If two shapes are similar, one is an enlargement of the other. This means that the two shapes will have the same angles and their sides will be in the same proportion (e.g. the sides of one triangle will all be 3 times the sides of the other etc.). angle A = angle D angle

# 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.

## Congruency

Basically, if two shapes are congruent, they are the same (shape and size). It is often useful to know whether two triangles are congruent. Two triangles are congruent if any one of the following is true: -All three sides of one triangle are the same length as all three sides of the other triangle (i.e.

## Three-figure Bearings

A bearing is the angle, measured clockwise from the north direction. Below, the bearing of B from A is 025 degrees (note 3 figures are always given). The bearing of A from B is 205 degrees. Example: A, B and C are three ships. The bearing of A from B is 045º. The bearing of

## Standard Deviation Formulas

Lower case sigma means ‘standard deviation’. Capital sigma means ‘the sum of’. x bar means ‘the mean’ The standard deviation measures the spread of the data about the mean value. It is useful in comparing sets of data which may have the same mean but a different range. For example, the mean of the following

## Sampling (Statistics)

When examining a particular population it is usually advisable to choose a small sample in such a way that everyone is represented. This is not easy and requires careful thought about sample size and composition. Often questionnaires are devised to identify the required information. These need to be idiot proof, so questions need to cover

## Representing Data

There are a number of ways of representing data diagrammatically. (See also Histograms). Scatter Graphs These are used to compare two sets of data. A line of best fit is drawn, which should pass through as many points as possible. It should have roughly the same number of points above and below it. The less

## Probability

Introduction Probability is the likelihood or chance of an event occurring. Probability = the number of ways of achieving success the total number of possible outcomes For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible

## Histograms

Histograms are similar to bar charts apart from the consideration of areas. In a bar chart, all of the bars are the same width and the only thing that matters is the height of the bar. In a histogram, the area is the important thing. Example: Draw a histogram for the following information. Frequency: Height

## Cumulative Frequency

This is the running total of the frequencies. On a graph, it can be represented by a cumulative frequency polygon, where straight lines join up the points, or a cumulative frequency curve. Example: Frequency: Cumulative frequency: 4 4 6 10 (4 + 6) 3 13 (4 + 6 +

## Average

Mean There are four types of average: mean, mode, median and range. The mean is what most people mean when they say ‘average’. It is found by adding up all of the numbers you have to find the mean of, and dividing by the number of numbers. So the mean of 3, 5, 7, 3