# Formula Sheet

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## Formula Sheet

### GCSE Maths Formula Sheet

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

* For example:* 5

^{4}x 5

^{3}= 5

^{4+3}= 5

^{7}

*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:* (3^{2})^{4} = 3^{2 x 4 }= 3^{8 }

*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:* 5

^{1}is just 5.

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

* For example:* 10

^{0}= 1, 2

^{0}= 1, x

^{0}= 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,* a ^{2 }+ b^{2} = c^{2}*

*Square:* Area = Length^{2}

*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 r^{2}

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

*Curved Surface of a Cylinder:* Area = 2π rh

*Surface of a Sphere: *Area = 4π r^{2}

*Curved Surface of a Cone: *Area = π rl

*Cube: *Volume = Length^{3}

*Cuboid: *Volume = Length x Width x Height

*Prism:* Volume = Area of Cross-section x Length

*Cylinder:* Volume = π r^{2}h

*Sphere:* Volume = ^{4}/_{3}π r^{3}

*Prism:* Volume = ^{1}/_{3}π 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 r^{2}

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

The gradient, m:

Quadratic functions are written in the form *y = ax ^{2} + bx + c *

Cubics are in the form *y = ax ^{3} + bx^{2} + 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)**