AQA A-level Mathematics 7357 and Further Mathematics 7367: the route map

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Mathematics 7357

Checked against AQA’s own 7357 specification, version 1.3, 31 January 2018, on 19 August 2026. That copy was taken from the board itself on the day of the check rather than from a landing page. The 7357 document remains the controlling text. The reference codes below are AQA’s; the short labels beside them are InkMaths summaries rather than AQA’s statement text. Each row links to the relevant lessons and records full, partial or missing coverage.

This page is the content. For the examination itself, what each paper is worth and where AQA publishes them: AQA 7357 past papers.

A-level Mathematics content is prescribed nationally. Use the table to check how each statement in this qualification maps to InkMaths; rows marked partial or not covered identify gaps.

3.1 Overarching themes · A Proof · B Algebra and functions · C Coordinate geometry in the (x, y) plane · D Sequences and series · E Trigonometry · F Exponentials and logarithms · G Differentiation · H Integration · I Numerical methods · J Vectors · K Statistical sampling · L Data presentation and interpretation · M Probability · N Statistical distributions · O Statistical hypothesis testing · P Quantities and units in mechanics · Q Kinematics · R Forces and Newton's laws · S Moments · 3.21 Use of data in statistics

3.1 Overarching themes

17 of 17 covered in full.

Ref	Specification statement	Taught in	Coverage
OT1.1	Presenting a mathematical argument	The structure of proof: deduction and exhaustion, Quadratic functions, Graphs, proportion and transformations, Compound angles and the harmonic form	Covered
OT1.2	Mathematical language and syntax	The structure of proof: deduction and exhaustion, Indices and surds, Functions, inverses and the modulus, Measures of location and spread	Covered
OT1.3	Set theory language and symbols	Simultaneous equations and inequalities, Quadratic functions, Probability and Venn diagrams	Covered
OT1.4	Functions, domain and range	Functions, inverses and the modulus, Graphs, proportion and transformations, Reciprocal and inverse trigonometric functions	Covered
OT1.5	Comprehending and critiquing arguments	The structure of proof: deduction and exhaustion, Disproof and proof by contradiction, Arithmetic series, Geometric series, The derivative from first principles	Covered
OT2.1	Recognising mathematical structure	Quadratic functions, Indices and surds, Trigonometric graphs and equations, Functions in modelling	Covered
OT2.2	Extended arguments on unstructured problems	Tangents, turning points and curve behaviour, Arithmetic series, Straight lines, Solving differential equations	Covered
OT2.3	Interpreting and communicating solutions	Straight lines, Log graphs and exponential models, Correlation and regression, Modelling, quantities and units	Covered
OT2.4	Why numerical methods are needed	Locating roots and iteration, The trapezium rule, The Newton-Raphson method	Covered
OT2.5	Evaluating accuracy and limitations	The trapezium rule, The Newton-Raphson method, Locating roots and iteration, The general binomial expansion, The normal distribution	Covered
OT2.6	The problem solving cycle	Functions in modelling, Trigonometric modelling, Sampling and the large data set, Representing and interpreting data	Covered
OT2.7	Diagrams as problem-solving tools	Forces and Newton's laws, Friction and inclined planes, Probability and Venn diagrams, Conditional probability, Representing and interpreting data, Locating roots and iteration	Covered
OT3.1	Translating a situation into a model	Functions in modelling, Modelling, quantities and units, Rates of change and building differential equations	Covered
OT3.2	Using a model to explore a situation	Functions in modelling, Trigonometric modelling, Log graphs and exponential models, Exponential functions and e	Covered
OT3.3	Interpreting a model's outputs	Functions in modelling, Trigonometric modelling, Solving differential equations, Straight lines	Covered
OT3.4	Refining a model and judging it	Functions in modelling, Log graphs and exponential models, Trigonometric modelling, Solving differential equations	Covered
OT3.5	Modelling assumptions	Modelling, quantities and units, Connected particles and pulleys, Conditional probability, The binomial distribution	Covered

A Proof

1 of 1 covered in full.

Ref	Specification statement	Taught in	Coverage
A1	Structure of proof, deduction, exhaustion, disproof and contradiction	The structure of proof: deduction and exhaustion, Disproof and proof by contradiction	Covered

B Algebra and functions

11 of 11 covered in full.

Ref	Specification statement	Taught in	Coverage
B1	Laws of indices for all rational exponents	Indices and surds	Covered
B2	Surds and rationalising the denominator	Indices and surds	Covered
B3	Quadratic functions, the discriminant and completing the square	Quadratic functions	Covered
B4	Simultaneous equations by elimination and substitution	Simultaneous equations and inequalities	Covered
B5	Linear and quadratic inequalities, and regions	Simultaneous equations and inequalities	Covered
B6	Polynomial algebra, division and the factor theorem	Polynomials and the factor theorem	Covered
B7	Graphs of functions, asymptotes and proportion	Graphs, proportion and transformations, Functions, inverses and the modulus, Simultaneous equations and inequalities	Covered
B8	Composite and inverse functions	Functions, inverses and the modulus	Covered
B9	Transformations of the graph of y = f(x)	Graphs, proportion and transformations	Covered
B10	Partial fractions	Partial fractions	Covered
B11	Functions in modelling	Functions in modelling	Covered

C Coordinate geometry in the (x, y) plane

4 of 4 covered in full.

