Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find positive powers of the complex numbers.

Express $\displaystyle \frac{a}{x + b} \pm  \frac{c}{x + d}$ as an algebraic single fraction over a common denominator. 

No description given

Given the exchange rate between two currencies, calculate how much of one currency you will get for $x$ amount of the other

Given the exchange rate between two currencies and the bank's commission rate, calculate how much of one currency you will get for $x$ amount of the other

Using geogebra to draw lines tangent to a curve and calculate their gradient.

Students are shown 4 network diagrams (randomly selected from a pool of 20) and asked to identify which of them are trees.

Students are awarded 1 mark for each correct identification, and lose 1 mark for each non-tree they select.

As the number of trees can change, the number of marks that this question is worth can also change, ranging from 1 to 4.

Integrating a polynomial functions which describe the rate of change of a population over time to find and use an equation that describes the total population according to time.

Example of an explore mode question. Student is given a 2x2 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvector is recognised by the marking algorithm, also multiples of the "obvious" one(s) (given the reduced row echelon form that we use to calculate them).

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

No description given

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.

Two questions testing the application of the Sine Rule when given two angles and a side. In this question, the triangle is always acute.

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Two questions testing the application of the Cosine Rule when given two sides and an angle. In these questions, the triangle is always acute and both of the given side lengths are adjacent to the given angle.

Example of an explore mode question. Student is given a 2x2 matrix with eigenvalues and eigenvectors, and is asked to decide if the matrix is invertible. If yes, second and third parts are offered where the student should give the eigenvalues and eigenvectors of the inverse matrix.

Assessed: remembering link between 0 eigenvalue and invertibility. Remembering link between eigenvalues and eigenvectors of matrix and its inverse.

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Questions asking for the factoring of simple case (a=1)

These first need to be changed to standard form.

Then use factors to solve.

Questions asking for the factoring of simple case (a=1)

These first need to be changed to standard form.

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.

The student is shown a Cartesian diagram containing a point $P$ and a circle. They must move the point and change its radius so that the point $P$ is touching the circle.

They can type the radius and coordinates in, or move the circle around on the diagram.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

Testing ability to read data accurately from graphs and apply percentage change equation

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.

No description given

Lets a student practice finding percentage changes.

Do not use this: JME marking algorithms are the best way to change marking behaviour now, instead of JavaScript.

A very simple example of a custom marking script for a "choose one from a list" part

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

No description given

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.