Finding probabilities from a survey giving a table of data on the alcohol consumption of males. This can be easily adapted to data from other types of surveys.

Eight questions on finding least upper bounds and greatest lower bounds of various sets.

Find a regression equation.

Given data on probabilities of three levels of success of three options and projections of the profits that the options will accrue depending on the level of success, find the expected monetary value (EMV) for each option and choose the one with the greatest EMV.

Find out whether the data presented in this question follows a Poisson distribution. Uses the $\chi^2$ test.

One question on determining whether statements are propositions.

Four questions on find truth tables for various logical expressions.

Statistics and probability. 2 questions. Both simple regression. First with 8 data points, second with 10. Find $a$ and $b$ such that $Y=a+bX$. Then find the residual value for one of the data points.

Find gcd g of two positive integers x, y and also find integers a, b such that ax+by=g with prescribed intervals for a and b.

Number Theory. 

Given $n \in \mathbb{N}$ find $\mu(n),\;\tau(n),\;\sigma(n),\;\phi(n).$

Given $\frac{a}{b} \in \mathbb{Q}$ for suitable choices of $a$ and $b$, find all $n \in \mathbb{N}$ such that $\phi(n)=\frac{a}{b}n$.

Given one solution of the quadratic equation in $\mathbb{Z}_n$ where $n=pq$ is a product of two primes find the other 3 solutions.

Given $m \in \mathbb{N}$, find all $n \in \mathbb{N}$ such that $\phi(n)=m$ and enter the largest and second largest if they exist.

Given $m \in \mathbb{N}$, find values of $n\in \mathbb{N}$ such that $\sigma(n)=m$.

There are at most two such solutions in this question.

Given $m \in \mathbb{N}$, find the smallest natural number $n \in \mathbb{N}$ with $\tau(n)=m$ divisors.

Solving an equation of the form $ax \equiv\;b\;\textrm{mod}\;n$  where $\operatorname{gcd}(a,n)|r$. In this case we can find all solutions. The user is asked for the two greatest.

Trying out something: get the student to enter a set for each of "regular singular points" and "essential singular points".

Find and classify singular points of a second-order ordinary differential equation.  One equation is chosen from a selection of 10.

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$.

Given a 3x3 matrix with very big elements, perform row operations to find a matrix with single-digit elements. Then reduce that to an upper triangular matrix, and hence find the determinant.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Exercise using a given uniform distribution $Y$, calculating the expectation and variance as well as asking for the CDF. Also finding  $P( b \lt Y \lt c)$ for given values of $b,\;c$.

Given 32 datapoints in a table find their minimum, lower quartile, median, upper quartile, and maximum.

Sample of size $24$ is given in a table. Find sample mean, sample standard deviation, sample median and the interquartile range.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Multiple correlation question. Given the correlation coefficent of $Y$ with $X_1$ is $r_{01}$, the correlation coefficent of $Y$ with $X_2$ is $r_{02}$ and the correlation coefficent of $X_1$ with $X_2$ is $r_{12}$ then explain the proportion of variablity of $Y$. Also find the partial corr coeff between $Y$ and $X_2$ after fitting $X_1$ and find how much of the remaining variability in $Y$ is explained by $X_2$ after fitting $X_1$.

Two numbers are drawn at random without replacement from the numbers m to n.

Find the probability that both are odd given their sum is even.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''-by=0$. Distinct roots.

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by'+cy=0$.

Find the solution of a first order separable differential equation of the form $a\sin(x)y'=by\cos(x)$.

Find the solution of a first order separable differential equation of the form $(a+x)y'=b+y$.