Edexcel GCSE Mathematics
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Papers 1, 2 and 3
1 Number
N1, N2 - Integers, decimals and written arithmeticCompare positive and negative numbers, understand what each digit is worth, and calculate with integers and decimals. Written methods and simple checks will help you spot an answer with the wrong sign or size.
N1, N2, N3 - Fractions, mixed numbers and cancellationCompare fractions, convert mixed numbers and use all four operations with exact fractional values. Equal-sized parts and inverse operations explain why the methods work, including when a quantity is negative.
N3, N6, N7 - Powers, roots and the order of operationsUse powers, roots and integer indices to calculate exactly. Brackets and operation order tell you what an expression means; inverse operations and familiar powers help you check the result.
N4, N5 - Primes, factors, multiples and systematic listsBuild whole numbers from prime factors, find shared factors and multiples, and choose the right method for grouping or repeating cycles. Organised lists will help you justify that you have found every possibility exactly once.
N5, N6 - The product rule and estimates of rootsCount successive choices efficiently, including choices with restrictions. Use familiar powers and carefully chosen trial values to locate unfamiliar roots and justify their rounding.
N7, N8, A4 - Fractional indices and exact surd calculationsUse fractional indices to connect powers and roots, then calculate exactly with surds. Simplify, collect and expand surd expressions, and rewrite fractions with rational denominators without changing their values.
N8, N9 - Exact multiples of pi and standard formKeep exact values intact and write very large or small numbers compactly. N8 develops exact calculations with fractions and multiples of pi; N9 develops standard form, its four operations and sensible interpretation of calculator displays.
N10, N12 - Fractions, decimals and percentage operatorsFractions, decimals and percentages are different ways to describe the same proportion. N10 connects terminating decimals with exact fractions; N12 uses fractions and percentages as operators, both to find a part and to recover its whole.
N10 - Recurring decimals and fractionsA recurring decimal can be an exact fraction even though its digits never stop. Learn why division repeats, how multiplication and subtraction recover the fraction, and how to handle a non-repeating start before the repeating digits.
N14, N15, N16 - Estimation, rounding and simple error intervalsN14 uses estimates to check answers, including calculator displays. N15 develops decimal places, significant figures and intervals from rounding or truncation. N16 uses these limits of accuracy to judge what a reported measurement really tells you.
N16 - Upper and lower bounds in calculationsRounded measurements can produce a range of calculated answers. Learn to find the extremes for sums, differences, products and quotients, interpret whether a boundary is included, and justify a reliable degree of accuracy for a compound measure.
2 Algebra
A1, A2, A3 - Algebraic notation, vocabulary and substitutionAlgebra lets you describe a calculation before you know its inputs. Learn to read its shorthand, distinguish expressions from mathematical statements, and substitute numbers into expressions and formulae, including scientific formulae.
A4 - Simplifying, expanding and common factorsThe same expression can be written as a sum, a product or a shorter expression with powers. Learn to collect like terms, expand a single bracket, extract common factors and apply integer index laws without changing the value.
A4, A18 - Quadratic expansion, factorisation and rootsTwo brackets can hide a quadratic expression, and a quadratic can hide two brackets. Learn to move between these forms, recognise a difference of squares and use factorisation to find the values that make a quadratic equation true.
A4 - Advanced factorisation and algebraic fractionsFactorisation makes larger expressions easier to handle. Learn to expand several brackets in stages, factorise quadratics with a non-unit leading coefficient, and calculate with algebraic fractions while keeping track of their original restrictions.
A5 - Rearranging formulaeA formula can be rewritten to calculate a different quantity. Learn to reverse operations, manage brackets and fractions, handle powers and roots, and collect a subject that appears more than once.
A6 - Equivalence, identities and algebraic argumentsA few matching answers can suggest a pattern, but algebra can explain whether it always works. Learn to distinguish equations from identities, show expressions are equivalent and assess a claim using a general argument or a counterexample.
A6 - Algebraic proofAlgebra can settle a claim about every integer without checking the integers one by one. You will represent whole families of numbers, prove parity and divisibility statements, and spot arguments that leave out cases or use invalid operations.
A7 - Functions as inputs and outputsA function turns each allowed input into one output. You will read rules, calculate input-output tables and recover an input by reversing a process, checking when an input is allowed and when an output is possible.
