E1 Understand and use the definitions of sine, cosine and tangent for all arguments; the sine and cosine rules; the area of a triangle in the form ½abSinC.
Work with radian measure, including use for arc length and area of sector.
 
TLMaths – E1: Trigonometry (google.com)
Trigonometry Basics | MME (mathsmadeeasy.co.uk)
Sine & Cosine Rules | MME (mathsmadeeasy.co.uk)
Arc Length & Area of a Sector | MME (mathsmadeeasy.co.uk)
 
E4 Understand and use the definitions of secant, cosecant and cotangent and of arcsin, arccos and arctan; their relationships to sine, cosine and tangent; understanding of their graphs; their ranges and domains.
 
TLMaths – E4: Further Trigonometry (google.com)
 
 
E2 Understand and use the standard small angle approximations of sine , cosine and
tangent . Sin θ ≈ θ, Cos θ ≈ 1 − θ²/2, Tan θ ≈ θ where θ is in radians
 
TLMaths – E2: Small Angle Approximation (google.com)
 
E6 Understand and use double angle formulae; use of formulae for sin (A ± B) , cos (A ± B) and tan (A ± B) ; understand geometrical proofs of these formulae.
Understand and use expressions for acos θ + bsin θ in the equivalent forms of Rcos(θ ± a) or rsin(θ ± a)
 
TLMaths – E6: Compound Angles & Equivalent Forms (google.com)
 
E3 Understand and use the sine, cosine and tangent functions, their graphs, symmetries and periodicity.
Know and use exact values of sin and cos for 0, π/6, π/4, π/3, π/2, π and multiples thereof and exact values of tan for 0, π/6, π/4, π/3, π/2, π and multiples thereof.
 
TLMaths – E3: Trig Graphs (google.com)
Trigonometry Basics | MME (mathsmadeeasy.co.uk)
Trig Graphs | MME (mathsmadeeasy.co.uk)
 
E5 Understand and use tan θ≡ cos θ/sin θ
Understand and use sin²θ +cos²θ ≡1; sec²θ ≡ 1 + tan²θ and cosec²θ ≡ 1 + cot²θ
 
TLMaths – E5: Trigonometric Identities (google.com)
Basic Trig Identities | MME (mathsmadeeasy.co.uk)
 
E8 Construct proofs involving trigonometric functions and identities.
 
TLMaths – E8: Proving Trigonometric Identities (google.com)
 

B7 Understand and sketch the modulus of linear functions.
Interpret algebraic solutions of equations graphically; use intersection points of graphs to solve equations.
 
TLMaths – B7: Graphs & Proportion (google.com)
The Modulus Function | Revision | MME (mmerevise.co.uk)

B8 Understand and use composite functions, inverse functions, and their graphs.
 
TLMaths – B8: Functions
Composite and Inverse Functions | Revision | MME (mmerevise.co.uk)
 
B6 Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use of the factor theorem. Simplify rational expressions including by factorising and cancelling, and algebraic division (by linear expressions only).
 
TLMaths – B6: Polynomials & Rational Expressions
Polynomials | Revision | MME (mmerevise.co.uk)
 
B10 Decompose rational functions into partial fractions (denominators not more complicated than squared linear terms and with no more than three terms, numerators constant or linear).
 
TLMaths – B10: Algebraic Fractions
Partial Fractions | Revision | MME (mmerevise.co.uk)
 

B9 Understand the effect of simple transformations on the graph of y = f(x) including sketching associated graphs: y = af(x), y = f(x) + a, y = f(x + a) and y = f(ax) and combinations of these transformations.
 
TLMaths – B9: Graph Transformations (google.com)
Graph Transformations | Revision | MME (mmerevise.co.uk)

A1 Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including proof by deduction, proof by exhaustion. Disproof by counter example. Proof by contradiction (including proof of the irrationality of 2 and the infinity of primes, and application to unfamiliar proofs)
 
TLMaths – A1: Proof (google.com)
Proof | Revision | MME (mmerevise.co.uk)
Proof by Contradiction | Revision | MME (mmerevise.co.uk)

J1 Use vectors in two dimensions and in three dimensions.
 
TLMaths – J1: Introducing Vectors (google.com)
 
J5 Use vectors to solve problems in pure mathematics and in context, including forces and kinematics.
 
TLMaths – J5: Vector Problems (google.com)
3D Vectors | Revision | MME (mmerevise.co.uk)
 

Q3 Understand, use and derive the formulae for constant acceleration for motion in a straight line; extend to 2 dimensions using vectors.
 
TLMaths – Q3: SUVAT (google.com)
SUVAT Equations | Revision | MME (mmerevise.co.uk)
 
Q4 Use calculus in kinematics for motion in a straight line:
v = dr/dt,  a = dv/dt = d²r/dt²,  r = ʃ v dt,  v = ʃa dt
Extend to 2 dimensions using vectors
 
TLMaths – Q4: Calculus in Kinematics
Non-Uniform Acceleration | Revision | MME (mmerevise.co.uk)
Vectors in Mechanics | Revision | MME (mmerevise.co.uk)
 
Q5 Model motion under gravity in a vertical plane using vectors; projectiles.
 
