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The topics listed below are for AQA GCSE Maths, with exam codes:
– Foundation 8300F
– Higher 8300H
The list provides everything you need for your AQA GCSE Maths exam, with topics broken in to the headings given by the exam board. More information is available here:
[https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-8300/specification-at-a-glance]
For samples questions and papers, please click this link:
Everything you need to know about your GCSE (9-1) Maths specifications can be found here.
Basic Foundation Content
order positive and negative integers, decimals and fractions use the symbols =, ≠, <, >, ≤, ≥
Notes: including use of a number line.
Basic Foundation Content
apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative understand and use place value (eg when working with very large or very small numbers, and when calculating with
decimals)
Notes: including questions set in context.
Knowledge and understanding of terms used in household finance, for example profit, loss, cost price, selling price, debit, credit, balance, income tax, VAT and interest rate.
Basic Foundation Content
recognise and use relationships between operations, including inverse operations (eg cancellation to simplify calculations and expressions) use conventional notation for priority of operations, including brackets, powers, roots and reciprocals
Basic Foundation Content
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
Notes: prime factor decomposition including product of prime factors written in index form.
Basic Foundation Content
apply systematic listing
strategies
Higher Content Only
including use of the product rule for counting
Notes: including using lists, tables and diagrams.
Basic Foundation Content
use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5
Higher Content Only
estimate powers and roots of any given positive number
Notes: including square numbers up to 15 × 15
Students should know that 1000 = 10³ and 1 million = 106
Additional Foundation Content
calculate with roots, and with integer indices
Higher Content Only
calculate with fractional indices
Basic Foundation Content
calculate exactly with fractions
Additional Foundation Content
calculate exactly with
multiples of π
Higher Content Only
calculate exactly with surds simplify surd expressions involving squares
(eg √12 = √(4×3)= √4 × √3=2 3 ) and rationalise denominators
Basic Foundation Content
calculate with and interpret
standard form A × 10n
, where
1 ≤ A < 10 and n is an integer
Notes: with and without a calculator.
Interpret calculator displays.
Basic Foundation Content
work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8 )
Higher Content Only
change recurring decimals into their corresponding fractions and vice versa
Notes: including ordering.
Basic Foundation Content
identify and work with fractions in ratio problems
Basic Foundation Content
interpret fractions and percentages as operators
Notes: including interpreting percentage problems using a multiplier.
Basic Foundation Content
use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
Notes: know and use metric conversion factors for length, area, volume and capacity.
Imperial/metric conversions will be given in the question.
Basic Foundation Content
estimate answers
check calculations using approximation and estimation, including answers obtained using technology
Notes: including evaluation of results obtained.
Basic Foundation Content
round numbers and measures to an appropriate degree of accuracy (eg to a specified number of decimal places or significant figures)
Additional Foundation Content
use inequality notation to specify simple error intervals due to truncation or rounding
Notes: including appropriate rounding for questions set in context.
Students should know not to round values during intermediate steps of a calculation.
Additional Foundation Content
apply and interpret limits of
accuracy
Higher Content Only
including upper and lower bounds
Basic Foundation Content
Notes: it is expected that answers will be given in their simplest form without an explicit instruction to
do so.
Basic Foundation Content
substitute numerical values into formulae and expressions, including scientific formulae
Notes: unfamiliar formulae will be given in the question.
See the Appendix for a full list of the prescribed formulae
Basic Foundation Content
understand and use the concepts and vocabulary of expressions, equations, formulae, inequalities, terms and factors
Additional Foundation Content
to include identities
Notes: this will be implicitly and explicitly assessed.
Basic Foundation Content
simplify and manipulate algebraic expressions by:
Additional Foundation Content
simplify and manipulate algebraic expressions (including those involving surds) by:
Higher Content Only
simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by:
Basic Foundation Content
understand and use standard mathematical formulae rearrange formulae to change the subject
Notes: including use of formulae from other subjects in words and using symbols.
See the Appendix for a full list of the prescribed formulae.
Basic Foundation Content
know the difference between an equation and an identity
argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments
Higher Content Only
to include proofs
Notes: including use of formulae from other subjects in words and using symbols.
See the Appendix for a full list of the prescribed formulae.
Basic Foundation Content
where appropriate, interpret simple expressions as functions with inputs and outputs
Higher Content Only
interpret the reverse process as the ‘inverse function’ interpret the succession of two functions as a ‘composite function’
Notes: understanding and use of f x , f(g) x and f–1 (x) notation is expected at Higher tier.
See the Appendix for a full list of the prescribed formulae.
Basic Foundation Content
work with coordinates in all four quadrants
Basic Foundation Content
plot graphs of equations that correspond to straight-line graphs in the oordinate plane
Additional Foundation Content
use the form y = mx + c to identify parallel lines find the equation of the line through two given points, or through one point with a given gradient’
Higher Content Only
use the form y = mx + c to identify perpendicular lines
Basic Foundation Content
identify and interpret gradients and intercepts of linear functions graphically and algebraically
Additional Foundation Content
identify and interpret roots, intercepts and turning points of quadratic unctions graphically deduce roots algebraically
Higher Content Only
deduce turning points by completing the square
Notes: including the symmetrical property of a quadratic.
