Practice to decide which quadrant a complex number lies in.

given trig function applied to tides. students need to find max depth, time of low tide and times between which a boat of given depth can use the port.

A couple of different ways of showing the correct answer to a single part as soon as the student submits an answer. One way allows the student to change their answer, while the other locks the part.

A third part includes a "reveal answers to this part" button, which allows the student to choose to reveal the answer to the part.

Think very carefully before using this: by revealing the answer, you are removing the opportunity for the student to later on realise they've got that step wrong, as a consequence of some further work. It's often possible to use adaptive marking to use the student's answer in place of the correct answer in later parts.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

A 2D linear programming problem: optimise the profit from producing two different kinds of product, which both use the same limited resources.

A JSXGraph diagram illustrates the problem and can be used to find an answer.

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

6 questions which introduce the user to the Numbas system.

These questions are part of a numerical reasoning test which focuses on comparing the data in different categories, or comparing total data.

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.

Determine for which value of \(t\) two vectors are parallel. In the first part, there is no real number \(t\) to make it work. In the second part, a value can be worked out.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Not randomized because it's the same as in our workbook. But the variables are made in a way that it should be easy to randomise the size of the matrix, and the to change the formula for the input in not too many places.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

A combination of tasks: checking which matrix products exist, calculating some of these products, calculating transpose matrices. Comparing product of transpose with transpose of product. Experiencing associativity of matrix multiplication. Not much randomisation, only in which matrix product is computed as second option.

Comprehensive solution written out in Advice.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

A combination of tasks: checking which matrix products exist, calculating some of these products, calculating transpose matrices. Comparing product of transpose with transpose of product. Experiencing associativity of matrix multiplication. Not much randomisation, only in which matrix product is computed as second option.

Comprehensive solution written out in Advice.

Use matrix multiplication to get an equation for \(k\) which is then to be solved.

Asking the student to create examples of two matrices which multiply to zero but are not themselves the zero matrix. Then getting the student to think about some features of these examples.

Give the student a larger area to write some free-form text, which isn't marked.

This exam uses a custom theme which provides a new logo image.

Defines a CSS class in the preamble which styles the "Lemma" environment, used in the statement.

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

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

The electrostatic potential due to a point charge is calculated at three points, who of which are at the same distance but different directions.  This relates to the idea that the equipoptentials of a point charge are spheres centred on the charge, so all points at the same distance are at the same potential.

This question requires unit conversion, numerical calculations and some critical evaluation.

Find moment of inertia of a shape which requires the use of the parallel axis theorem for a semicircle.

A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$.

Compute how many linear maps $\mathbb F_p^n\to \mathbb F_p^m$ exist which take prescribed values on a given set of elements in $\mathbb F_p^n$ (which is linearly dependent).