Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

$Y \sim \operatorname{Poisson}(p)$. Find $P(Y=a)$, $P(Y \gt b)$, $E[Y],\;\operatorname{Var}(Y)$.

3 Repeated integrals of the form $\int_a^b\;dx\;\int_c^{f(x)}g(x,y)\;dy$ where $g(x,y)$ is a polynomial in $x,\;y$ and $f(x)$ is a degree 0, 1 or 2 polynomial in $x$.

Repeated integral of the form: $\displaystyle I=\int_0^1\;dx\;\int_0^{x^{m-1}}mf(x^m+a)dy$

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

Determine if the following describes a probability mass function.

$P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$.

$X$ is a continuous uniform random variable defined on $[a,\;b]$. Find the PDF and CDF of $X$ and find  $P(X \ge c)$.

Find the centre and radius of a circle when given an equation in standard form.

Express the equation of the given line in the form $y=mx+c$.

Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions. 

No description given

Differentiate $f(x)=x^{m}\sin(ax+b) e^{nx}$.

The answer is of the form:
$\displaystyle \frac{df}{dx}= x^{m-1}e^{nx}g(x)$ for a function $g(x)$.

Find $g(x)$.

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

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

The derivative of $\displaystyle \frac{ax+b}{cx^2+d}$ is of the form $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

No description given

The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$. Find $p$.

The derivative of  $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$. Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$.

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

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

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

Write complex numbers in real-imaginary form.

Given a payoff table with two states and five actions, identify which actions are admissible, then the maximax, maximin, and minimax regret actions.

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.

Polar form of a complex number.

Expressing $\log(f(i))$ in the form $u+iv$.  Principal values of log.

For given optimisation problems, determine maximin, maximax, and minimax regret actions, expected value criteria, expected value of perfect information.