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WMA14 Pure Mathematics 4 — IAL Mathematics Unit 4 · Study-IAL

Subjects
Mathematics
WMA14

Pure Mathematics 4

WMA14Unit 47 topics · 18 questions

Practise this unit Practise weak topics

Topics

4.1Proof2 questions
4.2Algebra and functions: partial fractions2 questions
4.3Coordinate geometry: parametric equations2 questions

Key formulae

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

4.3Coordinate geometry: parametric equations

$\dfrac{dy}{dx} = \dfrac{dy/dt}{dx/dt}$

4.4Binomial expansion2 questions

4.5Differentiation3 questions

4.6Integration4 questions

4.7Vectors3 questions

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dx/dtdy/dt

gradient of a parametric curve

4.4Binomial expansion

$(1 + x)^n = 1 + nx + \dfrac{n(n-1)}{2!}x^2 + \dots$: any rational $n$ , valid for $|x| < 1$

4.6Integration

$\int u\dfrac{dv}{dx}\,dx = uv - \int v\dfrac{du}{dx}\,dx$: integration by parts
$V = \pi\int_a^b y^2\,dx$: volume of revolution about the -axis

4.7Vectors

$|\mathbf{a}| = \sqrt{x^2 + y^2 + z^2}$: magnitude of a vector
$\mathbf{a}\cdot\mathbf{b} = |\mathbf{a}||\mathbf{b}|\cos\theta$: scalar product and the angle between vectors
$\mathbf{r} = \mathbf{a} + \lambda\mathbf{b}$: line through $\mathbf{a}$ in direction $\mathbf{b}$

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