# A-level Mathematics/OCR/C2/Appendix A: Formulae

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

## Contents

## Dividing and Factoring Polynomials[edit]

### Remainder Theorem[edit]

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 Theorem[edit]

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 Function[edit]

### The Laws of Exponents[edit]

- where c is a constant

### Logarithmic Function[edit]

The inverse of is which is equivalent to

Change of Base Rule: can be written as

### Laws of Logarithmic Functions[edit]

When X and Y are positive.

## Circles and Angles[edit]

### Conversion of Degree Minutes and Seconds to a Decimal[edit]

where X is the degree, y is the minutes, and z is the seconds.

### Arc Length[edit]

Note: θ need to be in radians

### Area of a Sector[edit]

Note: θ need to be in radians.

## Trigonometry[edit]

### The Trigonometric Ratios Of An Angle[edit]

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

Cosine | |||||

Sine | |||||

Tangent |

### Important Trigonometric Values[edit]

You need to have these values memorized.

0 | 0 | 1 | 0 | |

1 | 0 | - |

### The Law of Cosines[edit]

### The Law of Sines[edit]

### Area of a Triangle[edit]

### Trigonometric Identities[edit]

## Integration[edit]

### Integration Rules[edit]

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 Integrals[edit]

- , 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 Rule[edit]

Where:

### Midpoint Rule[edit]

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**