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Shapes and Numeracy Tests

Many numeracy tests ask you to describe shapes in some way. You need to be able to identify different shapes and the number of sides each shape has.

Finding your angle

Angles are measured in degrees. For example, if a car spins 360 degrees, it spins all the way round, while the latitude of London is 53 degrees north of the equator. Confusingly, angle degrees are completely different from temperature degrees – the context usually makes clear which type of degrees you need to work with.

The four key types of angle you need to know about are:

  • An acute angle is less than 90º– a small angle that looks quite pointy. Remember this by thinking that a ‘cute’ angle is little.

  • A right angle is exactly 90º.

  • An obtuse angle is more than 90º but less than 180º.

  • A reflex angle is more than 180º. You can remember this by thinking of the doctor hitting the outside of your knee to test your reflexes – the angle on the outside of your knee is more than 180º!

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The shapes you need to know

The four basic two-dimensional (or flat) shapes you need to know and recognise are the square, rectangle, triangle and circle.

A few others you may need to know about are the pentagon (five sides), a hexagon (six sides) and an octagon (eight sides).

You may also need to know a few ways to describe triangles:

  • An equilateral triangle has three sides of the same length (‘equi-’ means ‘the same’, and ‘lateral’ means ‘side’). You may also need to know that each angle in an equilateral triangle is 60º.

  • An isosceles triangle has two sides of the same length and one different. Two of the angles in an isosceles triangle are the same, and the other different – it’s the one between the sausages that’s different.

  • A scalene triangle has sides of all different lengths.

  • A right-angled triangle has one corner with an angle of 90º – a right-angled triangle can be either scalene or isosceles.

In three dimensions, the main shapes you need to know about are these:

  • The cube: the shape of a die – a box where all six faces are equal-sized squares.

  • The cuboid: the shape of a shoe box – all six faces are rectangles.

  • The sphere: the shape of a ball.

  • The cone: the shape of an ice cream cone (at least, the pointy bit!)

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