England · AQASyllabus
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 determine the motion of an object, and how do you apply Newton's laws to solve problems?Force as a vector, the resultant of forces, Newton's three laws of motion, weight and the relationship between mass and weight, connected particles, and resolving forces in two dimensions.11 min answer →
- How does friction resist motion, and how do you decide whether an object stays still or slides?The nature of friction, the coefficient of friction, the limiting friction model with the inequality between friction and the normal reaction, and applying friction to objects on horizontal and inclined surfaces.11 min answer →
- How do you describe and calculate the motion of an object, using graphs and equations of constant acceleration?Displacement, velocity and acceleration, motion graphs and the meaning of their gradients and areas, the constant acceleration equations, motion under gravity, and using calculus to relate displacement, velocity and acceleration.11 min answer →
- How do you decide whether a rigid object will balance or turn, and where its supports must act?The moment of a force about a point, the principle of moments, equilibrium of a rigid body under coplanar forces, reactions at supports, and modelling uniform and non-uniform rods.10 min answer →
- How do you analyse the motion of an object launched into the air under gravity alone?Modelling projectile motion by resolving into independent horizontal and vertical components, using the constant acceleration equations, and finding range, maximum height, time of flight and the equation of the path.11 min answer →
- What are the basic quantities and units used in mechanics, and how do scalars and vectors differ?The base and derived SI units used in mechanics, the distinction between scalar and vector quantities, modelling assumptions such as particles and smooth surfaces, and the conventions for representing forces and motion.9 min answer →
Pure mathematics
Module overview →- How do you manipulate, factorise and transform algebraic expressions and functions accurately?Indices, surds, quadratics, simultaneous equations, inequalities, polynomials, the factor theorem, partial fractions, graphs of functions, composite and inverse functions, the modulus function and graph transformations.11 min answer →
- How do you describe straight lines, circles and curves using coordinates and equations?Equations of straight lines, gradients, parallel and perpendicular lines, the equation of a circle, tangents and chords, and parametric equations of curves.10 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, stationary points and their nature, and connected rates of change.11 min answer →
- How do exponential and logarithmic functions describe growth and decay, and how do you manipulate and solve equations involving them?The exponential function and its derivative, the natural logarithm, the laws of logarithms, solving exponential and logarithmic equations, and using logarithms to linearise data and model exponential growth and decay.11 min answer →
- How do you reverse differentiation to find areas, and what techniques let you integrate more complicated functions?Integration as the reverse of differentiation, indefinite and definite integrals, the area under a curve, integration of standard functions, integration by substitution and by parts, and using partial fractions to integrate rational functions.11 min answer →
- When you cannot solve an equation or integrate a function exactly, how do you find a reliable approximate answer?Locating roots by sign change, iterative methods including fixed point iteration and the Newton-Raphson method, the conditions under which they succeed or fail, and the trapezium rule for approximating definite integrals.11 min answer →
- How do you prove a mathematical statement is always true, and how do you disprove one?Methods of proof including proof by deduction, proof by exhaustion, disproof by counter-example and proof by contradiction, applied to statements about numbers and inequalities.10 min answer →
- How do you describe, sum and expand sequences and series?Arithmetic and geometric sequences and series, sigma notation, the conditions for convergence of a geometric series, the binomial expansion for positive integer and rational powers, and recurrence relations.10 min answer →
- How do the trigonometric functions, their identities and inverse functions let you model and solve problems involving angles?Radian measure, arc length and sector area, the trigonometric ratios and their graphs, exact values, identities, the reciprocal and inverse functions, the addition and double angle formulae, and solving trigonometric equations.11 min answer →
- How do vectors represent position and movement in two and three dimensions, and how do you calculate with them?Vectors in two and three dimensions, magnitude and direction, addition and scalar multiplication, unit vectors and components, position vectors, and using vectors to solve geometric problems.10 min answer →
Statistics
Module overview →- How do you summarise, display and interpret data, and how do you identify relationships and outliers?Measures of location and spread, histograms, box plots and cumulative frequency, identifying outliers, scatter diagrams, correlation and the use of regression lines.11 min answer →
- How do you use sample data to test a claim about a population, and decide whether the evidence is strong enough?Setting up null and alternative hypotheses, the significance level, one-tailed and two-tailed tests, hypothesis tests for a binomial proportion and for a normal mean, critical regions, and interpreting the conclusion in context.11 min answer →
- How do you calculate the likelihood of events, including when events depend on or exclude one another?Probability of events, mutually exclusive and independent events, the addition and multiplication rules, Venn diagrams and tree diagrams, and conditional probability.10 min answer →
- How do you model a random variable mathematically, and how do you use that model to find probabilities?Discrete random variables and their probability distributions, the requirement that probabilities sum to one, the use of statistical distributions to model real situations, and an introduction to the binomial and normal models.9 min answer →
- How do you select a sample that fairly represents a population, and what are the trade-offs of each method?Populations and samples, the advantages and limitations of sampling, simple random sampling, systematic, stratified, quota and opportunity sampling, and the importance of the large data set.9 min answer →
- How do you model the number of successes in a fixed number of independent trials, and find probabilities from that model?The conditions for a binomial model, the binomial probability formula, calculating individual and cumulative probabilities, the mean of a binomial distribution, and using the model in context.10 min answer →
- How do you model a continuous quantity that clusters symmetrically about a mean, and find probabilities from it?The normal distribution as a model for continuous data, its mean and standard deviation, calculating probabilities, the standard normal distribution and standardising, finding values from probabilities, and using the normal approximation to the binomial.11 min answer →