Maths (Year 13)
See Year 13s Maths ‘Schedule of Learning’ for the 2025/26 academic year:
| Topic Pure & Mechanics | Sub-topic | Topic Pure & Statistics | Sub-topic |
|---|---|---|---|
| Differentiation | -be able to find the derivative of sin x and cos x from first principles. -be able to differentiate functions involving ex, ln x and related functions such as 6e4x and 5 ln 3x and sketch the graphs of these functions; -be able to differentiate to find equations of tangents and normals to the curve. | Trigonometric Functions | -understand the secant, cosecant and cotangent functions, and their relationships to sine, cosine and tangent. -be able to sketch the graphs of secant, cosecant and cotangent -be able to solve identities involving sec, cosec and cot |
| Differentiation | -Differentiate functions using the chain, product and quotient rules | Trigonometric Functions | -know and be able to use the identities 1 + tan²x = sec²x and 1 + cot²x = cosec²x to prove other identities and solve equations in degrees and/or radians -be able to work with the inverse trig functions sin–1, cos–1 and tan–1 -be able to sketch the graphs of sin–1, cos–1 and tan–1 |
| Differentiation | -be able to differentiate parametric equations -be able to use implicit differentiation to differentiate an equation involving two variables – Use the second derivative to describe the behaviour of a function | Trigonometry and Modelling | -be able to prove geometrically the following compound angle formulae for sin (A ± B), cos (A ± B) and tan (A ± B) -be able to use compound angle identities to rearrange expression, prove other identities and rearrange equations into a different form and then solve |
| Differentiation | – Solve problems involving connected rate of change and construct simple differential equations | Trigonometry and Modelling | -be able to recall or work out double angle identities -be able to use double angle identities to rearrange expressions or prove other identities and rearrange equations into a different form and then solve ‘-be able to express acosθ+b sinθ as a single sine or cosine function and solve in a given interval ‘- Prove trigonometric identities using a variety of identities -Use trigonometric functions to model real-life situations |
| Vectors | – Understand 3D Cartesian coordinates -Use vectors in three dimensions -Use vectors to solve geometric problems | Parametric Equations | -Understand the difference between the Cartesian and parametric system of expressing coordinates; -be able to convert between parametric and Cartesian forms. -be able to plot and sketch curves given in parametric form; -recognise some standard curves in parametric form and how they can be used for modelling |
| Vectors | –Model 3D motion in mechanics with vectors | Parametric Equations | |
| Moments | -realise that a force can produce a turning effect; -know that a moment of a force is given by the formula force × distance giving Nm and know what the sense of a moment is; -understand that the force and distance must be perpendicular to one another; | Integration | -be able to integrate expressions by inspection using the reverse of differentiation – Integrate standard mathematical functions including trigonometric and exponential functions -be able to integrate expressions by inspection using the reverse of the chain rule (or function of a function) |
| Moments | -be able to draw mathematical models to represent horizontal rod problems; -realise what conditions are needed for a system to remain in equilibrium; -be able to solve problems when a bar is on the point of tilting | Integration | -be able to integrate a function expressed parametrically -recognise integrals of the form ∫(f^’ (x))/(f(x)) dx = ln |f(x)| + c; -be able to use trigonometric identities to manipulate and simplify expressions to a form which can be integrated directly |
| Forces and Friction | -understand the language relating to forces; -be able to identify the forces acting on a particle and represent them in a force diagram; -understand how to find the resultant force (magnitude and direction); -be able to find the resultant of several concurrent forces by vector addition -be able to resolve a force into components and be able to select suitable directions for resolution. | Integration | -be able to integrate expressions using an appropriate substitution; -be able to integrate an expression using integration by parts -be able to integrate rational expressions by using partial fractions that are linear in the denominator |
| Forces and Friction | -understand that a rough plane will have an associated frictional force, which opposes relative motion -understand that the ‘roughness’ of two surfaces is represented by a value called the coefficient of friction represented by µ; -know that 0 ≤ µ but that there is no theoretical upper limit for µ although for most surfaces it tends to be less than 1 and that a ‘smooth’ surface has a value of µ = 0; -be able to draw force diagrams involving rough surfaces which include the frictional force -understand and be able to use the formula F ≤ µR. | Integration | – Use integration to find the area under a curve -Use the trapezium rule to approximate the area under a curve -Solve simple differential equations and model real-life situations with differential equations |
