IGCSE Optical Fibres. Animated powerpoint covering the benefits of fibre optics over copper wire, basic construction and network infrastructure. 11 slides.

Summary of the Hubble Expansion and the Hubble-Lamaitre Law of linear proportionality between recessional velocity and distance. The predicted collision between the Andromeda and Milky Way galaxies. The predicted timetable for the Sun’s transition to red and white dwarf status and impact for Earth. 2 sides.

Introduction to the Cosmic Background Radiation (‘CBR’) that goes with the Big Bang. Briefly summarising the Big Bang and the search for & confirmation of CBR. 2 sides.

Turning the general circle equation into the standard equation by completing the square. From 3 circumference points to the circle equation in < 2 mins. The 3 points can be translated by the negative of the position vector of any one of the points to make the circumference pass through the origin, thereby enabling the general equation, x^2 + y^2 = 2xh + 2yk, to be used on the other two points to reveal the centre coordinates, (h, k), of the shifted circle. Pythagoras’ rule on the centre coordinates will reveal the radius and these centre coordinates should be translated back by the original position vector to reveal the centre of the original circle.

Parallelogram area in under a minute. Using the position vectors of 2 corners from another corner, (ai, bj) & (ci, dj), area = |ad - bc|. Geometric and algebraic proofs are included.

Indices and Logarithms to IGCSE level, covering the basic rules. Animated powerpoint. 13 slides.