Given percentages of males and females working on a project, and the percentage of the total staff who are male (or female), find the percentage of all staff working on the project.

Based on question 3 from section 3 of the maths-aid workbook on numerical reasoning.

Choose from one of several pre-defined scenarios, and set variables to the corresponding values. 

This question has three variables: city, population, and percent_like_chocolate. These differ for each city. 

Update: you can now use the conditional visibility button to do this more easily - see the documentation.

If the statement or advice for your question differs greatly depending on a random variable (for instance, if you're picking from a selection of scenarios), you only want to show content for the relevant scenario.

This question shows one way of doing that.

Introductory exercise about power sets.

No description given

Given  $P(A)$, $P(A\cup B)$, $P(B^c)$ find $P(A \cap B)$, $P(A^c \cap B^c)$, $P(A^c \cup B^c)$ etc..

Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

Choose from one of several pre-defined scenarios, and set variables to the corresponding values, defined in lists.

This question has three variables: city, population, and percent_like_chocolate. These differ for each city. We've defined a list for each variable, with the corresponding values. A variable called scenario picks a random position in the list, so the value of city, for example, is cities[scenario].

Some clever variable-substitution trickery to randomly pick two sides of a right-angled triangle to give to a student, and ask for the other.

The sides are set up so they're always Pythagorean triples, and the opposite side is always odd.

As ever, most of the tricky stuff is in the advice. 

Because this was created quickly to show how to set up the randomisation, there's no diagram. It would benefit greatly from a diagram.

This exam turns off all the feedback options, so students know nothing about how they've done.

The student has to compute $a^b$ and $b^a$, then decide which of the two is bigger.

This question shows how to set up a custom marking matrix for the "choose one from a list" part, based on values used elsewhere in the question. It could use adaptive marking to use the student's incorrect values for the comparison, but doesn't at the moment.

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.

List all vectors in a spanning set.

(repeated 3 times)

Given a set of vectors, find a basis which generates their span as a subspace of $\mathbb{Z}_n$.

Given a set of codewords generating a code, write down a generator matrix, encode three data vectors, and decode one codeword.

Given a set of codewords generating a code, give a generating matrix, encode three data vectors, and decode one codeword.

Given a set of codewords generating a code, give a generating matrix, encode three data vectors, and decode one codeword.

Cartesian form of the parametric representation of a surface, normal vector, and magnitude.

Accuracy for part c) should be made more stringent as can be marked correct for an incorrect answer. Use a different sample range rather than 0 to 1 would help as would setting accuracy to something less than 0.001.

Double integrals (2) with numerical limits

Unit normal vector to a surface, given in Cartesian form.

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

Given data on population mean and population standard deviation and three sampling sizes, calculate the probabilities that the sample means are within a specified distance from the population mean.

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 $t$. 

LSD and Tukey yardsticks on three treatments. Also one-way Anova test on same set of data.