AQA GCSE MATHS

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:

[https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-8300/assessment-resources?f.Resource+type%7C6=Question+papers]

Everything you need to know about your GCSE (9-1) Maths specifications can be found here.

3.1 Number

3.1.1 Structure and calculation

N1

Basic Foundation Content

order positive and negative integers, decimals and fractions use the symbols =, ≠, <, >, ≤, ≥

Notes: including use of a number line.

N2

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.

N3

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

N4

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.

N5

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.

N6

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

N7

Additional Foundation Content

calculate with roots, and with integer indices

Higher Content Only

calculate with fractional indices

N8

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

N9

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.

3.1.2 Fractions, Decimals and Percentages

N10

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.

N11

Basic Foundation Content

identify and work with fractions in ratio problems

N12

Basic Foundation Content

interpret fractions and percentages as operators

Notes: including interpreting percentage problems using a multiplier.

3.1.3 Measures and Accuracy

N13

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.

N14

Basic Foundation Content

estimate answers
check calculations using approximation and estimation, including answers obtained using technology

Notes: including evaluation of results obtained.

N15

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.

N16

Additional Foundation Content

apply and interpret limits of
accuracy

Higher Content Only

including upper and lower bounds

3.2 Algebra

3.2.1 Notation, Vocabulary and Manipulation

A1

Basic Foundation Content

use and interpret algebraic
notation, including:
ab in place of a × b
3y in place of y + y + y and 3 × y
a² in place of a × a, a³ in place of a × a × a, a² b in place of a × a × b
a/b in place of a ÷ b
coefficients written as fractions rather than as decimals
brackets

Notes: it is expected that answers will be given in their simplest form without an explicit instruction to
do so.

A2

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

A3

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.

A4

Basic Foundation Content

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

Additional Foundation Content

simplify and manipulate algebraic expressions (including those involving surds) by:

expanding products of two binomials
factorising quadratic expressions of the form x² + bx + c, including the difference of two squares

Higher Content Only

simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by:

expanding products of two or more binomials
factorising quadratic
expressions of the form ax² + bx + c

A5

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.

A6

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.

A7

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.

3.2.2 Graphs

A8

Basic Foundation Content

work with coordinates in all four quadrants

A9

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

A10

Basic Foundation Content

identify and interpret gradients and intercepts of linear functions graphically and algebraically

A11

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.

A12

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

A13

Higher Content Only

sketch translations and reflections of a given function

A14

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.

A15

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

A16

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

3.2.3 Solving Equations and Inequalities

A17

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

A18

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

A19

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

A20

Additional Foundation Content

find approximate solutions to equations numerically using iteration

Notes: including the use of suffix notation in recursive formulae.

A21

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.

A22

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.

3.2.4 Sequences

A23

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.

A24

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 rⁿwhere 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.

A25

Basic Foundation Content

deduce expressions to calculate the nth term of linear sequences

Higher Content Only

including quadratic sequences

3.3 Ratio, Proportion and Rates of Change

R1

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

R2

Basic Foundation Content

use scale factors, scale diagrams and maps

Notes: including geometrical problems

R3

Basic Foundation Content

express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1

R4

Basic Foundation Content

use ratio notation, including reduction to simplest form

R5

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.

R6

Basic Foundation Content

express a multiplicative relationship between two quantities as a ratio or a fraction

R7

Basic Foundation Content

understand and use proportion as equality of ratios

R8

Basic Foundation Content

relate ratios to fractions and to linear functions

Notes: see also N11, R14

R9

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

R10

Basic Foundation Content

solve problems involving direct and inverse proportion, including graphical and algebraic representations

R11

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.

R12

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

R13

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

R14

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

R15

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

R16

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

3.4 Geometry and Measures

3.4.1 Properties and Constructions

G1

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

G2

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°.

G3

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.

G4

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.

G5

Additional Foundation Content

use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)

G6

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

G7

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

G8

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

G9

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

G10

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.

G11

Basic Foundation Content

solve geometrical problems on coordinate axes.

G12

Basic Foundation Content

identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres.

G13

Basic Foundation Content

interpret plans and elevations of 3D shapes

Additional Foundation Content

construct and interpret plans and elevations of 3D shapes

3.4.2 Mensuration and calculation

G14

Basic Foundation Content

use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money etc.)

G15

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

G16

Basic Foundation Content

know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders)

G17

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

G18

Additional Foundation Content

calculate arc lengths, angles and areas of sectors of circles

Notes: see also N8, G17

G19

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

G20

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

G21

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

G22

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

G23

Higher Content Only

know and apply Area = 1/ 2 absinC to calculate the area, sides or angles of any triangle

3.4.3 Vectors

G24

Basic Foundation Content

describe translations as 2D vectors

Notes: See also G8

G25

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

3.5 Probability

P1

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.

P2

Basic Foundation Content

apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments

P3

Basic Foundation Content

relate relative expected frequencies to theoretical probability, using appropriate language and the 0 to 1 probability scale

P4

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

P5

Additional Foundation Content

understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size

P6

Basic Foundation Content

enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams

Additional Foundation Content

including using tree diagrams

P7

Basic Foundation Content

construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities

P8

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

P9

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

3.6 Statistics

S1

Additional Foundation Content

infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling

S2

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

including tables and line graphs for time series data

Notes: including choosing suitable statistical diagrams

S3

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

S4

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

• including box plots

• including quartiles and
inter-quartile range

Notes: students should know and understand the terms: primary data, secondary data, discrete data
and continuous data.

S5

Basic Foundation Content

apply statistics to describe a population

S6

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.