**Table of Contents**

** Unit 1 | Algebra**

Page 1 | Expressions and Formulae

Page 3| Solving Linear Equations

Page 4| Expanding and Factorising

Page 5| Factorising Quadratics and expanding double brackets

Page 6| Patterns and Sequences

Page 7| Simultaneous Equations

Page 8| Changing the subject of a Formula

Page 9| Adding , subtracting algebraic formulas

** Unit 2 |Graphs**

Page 1 | Straight line graphs

Page 2 | Graphs of Quadratic functions

** Unit 3 |Geometry and Measure **

Page 2 | Symmetry

Page 3 | Coordinates

Page 4 | Perimeter, Area, Volume

Page 6 | Measurement

Page 7 | Trigonometry

Page 8 | Pythagoras

Page 9 | Angles

Page 10 | Shapes

Page 11| Time

Page 12 | Locus

**Unit 4 | Numbers**

Page 1 | Speed, Distance and time

Page 2 | Rounding and estimating

Page 3 | Ratio and proportion

Page 4 | Factors, Multiples and primes

Page 5 | Powers and roots

Page 7 | Positive and negative numbers

Page 8 | Basic operations

Page 9 | Fractions

Page 10 | Percentages

** Unit 5 | Statistics and Probability **

Page 1 | Sampling data (MA)

Page 2 | Recording and representing data

Page 3 | Mean median range and mode

Page 4 | Standard deviation

**Unit 4 | Calculus **

*Equivalent Fractions*

**Fractions**represent a**portion of**the**whole**. Different fractions which represent an**equal amount of the whole**are called equivalent fractions.

- In order to
**find****different equivalent fractions**, we can**multiply**or**divide**both the**numerator**and**denominator**of the fractions we already have.

- For example, if we wanted to
**find**an**equivalent fraction of**, we could do this**multiplying both numbers by two**, which would give us**.**

**Example 1 :**

Take a look at this cake. We can cut it into **different numbers of slices** and still represent one half.

In the **first circle**, we can show a half by taking **one piece out of** a possible **two**, so this **is **

In the **second circle**, one half is shown by highlighting **2 pieces** **out of** a possible **four**, so this **is **

The third circle is and the fourth circle is .

As all of these **fractions **represent the same amount of space, we would say that they are **equivalent fractions**. We can see that the numerator and denominator of the first **fraction ** ** **have been **multiplied by 2, 3 **and **4** to get the other fractions.

4.** Equivalent fractions** can come in very useful when we need to **compare fractions** that have different **denominators**.

5.If we can use equivalent fractions to make **both fractions** have the same **denominator**, all we **have to do is compare **the** numerator**.

**Example 2 :**

Let’s say that we need to find out **whether ** ** **or is **larger **.

**First**, we need to**find a number**that both of the**denominators are factors**of (they fit into it a specific number of times).**8**and**12****both fit**into**24**so we’ll choose that as our new denominator. 7

**Secondly**, we need to find out what we need to multiply each fraction by so that it has a**denominator of 24**–**whatever**we’ve**done**to each of our**denominators**has to also be**done to the numerator**.

- If we
**compare the two fractions**, we can now clearly see that**6/8**must be**bigger than 8/12**, as the**numerator is bigger**when it is**converted**.

6. If you can see that the numerator and the denominator both have the same factor, you can divide them both by this factor, which is called **cancelling**.

7. Once a fraction cannot be cancelled anymore, it is said to be in its** simplest form**.

**Example 3 :**

The fraction we can use for our example is

Both 36 and 42 are in the 6 times table, so we can cancel by a factor of six.