Wales · WJECSyllabus
Maths syllabus, dot point by dot point
Every dot point in the Wales 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.
AS Unit 1 Pure Mathematics A
Module overview →- How do we manipulate surds, indices, quadratics, polynomials and inequalities, and transform graphs?Surds and indices, quadratic functions and the discriminant, simultaneous equations, inequalities, polynomial division and the factor theorem, and graph transformations.13 min answer →
- How do we describe straight lines and circles algebraically and find where they meet?Equations of straight lines, parallel and perpendicular gradients, the equation of a circle, tangents and chords, and intersections of lines and curves.12 min answer →
- How do we find the gradient of a curve at a point, and use it to locate tangents and turning points?Differentiation from first principles, differentiating powers of , gradients, tangents and normals, increasing and decreasing functions, and stationary points.13 min answer →
- How do exponential and logarithmic functions behave, and how do we use logs to solve equations and model growth?The exponential function and , logarithms and their laws, solving equations with logs, and fitting exponential models with a log-linear graph.12 min answer →
- How do we reverse differentiation, and use the definite integral to find the area under a curve?Integration as the reverse of differentiation, indefinite integrals with a constant, definite integrals and the limits, and the area under a curve.12 min answer →
- How do we prove a mathematical statement rigorously, and how do we show one is false?Proof by deduction, proof by exhaustion, and disproof by counterexample, with the language and structure WJEC rewards.11 min answer →
- How do we expand a bracket raised to a positive integer power without multiplying it out term by term?The binomial expansion of for positive integer , binomial coefficients and Pascal's triangle, and finding a specified term.11 min answer →
- How do we work with trig graphs, identities and equations, and solve triangles that are not right-angled?Graphs of sine, cosine and tangent, the identities and , solving trig equations, and the sine and cosine rules.13 min answer →
- How do we represent and combine vectors in two dimensions, and use position vectors in geometry?Vectors in two dimensions, magnitude and direction, addition and scalar multiplication, position vectors, and dividing a line segment in a given ratio.11 min answer →
AS Unit 2 Applied Mathematics A
Module overview →- How do Newton's laws relate force to acceleration, and how do we handle weight, tension, friction and connected particles?Newton's three laws, force diagrams, weight, normal reaction, tension, friction, and connected particles over a pulley.13 min answer →
- How do we describe motion in a straight line using graphs and the equations of constant acceleration?Quantities and units in mechanics, displacement, velocity and acceleration, motion graphs, and the constant-acceleration (suvat) equations including vertical motion under gravity.12 min answer →
- How do we calculate probabilities for combined events using Venn diagrams and the addition and multiplication rules?Probability of events, Venn diagrams and set notation, the addition rule, mutually exclusive and independent events, and tree diagrams.12 min answer →
- How do we model the number of successes in a fixed number of trials, and what is the binomial distribution?Discrete random variables and probability distributions, the binomial distribution and its conditions, and calculating binomial probabilities.12 min answer →
- How do we test a claim about a probability using a sample and the binomial distribution?Null and alternative hypotheses, one-tailed and two-tailed tests, the significance level, critical regions, and the binomial hypothesis test.13 min answer →
- How do we sample a population fairly, and how do we present and interpret the data we collect?Populations and samples, random and non-random sampling methods, and presenting and interpreting data with measures of location, spread, histograms and box plots.12 min answer →
A2 Unit 3 Pure Mathematics B
Module overview →- How do we handle the modulus function, composite and inverse functions, and split a rational expression into partial fractions?The modulus function and its graphs and equations, composite and inverse functions, and resolving rational expressions into partial fractions.13 min answer →
- How do we differentiate products, quotients, composite functions and implicit relations, and the standard functions?The chain, product and quotient rules, implicit differentiation, derivatives of exponential, logarithmic and trigonometric functions, and the second derivative and concavity.14 min answer →
- How do we integrate by parts, by substitution, and using partial fractions, and the standard functions?Integrating standard functions, integration by substitution, integration by parts, integration using partial fractions, and definite integrals for areas.14 min answer →
- How do we locate and approximate roots when there is no exact algebraic solution, and estimate an area numerically?Locating roots by change of sign, iterative methods, the Newton-Raphson method, and the trapezium rule for numerical integration.13 min answer →
- How do we describe a curve using a parameter, convert to Cartesian form, and find its gradient?Parametric equations of curves, converting between parametric and Cartesian forms, and differentiating parametrically to find gradients and tangents.12 min answer →
- How do we prove a statement by assuming it is false and deriving a contradiction?Proof by contradiction, the structure of the method, and the classic results proved this way (the irrationality of root 2, the infinitude of primes).11 min answer →
- How do we sum arithmetic and geometric series, handle infinite sums, and expand a binomial for any rational power?Arithmetic and geometric sequences and series, sigma notation, the sum to infinity of a convergent geometric series, and the binomial expansion for any rational index.13 min answer →
- How do we use radians, the reciprocal ratios, and the compound and double-angle identities to simplify and solve trig problems?Radian measure, the reciprocal functions secant, cosecant and cotangent, the compound and double-angle formulae, and the harmonic form R sin(theta + alpha).14 min answer →
A2 Unit 4 Applied Mathematics B
Module overview →- How does knowing one event has happened change the probability of another?Conditional probability, the conditional probability formula, the multiplication rule, independence, and probability from two-way tables and tree diagrams.12 min answer →
- How do we form and solve a differential equation to model a rate of change?Forming differential equations from a rate of change, solving first-order equations by separating the variables, and applying them to growth, decay and mechanics.13 min answer →
- How do we resolve forces on an inclined plane, model friction, and take moments to analyse equilibrium?Resolving forces on inclined planes, the friction model and the coefficient of friction, connected particles, and moments and the equilibrium of rigid bodies.14 min answer →
- How do we test for correlation, and test a claim about the mean of a Normal distribution?Hypothesis testing for a correlation coefficient, and hypothesis testing for the mean of a Normal distribution using the distribution of the sample mean.13 min answer →
- How do we use calculus for variable-acceleration motion, and analyse projectiles in two dimensions?Kinematics with calculus for variable acceleration, vectors in kinematics, and projectile motion resolved into horizontal and vertical components.13 min answer →
- How do we model continuous data with the Normal distribution and find probabilities and unknown parameters?Continuous random variables and the Normal distribution, standardising to the standard Normal, finding probabilities, and the Normal approximation to the binomial.13 min answer →