GCSE Maths Formula Sheet

Rule 1: When you multiply indices of the same number you add the powers.

For example: 5⁴x 5³= 5⁴⁺³= 5⁷

Rule 2: When you divide indices of the same number you subtract the powers.

For example:

Rule 3: Indices outside a bracket multiply.

For example: (3²)⁴ = 3^{2 x 4} = 3⁸

Rule 4: Negative indices mean reciprocal, i.e. 'one over....' or 'put on the bottom of a fraction'.

For example:

Rule 5: When the power is a fraction the top of the fraction (numerator) is a power and the bottom of the fraction is a root.

For example:

Rule 6: Anything to a power of 1 is just itself and we normally don't bother putting the 1 there.

For example: 5¹ is just 5.

Anything to a power of 0 is equal to 1, it doesn't matter what number it is!

For example: 10⁰ = 1, 2⁰ = 1, x⁰ = 1, etc.

n^th term = dn + (a - d)

For example: 6, 11, 16, 21, ... for this sequence d = 5, a = 6

Rule 1: Angles around a single point add up to 360^°.

Rule 2: Angles on a straight line add up to 180°.

Rule 3: Vertically opposite angles are equal. (This is when two straight lines cross!).

Rule 4: Angles in a triangle add up to 180°.

Rule 5: Angles in a quadrilateral add up to 360°.

When a straight line crosses two parallel lines there are more angle facts we can look for and use!

Rule 1: Corresponding angles are equal - these are angles in a letter 'F'.

Rule 2: Alternate angles are equal - these are angles in a letter 'Z'.

Rule 3: Supplementary angles add up to 180° - these are angles in a letter 'U' or 'C' (when the 'U' and the 'C' are made of three straight sides, of course).

SOHCAHTOA

Rule 1: Sine is Opposite over Hypotenuse

Rule 2: Cos is Adjacent over Hypotenuse

Rule 3: Tan is Opposite over Adjacent

Rule:

The square on the hypotenuse is equal to the sum of the squares on the other two sides

or, a² + b² = c²

Square: Area = Length²

Rectangle: Area = Length x Width

Right-angled Triangle: Area = ½ x Base x Height

Other Triangle: Area = ½ x Base x Perpendicular Height

Circle: Area = π r²

Trapezium: Area = Average of Parallel sides x Distance between them

Curved Surface of a Cylinder: Area = 2π rh

Surface of a Sphere: Area = 4π r²

Curved Surface of a Cone: Area = π rl

Cube: Volume = Length³

Cuboid: Volume = Length x Width x Height

Prism: Volume = Area of Cross-section x Length

Cylinder: Volume = π r²h

Sphere: Volume = ⁴/₃π r³

Prism: Volume = ¹/₃π r2h

For a regular polygon with 'n' sides, External angle:

For a regular polygon with 'n' sides, Internal angle:

Circumference = 2π r or, Circumference = πd

Area = π r²

The equation of a straight line is y = mx + c

The gradient, m:

Quadratic functions are written in the form y = ax² + bx + c

Cubics are in the form y = ax³ + bx² + cx + d

In a pie chart, to find out the frequency that each section represents measure the angle for the section then:

If we call a particular event 'A' then the probability of A happening is:

The 'and' rule:

p (A and B) = p (A) x p (B)

The 'or' rule:

p (A or B) = p (A) + p (B)