By the end of this module you will be expected to have learnt the following formulae:

## Contents

## Dividing and Factoring PolynomialsEdit

### Remainder TheoremEdit

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

### Logarithmic FunctionEdit

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.

### Arc LengthEdit

Note: θ need to be in radians

### Area of a SectorEdit

Note: θ need to be in radians.

## TrigonometryEdit

### The Trigonometric Ratios Of An AngleEdit

Function | Written | Defined | Inverse Function | Written | Equivalent to |
---|---|---|---|---|---|

Cosine | |||||

Sine | |||||

Tangent |

### Important Trigonometric ValuesEdit

You need to have these values memorized.

0 | 0 | 1 | 0 | |

1 | 0 | - |

### The Law of CosinesEdit

### The Law of SinesEdit

### Area of a TriangleEdit

### Trigonometric IdentitiesEdit

## IntegrationEdit

### Integration RulesEdit

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

### Trapezium RuleEdit

Where:

### Midpoint RuleEdit

Where: n is the number of strips.

and

*This is part of the C2 (Core Mathematics 2) module of the A-level Mathematics text.*

Dividing and Factoring Polynomials / Sequences and Series / Logarithms and Exponentials / Circles and Angles / Integration

**Appendix A: Formulae**