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Three equilateral triangles are divided equally into 3, 4 and 5 parts respectively. Calculate the distance between two marked points.

Based on a puzzle by Catriona Shearer, shared on Twitter.

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An example of using the GeoGebra extension to ask the student to create a geometric construction, with marking and steps.

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A question testing the application of the Area of a Triangle formula 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.

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

Two questions testing the application of the Sine Rule when given two sides and an angle. In this question, the triangle is always acute and one of the given side lengths is opposite the given angle.

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Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

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.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

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The custom function rectangle(width,height) draws a rectangle with the given dimensions, along with some labels.

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.

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

Find angle between plane $\Pi_1$, given by three points, and the plane $\Pi_2$ given in Cartesian form.

The calculation of $cos(\alpha)$ at the end of Advice has fractionNumbers switched on and so the result is presented as a fraction, which can be misleading. Best if calculation is followed through without using fractionNumbers.

(Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2-by \right)\;dx+\left(cy^2+px\right)\;dy$.

Find the cosine of the angle between two pairs of 3D and 4D vectors.

The calculations and answers are correct, however the Advice should display the interim calculations of the lengths of vectors and their products to say 6dps. At present the student may be mislead into using 2dps at each stage - the instruction at the start of Advice is somewhat confusing.

Intersection points, tangent vectors, angles between pairs of curves, given in parametric form.

Questions on right-angled triangles asking for the calculation of angles using inverse-trigonometrical functions.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always obtuse. A secondary application is finding the area of a triangle.

Two questions testing the application of the Sine Rule when given two angles and a side. In this question the triangle is obtuse. In one question, the two given angles are both acute. In the second, one of the angles is obtuse.

Two questions testing the application of the Sine Rule when given two sides and an angle. In this question, the triangle is always acute and one of the given side lengths is opposite the given angle.

A question testing the application of the Sine Rule when given two sides and an angle.  In this question the triangle is obtuse and the first angle to be found is obtuse.

This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.

The shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.

Author of gif: Picknick
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