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

Compound Angle Formulae

Summary Compound angle formulas are: Half angle formulas are: Function to trigonometric form: In Fig 1, and are acute angles and As Hence, Replacing B by -B in i) Also from the diagram: Hence, Also: We have derived the compound angle formulae above. All the compound angle formulas are listed below: Double Angle formulae We … Read more

Solving Trigonometric Equations

Summary To solve trigonometric equations, several identities and formulas are used i.e: For basic trigonometric equations, we follow the following steps to solve them: 1.    Make sine, cosine or tangent the subject. 2.    Use any method including a calculator to find basic angles. 3.    Using quadrants, find all solutions in the given range. Example #1 … Read more