England · WJEC EduqasSyllabus
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.
Algebra
Module overview →- How do you expand brackets, factorise expressions and change the subject of a formula?Simplify and manipulate algebraic expressions: collect like terms, expand single and double brackets, factorise (common factors, quadratics and the difference of two squares), and rearrange formulae to change the subject.11 min answer →
- How do you solve and represent inequalities, and recognise quadratic, cubic, reciprocal and exponential graphs?Solve linear inequalities and represent solutions on a number line; solve quadratic inequalities (Higher tier); and recognise and sketch the graphs of quadratic, cubic, reciprocal and exponential functions.10 min answer →
- How do you solve quadratic equations by factorising, the quadratic formula and completing the square?Solve quadratic equations by factorising, by the quadratic formula and by completing the square (Higher tier), and interpret the roots and the turning point of the curve.12 min answer →
- How do you find the nth term of linear and quadratic sequences and recognise special sequences?Generate sequences from a rule; find the nth term of a linear sequence and a quadratic sequence (Higher tier); and recognise arithmetic, geometric, square, cube, triangular and Fibonacci sequences.10 min answer →
- How do you solve simultaneous equations by elimination and substitution, including one linear and one quadratic?Solve two simultaneous linear equations by elimination and substitution; solve a linear and a quadratic equation simultaneously (Higher tier); and interpret the solution as the point of intersection.11 min answer →
- How do you solve linear equations, including with brackets, fractions and the unknown on both sides?Solve linear equations in one unknown, including those with brackets, fractions and the unknown on both sides, and form linear equations from worded and geometric contexts.10 min answer →
- How do you find the gradient, intercept and equation of a straight line, and identify parallel and perpendicular lines?Use the equation to find the gradient and intercept; find the equation of a line through given points; and identify parallel and perpendicular lines (perpendicular at Higher tier).10 min answer →
Geometry and measures
Module overview →- How do you use angle facts at points, on lines and in parallel lines, and find the angles of polygons?Use angle facts at a point, on a straight line and in parallel lines (alternate, corresponding and co-interior); and calculate the interior and exterior angles of polygons.11 min answer →
- How do you find the area and perimeter of 2D shapes and the surface area and volume of 3D solids?Calculate the area and perimeter of rectangles, triangles, parallelograms, trapezia, circles and sectors; and the surface area and volume of prisms, cylinders, pyramids, cones and spheres.12 min answer →
- What are the circle theorems and how do you use them to find angles and write proofs?Know and use the circle theorems (angle at the centre, angle in a semicircle, angles in the same segment, cyclic quadrilateral, tangent properties and alternate segment) to find angles and construct reasoned proofs (Higher tier).12 min answer →
- How do you carry out standard ruler-and-compass constructions and find loci of points satisfying a condition?Carry out standard constructions (perpendicular bisector, angle bisector, perpendicular from a point) with ruler and compasses, and find loci of points satisfying a given condition, including in combination.11 min answer →
- How do you use Pythagoras and the trigonometric ratios in right-angled triangles, and the sine and cosine rules in any triangle?Use Pythagoras' theorem and the trigonometric ratios in right-angled triangles; and apply the sine rule, cosine rule and the area formula in any triangle (Higher tier).12 min answer →
- How do you describe and perform translations, rotations, reflections and enlargements?Describe and perform the four transformations (translation, rotation, reflection and enlargement, including negative and fractional scale factors at Higher tier) and combine them.11 min answer →
- How do you add, subtract and scale vectors, and use them in geometric proofs?Use vector notation; add, subtract and multiply vectors by a scalar; and use vectors to construct geometric arguments and proofs (proof at Higher tier).11 min answer →
Number
Module overview →- How do you write a number as a product of primes, and use that to find the HCF and LCM?Identify primes; write a number as a product of its prime factors using index notation; and find the highest common factor (HCF) and lowest common multiple (LCM) of two numbers, including from prime factorisation.11 min answer →
- How do you calculate with fractions, convert between fractions, decimals and percentages, and find percentages of amounts?Carry out the four operations with fractions; convert between fractions, decimals and percentages (including recurring decimals to fractions at Higher tier); and find a percentage of an amount and one quantity as a percentage of another.12 min answer →
