When the coordinates of a function are expressed in terms of a third independent variable, parametric equations are produced. E.g. x = 3 s...

 Challenge Prove that FEGH in the following simulation is a cyclic quadrilateral. You can use the circle theorems and geometry to prove the ...

  Polygons A closed shape with many sides is a polygon. Sum of Interior Angles If the number of sides is n and the sum of interior angles is...

  Circle Theorems Circle Theorem 5 The angle between a radius and the tangent at the point of contact is a right angle. Circle Theorem 6 Two...

  Diffraction grating is a glass slide with a series of parallel transparent lines, called slits, on it. When a beam of monochromatic beam s...

  Cyclic Quadrilaterals   A quadrilateral whose vertices touch a circle is called a cyclic quadrilateral.  Fourth Circle Theorem The opposit...

The above simulations show the first three circle theorems.     You can practise them interactively with the following simulation: ...

The above simulation shows how a cube is formed from a net or vice a versa. The net of a triangular-based prism is as follows: In the GCSE o...

Let the EMF, internal resistance, load and the current of a circuit be E, r, R and I respectively. E = I(R + r) I = E/(R + r) The power of t...

Conservation of Mechanical Energy The sum of the kinetic energy and potential energy of an object that moves under gravity remains constant ...

  Credit: Olympus The diffraction of a beam of light through a single slit is given by the following equation. x = d sin θ, where x is the p...

  Modelling with Parametric Equations for A Level pure mathematics Parametric equations can be used to model real life situations. For examp...

  In 1926, Albert Michelson, the German-born American physicist, came up with a method to measure the speed of light to a high degree of acc...

  Euclid's Algorithm is one of the oldest algorithms known to  mankind. It was found in Euclid's Elements, something that dates back...

  The instantaneous velocity of an object can be found by the gradient of the displacement/time graph at a given time.  E.g. In the above gr...

  A histogram represents continuous grouped data as a running total in each group. The area of a each bar, as opposed to the height of each ...

  Refraction When light moves from a medium to another medium, its speed and the direction changes. This is called refraction of light. Snel...

Waves A wave carries energy from a point to another point in a medium / vacuum without the movement of the particles along with it. In the a...

  Inscribed Circle A circle that touches the three sides of a triangle from inside is called  an inscribed circle. In order to construct an ...

  A circle that touches the vertices of a tringle from outside is called a circumcircle. In order to construct it, the following simple step...

  If two lines are perpendicular, the gradient of one line is the negative reciprocal of the other line. E.g.1 Find the equation of the perp...

  When it comes to distances involved in the objects in space, three major units are used. They are, astronomical unit light-year parsec Ast...

  Resistors in series and parallel Resistors can be combined in two different methods; they are in series and in parallel. If two resistors,...

  The area under a curve and the x-axis can be found by integrating the curve between two chosen values of x. Area = ∫ x 2 /4 dx E.g. Are...