A7 - Inverse and composite functionsFunction notation lets you name a rule, reverse it and combine it with another rule. You will calculate with numerical and algebraic inputs, find inverse functions with appropriate restrictions, and solve equations involving compositions in either order.
A8, A9, A10 - Coordinates, straight lines and gradientsCoordinates place points precisely (A8). You will use straight-line equations to plot and find lines (A9), then read and interpret their gradients and intercepts (A10), including how to recognise parallel lines.
A9, A16 - Perpendicular lines, circles and tangentsPerpendicular gradients connect straight-line algebra (A9) to circle equations and tangents (A16). You will use circles centred at the origin, find a tangent at a given point and recover a contact point from a tangent line.
A11, A12, A18 - Quadratic graphs and approximate rootsA quadratic graph's shape, roots and turning point reveal its behaviour (A11 and A12). You will plot and interpret these curves, find roots using factors, and estimate equation solutions from graph intersections (A18).
A11, A18 - Completing the square and the quadratic formulaA11 links a quadratic's algebra to its turning point. A18 gives you ways to solve it even when its factors are awkward. You will complete the square, use the quadratic formula, choose a method, and handle parameters and algebraic fractions.
A12, A14 - Cubic, reciprocal and real-context graphsA12 helps you recognise cubic and reciprocal graphs. A14 uses graphs to explore unfamiliar rules and motion. You will calculate useful points, choose sensible joins and read distances, speeds and accelerations from labelled axes.
A12, A13, A14 - Exponential, trigonometric and transformed graphsA12 introduces graphs of repeated multiplication and repeating cycles. A13 moves and reflects a given graph, while A14 uses exponential graphs in context. You will recognise the shapes, find graph intersections and track important points without recalculating a whole table.
A15, R15 - Gradients, areas and rates on curved graphsA15 uses graph gradients and areas to interpret motion and money. R15 distinguishes average change from change at one moment. You will draw and read tangents, build area estimates from simple shapes, and use the axes to decide what the answer means.
A17, A21 - Linear equations and mathematical modelsA17 uses algebra and graph intersections to solve linear equations. A21 turns quantities and number procedures into equations, then interprets the answers. You will keep equality balanced, handle brackets and fractions, and check that a solution makes sense.
A19, A21 - Simultaneous linear equationsA19 finds a pair of values that satisfies two linear equations at once. A21 uses those equations to model linked quantities. You will solve by elimination, substitution and graph intersections, then interpret both values in context.
A19 - Linear and quadratic simultaneous equationsA line and a curve can share two points, one point or no points. You will use substitution to find their common coordinates, keep each solution pair together and connect the algebra with a graph.
A20 - Numerical solutions by iterationIteration feeds an answer back into the same calculation. You will build suitable rules, retain enough accuracy and check whether repeated values really approach a solution.
A22 - Linear inequalities and number linesAn inequality describes a range of possible values. You will solve linear inequalities, explain negative division, show solutions on number lines and choose permitted whole-number answers in a context.
A22 - Regions and quadratic inequalitiesSome inequalities select coordinate regions; others select intervals on a number line. You will use boundary lines, overlaps and quadratic signs to find these solutions, then express them clearly using set notation.
A23, A24, A25 - Sequence rules and linear nth termsA23 gives rules for generating terms, A24 develops familiar number patterns and A25 gives direct rules for arithmetic sequences. You will distinguish position from value, recognise sequences and find terms without writing every earlier one.
A24, A25 - Quadratic and surd sequencesA24 extends sequence recognition to surd ratios and other rules. A25 develops quadratic nth terms. You will use differences, exact arithmetic and equations to find rules, test membership and recover unknown parameters.
3 Ratio, proportion and rates of change
N11, R3, R4, R5, R6, R7, R8 - Ratios, fractions and proportional sharingRatios describe relative amounts rather than fixed totals. You will connect ratios to fractions and linear relationships, share quantities, combine linked ratios and track changes to mixtures. These methods help you keep a recipe's flavour while changing its size.
N13, R1, R11, G14 - Standard units and compound measuresA numerical answer gains meaning from its unit: a distance, an area and a speed need different conversions. You will convert standard and compound units, read times and timetables, and calculate speed, pay, unit prices, density and pressure using consistent units.