Ref	Specification statement	Taught in	Coverage
C1	Equation of a straight line, parallel and perpendicular	Straight lines	Covered
C2	Coordinate geometry of the circle	Circles	Covered
C3	Parametric equations and conversion	Parametric equations	Covered
C4	Parametric equations in modelling	Parametric equations, Implicit and parametric differentiation	Covered

D Sequences and series

6 of 6 covered in full.

Ref	Specification statement	Taught in	Coverage
D1	The binomial expansion, integer and rational n	The binomial expansion, The general binomial expansion, Partial fractions	Covered
D2	Sequences by formula and by recurrence	Sequences and sigma notation	Covered
D3	Sigma notation	Sequences and sigma notation	Covered
D4	Arithmetic sequences and series	Arithmetic series	Covered
D5	Geometric sequences and series	Geometric series	Covered
D6	Sequences and series in modelling	Arithmetic series, Geometric series	Covered

E Trigonometry

9 of 9 covered in full.

Ref	Specification statement	Taught in	Coverage
E1	Sine, cosine and tangent for all arguments; the rules; radians	Triangles and the sine and cosine rules, Trigonometric graphs and equations, Radians, arcs and small angles	Covered
E2	Small angle approximations	Radians, arcs and small angles	Covered
E3	Trigonometric graphs, symmetry, periodicity and exact values	Trigonometric graphs and equations, Radians, arcs and small angles	Covered
E4	Secant, cosecant, cotangent, arcsin, arccos and arctan	Reciprocal and inverse trigonometric functions	Covered
E5	The quotient identity and the Pythagorean identities	Trigonometric graphs and equations, Reciprocal and inverse trigonometric functions	Covered
E6	Compound and double angle formulae, and the harmonic form	Compound angles and the harmonic form	Covered
E7	Solving trigonometric equations in an interval	Trigonometric graphs and equations	Covered
E8	Constructing trigonometric proofs	Compound angles and the harmonic form, Reciprocal and inverse trigonometric functions	Covered
E9	Trigonometry in context, with vectors, kinematics and forces	Trigonometric modelling, Vectors in two dimensions, Projectiles, Forces and Newton's laws, Friction and inclined planes, Statics of a particle	Covered

F Exponentials and logarithms

7 of 7 covered in full.

Ref	Specification statement	Taught in	Coverage
F1	The functions a^x and e^x and their graphs	Exponential functions and e	Covered
F2	The gradient of e^kx and why the model suits	Exponential functions and e	Covered
F3	Logarithms as inverses, and the natural logarithm	Logarithms and their laws	Covered
F4	The laws of logarithms	Logarithms and their laws	Covered
F5	Solving equations of the form a^x = b	Logarithms and their laws	Covered
F6	Logarithmic graphs to estimate parameters	Log graphs and exponential models, Correlation and regression	Covered
F7	Exponential growth and decay in modelling	Log graphs and exponential models, Exponential functions and e, Functions in modelling, Solving differential equations	Covered

G Differentiation

6 of 6 covered in full.

Ref	Specification statement	Taught in	Coverage
G1	The derivative as a limit, first principles, and the second derivative	The derivative from first principles, Differentiating trig, exponentials and logs, Tangents, turning points and curve behaviour	Covered
G2	Differentiating powers, exponentials, trigonometric functions and ln x	Differentiating powers of x, Differentiating trig, exponentials and logs	Covered
G3	Gradients, tangents, normals, stationary points and inflections	Tangents, turning points and curve behaviour	Covered
G4	Product, quotient and chain rules, and connected rates	The product, quotient and chain rules, Rates of change and building differential equations, Implicit and parametric differentiation	Covered
G5	Implicit and parametric differentiation	Implicit and parametric differentiation	Covered
G6	Constructing differential equations	Rates of change and building differential equations	Covered

H Integration

8 of 8 covered in full.

Ref	Specification statement	Taught in	Coverage
H1	The Fundamental Theorem of Calculus	Integration as antidifferentiation, Definite integrals and areas	Covered
H2	Integrating powers and standard functions	Integration as antidifferentiation, Integrating standard functions	Covered
H3	Definite integrals and areas	Definite integrals and areas, Areas, parametric curves and the limit of a sum	Covered
H4	Integration as the limit of a sum	Areas, parametric curves and the limit of a sum	Covered
H5	Integration by substitution and by parts	Integration by substitution and by parts	Covered
H6	Integrating with partial fractions	Integrating rational functions	Covered
H7	Solving separable first order differential equations	Solving differential equations	Covered
H8	Interpreting the solution of a differential equation	Solving differential equations	Covered

I Numerical methods

4 of 4 covered in full.

