Solving a proportionality problem and then having to discuss the assumptions made in solving the problem.

An exam style question around a square based pyramid. Finding upper and lower bounds on the volume and then looking at the number of ways of recombining the lengths to create a square based pyramid. Answers are on page 2.

Given 3 lengths and 3 perpendiculars, which length is incorrect? If working with non-right-angled trigonometry can also bring in cosine rule and area to check by calculating areas from given lengths. Possibly also some Pythagoras links with the perpendiculars? Is there more than one possible answer?

Nice early composite function problem, is Harry doing it right?

Was moved to create this after seeing something similar on an AQA topic test. Allows pupils the opportunity to consider rotations for angles other than 90 or 180 degrees in a way that is potentially more accessible than doing this on squared paper. Shapes are placed onto a triangular grid, and pupils have to rotate through angles of 60 or multiples of 60.