**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 **

*Factors, Multiples and Primes*

L.O – To be able to find the multiples, factors and prime factors of numbers. Also, be able to find the LCM and HCF of numbers.

** **

__Multiples__

The multiples of a number are its times table.

For example, the multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 etc

11 are 11, 22, 33, 44, 55, 66 etc

25 are 25, 50, 75, 100, 125 etc

__Factors__

The factors of a number are all the numbers that divide into it (without remainders).

So, 2 and 9 are factors of 18. However 18 has many more factors including 3, 6 etc

By following the method below, you will be sure to find all the factors of a number.

**Example 1:**

Find the factors of 12

**1. **Draw a box in which you will insert all the factors. Write down 1at the front and 12 at the end

2.Work onwards from one to 2, 3, 4, 5, etc and see if these numbers divide into the number given in the question

– The next number is 2

2 x 6 = 12, so 2 and 6 are factors

The next number is 3

3 x 4 = 12

The next number is 4.

However we have already put 4 into the table. So this is where we stop

**Steps:**

- Draw a box. Put the number 1 at the front and the number given in the question at the end. These are the first pair of factors
- Work onwards from 1 to 2, 3, 4, 5 etc

- The next number is 2. See if 2 divides into the number given in the If it does put 2 in the next box at the beginning and its corresponding factor at the end.

E.g. if the number in the question was 12à 2 x 6 = 12

- The next number is 3. Repeat the same steps as above.
- Not all numbers will divide into the number in the question. If this is the case
**do not insert**this into the table. Then move onto the next number

- Eventually a factor will be
**repeated**. This is when you stop.

See the example above in order to understand these steps!

__Prime Factors__

Remember a prime number are numbers that don’t divide by anything apart from 1 and themselves. Examples include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 etc

In order the find the prime factors of a number, you must draw out a factor tree.

**Example 1:**

Find the prime factors of 210

– Start off with 210. Start ‘splitting the number up’ (this can be done in many ways).

– Then split the numbers again

– Once you reach prime numbers – put a circle around them/highlight them. These cannot be split anymore and are the prime factors.

The prime factors of 210 are 2, 3, 5 and 7

So, 210 **expressed as a product of its prime factors** = 2 x 3 x 5 x 7

In an exam, always write the numbers multiplied by one another

The steps are shown above for this type of question. Just remember to keep splitting the numbers up until you can’t split any futher!

__LCM – Lowest Common Multiple__

The lowest common multiple is the** smallest** positive number that is a multiple of two or more numbers i.e. it will divide by all the numbers in the question

In order to find the lowest common multiple you need to lists the multiples of the numbers in the question and find the smallest multiple which appears in all the lists.

**Example 1:**

Find the lowest common multiple (LCM) of 6 and 8.

- Multiples of 6 = 6, 12, 18,
**24**, 30, 36, 42, 48, 54, 60….

Multiples of 8 = 8, 16, **24**, 32, 40, 48, 56, 64, 72, 80….

- The smallest multiple that appears in both lists is 24

Therefore, the LCM of 6 and 8 is 24.

**Steps:**

- List the multiples of the numbers in the question i.e. write out their times tables.

Writeout 10 multiples to begin with, however you may need to go further into the times table if needed.

- Look at the lists you just wrote out. Find the
**smallest**number which appears in both lists.

This is the lowest common multiple.

__HCF – Highest Common Factor__

The highest common factor is the largest positive number which will divide into all the numbers in the question, without any remainders.

In order to find the highest common factor of numbers, you need to list the factors of all the numbers in the question. Then, find the largest factor which appears in all the lists.

**Example 1:**

Find the highest common factor (HCF) of 36 and 90

- Factors of 36 = 1, 2, 3, 4, 6, 9, 12,
**18**, 36

Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, **18**, 30, 45, 90

- The largest factor which appears in both lists is 18.

Therefore, the HCF of 36 and 90 is 18.

**Steps:**

- List all the factors of the numbers in the question.

You can do this using the method shown above under ‘Factors’

- Look at the lists you just wrote out. Find the largest number which appears in both lists.

This is the highest common factor (HCF).

Find the first 10 multiples of the following numbers

- 13
- 6
- 9
- 12

Find the prime factors of the following numbers. Give the answer as a product of prime factors

- 160
- 36
- 40
- 660

Find the HCF of the followingnumbers

- 72 and 96
- 128 and 320
- 48 and 84
- 45 and 27
- 24, 36 and 18

Find all the factors of the following numbers

- 35
- 64
- 84
- 13

Find the LCM of the following numbers

- 32 and 40
- 12 and 18
- 12 and 5
- 7 and 9
- 3, 6 and 7