By the end of this module you will be expected to have learnt the following formulae:
Dividing and Factoring PolynomialsEdit
If you have a polynomial f(x) divided by x - c, the remainder is equal to f(c). Note if the equation is x + c then you need to negate c: f(-c).
The Factor TheoremEdit
A polynomial f(x) has a factor x - c if and only if f(c) = 0. Note if the equation is x + c then you need to negate c: f(-c).
Formula For Exponential and Logarithmic FunctionEdit
The Laws of ExponentsEdit
- where c is a constant
The inverse of is which is equivalent to
Change of Base Rule: can be written as
Laws of Logarithmic FunctionsEdit
When X and Y are positive.
Circles and AnglesEdit
Conversion of Degree Minutes and Seconds to a DecimalEdit
where X is the degree, y is the minutes, and z is the seconds.
Note: θ need to be in radians
Area of a SectorEdit
Note: θ need to be in radians.
The Trigonometric Ratios Of An AngleEdit
|Function||Written||Defined||Inverse Function||Written||Equivalent to|
Important Trigonometric ValuesEdit
You need to have these values memorized.
The Law of CosinesEdit
The Law of SinesEdit
Area of a TriangleEdit
The reason that we add a + C when we compute the integral is because the derivative of a constant is zero, therefore we have an unknown constant when we compute the integral.
Rules of Definite IntegralsEdit
- , F is the anti derivative of f such that F' = f
- Area between a curve and the x-axis is
- Area between a curve and the y-axis is
- Area between curves is
Where: n is the number of strips.