R2, G15 - Scale drawings, maps and bearingsScale drawings preserve length proportions while bearings specify directions from north. You will convert map distances, construct and measure scale diagrams on paper, and use clockwise bearings to place points and interpret routes.
R9 - Percentage changes and financial mathematicsEvery percentage compares with a base quantity. You will calculate percentage changes, reverse them to recover an original value, use simple interest and compare the complete costs of financial offers.
R10, R13, R14 - Direct and inverse proportionSome quantities change by the same factor, while others change by reciprocal factors. You will solve numerical proportion problems, interpret given equations and graphs, and use a straight line's gradient as a rate of change.
R10, R13 - Constructing proportional relationshipsTurn statements about direct and inverse proportion into equations, then use known values to find the constant. You will also work with powers, roots and two changing quantities, and check whether a proposed model fits its data.
R16 - Compound interest, growth and decayRepeated percentage changes use a changing amount, so their effects build up by multiplication. Calculate growth, depreciation and compound interest, reverse changes to find a starting amount or rate, and decide what a model's predictions mean.
R16 - General iterative processesSome repeated changes combine a percentage with a fixed addition or removal. Form a rule for the next amount, use it repeatedly, undo its steps and explain whether its predictions settle towards a fixed value.
R12, G19 - Similarity ratios for lengths, areas and volumesUse corresponding lengths to scale areas and volumes of similar figures, then work backwards from area or volume information. Link these ratios to capacity, mass and coating, and explain why equal areas alone do not guarantee the same shape.
4 Geometry and measures
G1, G4 - Geometrical language, triangles and quadrilateralsA square is still a square when you turn it onto a corner. You will use precise geometrical language and diagram marks, recognise triangles and quadrilaterals from their properties, and turn written descriptions into drawings.
G3 - Angle facts, parallel lines and polygonsYou can find an angle without putting a protractor on a diagram. You will use straight lines and parallel lines to calculate angles, explain why every triangle totals 180°, and build polygon rules from that result.
G2 - Ruler and compass constructions and lociCompass arcs turn equal distances into accurate lines and shapes. You will construct bisectors and perpendiculars, build figures from given measurements, and combine loci to find every point satisfying a set of conditions.
G5, G6 - Triangle congruence and geometrical argumentsTwo triangles can match exactly even when one is turned or reflected. You will decide when their information guarantees a match, then use congruence, angle facts and similarity to explain triangle and quadrilateral properties and prove Pythagoras' theorem.
G7, G24 - Reflections, rotations, translations and enlargementsA shape can move, turn, reflect or change size in a precisely controlled way. You will construct images vertex by vertex, describe each transformation completely, use column vectors for translations, and recognise which properties stay unchanged.
G7, G8 - Negative enlargements and combined transformationsA negative enlargement reverses the direction from its centre. You will construct these images, follow transformations in order, and use unchanged properties to describe a combination as one transformation when that is possible.
G9, G17, G18 - Circles, circumference, arcs and sectorsA radius fixes a circle's size, and a central angle fixes a fraction of that circle. You will identify circle features, calculate lengths and areas, recover missing values, and trace the correct boundary of a circular shape.
G10 - Circle theorems and their proofsEqual radii, triangle angle facts and congruence explain circle theorems. You will prove the standard results, apply them to angles and lengths, and combine them into complete geometrical arguments.
G11 - Geometrical problems on coordinate axesCoordinates provide evidence about a shape's lengths, directions and midpoints. You will use that evidence to classify shapes, find missing vertices and justify geometrical conclusions, including perpendicular-gradient proofs at Higher tier.
G12, G13 - Three-dimensional shapes, plans and elevationsA solid has width, depth and height, while each flat view records only two of them. You will identify solid properties, draw plans and elevations, and decide what these views can reveal or hide.
G16, G17 - Perimeters, areas and composite shapesPerimeter measures the distance around a shape; area measures the space inside it. You will find missing boundary lengths, use perpendicular heights in area formulae, and split or subtract regions to solve composite-shape problems.
G16, G17 - Volumes and surface areas of solidsVolume measures the space inside a solid; surface area measures its boundary. You will calculate both for prisms, cylinders, pyramids, cones and spheres, then decide which volumes and surfaces count when solids are joined or cut.