| Projectiles | -be able to find the time of flight of a projectile; -be able to find the range and maximum height of a projectile; -be able to derive formulae to find the greatest height, the time of flight and the horizontal range (for a full trajectory | Regression, Correlation and Hypothesis Testing | -be able to change the variable in a regression line; be able to estimate values from regression line -understand correlation coefficients and interpret; be able to calculate the PMCC (calculator only); -be able to conduct a hypothesis test for a correlation coefficient. |
| Projectiles | ‘-know how to modify projectile equations to take account of the height of release; -be able to derive and use the equation of the path. | Conditional Probability | -understand and be able to use probability formulae using set notation; -be able to use tree diagrams, Venn diagrams and two-way tables -understand and be able to use the conditional probability formula P(A|B)=(P(A∩B))/(P(B)) |
| Application of Forces | -understand that a body is in equilibrium under a set of concurrent (acting through the same point) forces is if their resultant is zero; -know that vectors representing forces in equilibrium form a closed polygon; -understand how to solve problems involving equilibrium of a particle under coplanar forces, including particles on inclined planes and 2D vectors; -be able to solve statics problems for a system of forces which are not concurrent (e.g. ladder problems), thus applying the principle of moments for forces at any angle. | Conditional Probability | -be able to model with probability; -be able to critique assumptions made and the likely effect of more realistic assumptions. |
| Application of Forces | -know and understand the meaning of Newton’s second law; -be able to formulate the equation of motion for a particle in 1-dimensional motion where the resultant force is mass × acceleration; -be able to formulate the equation of motion for a particle in 2-dimensional motion where the resultant force is mass × acceleration; -be able to formulate and solve separate equations of motion for connected particles, where one of the particles could be on an inclined and/or rough plane. | Normal Distribution | -understand the properties of the Normal distribution; -be able to find probabilities using the Normal distribution; -know the position of the points of inflection of a Normal distribution. |
| Further Kinematics | -be able to recognise when the use of constant acceleration formulae is appropriate; -be able to write positions, velocities and accelerations in vector form and find the magnitude and direction of vectors. -be able to extend techniques for motion in 1D to 2D by using vectors; -know how to use velocity triangles to solve simple problems; -understand and use suvat formulae for constant acceleration in 2D and apply the equations of motion to i, j vector problems; -be able to use v = u + at , r = ut + 1/2at2 etc. with vectors given in i , j or column vector form. | Normal Distribution | -be able to find the mean and variance of a binomial distribution; -understand and be able to apply a continuity correction; -be able to use the Normal distribution as an approximation to the binomial distribution. |
| Further Kinematics | -be able to extend techniques for motion in 1 dimension to 2 dimensions by using calculus and vector versions of equations for variable force/acceleration problems; -understand the language and notation of kinematics appropriate to variable motion in 2 dimensions, i.e. knowing the notation r ̇ and r ̈ for variable acceleration in terms of time. | Normal Distribution | -be able to conduct a statistical hypothesis test for the mean of the Normal distribution; -be able to interpret the results in context. |
Exam Board – Edexcel
What will you study?
Algebraic Methods, Functions and Graphs, Sequences and Series, The Binomial Expansion, Radians, Trigonometric Functions, Trigonometry and Modelling, Regression and Correlation, Moments, Forces and Friction.
Parametric Equations, Differentiation, Numerical Methods, Integration, Conditional Probability, The Normal Distribution, Projectiles, Application of Forces
Integration, Further Kinematics.
Useful tips and resources
The Year 13 Curriculum covers aspects of Pure Mathematics, Statistics and Mechanics. It’s aim is to build on and extend the topics studied in Year 12, as well as introducing new topics. At A Level, the emphasis is on Using and Applying Mathematics ; in particular, relating it to the real world and looking at modelling. You should expect to be successful at A level, to be spending 10 hours per week on Mathematics, including lesson time, homework and independent practice.
Dr Frost Maths
Maths Genie
Corbett Maths
MME Revise
Save My Exams
What super curricular activities can KS3 students engage with at school for your subject?
UKMT Senior Maths Challenge
Hans Woyda Club – Autumn Term
Maths Stretch and Challenge – nrich.maths.org
The Winton Gallery – The Science Museum, London
The Bank of England – Financial History
Bletchley Park – Coding and Alan Turing
The History of Science Museum in Oxford