Ref	Specification statement	Taught in	Coverage
I1	Locating roots by change of sign, and how it fails	Locating roots and iteration	Covered
I2	Iterative methods, Newton-Raphson, and their failures	Locating roots and iteration, The Newton-Raphson method	Covered
I3	Numerical integration by the trapezium rule	The trapezium rule	Covered
I4	Numerical methods in context	The trapezium rule, The Newton-Raphson method	Covered

J Vectors

5 of 5 covered in full.

Ref	Specification statement	Taught in	Coverage
J1	Vectors in two and three dimensions	Vectors in two dimensions, Vectors in three dimensions	Covered
J2	Magnitude, direction and conversion between forms	Vectors in two dimensions, Vectors in three dimensions	Covered
J3	Vector addition, scalar multiples and their geometry	Vectors in two dimensions	Covered
J4	Position vectors and distance between points	Vectors in two dimensions, Vectors in three dimensions	Covered
J5	Vectors in pure problems and in context	Vectors in two dimensions, Vectors in three dimensions, Forces and Newton's laws, Kinematics with variable acceleration	Covered

K Statistical sampling

1 of 1 covered in full.

Ref	Specification statement	Taught in	Coverage
K1	Population, sample and sampling techniques	Sampling and the large data set	Covered

L Data presentation and interpretation

4 of 4 covered in full.

Ref	Specification statement	Taught in	Coverage
L1	Diagrams for single-variable data	Representing and interpreting data, The normal distribution	Covered
L2	Scatter diagrams, regression lines and correlation	Correlation and regression	Covered
L3	Central tendency, variation and standard deviation	Measures of location and spread	Covered
L4	Outliers, choosing a presentation, and cleaning data	Representing and interpreting data	Covered

M Probability

3 of 3 covered in full.

Ref	Specification statement	Taught in	Coverage
M1	Mutually exclusive and independent events	Probability and Venn diagrams, The binomial distribution, The normal distribution	Covered
M2	Conditional probability	Conditional probability	Covered
M3	Modelling with probability	Conditional probability, The binomial distribution	Covered

N Statistical distributions

3 of 3 covered in full.

Ref	Specification statement	Taught in	Coverage
N1	Discrete distributions and the binomial	The binomial distribution	Covered
N2	The Normal distribution	The normal distribution	Covered
N3	Selecting an appropriate distribution	The normal distribution, The binomial distribution	Covered

O Statistical hypothesis testing

3 of 3 covered in full.

Ref	Specification statement	Taught in	Coverage
O1	The language of hypothesis testing	Hypothesis testing with the binomial, Hypothesis testing: correlation and the normal	Covered
O2	Testing a binomial proportion	Hypothesis testing with the binomial	Covered
O3	Testing a Normal mean with known variance	Hypothesis testing: correlation and the normal	Covered

P Quantities and units in mechanics

1 of 1 covered in full.

Ref	Specification statement	Taught in	Coverage
P1	Fundamental and derived quantities and units	Modelling, quantities and units, Moments	Covered

Q Kinematics

5 of 5 covered in full.

Ref	Specification statement	Taught in	Coverage
Q1	The language of kinematics	Modelling, quantities and units, Kinematics with constant acceleration, Kinematics with variable acceleration	Covered
Q2	Kinematics graphs	Kinematics with constant acceleration	Covered
Q3	The constant acceleration formulae	Kinematics with constant acceleration, Projectiles	Covered
Q4	Calculus in kinematics	Kinematics with variable acceleration	Covered
Q5	Motion under gravity in a vertical plane, and projectiles	Projectiles, Kinematics with constant acceleration	Covered

R Forces and Newton's laws

6 of 6 covered in full.

Ref	Specification statement	Taught in	Coverage
R1	The concept of a force and Newton's first law	Forces and Newton's laws, Statics of a particle	Covered
R2	Newton's second law, including resolved forces	Forces and Newton's laws, Friction and inclined planes	Covered
R3	Weight and motion under gravity	Modelling, quantities and units, Kinematics with constant acceleration, Forces and Newton's laws	Covered
R4	Newton's third law, pulleys, connected particles and equilibrium	Forces and Newton's laws, Connected particles and pulleys, Statics of a particle, Friction and inclined planes	Covered
R5	Addition of forces, resultants and motion in a plane	Forces and Newton's laws, Statics of a particle	Covered
R6	The friction model, limiting friction and statics	Friction and inclined planes, Statics of a particle, Connected particles and pulleys	Covered

S Moments

1 of 1 covered in full.

Ref	Specification statement	Taught in	Coverage
S1	Moments in simple static contexts	Moments	Covered

3.21 Use of data in statistics

0 of 1 covered in full, 1 with the gap named.

Ref	Specification statement	Taught in	Coverage
3.21.1	Large data set	Sampling and the large data set, Representing and interpreting data, Measures of location and spread, Correlation and regression	Technique covered; the board’s context is not: AQA's own data set is not taught. Every board chooses its own, and AQA's is a government survey of household food and drink purchasing, published by the board and obtainable only from it. The lesson here is written around Pearson's set instead, and teaches its frame in detail: which stations, which two years, which months, which columns are words rather than numbers, and which southern-hemisphere station has its seasons the wrong way round. An AQA candidate needs none of that and will be asked about a table this library never shows them, so the familiarity the exam assumes has to be built from the board's own materials.

