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.

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.

IGCSE Physics - Waves Introduction, covering the classification and descriptive terms for waves. Introducing transverse waves (waves on a string, light waves), longitudinal waves (sound waves) and rotary waves (ocean waves). Introducing the wave speed formula, standing waves, wave interference, the rules for reflection and refraction, diffraction and the Doppler effect. (16 slides.)

IGCSE Physics - Electromagnetism. Electrons in motion create magnetic fields, with a relationship between current and field directions given by the ‘corkscrew’ rule. Introducing solenoid electromagnets. Basics of d.c. electric motors and Fleming’s Left Hand (motor) rule for the FBI directions (force (F), field (B) and current (I)). Basics of electric generators and Fleming’s Right Hand (generator) rule.

Factors, Prime Factors, HCF & LCM animated powerpoint. Defining factors and prime factors. Finding prime factors using divisibility rules and using a Venn diagram to find the highest common factor and lowest common multiple of a pair and a triplet of numbers. Finding prime numbers up to 100 in under 10 seconds. (6 slides.)

IGCSE Trigonometry animated powerpoint. Reviewing angle and triangle basics including the Pythagoras theorem in two and three dimensions. Defining the sine, cosine and tangent functions, using them to find side-lengths and angles. Deriving the sine and cosine rules and using them to find distances and bearings on maps. Exploring the shape of the sine, cosine and tangent functions. (17 slides.)

IGCSE Maths - Quadratics (Notes). Exploring the effect(s) of each coefficient on the shape of the parabola; use the Geogebra link to explore for yourself. Finding the coordinates for the turning point. Factorising a quadratic expression by inspection, completing the square, using the quadratic equation to obtain the roots. The discriminant of the quadratic equation and imaginary roots. (22 pages, 10 diagrams & 35 examples.)

IGCSE Force & Pressure, animated powerpoint. Force and pressure in a solid, liquid and a gas. ‘Head’ of pressure, and transmission of pressure by a fluid. Measuring pressure with a barometer and a manometer. Boyle’s Law and scuba diving. 22 slides.

(I)GCSE Newton’s Laws of Motion animated powerpoint. Starting with inertia, through momentum and impulse, Newton’s Laws of Motion are introduced, with 5 worked examples. 10 slides.

IGCSE Introduction to Calculus animated powerpoint. The gradient ratio as rise-over-run and the limit for a tangent to a curve as the ‘derivative’. Examples of the limit/derivative for straight line, a parabola and a cubic. The use of the derivative to find ‘turning points’, and the distinction between a local maximum and a local minimum. 15 slides.

Electrostatics, voltage and current, dangers and protection for devices and humans, measuring voltage, current, power and energy, series and parallel circuit resistance, introducing variable resistors, NTC thermistors, LDRs, diodes, capacitors, relays, transformers, rectifiers and inverters.

IGCSE Physics - Line of Force and Motion. Animated powerpoint, introducing torque/moment, the lever, centre of mass and centre of gravity, Fosbury flop, Earth-Moon barycentre, conditions for equilibrium, balance and stability, tipping angle, boat buoyancy, car rolling and pitching, fork-lift trucks and cranes ! 33 slides.

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

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

Multiplication of Two-digit Numbers. Animated powerpoint covering the ‘area method’, the ‘let’s try in our head’ method, + the multiples of 5 short-cut. 3 slides.

IGCSE Atomic Structure, animated powerpoint. Electrons, protons & neutrons. Introducing Isotopes, Atomic weight, the Billiard Ball model, the Plum pudding model, the Gold Foil experiments, the Nuclear model, the Electron Shell model & electron configuration. 22 slides.

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.

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.

IGCSE Solar System animated powerpoint. Distinguishing between the terrestrials, asteroids, gas giants, ice giants, comets and meteoroids. Planetary orbital data. Mass and radius vs gravitational field strength. Gravitational force and orbital speed. 22 slides.

IGCSE Radioactivity, animated powerpoint. Unstable nuclei, alpha/beta/gamma decay, decay equations, half-life, Ba-137m experiment, radioisotope uses, ionisation smoke detector, carbon-dating, background radiation, harmful effects of radiation, safety precautions. 34 slides.