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Table of Contents

 

 Unit 1 | Algebra

Page 1 | Expressions and Formulae

Page 2 | Index notation

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 1 | Transformations

Page 2 | Symmetry

Page 3 | Coordinates

Page 4 | Perimeter, Area, Volume

Page 5 | Circle geometry

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 6 | Decimals

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

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