Cauchy's integral theorem/formula for several functions $f(z)$ and $C$ the unit circle.

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Poles, residues, and contour integral of a complex-valued function.  Pair of pure imaginary poles.

Poles, residues, and contour integral of a complex-valued function.  Pair of real poles.

Poles, residues, and contour integral of a complex-valued function.  Single, simple pole.

Contour integral of $z^2$ along any path.

Contour integral of $\mathrm{e}^{-z}$ along any path.

Contour integral of a complex-valued function $f(z)$ with the poles of $f(z)$ either inside or outside the path $C$.

Express $f(z)$ in real-imaginary form, given that $z=x+iy$.

Express $f(z)$ in real-imaginary form, given that $z=x+iy$, where $f(z)$ involves hyperbolic functions.

Multiple response question (2 correct out of 4) covering properties of continuity and limits of functions. Selection of questions from a pool.

Use the chain rule to differentiate various functions.

Use the product rule to differentiate various functions.

Approximate $f(x)=(a+h)^{m/n}$ by $f(a)+hf^{\prime}(a)$ to 5 decimal places and compare with true value.

An object moves in a straight line, acceleration given by:

$\displaystyle f(t)=\frac{a}{(1+bt)^n}$. The object starts from rest. Find its maximum speed. 

Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots. 

Finding the coordinates and determining the nature of the stationary points on a polynomial function

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Modular arithmetic. Find the following numbers modulo the given number $n$. Three examples to do.

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

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A quadratic function $ax^2+bs+c$ is given. Six parabolas are sketched. Question is to select the correct parabola.  Need to consider the y-intercept, the coefficient of x^2, and the x-coordinate of the minimum/maximum point.

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