**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 **

*Polygons *

**L.O – To become familiar with the properties of regular polygons. Also be able to learn and use formulas associated with angles of polygons**

A polygon = a shape with many sides.

A **regular polygon** = a shape where all the sides and the angles are the same

Here are the regular polygons you should be familiar with;

**Equilateral Triangle:**

3 sides

3 lines of symmetry

Rotational symmetry order 3

**Square:**

4 sides

4 lines of symmetry

Rotational symmetry order 4

**Regular Pentagon:**

5 sides

5 lines of symmetry

Rotational symmetry order 5

**Regular Hexagon:**

6 sides

6 lines of symmetry

Rotational symmetry order 6

**Regular Heptagon:**

7 sides

7 lines of symmetry

Rotational symmetry order 7

**Regular Octagon:**

8 sides

8 lines of symmetry

Rotational symmetry order 8

*Also remember*

- Nonagon (9 sides)
- decagon (10 sides)

**Angles in Polygons:**

Make sure you understand what an interior and exterior angle is

Here are the relevant formulas that need to be learnt!

*As the examples show, you may need to use several formulas to work out an angle*

*Note – there may be more than one way to find the answer using these formulas. So if one way doesn’t work for you, try another formula/method!*

**Example 1:**

Find the interior angle of a regular hexagon

- Using, Sum of Interior Angles = (n – 2) x 180°, where n = 6

= (6 – 2) x 180°

= 4 x180°

= 720°

- 720° is the sum of interior angles. We need to divide this by the number of sides to find the value of a single interior angle

720°/6 = **120°**

- Interior angle =
**120°**

**Example 2:**

Calculate the exterior angle of a regular nonagon and hence, find the interior angle

- Sum of Exterior Angles = 360°
- To find the value of a single exterior angle, we need to divide 360° by the number of sides

360°/n = **40°**

- Interior Angle = 180° – Exterior Angle

= 180° – 40°

= **140°**

- Exterior Angle =
**40°**and Interior Angle =**140°**

**Example 3:**

The interior angles of a regular polygon are each 120°. Calculate the number of sides

- The interior angles are 120° so the exterior angles = 180° – interior angles

= 180° – 120°

= 60°

- We know that exterior angle = 360°/n

n = 360°/exterior angle (by rearranging above formula)

n = 360°/ 60°

n = **6**

– This regular polygon has **6** sides