Determine if the following describes a probability mass function.

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

Questions on right-angled triangles asking for the calculation of angles using inverse-trigonometrical functions.

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

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f\;'(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

Differentiate the function $(a + b x)^m  e ^ {n x}$ using the product rule.

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 $ (a+bx) ^ {m} \sin(nx)$

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

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

Use the quotient rule to differentiate various functions.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Spearman rank correlation calculated. 10 paired observations.

Spearman rank correlation calculated. 8 paired observations.

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.