**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 **

*Area and Perimeter*

L.O – To be able to calculate the area of rectangles, triangles, parallelograms, trapeziums and also more complex shapes.

__Area of a rectangle__

The formula for the area of a rectangle is:

**Area = base x height**

**A = b x h**

**Example 1:**

**Steps:**

- Identify the length of the base and the height of the rectangle.
- Using the formula, A= b x h, substitute b and h for the values identified in step 1.Remember units! For area always add a
^{2 }, e.g. cm^{2}, m^{2}, km^{2}etc

__Area of a triangle__

The formula for the area of a triangle is:

**Area = **^{1}**/**_{2}** × base × height**

**A = **^{1}**/**_{2}**x b x h **

The height used must be the **perpendicular height**! This is especially important is you are not given a right angled triangle.

**Steps:**

- Identify the length of the base and the height of the triangle.
- Using the formula, A=
^{1}/_{2}x b x h, substitute b and h for the values identified in step 1.

**Example 1:**

**Steps:**

- Split the shape up into simpler shapes e.g. triangles, squares and rectangles Draw each shape out separately and label the lengths of the sides (base and heights).You may need to work out some new lengths using the diagram and the lengths given.
- Find the area of each of the separate shapes.
- Add the areas of the separate shapes together. This will give you the area of the complex shape!

__Area of complex shapes__

Sometimes, you will have to split up a complex shape into smaller shapes. You find the area of these smaller shapes and add them up to find the area of the original shape.

**Example 1:**

1.The two shapes that this complex shape is made up of

2.Area of rectangle = 4 x 6 = 24cm^{2}

Area of triangle = ½ x 4 x 6 = 12cm^{2}

3.Total area of complex shape = area of rectangle + area of triangle

=24cm^{2} + 12cm^{2}

=** 36cm ^{2}**

**Steps:**

- Split the shape up into simpler shapes e.g. triangles, squares and rectangles Draw each shape out separately and label the lengths of the sides (base and heights).You may need to work out some new lengths using the diagram and the lengths given.
- Find the area of each of the separate shapes.
- Add the areas of the separate shapes together. This will give you the area of the complex shape!

__Area of a parallelogram__

The formula for area of a parallelogram is;

Area = base x perpendicular height

A = b x h

It is really important that you use the **perpendicular height** and not just the height of one of the slanted sides for h!

**Example 1:**

- The length of the base = 7cm

The perpendicular height = 6cm

- A = b x h

= 7cm x 6cm

=** 42cm ^{2} **

**Steps:**

- Identify the length of the base and the perpendicular height of the parallelogram.
- Using the formula, A= b x h, substitute b and h for the values identified in step 1. Remember units!

Don’t forget à **use perpendicular height**!

__Area of a trapezium__

The formula for the area of a trapezium is;

A = ^{1}/_{2} × h × (a + b)

You must use the perpendicular height!

a and b are the lengths of the **two parallel sides** of the trapezium. It doesn’t matter which length is a/b.

**Example 1:**

- Length of the base = 6cm

Perpendicular height = 5cm

Length of a = 4cm

Length of b = 6cm

- A =
^{1}/_{2}× h × (a + b)

A = ½ x 5cm x (4cm +6cm)

A =** 25cm ^{2}**

__Perimeter__

** **The perimeter of a shape is the **distance around it.**

To work out the perimeter, all you have to do is add all of the sides of the shape together!

If you are given a complex shape, you may have to work out the length of some of the sides before you can find the perimeter.

**Steps:**

- Identify the length of the base and the height of the triangle.Also identify the lengths of the two parallel sides of the trapezium, a and b.
- Using the formula, A =
^{1}/_{2}× h × (a + b), substitute b, h, a and b for the values identified in step 1.