# A-level Mathematics/OCR/C3/Formulae

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< A-level Mathematics | OCR | C3

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

## Contents

## Transformations of Graphs[edit]

#### Reflection[edit]

- is a reflection of through the x axis.
- is a reflection of through the y axis.
- is a reflection of when y < 0, through the x-axis.
- is a reflection of when x < 0, through the y-axis.
- is a reflection of through the line y = x.

Note: exists only if is bijective, that is, one-to-one and onto.

#### Stretching[edit]

- is stretched toward the x-axis if and stretched away from the x-axis if . In both cases the change is by a units.
- is stretched away from the y-axis if and stretched toward the y-axis if . In both cases the change is by b units.

### Translations[edit]

- is a translation of f(x) by h units to the right.
- is a translation of f(x) by h units to the left.
- is a translation of f(x) by k units upwards.
- is a translation of f(x) by k units downwards.

## Natural Functions[edit]

- , where y(t) is the final value, is the initial value, k is the growth constant, t is the elapsed time.
- , k for calculations involving half-lives.

## Trigonometry[edit]

### Reciprocal Trigonometric Functions and their Inverses[edit]

### Angle Sum and Difference Identities[edit]

Note: The sign means that if you add the angles (A+B) then you subtract in the identity and vice versa. It is present in the cosine identity and the denominator of the tangent identity.

### Double Angle Identities[edit]

### Combination of Trigonometric Functions[edit]

Using radians r = amplitute α = phase.

*where*

*where*

## Differentiation[edit]

- If , then
- If , then
- If , then
- If , then
- If , then

## Integration[edit]

For volumes of revolution:

## Numerical Methods[edit]

**Simpson's Rule**

where and n is even

*This is part of the C3 (Core Mathematics 3) module of the A-level Mathematics text.*