Basic Foundation Content
recognise, sketch and interpret graphs of linear functions and quadratic functions
Additional Foundation Content
including simple cubic functions and the reciprocal function y = 1/x with x ≠ 0
Higher Content Only
including exponential functions y = kx for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size
Higher Content Only
sketch translations and reflections of a given function
Basic Foundation Content
plot and interpret graphs, and graphs of non-standard functions in real contexts, to
find approximate solutions to problems such as simple
kinematic problems involving distance, speed and acceleration
Additional Foundation Content
including reciprocal graphs
Higher Content Only
including exponential graphs
Notes: including problems requiring a graphical solution.
Higher Content Only
calculate or estimate gradients of graphs and areas under graphs (including quadratic and other nonlinear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts
Notes: see also A14, R14 and R15
Higher Content Only
recognise and use the equation of a circle with centre at the origin find the equation of a tangent to a
circle at a given point
Basic Foundation Content
solve linear equations in one unknown algebraically find approximate solutions using a graph
Additional Foundation Content
including those with the unknown on both sides of the equation
Notes: including use of brackets
Basic Foundation Content
solve quadratic equations algebraically by factorising
find approximate solutions using a graph
Additional Foundation Content
including those that require rearrangement including completing the square and by using the quadratic formula
Notes: see also A11
Additional Foundation Content
solve two simultaneous equations in two variables (linear/linear) algebraically find approximate solutions using a graph
Higher Content Only
including linear/quadratic
Additional Foundation Content
find approximate solutions to equations numerically using iteration
Notes: including the use of suffix notation in recursive formulae.
Additional Foundation Content
translate simple situations or procedures into algebraic expressions or formulae derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution
Notes: including the solution of geometrical problems and problems set in context.
Additional Foundation Content
solve linear inequalities in one variable
represent the solution set ona number line
Higher Content Only
solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable represent the solution set on a number line, using set notation and on a graph
Notes: 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. See also N1
In graphical work the convention of a dashed line for strict inequalities and a solid line for an included
inequality will be required.
Basic Foundation Content
generate terms of a sequence from either a term-to-term or a position-to-term rule
Notes: including from patterns and diagrams.
Basic Foundation Content
recognise and use sequences of triangular, square and cube numbers and simple arithmetic progressions
Additional Foundation Content
including Fibonacci-type sequences, quadratic sequences, and simple geometric progressions rn where n is an integer and r is a rational number > 0)
Higher Content Only
including other sequences
including where r is a surd
Notes: other recursive sequences will be defined in the question.
Basic Foundation Content
deduce expressions to calculate the nth term of linear sequences
Higher Content Only
including quadratic sequences
Basic Foundation Content
change freely between related standard units (eg time, length, area, volume/capacity, mass)
and compound units (eg speed, rates of pay, prices) in numerical contexts
Additional Foundation Content
compound units (eg density, pressure)
in numerical and algebraic contexts
Basic Foundation Content
use scale factors, scale diagrams and maps
Notes: including geometrical problems
Basic Foundation Content
express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
Basic Foundation Content
use ratio notation, including reduction to simplest form
Basic Foundation Content
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 (such as those involving conversion, comparison, scaling, mixing, concentrations)
Notes: including better value or best-buy problems.
Basic Foundation Content
express a multiplicative relationship between two quantities as a ratio or a fraction
Basic Foundation Content
understand and use proportion as equality of ratios
Basic Foundation Content
relate ratios to fractions and to linear functions
Notes: see also N11, R14
Basic Foundation Content
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
Notes: see also N11, R14
Basic Foundation Content
solve problems involving direct and inverse proportion, including graphical and algebraic representations
Basic Foundation Content
use compound units such as speed, rates of pay, unit pricing
Additional Foundation Content
use compound units such as density and pressure
Notes: including making comparisons.
Basic Foundation Content
compare lengths, areas and volumes using ratio notation
scale factors
Additional Foundation Content
make links to similarity
(including trigonometric
ratios)
Notes: see also G19, G20
Additional Foundation Content
understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y
interpret equations that describe direct and inverse proportion
Higher Content Only
construct and interpret equations that describe direct and inverse proportion
Additional Foundation Content
interpret the gradient of a straight-line graph as a rate of change recognise and interpret graphs that illustrate direct and inverse proportion
Notes: see also A15, R8
Higher Content Only
interpret the gradient at a point on a curve as the instantaneous rate of change apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts
Notes: see also A15
Additional Foundation Content
set up, solve and interpret the answers in growth and decay problems, including compound interest
Higher Content Only
and work with general iterative processes
Basic Foundation Content
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
Additional Foundation Content
use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle) use these to construct given figures and solve loci problems know that the perpendicular distance from a point to a line is the shortest distance to the line
Notes: including constructing an angle of 60°.
