 # Formula Sheet

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## Formula Sheet

### GCSE Maths Formula Sheet

#### Rules of Indices

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 = 32 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.

#### The nth Term

nth term = dn + (a - d)

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

#### Angle Formulae

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°.

#### Parallel Lines

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).

#### Sin, Cos, Tan

SOHCAHTOA

Rule 1: Sine is Opposite over Hypotenuse

Rule 2: Cos is Adjacent over Hypotenuse

Rule 3: Tan is Opposite over Adjacent

#### Pythagoras

Rule:

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

or, a2 + b2 = c2

#### Area

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

#### Surface Area

Curved Surface of a Cylinder: Area = 2π rh

Surface of a Sphere: Area = 4π r2

Curved Surface of a Cone: Area = π rl

#### Volume

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

#### Polygons and their angles

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

Circumference = 2π r or, Circumference = πd

Area = π r2

#### Similarity #### Graphs

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

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)

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