Curve Sketching

Summary Gradient Intercept Form of an equation of a line helps plot the graph: If we are to sketch a curve, we find the gradient by differentiating the equation to find the derivative. An asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one … Read more


Summary Unit vector is defined as:  Position vector of two points is:  Equation of a vector line is    where a is the point on the line and b is the direction Angle between two vectors is  Vector quantities are extremely useful in physics. The important characteristic of a vector quantity is that it has … Read more

Equation Of A Circle

Summary Formula for equation of a circle is: Where (a, b) is the center of the circle and r is the radius. Before we move on to the equation of a circle, let’s just recap Pythagoras theorem from your GCSE studies: We know that Pythagoras Theorem can be applied when we have a right angle … Read more

Coordinate Geometry

Summary Midpoint of a line: Distance between two points: Gradient of a straight line 3 forms of equation of a straight line: Gradient Intercept Form: Gradient Point Form: Two Point Form: What is coordinate geometry? As we know from GCSE’s geometry is basically about how shapes, points, lines all relate to each other. When we … Read more

Newton’s Law of Restitution

Summary Newton’s law of restitution states that when two bodies collide, the speed with which they move after the collision actually depends on the material from which they are made. The Coefficient of Restitution (e) tells us about the bounciness, or elasticity, of the collision. When e = 1, no kinetic energy is lost When … Read more

Motion In A Circle

Summary So for an object moving in a circle, there is an inward force acting upon it in order to cause its inward acceleration. This is known as Centripetal Force. Angular velocity is basically the rate of change of angle when an object is in a circular motion:  .  Where f is the frequency of … Read more