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Inverse and division of complex numbers.  Four parts.

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $ f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.

Find the determinant of a $4 \times 4$ matrix.

Find the determinant of a $3 \times 3$ matrix.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

Differentiate $\displaystyle \cos(e^{ax}+bx^2+c)$

Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$.

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

Moving averages, regression and seasonal adjustments.

Centred moving averages.

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.

Differentiate $\displaystyle (ax^m+b)^{n}$.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$. 

Elementary Exercises in multiplying matrices. 

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.

Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.

Differentiate

\[ \sqrt{a x^m+b})\]

Differentiate $\displaystyle (ax^m+bx^2+c)^{n}$.

Differentiate $\displaystyle \ln((ax+b)^{m})$

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Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

Preparing solutions to given concentrations/dilutions.