Discriminants

Polynomial You must have heard the word ‘polynomial’ or a ‘polynomial equation’. Algebra is obsessed with polynomials. You will find them everywhere. So, what is a polynomial then? Polynomial is just an expression that involves variables and constants with arithmetic operators (‘+’, ‘-‘, ‘×’, ‘÷’) in between. An example of a polynomial is, As you … Read more

Algebra Functions

Function Many people muddle up the concepts of ‘Equation’ and ’Function’. They are related but they are definitely not the same. You will see how. Let us first understand the idea of an ‘Equation’. An equation is defined as a mathematical relation (involving the ‘=’ symbol) between two or more variables. For instance, the following … Read more

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

Vectors

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