**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 **

*Fractions*

L.O- To be able to multiply, divide, add and subtract fractions. Students should also be able to equalise the denominators of fractions and use this in more complicated fraction questions.

**Multiplying Fractions**

To multiply fractions, simply multiply the top and bottom separately.

**Example 1:**

**Steps:**

Multiply the ‘top numbers’ of the fractions together à this gives you the ‘top number’ of your answer.

Multiply the ‘bottom numbers’ of the fractions together à this gives you the ‘bottom number’ of your answer.

‘top numbers’ = numerators

‘bottom numbers’ = denominators

**Dividing Fractions**

To divide fractions, turn the 2^{nd} fraction upside down and then multiply the fractions as normal.

**Example 1:**

**Steps:**

- Turn the 2
^{nd}fraction upside down - Now, multiply the two fractions (as done above)

**Adding Fractions**

To add fractions, you add the **top line only** but only if the denominators (bottom numbers) are the same.

**Example 1:**

**Example 2:**

**Steps:**

Check whether the denominators of the fractions are the same. If they are the same;

- add the ‘top numbers’ of the fractions together à this gives you the top number of your answer
- the bottom number does not change

If they are different – there is an extra step before you can carry out the main steps.

you will need to **equalize the denominators** i.e. ‘make the denominators of the fractions the same’

**Subtracting Fractions**

To subtract fractions, you subtract the **top line only**, but only if the denominators (bottom numbers) are the same.

**Example 1:**

**Example 2:**

**Steps:**

Check whether the denominators of the fractions are the same. If they are the same;

- Subtract the ‘top numbers’ of the fractions à this gives you the top number of your answer
- the bottom number does not change

If they are different – there is an extra step before you can carry out the main steps

- you will need to equalize the denominators FIRST i.e. ‘make the denominators of the fractions the same’

**Equalizing the denominator**

This means ‘*making the denominators of fractions the same*.’

This will need to be done during addition/subtraction of fractions when the denominators of the fractions are not the same. It is also done when ordering fractions.

**Example 1:**

Equalize the denominator of the following fractions

The multiplier in this case is 2

Then, multiply the current numerator by this multiplier

**Steps:**

- Find a common denominator of the two fractions.

You can multiply the two denominators together and this will give you a common denominator!

- Next, we need to put both fractions over 14 i.e. make 14 the denominator for both of them

In order to do this;

- Work out what the current denominator must be multiplied by to become the common denominator. This number is ‘the multiplier’
- Multiply the numerator by this number

This will give you your new fraction.

- Repeat step 2 for the other fractions in the question.

Here is a question in which you first need to equalize the denominators.

**Example 1:**

This is an addition (see above).

The denominators are not the same, so first you must equalize the denominators of these true fractions.

The multiplier for the first fraction is 10.

The multiplier for the second fraction is 9.

The same method would be carried out if you had to subtract fractions with different denominators.

**Ordering fractions**

You will need to equalize the denominator for all the fractions before you can put them in order.

**Example 1:**

**Steps:**

- Find a common denominator of the fractions
- Equalize the denominator of the fractions
- Place the fractions in the order stated in the question

Remember Ascending order = fractions increase in size

Descending order = fractions decrease in size