Geometry and Measure

To draw constructions you need a pencil, ruler and a pair of compasses. Loci are used to identify areas that satisfy criteria such as a given distance from a point or halfway between two lines.

Pythagoras’ theorem allows us to calculate lengths in right-angled triangles. Right-angled triangles are seen in everyday life – from the dimensions of a television to a ladder resting against a wall.

Trigonometric relationships are very important in the construction and planning industry and allow precise calculation of unknown lengths and angles.

Scale factors ensure that a shape stays in the same proportions when the size is changed. This may be important when resizing photos or company logos to ensure the image does not become distorted.

Maps and scale drawings form a crucial part of everyday life. Scale drawings are useful in a variety of careers from surveyors, to town planning and architecture. We also need to understand bearings.

With international collaboration so important to industry and the economy, it is vital to be able to convert between metric and imperial units. Read through this GCSE maths study guide and learn how to convert kilometres to miles, calculate centimetres and millimetres to inches and feet, and learn the differences between litres, pints and gallons.

Dimensional analysis allows us to make inferences and deductions about formulae. It provides us with an alternative way to check our own calculations and those of others.

Compound measures are types of measure that involve two or more different units. Examples of compound measures include m/s, g/cm³, population per km² and miles per gallon.

Knowing how to find the perimeter or area of a shape can be useful in everyday life - from wrapping a present to buying a carpet. Use it in calculations to find the amount of materials needed or cost.

We can calculate the volume of 3D shapes to find their capacity or the amount of space they occupy. We can also find the surface area which indicates the total area of each of their faces.