The gradient of a straight line is how steep it is. It can be calculated from a given set of coordinate points. There are three special cases of straight lines: parallel, horizontal and vertical.

Arc length is a fraction of circumference. Area of a sector is a fractions of the area of a circle. Both can be calculated using the angle at the centre and the diameter or radius.

The volumes of standard 3D solids can be found using specific formulae. In this SQA National 5 Maths revision guide, we'll go through how to work out the volume of a cylinder, sphere, hemisphere, cone, prism, and composite shapes.

Pythagoras Theorem states that for a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Angles in a triangle add up to 180° and quadrilaterals add up to 360°. Angles can be calculated inside semicircles and circles, as well as with perpendicular bisectors and tangents.

Similar figures are identical in shape, but not necessarily in size. A missing length, area or volume on a reduction/enlargement figure can be calculated by first finding the scale factor.

A vector describes a movement from one point to another. 2D vectors are added from nose to tail giving a new line from the starting point to the final point..

A vector describes a movement from one point to another. 3D vectors exist in the xyz plane. The 3D coordinates for any point have three values.

Vector components describe the separate x, y and z values of a vector. When working with vectors, components can be added or subtracted separately.

The magnitude of a vector is its size. It can be calculated from the square root of the total of the squares of of the individual vector components.