Further Mathematics 7367

Checked against AQA’s own 7367 specification, version 1.1, 20 October 2017, on 19 August 2026. That copy was taken from the board itself on the day of the check rather than from a landing page. The 7367 document remains the controlling text. The reference codes below are AQA’s; the short labels beside them are InkMaths summaries rather than AQA’s statement text. Each row links to the relevant lessons and records full, partial or missing coverage.

This page is the content. For the examination itself, what each paper is worth and where AQA publishes them: AQA 7367 past papers.

This qualification includes compulsory content and two of three optional applications. Use the section links to find the papers you take. Option content differs between awarding organisations, so treat every recorded gap as qualification-specific.

Compulsory content: A Proof · B Complex numbers · C Matrices · D Further algebra and functions · E Further calculus · F Further vectors · G Polar coordinates · H Hyperbolic functions · I Differential equations · J Numerical methods
Optional application 1, mechanics: MA Dimensional analysis · MB Momentum and collisions · MC Work, energy and power · MD Circular motion · ME Centres of mass and moments
Optional application 2, statistics: SA Discrete random variables and expectation · SB Poisson distribution · SC Type I and Type II errors · SD Continuous random variables · SE Chi squared tests for association · SF Exponential distribution · SG Inference: one sample t-distribution · SH Confidence intervals
Optional application 3, discrete mathematics: DA Graphs · DB Networks · DC Network flows · DD Linear programming · DE Critical path analysis · DF Game theory for zero-sum games · DG Binary operations

A Proof

1 of 1 covered in full.

Ref	Specification statement	Taught in	Coverage
A1	Proof by mathematical induction	Proof by induction: sums and series, Induction: divisibility and matrices	Covered

B Complex numbers

11 of 11 covered in full.

Ref	Specification statement	Taught in	Coverage
B1	Solving quadratic, cubic and quartic equations	Complex arithmetic and the Argand diagram, Roots of polynomials	Covered
B2	Arithmetic in the form x + iy	Complex arithmetic and the Argand diagram	Covered
B3	The complex conjugate and conjugate root pairs	Complex arithmetic and the Argand diagram, Roots of polynomials	Covered
B4	Argand diagrams	Complex arithmetic and the Argand diagram, Modulus, argument and loci	Covered
B5	Cartesian and modulus-argument form	Modulus, argument and loci	Covered
B6	Multiplying and dividing in modulus-argument form	Modulus, argument and loci	Covered
B7	Loci in the Argand diagram	Modulus, argument and loci, Further loci and regions in the Argand diagram	Covered
B8	De Moivre's theorem, multiple angles and sums of series	De Moivre's theorem and trigonometric identities, Roots of unity and complex roots, Geometric series	Covered
B9	The exponential form	De Moivre's theorem and trigonometric identities, Roots of unity and complex roots, Maclaurin series	Covered
B10	The n distinct nth roots and their polygon	Roots of unity and complex roots	Covered
B11	Roots of unity in geometric problems	Roots of unity and complex roots	Covered

C Matrices

11 of 11 covered in full.

Ref	Specification statement	Taught in	Coverage
C1	Matrix addition, multiplication and scalar multiples	Matrix algebra and transformations	Covered
C2	Zero and identity matrices	Matrix algebra and transformations	Covered
C3	Matrices as linear transformations, in 2D and 3D	Matrix algebra and transformations	Covered
C4	Invariant points and invariant lines	Systems of equations and invariance, Eigenvalues and eigenvectors	Covered
C5	Determinants of 2 x 2 and 3 x 3 matrices as scale factors	Determinants and inverses, Matrix algebra and transformations	Covered
C6	Singular and non-singular matrices, and inverses	Determinants and inverses	Covered
C7	Three equations in three unknowns by inverse matrix	Systems of equations and invariance, Determinants and inverses	Covered
C8	Geometry of three simultaneous equations	Systems of equations and invariance	Covered
C9	Factorising determinants by row and column operations	Determinants and inverses	Covered
C10	Eigenvalues, eigenvectors and the characteristic equation	Eigenvalues and eigenvectors	Covered
C11	Diagonalisation and powers of a matrix	Diagonalisation and the Cayley-Hamilton theorem	Covered

D Further algebra and functions

16 of 16 covered in full.

