England · Pearson EdexcelSyllabus
Maths syllabus, dot point by dot point
Every dot point in the England Mathssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Mechanics
Module overview →- How do forces cause acceleration, and how do you analyse the forces acting on a body?Newton's three laws of motion, weight and the relationship between mass and force, resolving forces, friction and the coefficient of friction, and connected particles.11 min answer →
- How do you describe and calculate motion using displacement, velocity, acceleration and time?Displacement, velocity and acceleration, motion graphs, the constant acceleration formulae, and using calculus to relate displacement, velocity and acceleration that vary with time.10 min answer →
- How do you analyse the turning effect of forces and the conditions for a rigid body to balance?The moment of a force about a point, the principle of moments, equilibrium of a rigid body, and problems involving rods, beams and reactions at supports.8 min answer →
- How do you analyse the motion of a body launched into the air under gravity?Projectile motion resolved into horizontal and vertical components, the independence of the two motions, and finding range, maximum height, time of flight and the path.9 min answer →
- What are the basic quantities and units of mechanics, and how do you model real situations to apply them?Fundamental and derived quantities and their SI units, scalar and vector quantities, and the modelling assumptions used to simplify mechanics problems.7 min answer →
Pure mathematics
Module overview →- How do you manipulate expressions, solve equations and inequalities, and transform graphs?Algebra and functions including indices and surds, quadratics, simultaneous equations, inequalities, polynomials, graphs, functions and transformations, the binomial expansion and partial fractions.12 min answer →
- How do you describe lines, circles and curves with equations and use them?Coordinate geometry in the x and y plane including straight lines, the equation of a circle, tangents, chords and parametric equations of curves.11 min answer →
- How do you find the rate at which a quantity changes, and how do you use that to analyse curves and solve optimisation problems?Differentiation from first principles, the rules for powers, the chain, product and quotient rules, derivatives of standard functions, implicit and parametric differentiation, stationary points and connected rates of change.11 min answer →
- How do you work with exponential growth and decay, and how do logarithms undo exponentials?The exponential function and the number e, the natural logarithm, the laws of logarithms, solving exponential equations, and using logarithms to linearise and model real data.9 min answer →
- How do you reverse differentiation to find areas, volumes and total change?Indefinite and definite integrals, areas under curves, integrals of standard functions, integration by substitution and by parts, integration using partial fractions, and differential equations.11 min answer →
- How do you find roots and areas approximately when an exact answer is not available?Locating roots by change of sign, iterative methods including the Newton-Raphson method, the trapezium rule for numerical integration, and the conditions under which these methods fail.9 min answer →
- How do you prove a statement is always true, and how do you show one is false?Structure of mathematical proof including proof by deduction, proof by exhaustion, disproof by counter-example and proof by contradiction, applied to statements about numbers and inequalities.9 min answer →
- How do you describe and sum patterns of numbers, and expand binomials for any power?Sequences and series including arithmetic and geometric sequences, sigma notation, sums to infinity, recurrence relations, and the binomial expansion for any rational power.9 min answer →
- How do you work with angles, trigonometric functions and identities to solve equations and model periodic behaviour?Radian measure, arc length and sector area, exact values, the Pythagorean and addition identities, reciprocal and inverse functions, and solving trigonometric equations.11 min answer →
- How do you represent quantities with both magnitude and direction, and use them in geometry and motion?Vectors in two and three dimensions, magnitude and direction, addition and scalar multiplication, position vectors, unit vectors, and geometric applications.9 min answer →
Statistics
Module overview →- How do you summarise, display and interpret data, and how do you measure how two variables are related?Measures of location and spread, diagrams for single and bivariate data, outliers and cleaning, correlation and the equation of a regression line, and interpolation versus extrapolation.10 min answer →
- How do you use sample evidence to decide whether to accept or reject a claim about a population?Null and alternative hypotheses, one- and two-tailed tests, significance levels and critical regions, hypothesis tests for a binomial proportion, and for a correlation coefficient and a normal mean.11 min answer →
- How do you measure the chance of events, and how do you combine probabilities of related events?Probability of events, mutually exclusive and independent events, the addition and multiplication laws, conditional probability, and Venn and tree diagrams.9 min answer →
- How do you model a discrete random variable, and when is the binomial distribution the right model?Discrete random variables and probability distributions, the binomial distribution, its conditions, and calculating binomial probabilities with technology.9 min answer →
- How do you select a representative sample from a population, and what are the trade-offs of each method?Populations and samples, census and sampling, random and non-random sampling methods, and the advantages and limitations of each in context.8 min answer →
- How do you model continuous data with the normal distribution, and how do you find probabilities and unknown parameters?The normal distribution as a model for continuous data, finding probabilities, the standard normal distribution, using the inverse normal, and approximating the binomial.10 min answer →