# A-level Mathematics/AQA/MPC3

## Contents

## Functions[edit]

### Domain and range of a function[edit]

In general:

- is called the
**image**of . - The set of permitted values is called the
**domain**of the function - The set of all images is called the
**range**of the function

### Modulus function[edit]

The **modulus** of , written , is defined as

## Differentiation[edit]

### Chain rule[edit]

The **chain rule** states that:

If is a function of , and is a function of ,

### Product rule[edit]

The **product rule** states that:

If , where and are both functions of , then

An alternative way of writing the product rule is:

### Quotient rule[edit]

The **quotient rule** states that:

If , where and are functions of , then

An alternative way of writing the quotient rule is:

*x* as a function of *y*[edit]

In general,

## Trigonometric functions[edit]

### The functions cosec *θ*, sec *θ* and cot *θ*[edit]

### Standard trigonometric identities[edit]

### Differentiation of sin *x*, cos *x* and tan *x*[edit]

### Integration of sin(*kx*) and cos(*kx*)[edit]

In general,

## Exponentials and logarithms[edit]

### Differentiating exponentials and logarithms[edit]

In general,

### Natural logarithms[edit]

If , then

It follows from this result that

## Integration[edit]

### Integration by parts[edit]

### Standard integrals[edit]

### Volumes of revolution[edit]

The volume of the solid formed when the area under the curve , between and , is rotated through 360° about the -axis is given by:

The volume of the solid formed when the area under the curve , between and , is rotated through 360° about the -axis is given by:

## Numerical methods[edit]

### Iterative methods[edit]

An **iterative** method is a process that is repeated to produce a sequence of approximations to the required solution.

### Numerical integration[edit]

**Mid ordinate rule**

**Simpson's rule**