Ref	Specification statement	Taught in	Coverage
D1	Roots and coefficients up to quartics	Roots of polynomials	Covered
D2	Forming an equation with transformed roots	Roots of polynomials	Covered
D3	Sums of integers, squares and cubes	Summing series and the method of differences	Covered
D4	The method of differences	Summing series and the method of differences, Partial fractions	Covered
D5	Maclaurin series, including the general term	Maclaurin series	Covered
D6	The standard Maclaurin series and their validity	Maclaurin series, The general binomial expansion	Covered
D7	Limits by series or by l'Hopital's rule	Limits and L'Hôpital's rule, Maclaurin series	Covered
D8	Cubic and quartic inequalities	Inequalities and inequations, Graphs, proportion and transformations, Simultaneous equations and inequalities	Covered
D9	Algebraic solution of rational inequalities	Inequalities and inequations	Covered
D10	Modulus of functions and modulus inequalities	Inequalities and inequations, Functions, inverses and the modulus	Covered
D11	Graphs of the modulus and the reciprocal of a function	Graphs, proportion and transformations, Functions, inverses and the modulus	Covered
D12	Graphs of linear-over-linear rational functions	Graphs, proportion and transformations, Inequalities and inequations	Covered
D13	Graphs of quadratic-over-quadratic rational functions	Graphs, proportion and transformations, Conic sections	Covered
D14	Range and stationary points by quadratic theory	Graphs, proportion and transformations, Quadratic functions, Tangents, turning points and curve behaviour, Simultaneous equations and inequalities	Covered
D15	Sketching the standard conics	Conic sections	Covered
D16	Transformations of curves, single and composite	Graphs, proportion and transformations, Matrix algebra and transformations, Functions, inverses and the modulus	Covered

E Further calculus

9 of 9 covered in full.

Ref	Specification statement	Taught in	Coverage
E1	Improper integrals	Mean values and improper integrals	Covered
E2	Volumes of revolution	Volumes of revolution	Covered
E3	The mean value of a function	Mean values and improper integrals	Covered
E4	Integrating with partial fractions, including a quadratic factor	Calculus with inverse trigonometric functions, Integrating rational functions, Partial fractions	Covered
E5	Differentiating inverse trigonometric functions	Calculus with inverse trigonometric functions	Covered
E6	The two standard inverse-trigonometric integrals and substitutions	Calculus with inverse trigonometric functions	Covered
E7	Arc length and surface of revolution	Arc length and surface area	Covered
E8	Reduction formulae	Reduction formulae	Covered
E9	Two named limits applied to improper integrals	Limits and L'Hôpital's rule, Mean values and improper integrals, Reduction formulae	Covered

F Further vectors

6 of 6 covered in full.

Ref	Specification statement	Taught in	Coverage
F1	Vector and Cartesian forms of a line in three dimensions	Lines and planes in three dimensions	Covered
F2	Vector and Cartesian forms of a plane	Lines and planes in three dimensions	Covered
F3	The scalar product, and angles between lines and planes	Intersections, angles and distances, Lines and planes in three dimensions	Covered
F4	Testing vectors for perpendicularity	Lines and planes in three dimensions, Intersections, angles and distances, The vector product and the scalar triple product	Covered
F5	The vector product, the line through a point, and areas	The vector product and the scalar triple product	Covered
F6	Intersections and perpendicular distances	Intersections, angles and distances, Lines and planes in three dimensions, The vector product and the scalar triple product	Covered

G Polar coordinates

3 of 3 covered in full.

Ref	Specification statement	Taught in	Coverage
G1	Polar coordinates and conversion	Polar curves	Covered
G2	Sketching polar curves	Polar curves	Covered
G3	Area enclosed by a polar curve	Areas with polar coordinates	Covered

H Hyperbolic functions

7 of 7 covered in full.

Ref	Specification statement	Taught in	Coverage
H1	Definitions, domains, ranges and graphs of the six hyperbolic functions	Hyperbolic functions and identities	Covered
H2	Differentiating and integrating hyperbolic functions	Calculus with hyperbolic functions	Covered
H3	The inverse hyperbolic functions, domains and ranges	Hyperbolic functions and identities	Covered
H4	Logarithmic forms of the inverse hyperbolic functions	Hyperbolic functions and identities, Calculus with hyperbolic functions	Covered
H5	The two hyperbolic standard integrals and substitutions	Calculus with hyperbolic functions	Covered
H6	The hyperbolic identities	Hyperbolic functions and identities	Covered
H7	Proofs with hyperbolic functions and identities	Hyperbolic functions and identities, Calculus with hyperbolic functions, Arc length and surface area	Covered

I Differential equations

11 of 11 covered in full.

Ref	Specification statement	Taught in	Coverage
I1	Integrating factors	First order equations and integrating factors	Covered
I2	General and particular solutions	First order equations and integrating factors, Second order equations, Solving differential equations	Covered
I3	Differential equations in modelling	Modelling with differential equations, Solving differential equations, Rates of change and building differential equations	Covered
I4	Second order homogeneous equations by the auxiliary equation	Second order equations	Covered
I5	Second order equations with a right-hand side	Second order equations	Covered
I6	The discriminant and the form of the solution	Second order equations, Modelling with differential equations	Covered
I7	Simple harmonic motion and its solution	Modelling with differential equations, Simple harmonic motion	Covered
I8	Damped oscillations and the three regimes	Modelling with differential equations	Covered
I9	Coupled first order systems	Modelling with differential equations	Covered
I10	Formulating simple harmonic motion from Hooke's law	Oscillations on strings and springs, Hooke's law and elastic strings, Simple harmonic motion	Covered
I11	Damping proportional to velocity	Modelling with differential equations, Newton's laws with a variable force	Covered

J Numerical methods

3 of 3 covered in full.

