**Table of Contents**

**Algebra**

- Expressions and Formulae
- Writing Formulae
- Solving Formulae
- Changing the Subject of a Formulae

- Inequalities
- Number Lines
- Solving Inequalities

- Equations
- Solving Equations
- Equations with Brackets
- Equations with Fraction

- Graphs
- Straight Line Graphs ( y = mx + c )

- Patterns and Sequences
- Basic Patterns
- Linear Sequences & n
^{th}term - Quadratic Equations

*Writing Formula *

**L.O to be able to write and understand algebraic formulae for word problems** Formulae are a way of **rewriting problems** or **describing a rule**. They are written in **algebraic form** which means that **letters** are used. However the main element that shows that something is a **formulae** is that it will contain an **= sign**. Without even thinking about it, you have already been using formulae in maths before; for instance when working out the **area of a triangle**. Here the **base** and **perpendicula****r height**have been **abbreviated**, shortened, to** b** and** h**. This is exactly the point of formulas, to make solving problems later on easier, in such a way that any measurement can be applied to the formulae. Similarly you have already used **formulas** when working out other problems (notably areas) for example: Note how each of these formulas have an = sign. Now you are familiar with what formulas look like, it is now time to substitute values into formula As shown above, **formulae** can be used to help solve problems. However you need to be able to **write formulae** before you can **solve** or manipulate them further. For instance if in a supermarket you see an **apple** for **20p** and you wanted to buy **3apples**, you would mentally apply the following calculation: **1**apple is **20p** **2** apples are (20 X **2**) = 40p **3** apples are (20 X** 3**) = 60p So the **formula** to work out the cost of buying a number of apples is: . Cake baskets are £50 each. Samantha has many friends coming and wants a formula to help calculate the cost. In this example you would do as before: 1 basket = £50 **2** baskets are (50 X **2**) = £100 **3** baskets are (50 X **3**) = £150

**Cost = 50 x number of basket being bought**

Example 1: Jane is going to order some parcels online. Each parcel costs £5 but also has a small administration fee of £2.50 for each order processed. Write a formula to calculate the cost of one of Jane’s orders. Example 2: Aqif is having a banquet. The cost of a 3 course meal per adults is £15, per child is £6 and for younger children is £3. There is also a fee of £35 for hiring the hall. Write a formula to calculate the cost of Aqif’s banquet. Example 3: A group of 6 friends are making a fruit basket containing: apples at 60p each, pears at 40p and oranges at 80p each. They decide to split the cost of the basket equally between them. Write a formula for the cost of each person. Example 4: Sarah is having a birthday party and wants to make 5 bags that contain a different number of toys (30p), sweets (50p) and messages (55p). Write a formula for a given number of items for 5 party bags.