Transformations Transformations of a figure are changed in the image or the way the figured is presented. Methods to transform figures are translation, rotation, reflection and enlargement. Translation Sliding down on a sliding board or moving an object, this motion is an example of translation. Translation is moving a figure from one place to another.

# 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.

## Surds

Surds are an expression in root form such as square root, cube root and other in a root symbol. A surd cannot be simplified to remove the root symbol. It does not have an exact decimal value and cannot be represented by a fraction. The decimal value just continues on and on to infinity, neither

## Standard Deviation Formulas

As we know, random variables have few common numerical characteristic – average value, variation and standard deviation. Now we consider standard deviation of the random variable X. Formulas for calculation variation are next: 1. Population variation for random variable, which is defined by sequence \(x_{i}\) : \(\sigma^2 = \frac{1}{n}\sum_{i=1}^n (x_{i}-\overline{x})^2\) or for discrete random variable:

## Sampling (Statistics)

Several boxes of apples are undergoing a quality check. What will be the easiest way to do it? Checking all the apples piece by piece will be time-consuming. Taking a few apples from each box to examine is the most convenient way. This process is called sampling. The number of all the apples in every

## Ruler and Compass Construction

Let’s learn to construct geometric figures using a ruler and compass. Shapes, angles and lines must be drawn accurately. A ruler is used for a straightedge or drawing straight lines. A compass is used to draw a circle. When making constructions measuring devices are not necessarily used to measure distances because they’re used to make

## Representing Data

Representing Data This is the process of selecting samples through different sampling techniques. Then, gather the necessary information. The next step is to organise and present information in a way that can easily analysed and interpreted. There are many ways to represent the data. Scatter Diagrams Scatter diagrams are used to describe and compare two

## Quadratic Equations

A quadratic equation is an equation whose power is in the second degree. In an equation, at least one of the variables is squared. In finding the missing value, it can be solved by factoring, completing the square and using the quadratic formula. Example: \( x^2\) + 2x +1 = 0 The first term \(x^2\)

## Proportions

Proportion is represented by two equal ratios. There is direct and indirect proportion. With direct proportion, the two variables change at the same rate. Direct Proportion With direct proportion, the two variable change at the same time. In direct proportion, as the first variable increases (decreases), the second variable also increases (decreases). In mathematical statements,

## Matrices

A matrix is an arrangement of numbers to organise data and solve variables. It’s a way to represent information using a table of numbers. Matrices organise numbers inside a big bracket. The order of the matrix states the size of matrices. The numbers are arranged in rows and columns. Example 1: \(A=\begin{bmatrix}2 & 4 \\-3

## Histograms

Histograms A histogram is a graph that is made up of vertical lines of equal bases centred at the class midpoints. It is similar to bar charts. However, in bar charts, all bars are the same width in the bar and the height shows the difference. The area of the bases is important in a

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