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 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.)

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.)

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 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.

CAIE A2 9709 Maths Integration I. Animated powerpoint. Integration as area, basic rules (incl. 6 trig), numerical integration, reverse chain rule (substitution). 16 slides.

CAIE A2 9709 Maths Differentiation animated powerpoint. Product and Quotient rules, Ln and exponentials, the 6 Trig derivatives, Explicit and Parametric differentiation. 18 slides.

CAIE A2 9709 Trigonometry animated powerpoint. Covering compound angle formulae, double angle formulae, and the conversion into polar form. Incl examples, 10 + 8 slides.

CAIE AS 9709 Maths Trigonometry animated powerpoint with Geogebra add-ins. Values and patterns of the trig functions, rules and transformations. Radian. 19 slides. Explore all three main functions using the GeoGebra add-ins, including mapping the functions to rotation around the unit circle, transforming the functions by adjusting all four coefficients, and wrapping a radius (multiple) around a circle to see how the radian is defined.

CAIE A2 9709 Maths Numerical Solution of Equations animated powerpoint. Interval estimation, change of sign, point-and-gradient, fixed point iteration. 21 slides.

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

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.