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.
Algebra
Module overview →- How do you expand brackets, factorise expressions, simplify algebraic fractions and rearrange formulae?Algebraic manipulation: simplifying expressions, expanding single and double brackets, factorising (common factors, quadratics and the difference of two squares), and rearranging (changing the subject of) formulae.10 min answer →
- How do you solve and represent inequalities, and recognise and sketch quadratic, cubic, reciprocal and exponential graphs?Solving linear and quadratic inequalities and representing solutions on number lines and graphs, and recognising and sketching 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?Solving quadratic equations by factorising, by the quadratic formula and by completing the square (Higher tier), and interpreting the roots and the turning point of the curve.11 min answer →
- How do you find the nth term of linear and quadratic sequences, and recognise special sequences?Sequences: generating terms, finding the nth term of a linear (arithmetic) sequence and a quadratic sequence (Higher tier), and recognising geometric, triangular, square, cube and Fibonacci sequences.9 min answer →
- How do you solve simultaneous equations by elimination, substitution and graphically, including one linear and one quadratic?Solving simultaneous equations: two linear equations by elimination and by substitution, finding the solution graphically, and solving one linear and one quadratic equation (Higher tier).10 min answer →
- How do you solve linear equations, including those with brackets, fractions and the unknown on both sides?Solving linear equations in one unknown, including equations with brackets, equations with the unknown on both sides, and equations involving fractions, and forming equations from worded contexts.9 min answer →
- How do you find the gradient and intercept of a line, use y = mx + c, and find equations of parallel and perpendicular lines?Straight line graphs: plotting lines, finding the gradient and y-intercept, using the equation y = mx + c, finding the equation of a line through two points, and parallel and perpendicular lines (Higher tier).10 min answer →
Geometry and measures
Module overview →- How do you use angle facts on lines and in triangles, and find the interior and exterior angles of polygons?Angle facts: angles on a line and around a point, vertically opposite angles, angles in parallel lines (alternate, corresponding and co-interior), angles in triangles and quadrilaterals, and the interior and exterior angles of polygons.10 min answer →
- How do you find the area of 2D shapes and the surface area and volume of prisms, cylinders, cones and spheres?Area of triangles, parallelograms and trapeziums; circumference and area of circles; volume and surface area of prisms and cylinders; and the volume and surface area of cones, spheres and pyramids (Higher tier).10 min answer →
- How do you find arc lengths and sector areas, and apply the circle theorems to find angles?Parts of a circle, arc length and sector area, and the circle theorems including the angle at the centre, angles in a semicircle, angles in the same segment, cyclic quadrilaterals, the tangent-radius angle and the alternate segment theorem (Higher tier).10 min answer →
- How do you carry out standard ruler-and-compass constructions and use them to find loci and regions?Standard constructions with ruler and compasses (perpendicular bisector of a line, perpendicular from a point, angle bisector), constructing triangles, and finding loci and regions satisfying given conditions.9 min answer →
- How do you use Pythagoras' theorem and trigonometry to find sides and angles, including the sine and cosine rules?Pythagoras' theorem in right-angled triangles, the trigonometric ratios sine, cosine and tangent, exact trig values, and the sine rule, cosine rule and area formula for any triangle (Higher tier).11 min answer →
- How do you describe and carry out translations, reflections, rotations and enlargements, including negative and fractional scale factors?The four transformations: translation by a vector, reflection in a line, rotation about a point, and enlargement by a scale factor including fractional and negative scale factors (Higher tier), and describing a single transformation fully.9 min answer →
- How do you add, subtract and scale vectors, and use them to prove geometric results such as parallel or collinear points?Vectors: column vectors, adding, subtracting and multiplying vectors by a scalar, the magnitude of a vector, and using vectors in geometric proofs including parallel lines and points lying on a straight line (Higher tier).9 min answer →
Number
Module overview →- How do you find prime factors, the highest common factor and the lowest common multiple of numbers?Factors, multiples and primes: prime factor decomposition (product of prime factors), the highest common factor (HCF) and lowest common multiple (LCM), and using Venn diagrams to find them.8 min answer →
- How do you calculate with fractions, convert between fractions, decimals and percentages, and find percentages of amounts?Calculating with fractions (the four operations, including mixed numbers), converting between fractions, decimals and percentages including recurring decimals, and working with percentages of amounts.10 min answer →