Ref	Specification statement	Taught in	Coverage
J1	The mid-ordinate rule and Simpson's rule	Numerical methods for differential equations, The trapezium rule	Covered
J2	Euler's step by step method	Numerical methods for differential equations	Covered
J3	The improved Euler method	Numerical methods for differential equations	Covered

MA Dimensional analysis (Optional application 1, mechanics)

2 of 2 covered in full.

Ref	Specification statement	Taught in	Coverage
MA1	Dimensions of quantities and dimensional consistency	Modelling, quantities and units	Covered
MA2	Predicting formulae by finding powers	Modelling, quantities and units	Covered

MB Momentum and collisions (Optional application 1, mechanics)

4 of 4 covered in full.

Ref	Specification statement	Taught in	Coverage
MB1	Conservation of momentum, in one and two dimensions	Momentum and impulse, Impulse and momentum as vectors	Covered
MB2	Restitution, direct collisions and impact with a surface	Direct impact and Newton's law of restitution, Oblique impact and impact with a smooth surface	Covered
MB3	Impulse and its relation to momentum	Momentum and impulse, Impulse and momentum as vectors	Covered
MB4	Impulse of a variable force	Momentum and impulse, Newton's laws with a variable force	Covered

MC Work, energy and power (Optional application 1, mechanics)

7 of 7 covered in full.

Ref	Specification statement	Taught in	Coverage
MC1	Work done by a force	Work, energy and power	Covered
MC2	Gravitational potential energy	Work, energy and power, Motion in a vertical circle	Covered
MC3	Kinetic energy	Work, energy and power, Elastic potential energy, Direct impact and Newton's law of restitution	Covered
MC4	Hooke's law and the modulus of elasticity	Hooke's law and elastic strings	Covered
MC5	Work done by a variable force	Newton's laws with a variable force, Work, energy and power, Elastic potential energy	Covered
MC6	Elastic potential energy	Elastic potential energy	Covered
MC7	Power	Work, energy and power	Covered

MD Circular motion (Optional application 1, mechanics)

6 of 6 covered in full.

Ref	Specification statement	Taught in	Coverage
MD1	Motion in a circle at constant speed	Angular speed and horizontal circular motion	Covered
MD2	Angular speed, in radians and in revolutions	Angular speed and horizontal circular motion, Radians, arcs and small angles	Covered
MD3	Speed, angular speed, radius and acceleration	Angular speed and horizontal circular motion	Covered
MD4	Position, velocity and acceleration as vectors in circular motion	Angular speed and horizontal circular motion, Motion in a vertical circle, Kinematics with variable acceleration	Covered
MD5	The conical pendulum	Angular speed and horizontal circular motion	Covered
MD6	Circular motion in a vertical plane	Motion in a vertical circle	Covered

ME Centres of mass and moments (Optional application 1, mechanics)

6 of 6 covered in full.

Ref	Specification statement	Taught in	Coverage
ME1	Centre of mass of a system of particles	Centre of mass of a discrete distribution	Covered
ME2	Centre of mass of a composite body	Centres of mass of plane figures and frameworks	Covered
ME3	Centre of mass of a lamina by integration	Centres of mass by integration	Covered
ME4	Centre of mass of a solid of revolution	Centres of mass by integration	Covered
ME5	Sliding, toppling and suspension	Equilibrium, suspension, toppling and sliding	Covered
ME6	Forces on a rigid body in equilibrium, moments and couples	Equilibrium, suspension, toppling and sliding, Moments, Centres of mass of plane figures and frameworks, Statics of a particle	Covered

SA Discrete random variables and expectation (Optional application 2, statistics)

7 of 7 covered in full.

Ref	Specification statement	Taught in	Coverage
SA1	Discrete random variables given by table or function	Discrete random variables and expectation, The binomial distribution	Covered
SA2	Evaluating probabilities for a discrete random variable	Discrete random variables and expectation, The binomial distribution	Covered
SA3	Average and spread for a discrete random variable	Discrete random variables and expectation, Measures of location and spread	Covered
SA4	Expectation and variance formulae	Discrete random variables and expectation	Covered
SA5	Expectation of functions and of linear functions	Discrete random variables and expectation	Covered
SA6	The discrete uniform distribution as a model	The binomial distribution, Goodness-of-fit tests	Covered
SA7	Proof of the mean and variance of the discrete uniform distribution	Discrete random variables and expectation, Summing series and the method of differences	Covered

SB Poisson distribution (Optional application 2, statistics)

5 of 5 covered in full.