TLMaths – Q5: Projectiles
Projectiles | Revision | MME (mmerevise.co.uk)
 

R1 Understand the concept of a force; understand and use Newton’s first law.
 
TLMaths – R1: Introducing Forces & Newton’s First Law
Forces | Revision | MME (mmerevise.co.uk)
 
R2 Understand and use Newton’s second law for motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2-D vectors); extend to situations where forces need to be resolved (restricted to 2 dimensions).
 
TLMaths – R2: Newton’s Second Law
 
R4 Understand and use Newton’s third law; equilibrium of forces on a particle and motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2-D vectors); application to problems involving smooth pulleys and connected particles; resolving forces in 2 dimensions; equilibrium of a particle under coplanar forces.
 
TLMaths – R4: Newton’s Third Law and Pulleys
Connected Particles | Revision | MME (mmerevise.co.uk)
 
R5 Understand and use addition of forces; resultant forces; dynamics for motion in a plane.
 
TLMaths – R5: F=ma & Differential Equations
 
R6 Understand and use the F ≤ µR model for friction; coefficient of friction; motion of a body on a rough surface; limiting friction and statics.
 
TLMaths – R6: The Coefficient of Friction
Friction | Revision | MME (mmerevise.co.uk)
 
 

S1 Understand and use moments in simple static contexts.
 
TLMaths – S1: Moments
Moments | Revision | MME (mmerevise.co.uk)

I1 Locate roots of f(x) = 0 by considering changes of sign of f(x) in an interval of x on which f(x) is sufficiently well-behaved. Understand how change of sign methods can fail.
 
TLMaths – I1: The Change of Sign Method
 
 
I2 Solve equations approximately using simple iterative methods; be able to draw associated cobweb and staircase diagrams.
Solve equations using the Newton-Raphson method and other recurrence relations of the form x_{n + 1}= g(x_n) .
Understand how such methods can fail.
 
TLMaths – I2: The x=g(x) Method & The Newton-Raphson Method
Newton-Raphson Method | Revision | MME (mmerevise.co.uk)
 
I3 Understand and use numerical integration of functions, including the use of the trapezium rule and estimating the approximate area under a curve and limits that it must lie between.
 
TLMaths – I3: Numerical Integration
 
I4 Use numerical methods to solve problems in context.
 
TLMaths – I4: Numerical Methods in Context
Locating Roots | Revision | MME (mmerevise.co.uk)
 
H4 Understand and use integration as the limit of a sum.
 
TLMaths – H4: Integration as the Limit of a Sum
 

D2 Work with sequences including those given by a formula for the nth term and those generated by a simple relation of the form x_n+1 = f(x_n); increasing sequences; decreasing sequences; periodic sequences.
 
TLMaths – D2: Sequences
 
D3 Understand and use sigma notation for sums of series.
 
TLMaths – D3: Sigma Notation
 
D4 Understand and work with arithmetic sequences and series, including the formulae for nth term and the sum to n terms.
 
TLMaths – D4: Arithmetic Sequences
Arithmetic Series | Revision | MME (mmerevise.co.uk)
 
D5 Understand and work with geometric sequences and series including the formulae for the nth term and the sum of a finite geometric series; the sum to infinity of a convergent geometric series, including the use of |r| < 1; modulus notation.
 
TLMaths – D5: Geometric Sequences
Geometric Series | Revision | MME (mmerevise.co.uk)
 
D6 Use sequences and series in modelling.
 
TLMaths – D6: Modelling with Sequences
 

D1 Understand and use the binomial expansion of (a + bx)ⁿ for positive integer n; the notations n! and nCr; link to binomial probabilities.
Extend to any rational n, including its use for approximation; be aware that the expansion is valid for ǀ bx/a ǀ < 1 (Proof not required.)
 
TLMaths – D1: Binomial Expansion
Binomial Expansion | Revision | MME (mmerevise.co.uk)

G1 Understand and use the derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a general point (x, y); the gradient of the tangent as a limit; interpretation as a rate of change; sketching the gradient function for a given curve; second derivatives; differentiation from first principles for small positive integer powers of x and for sin x and cos x.
Understand and use the second derivative as the rate of change of gradient; connection to convex and concave sections of curves and points of inflection.
 
TLMaths – G1: Differentiation from First Principles
Differentiation from First Principles | Revision | MME (mmerevise.co.uk)
 
G2 Differentiate xⁿ, for rational values of n, and related constant multiples, sums and differences.
Differentiate e^kx and a^kx, sin kx, cos kx and tan kx related sums, differences and constant multiples.
Understand and use the derivative of ln x.
 
TLMaths – G2: Differentiation
More Differentiation | Revision | MME (mmerevise.co.uk)
 
G3 Apply differentiation to find gradients, tangents and normals, maxima and minima and stationary points. Identify where functions are increasing or decreasing.
 
TLMaths – G3: Gradients
 
G4 Differentiate using the product rule, the quotient rule and the chain rule
 
TLMaths – G4: Further Differentiation
Product Rule | Revision | MME (mmerevise.co.uk)
Quotient Rule | Revision | MME (mmerevise.co.uk)
Chain Rule | Revision | MME (mmerevise.co.uk)
 
G5 Differentiate simple functions and relations defined implicitly for first derivative only.
 
