GCSE Maths guides
Free, clear guides to GCSE Maths: topics, equations, exam technique and revision plans.
- GCSE Maths revision: a plan that worksA practical GCSE Maths revision plan: what to revise first, how to use past papers, and a week-by-week plan for Foundation and Higher tier.
- Circle theorems, explainedAll eight GCSE circle theorems explained in plain English, with how to spot them in exam questions and how to give reasons for full marks.
- GCSE Maths topics: the full listThe full list of GCSE Maths topics for Foundation and Higher tier, grouped into the six content areas, with the Higher-only topics marked.
- GCSE Maths vectorsGCSE Maths vectors explained: column vectors, adding and multiplying vectors, and how to answer Higher tier vector proof questions.
- GCSE Maths trigonometryGCSE Maths trigonometry explained: SOHCAHTOA, exact values, the sine rule, the cosine rule and the area of a triangle, with when to use each.
- GCSE Maths surdsSurds for GCSE Maths Higher explained: what a surd is, simplifying, adding and multiplying surds, expanding brackets and rationalising the denominator.
- Mean, median, mode and range, explainedMean, median, mode and range explained for GCSE Maths: averages from frequency tables and grouped data, missing values, and practice with answers.
- Bearings, explained with examplesBearings explained for GCSE Maths: the three rules, measuring and drawing, back bearings, and bearings with trigonometry, with practice questions and answers.
- Upper and lower bounds, explained with examplesUpper and lower bounds explained for GCSE Maths: bounds from rounding, error intervals, and bounds in calculations, with practice questions and answers.
- Box plots, explained with examplesBox plots explained for GCSE Maths: the five-number summary, quartiles, drawing a box plot, IQR, outliers and comparing distributions, with practice.
- Area of a circle, explained with examplesArea of a circle explained for GCSE Maths: A = πr², using the diameter, answers in terms of π, finding the radius, semicircles and sectors, with practice.
- Compound interest, explained with examplesCompound interest explained for GCSE Maths: the multiplier method, the formula, compound vs simple interest, depreciation and reverse problems, with practice.
- Completing the square, explained with examplesCompleting the square explained for GCSE and A level Maths: the method, when a is not 1, solving equations and finding turning points, with practice.
- Cumulative frequency, explained with examplesCumulative frequency explained for GCSE Maths: the table, plotting the graph, reading the median, quartiles and IQR, with practice questions and answers.
- Volume of a cylinder, explained with examplesVolume of a cylinder explained for GCSE Maths: V = πr²h, using the diameter, finding the height or radius, capacity in litres and surface area, with practice.
- Factorising quadratics, explained with examplesFactorising quadratics explained for GCSE Maths: common factors, x² + bx + c, difference of two squares, and the ac method when a is not 1, with practice.
- Histograms, explained with examplesHistograms explained for GCSE Maths: frequency density, unequal class widths, reading frequencies and estimating within a class, with practice and answers.
- Index laws, explained with examplesLaws of indices explained for GCSE Maths: multiplying and dividing powers, zero, negative and fractional indices, and solving index equations, with practice.
- Inequalities, explained with examplesInequalities explained for GCSE Maths: number lines, solving linear inequalities, flipping the sign, integer solutions, quadratic inequalities and regions.
- Straight line graphs, explained with examplesStraight line graphs explained for GCSE Maths: gradient, y = mx + c, the equation from two points, parallel and perpendicular lines, with practice and answers.
- The nth term, explained with examplesThe nth term explained for GCSE Maths: linear sequences, checking if a number is in a sequence, quadratic and geometric sequences, with practice and answers.
- Percentage change, explained with examplesPercentage change explained for GCSE Maths: the formula, increase and decrease, profit and loss, multipliers, reverse percentages and repeated changes.
- Pie charts, explained with examplesPie charts explained for GCSE Maths: calculating angles, drawing accurately, reading frequencies and percentages, and comparing two pie charts, with practice.
- Prime factors, HCF and LCM, explainedPrime factors, HCF and LCM explained for GCSE Maths: factor trees, products of primes, and HCF and LCM with Venn diagrams and word problems, with practice.
- Pythagoras' theorem, explained with examplesPythagoras' theorem explained for GCSE Maths: finding the hypotenuse and shorter sides, triples, distance between points and 3D problems, with practice.
- The quadratic formula, explained with examplesThe quadratic formula explained for GCSE Maths: when to use it, substituting without sign errors, the discriminant, surd answers and practice with answers.
- Ratio, explained with examplesRatio explained for GCSE Maths: simplifying, sharing in a ratio, finding totals from one part, combining ratios, best buys and scale, with practice and answers.
- Speed, distance and time, explained with examplesSpeed, distance and time explained for GCSE: the formula and triangle, unit conversions, average speed, distance-time graphs and km/h to m/s, with practice.
- Simultaneous equations, explained with examplesSimultaneous equations explained for GCSE Maths: elimination and substitution, linear and quadratic pairs, graphical solutions and word problems, with practice.
- The sine rule and cosine rule, explainedThe sine and cosine rules explained for GCSE and A level: finding sides and angles, which rule to use, the ambiguous case and ½ab sin C, with practice.
- Standard form, explained with examplesStandard form explained for GCSE Maths: writing large and small numbers, converting back, and multiplying, dividing, adding and subtracting, with practice.
- Area of a trapezium, explained with examplesArea of a trapezium explained for GCSE Maths: ½(a + b)h, why it works, finding a missing side or height, and compound shapes, with practice and answers.
- Probability tree diagrams, explained with examplesProbability tree diagrams explained for GCSE Maths: drawing them, multiplying and adding, with and without replacement, and conditional probability.
- Venn diagrams, explained with examplesVenn diagrams explained for GCSE Maths: two- and three-set diagrams, set notation, probabilities and conditional probability, with practice and answers.