Inverse and division of complex numbers.  Four parts.

Find the coordinates of the stationary point for $f: D \rightarrow \mathbb{R}$: $f(x,y) = a + be^{-(x-c)^2-(y-d)^2}$, $D$ is a disk centre $(c,d)$.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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Laplace from tables: e^(at), cos(bt), sin(bt).

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Laplace of constants and powers of t

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Warning: may take up to 60 seconds to load question!

Students are given six graphs, corresponding to curves $\gamma(t)$. They must match each with its signed curvature function, $\kappa(t)$.

The graphs are generated by calculating $\theta(t)=\int \kappa(t) \mathrm{d}t$ (by hand: these are given to the question as functions of a variable '#', in string form), and solving $x^{\prime}=\cos(\theta(t)-\theta(0))$ and $y^{\prime}(t)=\sin(\theta(t)-\theta(0))$ numerically (using the RKF method) with a JavaScript extension.

Equations which can be written in the form

\[\dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(y),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x)f(y)\]

can all be solved by integration.

In each case it is possible to separate the $x$'s to one side of the equation and the $y$'s to the other

Solving such equations is therefore known as solution by separation of variables

Find the solution of $\displaystyle \frac{dy}{dx}=\frac{1+y^2}{a+bx}$ which satisfies $y(1)=c$

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Converting Radians to Degrees

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Converting Degrees to Radians

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25 questions on solving quadratic equations

25 questions on solving quadratic equations

Find i using compound interest formula A=P(1+i)^n

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Transposing formulae

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Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Scientific Notation

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Scientific Notation

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Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Find the dot product and the angle between two vectors

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Questions about percentage and ratio, applied to finance.

Based on section 3.2 of the Maths-Aid workbook on numerical reasoning.

Some questions of relevance to consumers.

Some questions of relevance to consumers.

25 questions on solving quadratic equations

Definite Integrals

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Antiderivatives

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