TLMaths – G5: Implicit Differentiation & Parametric Differentiation
Implicit Differentiation | Revision | MME (mmerevise.co.uk)
 

C3 Understand and use the parametric equations of curves and conversion between Cartesian and parametric forms.
 
TLMaths – C3: Parametric Equations
 
C4 Use parametric equations in modelling in a variety of contexts.
 
TLMaths – C4: Parametric Equation Modelling
Parametric Equations | Revision | MME (mmerevise.co.uk)
 
G4 Using differentiation to solve problems involving connected rates of change and inverse functions.
 
TLMaths – G4: Further Differentiation
 
G5 Differentiate simple functions and relations defined parametrically, for first derivative only.
 
TLMaths – G5: Implicit Differentiation & Parametric Differentiation
Differentiating Parametric Equations | Revision | MME (mmerevise.co.uk)
 

H2  Integrate xⁿ (excluding n= –1), and related sums, differences, and constant multiples.
Integrate e^kx,1/x, sin kx, cos kx and related sums, differences, and constant multiples.
 
TLMaths – H2: Indefinite Integrals
Integrating Trig Functions | Revision | MME (mmerevise.co.uk)
 
H3 Evaluate definite integrals; use a definite integral to find the area under a curve and the area  between two curves.
 
TLMaths – H3: Definite Integrals & Parametric Integration
 
H5 Carry out simple cases of integration by substitution and integration by parts; understand these methods as the inverse processes of the chain and product rules respectively.
(Integration by substitution includes finding a suitable substitution and is limited to cases where one substitution will lead to a function which can be integrated; integration by parts includes more than one application of the method but excludes reduction formulae.)
 
TLMaths – H5: Further Integration
Integration by Substitution | Revision | MME (mmerevise.co.uk)
Integration by Parts | Revision | MME (mmerevise.co.uk)
 
H6 Integrate using partial fractions that are linear in the denominator.
 
TLMaths – H6: Integration with Partial Fractions
 

G6 Construct simple differential equations in pure mathematics and in context, (contexts may include kinematics, population growth and modelling the relationship between price and demand).
 
TLMaths – G6: Forming Differential Equations
 
H7 Evaluate the analytical solution of simple first order differential equations with separable variables, including finding particular solutions. (Separation of variables may require factorisation involving a common factor.)
 
TLMaths – H7: Differential Equations
 
H8 Interpret the solution of a differential equation in the context of solving a problem, including identifying limitations of the solution; includes links to kinematics.
 
TLMaths – H8: Differential Equations in Context
Differential Equations | Revision | MME (mmerevise.co.uk)
 

M2 Understand and use conditional probability, including the use of tree diagrams, Venn diagrams, two-way tables.
Understand and use the conditional probability formula P(AǀB) = P(AՈB)/P(B)
 
TLMaths – M2: Conditional Probability
Conditional Probability and Tree Diagrams | Revision | MME (mmerevise.co.uk)
 
M3 Modelling with probability, including critiquing assumptions made and the likely effect of more realistic assumptions.
 
TLMaths – M3: Modelling with Probability
Probability and Venn Diagrams | Revision | MME (mmerevise.co.uk)
 

N2 Understand and use the Normal distribution as a model; find probabilities using the Normal distribution. Link to histograms, mean, standard deviation, points of inflection and the binomial distribution.
 
TLMaths – N2: The Normal Distribution
The Normal Distribution | Revision | MME (mmerevise.co.uk)
The Standard Normal Distribution | Revision | MME (mmerevise.co.uk)
 
N3 Select an appropriate probability distribution for a context, with appropriate reasoning, including recognising when the binomial or Normal model may not be appropriate.
 
TLMaths – N3: Appropriate Distributions
Selecting a Distribution | Revision | MME (mmerevise.co.uk)
 

O1  Understand and apply the language of statistical hypothesis testing, developed through a binomial model: null hypothesis; alternative hypothesis, significance level, test statistic, 1-tail test, 2-tail test, critical value, critical region, acceptance region, p-value; extend to correlation coefficients as measures of how close data points lie to a straight line and be able to interpret a given correlation coefficient using a given p-value or critical value (calculation of correlation coefficients is excluded).
 
TLMaths – O1: Introducing Hypothesis Testing
Hypothesis Testing | Revision | MME (mmerevise.co.uk)
 
O2 Conduct a statistical hypothesis test for the proportion in the binomial distribution and interpret the results in context.
Understand that a sample is being used to make an inference about the population and appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis.
 
TLMaths – O2: Binomial Hypothesis Testing
Binomial Distribution Hypothesis Tests | Revision | MME (mmerevise.co.uk)
 
O3 Conduct a statistical hypothesis test for the mean of a Normal distribution with known, given or assumed variance and interpret the results in context.
 
TLMaths – O3: Sample Means Hypothesis Testing
Normal Distribution Hypothesis Tests | Revision | MME (mmerevise.co.uk)