- How do you round, estimate a calculation, and find the upper and lower bounds of a rounded value?Round to a given number of decimal places or significant figures; estimate calculations by rounding to one significant figure; and find upper and lower bounds and use them in calculations (Higher tier).11 min answer →
- How do the laws of indices work, and how do you calculate with numbers in standard form?Apply the laws of indices (including zero, negative and fractional indices at Higher tier); and write numbers in standard form and calculate with them, both with and without a calculator.12 min answer →
- How do you order numbers and calculate accurately with the four operations, directed numbers and the correct order of operations?Order positive and negative integers, decimals and fractions; use the four operations with whole numbers, decimals and directed numbers; and apply the correct order of operations (BIDMAS), including brackets, powers and roots.11 min answer →
- How do you simplify surds, carry out the four operations with them, and rationalise a denominator?Simplify surds, carry out the four operations with surds, expand brackets containing surds, and rationalise the denominator of a fraction (Higher tier).11 min answer →
Probability
Module overview →- How do you use the probability scale, find probabilities of single and combined events, and use sample space diagrams?Use the probability scale from 0 to 1; calculate probabilities of single events from equally likely outcomes; use the fact that probabilities sum to 1; and list combined outcomes using sample space diagrams.11 min answer →
- How do you use relative frequency to estimate probability and calculate expected outcomes?Use relative frequency (experimental probability) to estimate probabilities from data, understand how more trials improve the estimate, and calculate expected numbers of outcomes.10 min answer →
- How do you use tree diagrams to find probabilities of combined events, with and without replacement?Draw and use tree diagrams to calculate probabilities of combined events, including independent events and conditional events without replacement (Higher tier).11 min answer →
- How do you use Venn diagrams and set notation to organise data and find probabilities?Use Venn diagrams and set notation (union, intersection and complement) to represent and count outcomes and to calculate probabilities, including conditional probability (Higher tier).11 min answer →
Ratio, proportion and rates of change
Module overview →- How do you calculate with compound measures such as speed, density and pressure, including unit conversions?Use compound measures including speed, density and pressure; rearrange the defining formulae; and convert between units such as m/s and km/h.11 min answer →
- How do you solve direct and inverse proportion problems and form proportion equations using a constant of proportionality?Solve problems involving direct and inverse proportion, including using the unitary method and forming proportion equations of the form or with a constant of proportionality (Higher tier).11 min answer →
- How do you model growth and decay over time and interpret the gradient and area of a real-life graph as a rate of change?Model exponential growth and decay over repeated periods; and interpret the gradient of a graph as a rate of change and the area under a graph in real-life contexts (Higher tier).11 min answer →
- How do you work out percentage change, reverse percentages and compound interest using a multiplier?Calculate percentage increase and decrease, find the percentage change between two values, solve reverse percentage problems, and apply repeated percentage change including compound interest using multipliers.12 min answer →
- How do you simplify ratios, divide a quantity in a given ratio, and use ratios with scale and similar shapes?Use ratio notation; simplify ratios and express them in the form ; divide a quantity in a given ratio; and apply ratio to scale drawings, maps and similar shapes.11 min answer →
Statistics
Module overview →- How do you find and compare the mean, median, mode and range, including from frequency tables?Calculate the mean, median, mode and range; find the mean from a frequency table and an estimated mean from grouped data; and compare distributions using an average and the range (and quartiles at Higher tier).11 min answer →
- How do you identify types of data, design a sample, and recognise bias in data collection?Identify types of data (qualitative and quantitative, discrete and continuous); understand populations and samples; use random and stratified sampling; and recognise sources of bias.10 min answer →
- How do you interpret correlation on a scatter graph, draw a line of best fit, and use it to make predictions?Plot and interpret scatter graphs; describe correlation; draw a line of best fit; use it to estimate values; and understand interpolation, extrapolation and the difference between correlation and causation.10 min answer →
- How do you draw and interpret bar charts, pie charts, frequency polygons, histograms and box plots?Draw and interpret statistical charts including bar charts, pie charts, frequency polygons, stem-and-leaf diagrams, box plots and histograms with unequal class widths (histograms at Higher tier).11 min answer →