$x = f(t)$ , $y = g(t)$

As $t$ varies, $(x(t), y(t))$ traces out

A curve in the $xy$ -plane

First step in sketching parametric graphs

Choose appropriate range for parameter $t$

Why note order of plotting as $t$ increases?

Shows direction of the curve

How to show direction of increasing $t$ on curve

With an arrow on the curve

$x = \cos t$ , $y = \sin t$ ( $t$ in $[0,2\pi]$ ) forms

Circle with radius 1 at origin

Direction of $x=\cos t$ , $y=\sin t$ as $t$ increases

Counter clockwise

$x = 2\cos t$ , $y = \sin t$ forms

An ellipse

Key features to identify in parametric curves

Intercepts, maxima, minima, direction changes

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Parametric Equations

Further Parametric Equations

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Parametric Equations

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Parametric Equations

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Parametric Equations

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

Practise the cards

Parametric equations define xxx & yyy in terms of

General form of parametric equations

As ttt varies, (x(t),y(t))(x(t), y(t))(x(t),y(t)) traces out

First step in sketching parametric graphs

Why note order of plotting as ttt increases?

How to show direction of increasing ttt on curve

x=cos⁡tx = \cos tx=cost, y=sin⁡ty = \sin ty=sint (ttt in [0,2π][0,2\pi][0,2π]) forms

Direction of x=cos⁡tx=\cos tx=cost, y=sin⁡ty=\sin ty=sint as ttt increases

x=2cos⁡tx = 2\cos tx=2cost, y=sin⁡ty = \sin ty=sint forms

Key features to identify in parametric curves

Explore AQA A-Level Mathematics Revision Notes by Topics

Parametric Equations

Further Parametric Equations

Explore AQA A-Level Mathematics Model Answers by Topics

Parametric Equations

Further Parametric Equations

Explore AQA A-Level Mathematics Quizzes by Topics

Parametric Equations

Further Parametric Equations

Explore AQA A-Level Mathematics Exam Questions by Topics

Parametric Equations

Further Parametric Equations

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

Parametric equations define $x$ & $y$ in terms of

As $t$ varies, $(x(t), y(t))$ traces out

Why note order of plotting as $t$ increases?

How to show direction of increasing $t$ on curve

$x = \cos t$ , $y = \sin t$ ( $t$ in $[0,2\pi]$ ) forms

Direction of $x=\cos t$ , $y=\sin t$ as $t$ increases

$x = 2\cos t$ , $y = \sin t$ forms