Students are randomly shown one of two networks. They are shown four sub-networks, and asked to identify which one is a minimum spanning tree for the network. Thus, there are 2 versions of this question.

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.

https://numbas.mathcentre.ac.uk/question/22664/addition-and-subtraction-of-fractions/ by Lauren Richards

Translated to German and Part d) added.

Given a population size and data on a test for a condition on that population, use a tabular approach to find the increase in risk after a positive test in which there is a small chance of a false positive i.e. the probability that the test is positive even though  the condition is not present. See Advice for a graphical version.

This question uses the technique of allocating zero marks to gaps so that they act as holders of values input by the user but are not assessed. The values so input are then gathered using the code found in the preamble and suitable combinations are assigned as answers to gap fills which are then assessed to see if they meet the requirements of the question. Note that is a gap fill is created, but not addressed in the prompt of the part then it is hidden from the user.

Find a regression equation.

Now includes a graph of the regression line and another interactive graph gives users the opportunity to move the regression line around. Could be used for allowing users to experiment with what they think the line should be and see how this compares with the calculated line.

Also includes an updated SSE to see how the sum of the squares of the residuals varies with the regression line.

Nature of fixed points of a 2D dynamical system.

These examples are either centres or spirals.

Deduce some properties of elements of $\mathbb F_4$, given its multiplication table. (E.g., which element is the zero, the one element, ...)

Used for LANTITE preparation (Australia). NC = Non Calculator strand. SP = Statistics & Probability strand.This question provides a list of data to the student. They are asked to find the difference between the mean and the median. This question was based on a Newcastle Uni question which also asked the mode, hence the surplus legacy variables (too tricky to delete).

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are asked to obtain a percentage from an infographic, then choose the fraction which is closest. There are 7 different versions of this question.

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.

Original: https://numbas.mathcentre.ac.uk/question/11698/equation-of-a-straight-line/ by Newcastle University Mathematics and Statistics,

translated to German, added Parts b), c), d), e)

Two trains arrive at the same platform with different periods. Compute the LCM of the two periods to find the time they clash.

This is a context question testing the student's ability to identify the lowest common multiple of two integer values which are not multiples of each other. 

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

Questions which ask the student to intepret vector diagrams in order to write out the components in terms of base vectors. Also addition and subtraction of vectors and vector magnitude.

No description given

Students are given a formula and asked to evaluate it for a given input value, which is randomised.

A few questions which use the GeoGebra extension.

Solve $\displaystyle ax + b =\frac{f}{g}( cx + d)$ for $x$.

A video is included in Show steps which goes through a similar example.

Find the stationary points of a cubic which has 2 turning points.

Given a table of the number of days in which sales were between £x1000 and £(x+1)1000 find the relative percentage frequencies of these volume of sales.

Find a regression equation.

Find a regression equation.

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. 8 paired observations.

Spearman rank correlation calculated. 10 paired observations.

Find $p$ and $q$ such that $ax^2+bx+c = a(x+p)^2+q$. 

Hence, or otherwise, find roots of  $ax^2+bx+c=0$.

Includes a video which shows how to solve a quadratic by completing the square.

Express $\displaystyle \frac{a}{x + b} + \frac{cx+d}{x^2 +px+ q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

This is an old demo. For a demonstration of Numbas's current features, please see the newest demo exam.

A few questions which show off various features of Numbas.

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.