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In algebra, letters are used to represent arbitrary numbers. The various techniques of algebra, for example, collecting like terms or factorising etc. can be applied quite generally. As a result, many problems can be solved easily by expressing them in the form of an equation to which these general techniques can be applied. The origin of the term algebra lies in the Arabic ‘al-jabr w’al-muqabala’ which means ‘restoration and reduction’. It appears first in the writing of the mathematician Muhammad al-Khwarizmi (c780 to 850 AD). The topics are listed here in approximately the order they should be studied, though the order becomes less important further down the list.

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Of all the branches of GCSE Maths, the topics concerned with numbers are those which occur most frequently in everyday life. Simple arithmetic: addition, subtraction, multiplication and division through to fractions, percentages and ratios are used routinely by many both at home and at work.

The number system we use today originated from India, dating back at least to 595 AD. Introduction of this system to the West was largely due to translations of the work of the Arab mathematician Muhammad al-Khwarizmi - see the introduction to algebra (al-jabr). Interestingly, the earliest appearance of zero in this number system is almost 300 years later in 876 AD. The topics are listed here in approximately the order they should be studied, though the order becomes less important further down the list.

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The shape topic in GCSE Maths deals with a broad range of ideas connected with the properties of 2-d and 3-d shapes. Topics such as area, volume and symmetry are concerned mostly with the shapes themselves. Other topics, such as trigonometry and Pythagoras' theorem use the properties of triangles to calculate angles and distances in other contexts. The topics are listed here in approximately the order they should be studied, though the order becomes less important further down the list.

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