A percentage is a fraction whose denominator is 100 (the numerator of a fraction is the top term, the denominator is the bottom term). So 30% = 30/100 = 3/10 = 0.3 To change a decimal into a percentage, multiply by 100. So 0.3 = 0.3 × 100 = 30% . Example: Find 25% of

# GCSE Maths Revision Notes & Study Guide for Students

Here you will find comprehensive GCSE Maths revision notes for students, including worksheets & PowerPoint lessons, that will save you 100's of hours of GCSE maths revision prep.

## Fractions

Introduction 1/2 means 1 divided by 2. If you try this on a calculator, you will get an answer of 0.5 . 3/6 means 3 divided by 6. Using a calculator, you will find that this too gives an answer of 0.5 . That is because 1/2 = 3/6 = 0.5 . Fractions such as

## Directed Numbers

Numbers can either be positive or negative. Often brackets are put around negative numbers to make them easier to read, e.g. (-2). If a number is positive, the + is usually missed out before the number. So 3 is really (+3). Adding and multiplying combinations of positive and negative numbers can cause confusion and so

## Travel Graphs – Distance & Time

Speed, Distance and Time The following is a basic but important formula which applies when speed is constant (in other words the speed doesn’t change): Speed = distance time Remember, when using any formula, the units must all be consistent. For example speed could be measured in m/s, distance in metres and time in seconds.

## Graphs

Equations of straight lines are in the form y = mx + c (m and c are numbers). m is the gradient of the line and c is the y-intercept (where the graph crosses the y-axis).

## Gradients

Finding the gradient of a straight-line graph It is often useful or necessary to find out what the gradient of a graph is. For a straight-line graph, pick two points on the graph. The gradient of the line = (change in y-coordinate)/(change in x-coordinate) . In this graph, the gradient = (change in y-coordinate)/(change in

## Quadratic Equations

A quadratic equation is an equation where the highest power of x is x². There are various methods of solving quadratic equations, as shown below. NOTE: If x² = 36, then x = +6 or -6 (since squaring either of these numbers will give 36). However, Ö36 = + 6 only. Completing the Square 9

## Matrices

Matrices are tables of numbers. The numbers are put inside big brackets. Matrices are given ‘orders’, which basically describe the size of the matrices. The order is the number of rows ‘by’ the number of columns. So a 2 by 3 matrix has 2 rows and 3 columns. Adding and Subtracting Adding and subtracting matrices

## Inequalities

a < b means a is less than b (so b is greater than a) a £ b means a is less than or equal to b (so b is greater than or equal to a) a ³ b means a is greater than or equal to b etc. a > b

## Indices

Indices/ Powers 3³ (‘3 to the power of 3’) and 5² (5 ‘to the power’ of 2) are example of numbers in index form. 3³ = 3×3×3 2¹ = 2 2² = 2×2 2³ = 2×2×2 etc. The ² and ³ are known as indices. Indices are useful (for example they allow us to represent

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