Students are shown a right angled triangle and asked to compute a side length using a trig identity.

The triangle is a fixed image, but the angles and side lengths are randomly selected.

The angle is given in degrees and minutes, and students are asked for the side length correct to 1 decimal place.

There are 4 different triangle orientations that can display.

Given two side-lengths and an angle of a triangle, use the sine rule to calculate an unknown angle.

Draws a triangle based on 3 side lengths.  Randomises asking angle or side.

Draws a triangle based on 3 side lengths.  Randomises asking angle or side.

Draws a triangle based on 3 side lengths.  Randomises asking angle or side.

Draws a triangle based on 3 side lengths.
NOT ACCESSIBLE

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

A question testing the application of the Cosine Rule when given two sides and an angle. In this question, the triangle is always obtuse and both of the given side lengths are adjacent to the given angle (which is the obtuse angle).

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.

Calculate the distance between two points along the surface of a sphere using the cosine rule of spherical trigonometry. Context is two places on the surface of the Earth, using latitude and longitude.

The question is randomised so that the numerical values for Latitude for A and B will be positive and different (10-25 and 40-70 degrees). As will the values for Longitude (5-25 and 50-75). The question statement specifies both points are North in latitude, but one East and one West longitude, This means that students need to deal with angles across the prime meridian, but not the equator.

Students first calculate the side of the spherical triangle in degrees, then in part b they convert the degrees to kilometers. Part a will be marked as correct if in the range true answer +-1degree, as long as the answer is given to 4 decimal places. This allows for students to make the mistake of rounding too much during the calculation steps.

Consider a binary tree with $2^n$ nodes.

We give generators for the isomorphisms of the tree: at each non-leaf vertex, swap the branches descending from that node.

• What is the action of a given word?
• Write a word which produces the required isomorphism
• Which generators commute?
• What is the order of each generator?
• Write one of the (non-root) generators in terms of the others.
• Which permutations of the leaves are possible?
• What is the order of the group of isomorphisms?
• What is the order of the quotient group obtained by identifying all the leaves of one branch?

Draws a triangle based on 2 angles and a side length.

Draws a triangle based on 3 side lengths.

Draws a triangle based on 2 angles and a side length.

Draws a triangle based on 2 angles and a side length.

Using Pythagoras' theorem to determine a non-hypotenuse side, where side lengths include surds and students enter using sqrt syntax

Shows how the \text command is rendered using the plain-text font, not the LaTeX one. Useful for displaying units of measurement and English words inside equations.

This shows how to use variable name annotations inside \simplify to display a 3D vector in terms of the standard unit vectors $\boldsymbol{i}$, $\boldsymbol{j}$, $\boldsymbol{k}$

In progress!

The student is shown two number entry gaps on either side of a 'less than' sign. Their answer is marked correct if the first number is less than the second, using a custom marking algorithm.

This shows how to mark the gaps in a gap-fill part together, rather than independently.

Shows how to create a simplified JME subexpression, and substitute it into a string variable.

To prevent students from giving a trivial answer for a part which is used later in adaptive marking, you can consider it as invalid.

Part a of this question has a custom marking algorithm which marks an answer of zero as invalid. Any other answer is used in adaptive marking for part b.

Used when running a test standalone outside a VLE. This version warns that their answer will show as incorrect.

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This question uses the GeoGebra extension so it can ask the student to create an equilateral triangle. It doesn't matter how they do it, as long as they end up with a polygon with three vertices whose sides are all the same length.

This question uses the GeoGebra extension so it can ask the student to create an equilateral triangle. It doesn't matter how they do it, as long as they end up with a polygon with three vertices whose sides are all the same length.

This question uses the GeoGebra extension so it can ask the student to create an equilateral triangle. It doesn't matter how they do it, as long as they end up with a polygon with three vertices whose sides are all the same length.

This question uses the GeoGebra extension so it can ask the student to create an equilateral triangle. It doesn't matter how they do it, as long as they end up with a polygon with three vertices whose sides are all the same length.

This question uses the GeoGebra extension so it can ask the student to create an equilateral triangle. It doesn't matter how they do it, as long as they end up with a polygon with three vertices whose sides are all the same length.