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WMA13 Pure Mathematics 3 — IAL Mathematics Unit 3 · Study-IAL

Subjects
Mathematics
WMA13

Pure Mathematics 3

WMA13Unit 36 topics · 17 questions

Practise this unit Practise weak topics

Topics

3.1Algebra and functions3 questions
3.2Trigonometry3 questions
3.3Exponentials and logarithms3 questions

Key formulae

The relationships this unit leans on most. Check your formulae or data booklet for which ones the exam gives you.

3.2Trigonometry

$1 + \tan^2\theta = \sec^2\theta$

3.4Differentiation3 questions

3.5Integration3 questions

3.6Numerical methods2 questions

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θ

and $1 + \cot^2\theta = \operatorname{cosec}^2\theta$

$\sin 2A = 2\sin A\cos A$

double angle

$\cos 2A = \cos^2 A - \sin^2 A$

also $2\cos^2 A - 1$ and $1 - 2\sin^2 A$

$a\cos\theta + b\sin\theta = R\cos(\theta - \alpha)$

with $R = \sqrt{a^2 + b^2}$ and $\tan\alpha = \tfrac{b}{a}$

3.3Exponentials and logarithms

$e^{\ln x} = x, \quad \ln e^x = x$: $e^x$ and $\ln x$ undo each other

3.4Differentiation

$\dfrac{d}{dx}e^{kx} = ke^{kx}, \quad \dfrac{d}{dx}\ln x = \dfrac{1}{x}$: exponentials and logs
$\dfrac{dy}{dx} = \dfrac{dy}{du}\cdot\dfrac{du}{dx}$
$\dfrac{d}{dx}(uv) = u\dfrac{dv}{dx} + v\dfrac{du}{dx}$
$\dfrac{d}{dx}\left(\dfrac{u}{v}\right) = \dfrac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^2}$

3.6Numerical methods

$x_{n+1} = x_n - \dfrac{f(x_n)}{f'(x_n)}$: Newton–Raphson

dy

⋅

dxdu

chain rule

dx

dv

+

vdxdu

product rule

v

u

)

=

v2vdxdu−udxdv

quotient rule