7/8 : Ralph :
* 3-Powerful numbers. 1^3+5^3+3^3 = ? 4^3+0^3+7^3 = ? Find two other consecutive powerful numbers between these two. Find all 2-powerful numbers.* Prove (-1)x(-1) = +1 starting from (-1)+(1) = 0 and using the axioms a x 0 = 0, a + 0 = a, a x 1 = a, a x (b+c) = (axb) + (axc), (a+b) x c = (axc) + (bxc).9 : Keeley, Josh :
* Group Theory : A notion of a set, common sets such as N, Z and R, The four group axioms were introduced. How common sets could be made into groups was then explored.10 : Tamiru :
Geometry and Number theory* Explain the relationship between arc length and subtended angle.* Find the perimeter of the void between three equal touching circles of radius R.* Extra : Find the radius of the largest incircle that fits in the void.* Prove that p^2-1 is divisible by 24 for all primes >= 5.* Generalise Gauss' trick to sum arbitrary arithmetic progressions.11/12 : David and William :
* Find the mistake in the Kandelhardt Paradox.* Ralph's favourite problems.These topics rotated from class to class over the course of the term --- with extensions where necessary.