By the end of this module you will be expected to have learned the following formulae:
The Laws of Indices
The Laws of Surds
If f(x) is in the form
- -b is the axis of symmetry
- c is the maximum or minimum y value
Axis of Symmetry =
Completing the Square
The Quadratic Formula
- The solutions of the quadratic are:
- The discriminant of the quadratic is
Gradient of a line
The equation of a line passing through the point and having a slope m is .
Lines are perpendicular if
Distance between two points
Mid-point of a line
General Circle Formulae
Equation of a Circle
, where (h,k) is the center and r is the radius.
- Derivative of a constant function:
- The Power Rule:
- The Constant Multiple Rule:
- The Sum Rule:
- The Difference Rule:
Rules of Stationary Points
- If and , then c is a local maximum point of f(x). The graph of f(x) will be concave down on the interval.
- If and , then c is a local minimum point of f(x). The graph of f(x) will be concave up on the interval.
- If and and , then c is a local inflection point of f(x).