Students keep making the same mistakes in their GCSE Maths exams. Inspired by the examiner's reports find out where students are losing vital marks, so that you can avoid the common slip-ups!

# 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)**