Ref	Specification statement	Taught in	Coverage
SB1	Conditions for a Poisson model, and its notation	The Poisson distribution	Covered
SB2	The Poisson formula and Poisson probabilities	The Poisson distribution	Covered
SB3	Mean, variance and standard deviation of a Poisson distribution	The Poisson distribution, Discrete random variables and expectation	Covered
SB4	Sums of independent Poisson distributions	The Poisson distribution	Covered
SB5	Hypothesis test for a Poisson mean	Hypothesis tests for Poisson and geometric models	Covered

SC Type I and Type II errors (Optional application 2, statistics)

2 of 2 covered in full.

Ref	Specification statement	Taught in	Coverage
SC1	Type I and Type II errors, and the probability of a Type I error	Type I and Type II errors, test size and power, Hypothesis tests for Poisson and geometric models, Hypothesis testing with the binomial, Hypothesis testing: correlation and the normal	Covered
SC2	Power of a test and the probability of a Type II error	Type I and Type II errors, test size and power	Covered

SD Continuous random variables (Optional application 2, statistics)

8 of 8 covered in full.

Ref	Specification statement	Taught in	Coverage
SD1	Probability density functions, and mixed distributions	Continuous random variables: density and distribution functions, Discrete random variables and expectation	Covered
SD2	Probability of an observation in an interval	Continuous random variables: density and distribution functions	Covered
SD3	Median and quartiles from a density	Continuous random variables: density and distribution functions, Mean, variance and skewness of continuous variables	Covered
SD4	Mean, variance and standard deviation from a density	Mean, variance and skewness of continuous variables	Covered
SD5	Linear functions and functions of a continuous variable	Mean, variance and skewness of continuous variables, Discrete random variables and expectation	Covered
SD6	The cumulative distribution function	Continuous random variables: density and distribution functions	Covered
SD7	The rectangular distribution	The continuous uniform distribution	Covered
SD8	Expectation and variance of a sum of independent variables	Combinations of normal random variables	Covered

SE Chi squared tests for association (Optional application 2, statistics)

5 of 5 covered in full.

Ref	Specification statement	Taught in	Coverage
SE1	Constructing contingency tables	Contingency tables	Covered
SE2	The chi squared statistic and its degrees of freedom	Contingency tables, Goodness-of-fit tests	Covered
SE3	The convention on expected frequencies	Goodness-of-fit tests, Contingency tables	Covered
SE4	Identifying sources of association	Contingency tables	Covered
SE5	Yates' correction	Contingency tables, Goodness-of-fit tests	Covered

SF Exponential distribution (Optional application 2, statistics)

4 of 4 covered in full.

Ref	Specification statement	Taught in	Coverage
SF1	Conditions for an exponential model, and its two functions	Continuous random variables: density and distribution functions, The Poisson distribution	Covered
SF2	Probabilities from an exponential distribution	Continuous random variables: density and distribution functions	Covered
SF3	Proofs of the mean and variance of an exponential distribution	Mean, variance and skewness of continuous variables, Continuous random variables: density and distribution functions, Reduction formulae	Covered
SF4	Intervals between Poisson events	Continuous random variables: density and distribution functions, The Poisson distribution	Covered

SG Inference: one sample t-distribution (Optional application 2, statistics)

1 of 1 covered in full.

Ref	Specification statement	Taught in	Coverage
SG1	One sample t-test for a normal mean	Confidence intervals and tests with the t-distribution	Covered

SH Confidence intervals (Optional application 2, statistics)

4 of 4 covered in full.

Ref	Specification statement	Taught in	Coverage
SH1	Confidence interval for a mean with known variance	Estimators, standard error and confidence intervals	Covered
SH2	Confidence interval from a large sample with unknown variance	Estimators, standard error and confidence intervals, Confidence intervals and tests with the t-distribution	Covered
SH3	Inferences from a confidence interval	Estimators, standard error and confidence intervals, Confidence intervals and tests with the t-distribution	Covered
SH4	Confidence interval from a small sample using the t-distribution	Confidence intervals and tests with the t-distribution	Covered

DA Graphs (Optional application 3, discrete mathematics)

7 of 7 covered in full.

Ref	Specification statement	Taught in	Coverage
DA1	The language of graphs	Graphs: order, Eulerian paths and planarity, Route inspection, Minimum spanning trees: Prim and Kruskal	Covered
DA2	Eulerian, semi-Eulerian and Hamiltonian graphs	Graphs: order, Eulerian paths and planarity, Route inspection, The travelling salesman problem	Covered
DA3	Euler's formula for connected planar graphs	Graphs: order, Eulerian paths and planarity	Covered
DA4	Kuratowski's theorem	Graphs: order, Eulerian paths and planarity	Covered
DA5	Complete and bipartite graphs, adjacency matrices and complements	Graphs: order, Eulerian paths and planarity, Minimum spanning trees: Prim and Kruskal, Shortest paths: Dijkstra and Floyd	Covered
DA6	Simple graphs, simple-connected graphs and trees	Minimum spanning trees: Prim and Kruskal, Graphs: order, Eulerian paths and planarity, Critical path analysis	Covered
DA7	Isomorphism between graphs	Graphs: order, Eulerian paths and planarity, Subgroups, Lagrange's theorem and isomorphism	Covered

DB Networks (Optional application 3, discrete mathematics)

5 of 5 covered in full.