G19, R12 - Congruence and similarity of lengthsCongruent figures have the same size and shape; similar figures keep the same shape while allowing a change of size. You will match corresponding sides, use length scale factors in either direction, and explain why similar right triangles have equal side ratios.
G6, G20 - Pythagoras theorem in two dimensionsPythagoras' theorem links the three side lengths of a right-angled triangle. You will understand its area relationship, find missing lengths, test whether an angle is right, and choose the useful right triangles inside larger two-dimensional problems.
G20, G21 - Right-angle trigonometry and exact valuesTrigonometry connects an angle in a right-angled triangle to ratios of side lengths. You will choose sine, cosine or tangent to find sides and angles, derive exact special-angle values, and calculate heights and distances from observations.
G22, G23 - Sine rule, cosine rule and triangle areaA triangle need not contain a right angle for you to calculate its missing measurements. G22 gives you the sine and cosine rules for lengths and angles; G23 connects two sides and their included angle to the area. You will learn which information each rule needs and how to combine the rules witho...
G20 - Pythagoras and trigonometry in three dimensionsA solid can hide a familiar triangle. You will learn to choose a flat section through a cuboid or pyramid, calculate spatial lengths in stages, and identify the angle between a line and a plane or between two lines. The triangle methods stay the same; choosing the correct triangle is the new skill.
G25 - Vector notation and arithmeticA vector records a movement, including its direction. You will connect arrows with column notation, add and subtract displacements, scale them, and use routes to find missing vectors. These ideas describe the same movement even when the arrow is drawn in a different place.
G25 - Vector arguments and proofsVectors can prove a geometric statement for every figure satisfying the given conditions. You will describe positions and ratios, distinguish parallelism from collinearity, find unknown scalars, and build general midpoint and diagonal proofs. The important final step is to explain what the vector...
5 Probability
P1, P2, P3, P4, P5 - Probability, relative frequency and expected outcomesProbability describes uncertainty; frequency records what actually happened. P1–P3 connect experimental records, fair models and predictions, P4 explains how complete outcomes fit together, and P5 explains why more unbiased evidence usually improves an estimate. You will calculate chances and exp...
P6, P7 - Sample spaces, sets and Venn diagramsP6 uses lists, tables, grids, Venn diagrams and trees to organise possibilities without omissions or repeats. P7 turns equally likely outcomes into theoretical probabilities. You will also complete two-way tables and separate overlapping groups before counting them.
P8 - Combined events and probability treesP8 combines events through independent or dependent stages. You will build probability trees, multiply along complete paths and add successful alternatives, checking what the procedure assumes about replacement and independence. The final Higher part uses probability to find an unknown count.
P9 - Conditional probabilityP9 studies how a condition changes the group of possible outcomes. You will calculate conditional probabilities using expected frequencies, two-way tables, Venn diagrams and trees, and distinguish a condition from its reverse. Each part develops Higher content.
6 Statistics
S1, S5 - Samples, populations and statistical inferenceHow can a small survey say anything about a much larger group? S1 explains how samples support an inference and why their selection matters. S5 uses those results to describe a population, with a clear distinction between an observed count and an estimate.
S2 - Tables, charts and time-series dataThe same counts can look very different in different displays. Learn to organise one-way and two-way tables, choose and construct charts for categories, discrete values and time series, and preserve the meaning of the original data when plotting.
S4 - Averages, range and grouped-data estimatesA single “average” can hide very different stories. Learn to calculate and choose measures of centre and spread, work with frequency tables and grouped estimates, and recover or combine totals when a mean is given.
S6 - Scatter graphs, correlation and predictionA scatter graph keeps two measurements from each case together. Learn to plot paired observations, recognise correlation, estimate a line of best fit and make predictions whose limits are clear.
S3 - Histograms and frequency densityA histogram uses area to represent frequency, so unequal class widths need more than a comparison of heights. Learn to construct and read histograms, recover frequencies and scales, and estimate a median or probability from grouped data with the assumptions stated.
S3, S4 - Cumulative frequency, quartiles and box plotsHow can you compare two groups without listing every measurement? S3 uses cumulative frequency to estimate positions in grouped data. S4 uses quartiles, box plots and spread to compare typical values and consistency, while keeping the limits of these summaries clear.