Basic Foundation Content
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 (eg to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)
Notes: colloquial terms such as Z angles are not acceptable and should not be used.
Basic Foundation Content
derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus and triangles and other plane figures using appropriate language
Notes: including knowing names and properties of isosceles, equilateral, scalene, right-angled, acuteangled, obtuse-angled triangles. Including knowing names and using the polygons: pentagon, hexagon, octagon and decagon.
Additional Foundation Content
use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)
Additional Foundation Content
apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs
Basic Foundation Content
identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement
Additional Foundation Content
including fractional scale factors
Higher Content Only
including negative scale factors
Higher Content Only
describe the changes and invariance achieved by combinations of rotations, reflections and translations
Notes: including using column vector notation for translations. See also G24
Basic Foundation Content
identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference
Additional Foundation Content
including: tangent, arc, sector and segment
Higher Content Only
apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use
them to prove related results
Notes: including angle subtended by an arc at the centre is equal to twice the angle subtended at any point on the circumference, angle subtended at the circumference by a semicircle is 90°, angles in the same segment are equal, opposite angles in a cyclic quadrilateral sum to 180°, tangent at any point on a circle is perpendicular to the radius at that point, tangents from an external point are equal in length, the perpendicular from the centre to a chord bisects the chord, alternate segment theorem.
Basic Foundation Content
solve geometrical problems on coordinate axes.
Basic Foundation Content
identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres.
Basic Foundation Content
interpret plans and elevations of 3D shapes
Additional Foundation Content
construct and interpret plans and elevations of 3D shapes
Basic Foundation Content
use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money etc.)
Basic Foundation Content
measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings
Notes: including the eight compass point bearings and three-figure bearings
Basic Foundation Content
know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders)
Basic Foundation Content
know the formulae: circumference of a circle = 2πr = πd
area of a circle = πr²
calculate perimeters of 2D shapes, including circles
areas of circles and composite shapes
Additional Foundation Content
surface area and volume of spheres, pyramids, cones and composite solids
Notes: including frustums.
Solutions in terms of π may be asked for. See also N8, G18
Additional Foundation Content
calculate arc lengths, angles and areas of sectors of circles
Notes: see also N8, G17
Additional Foundation Content
apply the concepts of congruence and similarity, including the relationships between lengths in similar figures
Higher Content Only
including the relationships between lengths, areas and volumes in similar figures
Notes: see also R12
Additional Foundation Content
know the formulae for:
Pythagoras’ theorem, a² + b² = c² and the trigonometric ratios, sinπ = opposite/ hypotenuse ,
cosπ = adjacent/hypotenuse and tanπ = opposite/adjacent
apply them to find angles and lengths in right-angled triangles in two dimensional figures
Higher Content Only
apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures
Notes: see also R12
Additional Foundation Content
know the exact values of sinΘ and cosΘ for Θ = 0°, 30°, 45° , 60° and 90° know the exact value of tanΘ for Θ = 0°, 30°, 45° , 60°
Notes: see also A12
Higher Content Only
know and apply the sine rule,
a/sinA = b/sinB = c/sinC
and cosine rule,
a² = b² + c² − 2bccosA
to find unknown lengths and angles
Higher Content Only
know and apply Area = 1/ 2 absinC to calculate the area, sides or angles of any triangle
Basic Foundation Content
describe translations as 2D vectors
Notes: See also G8
Additional Foundation Content
apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors
Higher Content Only
use vectors to construct geometric arguments and proofs
Basic Foundation Content
record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees
Notes: probabilities should be written as fractions, decimals or percentages.
Basic Foundation Content
apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
Basic Foundation Content
relate relative expected frequencies to theoretical probability, using appropriate language and the 0 to 1 probability scale
Basic Foundation Content
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
Additional Foundation Content
understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
Basic Foundation Content
enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams
Additional Foundation Content
including using tree diagrams
Basic Foundation Content
construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities
Additional Foundation Content
calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions
Notes: including knowing when to add and when to multiply two or more probabilities
Higher Content Only
calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams
Notes: including knowing when to add and when to multiply two or more probabilities
Additional Foundation Content
infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling
Basic Foundation Content
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
Additional Foundation Content
Higher Content Only
construct and interpret diagrams for grouped discrete data and continuous data, ie histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use
Basic Foundation Content
interpret, analyse and compare the distributions of data sets from univariate empirical distributions through:
• appropriate graphical representation involving discrete, continuous and grouped data
• appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers)
Higher Content Only
Basic Foundation Content
apply statistics to describe a population
Basic Foundation Content
use and interpret scatter graphs
of bivariate data
recognise correlation
Additional Foundation Content
know that it does not indicate causation
draw estimated lines of best fit
make predictions
interpolate and extrapolate apparent trends whilst knowing the dangers of so doing
Notes: students should know and understand the terms: positive correlation, negative correlation, no
correlation, weak correlation and strong correlation.