One method of randomly choosing names for variables. For each variable, we have 4 options. Create a list of 4 numbers, which is 1 for the name we want to use, and 0 otherwise.

Then, whenever we use that variable, multiply each of the possible names by the corresponding number in the list. When the expression is simplified, the unwanted names will cancel to 0, leaving only the name we want.

This is quite clunky!

(This question also uses a custom marking script to check that the student has simplified the expression)

Load data about members of the Scottish parliament from a JSON object, and display a table of 5 randomly picked MSPs.

Load data on some items held in the Cooper Hewitt collection, and show a table of 5 randomly picked items.

A randomly generated list of numbers is shown to the student. They must tick every occurrence of the lowest number. The number of occurrences isn't always the same - sometimes the minimum is unique and sometimes it is repeated. The map function makes it easy to construct a marking matrix.

A mathematical expression part whose answer is the product of two matrices, $X \times Y$.

By setting the "variable value generator" option for $X$ and $Y$ to produce random matrices, we can ensure that the order of the factors in the student's answer matters: $X \times Y \neq Y \times X$.

Construct a line in a GeoGebra worksheet by writing its definition string by hand.

This isn't a very neat way of doing this. It's easier to define two points in GeoGebra, then make a line through those points. You can set the positions of the points from Numbas using vectors.

Construct a line through two points in a GeoGebra worksheet. Change the line by setting the positions of the two points when the worksheet is embedded into the question.

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.
This version of the question asks for 10 fields to be filled rather than the full 25, although the question statement asks for 25. I am sure that the first version asked for all 25.

Deciding whether or not three sampling methods are simple random sampling, stratified sampling, systematic or judgemental sampling. 

A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.

Given a linear combination $Y$ of three independent random variables with given means and variances, find the mean of variance of $Y$.

Given a discrete random variable $X$ find the expectation of $1/X$ and $e^X$.

Using a random sample from a population with given mean and variance, find the expectation and variance of three estimators of $\mu$. Unbiased, efficient?

Given a PDF $f(x)$ on the real line with unknown parameter $t$ and three random observations, find log-likelihood and MLE $\hat{t}$ for $t$. 

Abstract simplex method question. Given optimal tableau, student must identify optimal solution and objective value.

Given descriptions of  3 random variables, decide whether or not each is from a Poisson or Binomial distribution.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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

Choosing whether given random variables are qualitative or quantitative.

Deciding whether or not  three sampling methods are simple random sampling, stratified sampling, systematic or judgemental sampling. Also whether or not the method of selection is random, quasi-random or non-random.

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

Independent events in probability. Choose whether given three given pairs of events are independent or not.

Find a regression equation.

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

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.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Given the following three vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3$ Find out whether they are a linearly independent set are not. Also if linearly dependent find the relationship $\textbf{v}_{r}=p\textbf{v}_{s}+q\textbf{v}_{t}$ for suitable $r,\;s,\;t$ and integers $p,\;q$.