GCSE maths is a demanding subject and the syllabus covers a number of subjects. If you’re overwhelmed by the task that lies ahead, you’re in the right place. At Exam Papers Plus, we publish GCSE maths revision packs and have plenty of experience about how to perform well in the exam. In this article, will delve a little deeper into the GCSE maths syllabus, helping you to prepare for the exam.
The GCSE maths test subjects are:
 Number
 Algebra
 Ratio, proportion and rates of change
 Geometry and measures
 Probability
 Statistics
GCSE maths has a Foundation tier (grades 1 – 5) and a Higher tier (grades 4 – 9). Students must take three question papers at the same tier and all question papers must be taken in the same series.
The six subject areas on the GCSE maths syllabus are split into individual topics. Below we have provided a useful breakdown of each:

Number
Structure and Calculation
 Order positive and negative integers, decimals and fractions
 Use the symbols =, ≠, <, >, ≤, ≥
 Apply the four operations to integers, decimals and simple fractions and mixed numbers – both positive and negative
 Understand and use place value
 Recognise and use relationships between operations, including inverse operations
 Use conventional notation for priority of operations, including brackets, powers, roots and reciprocals
 Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem
 Apply systematic listing strategies
 Use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5
 Calculate exactly with fractions
 Calculate with and interpret standard form A × 10n, where 1 ≤ A < 10 and n is an integer (with and without a calculator)
Fractions, Decimals and Percentages
 Work interchangeably with terminating decimals and their corresponding fractions
 Change recurring decimals into their corresponding fractions and vice versa (Higher Tier only)
 Interpret fractions and percentages as operators
Measures and Accuracy
 Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
 Estimate answers
 Check calculations using approximation and estimation, including answers obtained using technology
 Round numbers and measures to an appropriate degree of accuracy

Algebra
Notation, Vocabulary and Manipulation
 Use and interpret algebraic notation
 Coefficients written as fractions rather than as decimals
 Use of brackets
 Substitute numerical values into formulae and expressions, including scientific formulae
 Understand and use the concepts and vocabulary of expressions, equations, formulae, inequalities, terms and factors
 Simplify and manipulate algebraic expressions by: collecting like terms; multiplying a single term over a bracket; taking out common factors; simplifying expressions involving sums, products and powers, including the laws of indices
 Understand and use standard mathematical formulae
 Rearrange formulae to change the subject
 Interpret simple expressions as functions with inputs and outputs
Graphs
 Work with coordinates in all four quadrants
 Plot graphs of equations that correspond to straightline graphs in the coordinate plane
 Identify and interpret gradients and intercepts of linear functions graphically and algebraically
 Recognise, sketch and interpret graphs of linear functions and quadratic functions
 Plot and interpret graphs, and graphs of nonstandard functions in real contexts
Solving Equations and Inequalities
 Solve linear equations in one unknown algebraically
 Find approximate solutions using a graph
 Students should know the conventions of an open circle on a number line for a strict inequality and a closed circle for an included boundary
Sequences
 Generate terms of a sequence from either a termtoterm or a positiontoterm rule
 Recognise and use sequences of triangular, square and cube numbers and simple arithmetic progressions
 Deduce expressions to calculate the nth term of linear sequences

Ratio, Proportion and Rates of Change
 Change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g. speed, rates of pay, prices) in numerical contexts
 Use scale factors, scale diagrams and maps
 Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
 Use ratio notation, including reduction to simplest form
 Divide a given quantity into two parts in a: given part : part or part : whole ratio
 Express the division of a quantity into two parts as a ratio
 Apply ratio to real contexts and problems
 Express a multiplicative relationship between two quantities as a ratio or a fraction
 Understand and use proportion as equality of ratios
 Relate ratios to fractions and to linear functions
 Define percentage as ‘number of parts per hundred’
 Interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively
 Express one quantity as a percentage of another
 Compare two quantities using percentages
 Work with percentages greater than 100%
 Solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematics
 Solve problems involving direct and inverse proportion, including graphical and algebraic representations
 Use compound units such as speed, rates of pay, unit pricing
 Compare lengths, areas and volumes using ratio notation scale factors

Geometry and Measures
Properties and Constructions
 Use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries
 Use the standard conventions for labelling and referring to the sides and angles of triangles Draw diagrams from written description
 Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
 Understand and use alternate and corresponding angles on parallel lines
 Derive and use the sum of angles in a triangle
 Derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus
 Identify, describe and construct congruent and similar shapes
 Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference
Mensuration and Calculation
 Use standard units of measure and related concepts
 Measure line segments and angles in geometric figures
 Know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms
Vectors
 Describe translations as 2D vectors
 Use vectors to construct geometric arguments and proofs (Higher Tier only)

Probability
 Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees
 Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
 Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 to 1 probability scale
 Apply the property that the probabilities of an exhaustive set of outcomes sum to 1 apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to 1
 Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams
 Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities

Statistics
 Interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, and know their appropriate use
 Interpret, analyse and compare the distributions of data sets from empirical distributions
 Apply statistics to describe a population
 Use and interpret scatter graphs of bivariate data
 Recognise correlation
For further detail about the GCSE maths syllabus, please visit the AQA website.
One of the most effective ways to revise for the GCSE maths exam is to use practice tests under exam conditions. When introduced early into your revision schedule, our GCSE maths practice packs can help to improve your confidence in the lead up to test day.
Our practice packs are all written and developed by former GCSE maths examiners and markers. We’ve also included questions that students find challenging, so you’ll have experience of tackling the most difficult questions.
If you are preparing for the GCSE maths exam, we can highly recommend the following practice resource:
GCSE Mathematics: Key Skills
All of our GCSE packs are available immediately after download.
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