Shannen's spaghetti trigonometry graphs were truly a great inspiration. We had a discussion about how some sinus waves can be listened by the human ear if they are between 16Hz and 20KHz.

In this geogebra file you can listen sinus waves based on 440Hz frequency which is the A tune.
It is quite interesting to notice how frequency not only affects the graph but also the pitch of the sound. The amplitude affects the volume.

 Moreover adding two sinus waves you can have a weird but very interesting effect where the resulting sound 'sounds' somehow trembling. If the two frequencies are close the effect is more intense (we are listening to the so called 'beats'). Thinking about the A level maths, we can use the compound angle formula to prove that the two interfering waves at some time reinforce each other and some other time cancel each other.

Happy by founding out a new (for me) Geogebra command: PlaySound[function,min value, max value] and the ear-saving PlaySound[false]
:) :) :)

parametric plots, compound functions and discussions that make the difference in marks

Consider the following pairs of parametric equations

Show that all of them have the same Cartesian form and explain the differences in sketching the corresponding curves. 

Algegra of vectors: from the dot product to group theory

A nice video to watch about group theory and symmetry is : https://youtu.be/ylAXYqgbp4M

Ultimately,a challenging question (STEP I, 2013)

CHALLENGE 2 CORE 4 INTEGRALS

CHALLENGE CORE 4 INTEGRALS