**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 **

*Scatter Graphs*

**L.O- To be able to draw scatter graphs along with a line of best fit. Also, understand and be able to identify a positive, negative or no correlation shown by graphs.**

A scatter graph is a diagram which is used to compare two variables.

**Example 1:**

Draw a scatter graph using the following results

- Label one axis of the graph as Age and the other axis of the graph as Shoe Size. Also, work out the scale of each graph.

2.Plot the graph. The data is simply used as coordinates

.

**Steps:**

- Label the two axis of the graph with the two variables. Also work out the scale of each axis using the range of data in each variable.
- Plot the graph! This is very simply as you use the data provided as coordinates.

Draw a line of best fit if possible (sometimes the points will be too scattered and you will not be able to draw a line of best fit).

A line of best fit should go through as many points as possible. There should be approximately the same number of points above and below the line as well.

__Correlation__

Scatter Diagrams tells us whether there is a relationship between the two variables that have been plotted. The relationship is described as a correlation. A scatter graph may show positive correlation, negative correlation or no correlation.

Positive Correlation

This graph tells us that as the age of a person increases, their height also increases. This type of correlation tells you that as one variable increases, the other variable also increases

__Negative Correlation__

This type of correlation tells you that as one variable increases, the other variable decreases.

This graph tells us that as the age of a car increases, its value decreased.

__No Correlation__

This type of correlation tells you that there is no relationship between the two variables.

This graph tells us that there is not relationship between shoe size and yearly income.

__Using the Line of Best Fit__

The line of best fit can be used to predict the value of one variable when the other is known.

**Example 1:**

Use this scatter graph and the line of best fit which has already been drawn to predict the shoe size of somebody aged 5.

- Extrapolate the line of best fit so that is extends down to age 5.

2.From Age 5 on the x axis ( the value given in the question) , move up until you reach the line of best fit and read off the shoe size value.

**Steps:**

- Extrapolate the line of best fit as needed so that is extends up/down to the value you are trying to predict.
- From the value you are given in the question move up/across to the line of best fit and read off the corresponding value on the x/y axis.