- How do you round to significant figures, estimate calculations and find the upper and lower bounds of a rounded value?Rounding to decimal places and significant figures, estimating calculations using rounding, and finding the upper and lower bounds of measurements, including error intervals and bounds in calculations (Higher tier).9 min answer →
- How do you use the laws of indices and write and calculate with numbers in standard form?The laws of indices including zero, negative and fractional powers, and standard form: writing very large and very small numbers and calculating with them.9 min answer →
- How do you use the four operations, place value, negative numbers and the priority of operations accurately without a calculator?The structure of the number system: ordering integers and decimals, the four operations with positive and negative numbers, place value, the priority of operations (BIDMAS), and inverse operations.9 min answer →
- How do you simplify surds, calculate with them and rationalise a denominator?Surds: simplifying surds, the four operations with surds, expanding brackets containing surds, and rationalising the denominator (Higher tier).9 min answer →
Probability
Module overview →- How do you use the probability scale, calculate probabilities of single and combined events, and use sample spaces?The probability scale and notation, probabilities of single events, mutually exclusive and exhaustive events, the AND and OR rules for combined events, and listing outcomes using sample space diagrams.9 min answer →
- How do you estimate probability from experiments using relative frequency, and predict expected numbers of outcomes?Estimating probability from experimental data using relative frequency, comparing experimental and theoretical probability, and calculating the expected number of outcomes from a probability.9 min answer →
- How do you use tree diagrams for combined events, including independent and conditional (without replacement) probability?Tree diagrams for two or more events, multiplying along branches and adding between paths, and conditional probability where the second event depends on the first (without replacement) at Higher tier.10 min answer →
- How do you use Venn diagrams and set notation to organise data and calculate probabilities?Venn diagrams for two or three sets, set notation (union, intersection and complement), and using a completed Venn diagram to find probabilities including conditional probability (Higher tier).9 min answer →
Ratio, proportion and rates of change
Module overview →- How do you use the formulae for speed, density and pressure, and convert between compound units?Compound measures: speed, distance and time; density, mass and volume; pressure, force and area; and converting between compound units such as metres per second and kilometres per hour.9 min answer →
- How do you solve direct and inverse proportion problems, including using the unitary method and proportion formulae?Direct and inverse proportion: the unitary method, recognising and using proportion relationships, and forming and using proportion equations with a constant of proportionality (Higher tier).9 min answer →
- How do you model repeated growth and decay, and find rates of change from graphs including gradients and areas?Growth and decay problems (including compound growth and depreciation), interpreting the gradient of a graph as a rate of change, and estimating the gradient of a curve and the area under a graph (Higher tier).9 min answer →
- How do you calculate percentage change, use multipliers for increase and decrease, find a reverse percentage, and work out compound interest?Percentage change: percentage increase and decrease using multipliers, percentage profit and loss, reverse percentages (finding the original amount), and simple and compound interest.10 min answer →
- How do you simplify ratios, divide a quantity in a given ratio, and use scale factors and scale drawings?Ratio: simplifying ratios, dividing a quantity in a given ratio, expressing ratios as fractions and unit ratios, combining ratios, and using scale factors, maps and scale drawings.10 min answer →
Statistics
Module overview →- How do you find the mean, median, mode and range, including from frequency tables and grouped data?The mean, median, mode and range; finding averages from frequency tables and from grouped data using the midpoint and an estimated mean; and comparing distributions using an average and the range.10 min answer →
- How do you choose a representative sample, classify types of data, and design fair data collection?Populations and samples, representative and biased sampling, random sampling, types of data (qualitative and quantitative, discrete and continuous), and designing questionnaires and data collection.9 min answer →
- How do you draw and interpret scatter graphs, describe correlation, and use a line of best fit?Scatter graphs and bivariate data, describing correlation (positive, negative or none), drawing and using a line of best fit to estimate values, and recognising the dangers of extrapolation and correlation versus causation.9 min answer →
- How do you draw and interpret bar charts, pie charts, frequency polygons, cumulative frequency graphs and box plots?Drawing and interpreting statistical diagrams: bar charts, pictograms, pie charts, frequency polygons, cumulative frequency graphs and box plots, and finding the median, quartiles and interquartile range (Higher tier).10 min answer →