Ref	Specification statement	Taught in	Coverage
DB1	The language of networks	Minimum spanning trees: Prim and Kruskal, Shortest paths: Dijkstra and Floyd, Flows in networks: cuts and capacity, Route inspection	Covered
DB2	Network optimisation with spanning trees	Minimum spanning trees: Prim and Kruskal, The travelling salesman problem	Covered
DB3	Route inspection problems	Route inspection	Covered
DB4	Upper and lower bounds for the travelling salesperson problem	The travelling salesman problem	Covered
DB5	Evaluating, modifying and refining network models	Route inspection, The travelling salesman problem, Flows in networks: cuts and capacity	Covered

DC Network flows (Optional application 3, discrete mathematics)

7 of 7 covered in full.

Ref	Specification statement	Taught in	Coverage
DC1	Interpreting flow problems on directed networks	Flows in networks: cuts and capacity, Maximum flow and the labelling procedure	Covered
DC2	The value of a cut	Flows in networks: cuts and capacity	Covered
DC3	The maximum flow minimum cut theorem	Maximum flow and the labelling procedure	Covered
DC4	Supersources and supersinks	Flows in networks: cuts and capacity	Covered
DC5	Augmenting a flow to the maximum	Maximum flow and the labelling procedure	Covered
DC6	Arcs with upper and lower capacities	Maximum flow and the labelling procedure, Flows in networks: cuts and capacity	Covered
DC7	Nodes of restricted capacity	Flows in networks: cuts and capacity	Covered

DD Linear programming (Optional application 3, discrete mathematics)

4 of 4 covered in full.

Ref	Specification statement	Taught in	Coverage
DD1	Formulating constrained optimisation problems	Linear programming: formulation and graphical solution	Covered
DD2	Graphical solution	Linear programming: formulation and graphical solution	Covered
DD3	The Simplex algorithm	The Simplex algorithm	Covered
DD4	Interpreting a Simplex tableau	The Simplex algorithm	Covered

DE Critical path analysis (Optional application 3, discrete mathematics)

6 of 6 covered in full.

Ref	Specification statement	Taught in	Coverage
DE1	Constructing a precedence network with activity-on-node	Critical path analysis	Covered
DE2	Earliest and latest start and finish times	Critical path analysis	Covered
DE3	Critical activities, critical paths and float	Critical path analysis, Float, Gantt charts and scheduling	Covered
DE4	Refining models and the implications of changes	Critical path analysis, Float, Gantt charts and scheduling	Covered
DE5	Gantt charts and resource histograms	Float, Gantt charts and scheduling	Covered
DE6	Resource levelling and restricted resources	Float, Gantt charts and scheduling	Covered

DF Game theory for zero-sum games (Optional application 3, discrete mathematics)

6 of 6 covered in full.

Ref	Specification statement	Taught in	Coverage
DF1	Pay-off matrices	Game theory: play safe and stable solutions	Covered
DF2	Play-safe strategies and the value of the game	Game theory: play safe and stable solutions, Mixed strategies in game theory	Covered
DF3	Existence or non-existence of a stable solution	Game theory: play safe and stable solutions	Covered
DF4	Dominated strategies	Game theory: play safe and stable solutions, Mixed strategies in game theory	Covered
DF5	Optimal mixed strategies and graphical solution	Mixed strategies in game theory	Covered
DF6	Converting higher order games to linear programming	Mixed strategies in game theory, The Simplex algorithm, Linear programming: formulation and graphical solution	Covered

DG Binary operations (Optional application 3, discrete mathematics)

12 of 12 covered in full.

Ref	Specification statement	Taught in	Coverage
DG1	Binary operations, modular arithmetic and matrix multiplication	Groups and their axioms, Modular arithmetic and Fermat's little theorem, Matrix algebra and transformations	Covered
DG2	Commutativity of a binary operation	Groups and their axioms, Matrix algebra and transformations	Covered
DG3	Associativity of a binary operation	Groups and their axioms	Covered
DG4	Cayley tables	Groups and their axioms	Covered
DG5	The identity element	Groups and their axioms, Matrix algebra and transformations	Covered
DG6	Inverses of elements	Groups and their axioms, Determinants and inverses, Modular arithmetic and Fermat's little theorem	Covered
DG7	The language of groups	Groups and their axioms, Subgroups, Lagrange's theorem and isomorphism	Covered
DG8	The group axioms	Groups and their axioms	Covered
DG9	Finite and infinite groups, symmetries, cyclic and abelian groups	Groups and their axioms, Subgroups, Lagrange's theorem and isomorphism	Covered
DG10	Lagrange's theorem	Subgroups, Lagrange's theorem and isomorphism, Groups and their axioms	Covered
DG11	Generators of a group	Groups and their axioms	Covered
DG12	Isomorphism between groups of finite order	Subgroups, Lagrange's theorem and isomorphism	Covered

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