Every formula, every topic.
Free formula sheets for every GCSE Maths topic — definitions, formulas, worked examples, common mistakes and exam tips. Each sheet is print-ready: click Print / Save as PDF on any sheet to download it.
Jump to strand
Number
Integers, fractions, percentages, ratio, indices, standard form, surds, bounds.
Fractions –
Master fractions for GCSE Maths with step-by-step methods, worked examples, and practice questions for Foundation and Higher tiers…
Decimals –
Learn how to work with decimals in GCSE Maths including ordering, rounding, and the four operations with clear examples.
Percentages –
Complete guide to GCSE Maths percentages covering percentage change, reverse percentages, and compound interest with worked exampl…
Powers and Roots
Understand squares, cubes, square roots, and cube roots for GCSE Maths with clear methods and exam-style practice questions.
Standard Form –
Master standard form for GCSE Maths with step-by-step methods for writing, calculating, and converting standard form numbers.
Surds –
Learn how to simplify, add, multiply, and rationalise surds for GCSE Maths Higher tier with step-by-step examples.
Bounds and Error Intervals –
Master bounds and error intervals for GCSE Maths Higher tier with clear rules for upper and lower bounds in calculations.
Indices and Index Laws –
Complete guide to index laws for GCSE Maths covering multiplying, dividing, negative and fractional indices with worked examples.
Prime Factorisation, HCF and LCM –
Learn prime factorisation, HCF and LCM for GCSE Maths with factor trees, Venn diagrams, and step-by-step worked examples.
Order of Operations (BIDMAS) –
Master BIDMAS for GCSE Maths with clear explanations of operation order, worked examples, and common exam pitfalls to avoid.
Adding and Subtracting Fractions –
Learn how to add and subtract fractions with different denominators using the LCD method. Worked examples and practice for GCSE Ma…
Multiplying and Dividing Fractions –
Master multiplying and dividing fractions for GCSE Maths. Learn cross-cancelling, Keep-Change-Flip, and practise with worked examp…
Percentage of an Amount –
Learn how to find a percentage of an amount with and without a calculator. Step-by-step methods, worked examples and GCSE practice…
Percentage Change –
Learn the percentage change formula for GCSE Maths. Step-by-step method for finding percentage increase and decrease between two v…
Percentage Multipliers –
Master decimal multipliers for percentage increase, decrease and repeated change. GCSE Maths worked examples and practice question…
Simplifying Surds –
Learn how to simplify surds, add and subtract surds, and multiply surds for GCSE Maths Higher tier with worked examples and practi…
Rationalising the Denominator –
Learn how to rationalise the denominator for GCSE Maths Higher tier. Single surds and conjugate pairs with worked examples and pra…
Negative and Fractional Indices –
Master negative and fractional indices for GCSE Maths Higher tier. Learn x to the power -1, 1/2, 2/3 with worked examples and prac…
HCF and LCM –
Learn how to find the HCF and LCM using prime factorisation, Venn diagrams, and listing. GCSE Maths worked examples and practice q…
Equivalent Fractions and Simplifying –
Learn how to find equivalent fractions, simplify fractions by dividing by the HCF, and compare fractions using cross-multiplicatio…
Fractions of Amounts –
Learn how to find a fraction of an amount for GCSE Maths with clear methods, worked examples at Foundation and Higher, and practic…
Converting Fractions, Decimals and Percentages –
Master converting between fractions, decimals and percentages for GCSE Maths with key equivalences, methods, and worked examples.
Recurring Decimals to Fractions –
Learn the algebraic method for converting recurring decimals to fractions for GCSE Maths Higher tier with worked examples and prac…
Square Numbers and Cube Numbers –
Learn square numbers, cube numbers, square roots and cube roots for GCSE Maths with key values to memorise and worked examples.
Estimating Square Roots –
Learn how to estimate square roots without a calculator for GCSE Maths by finding surrounding perfect squares with worked examples…
Rounding: Decimal Places and Significant Figures –
Master rounding to decimal places and significant figures for GCSE Maths with clear rules, worked examples, and common exam pitfal…
Multiplying and Dividing Decimals –
Learn non-calculator methods for multiplying and dividing decimals for GCSE Maths with step-by-step techniques and worked examples…
Factors, Multiples and Primes –
Learn factors, multiples, and prime numbers for GCSE Maths with factor pairs, prime factor trees, and product of primes worked exa…
Writing in Standard Form –
Learn how to convert large and small numbers to standard form (A times 10 to the n) for GCSE Maths with clear rules and worked exa…
Calculating with Standard Form –
Learn how to multiply, divide, add and subtract numbers in standard form for GCSE Maths with step-by-step methods and worked examp…
Expressing One Quantity as a Percentage –
Learn how to express one quantity as a percentage of another for GCSE Maths using the (part/whole) times 100 method with worked ex…
Algebra
Expressions, equations, graphs, quadratics, sequences, functions, iteration.
Simplifying Expressions –
Learn how to simplify algebraic expressions for GCSE Maths by collecting like terms and using index laws with worked examples.
Expanding Brackets
Master expanding single and double brackets in GCSE Maths with step-by-step methods, worked examples, and practice questions.
Factorising Expressions –
Learn how to factorise algebraic expressions at GCSE level with worked examples, step-by-step methods, and practice questions.
Solving Linear Equations –
Master solving linear equations for GCSE Maths with clear steps, worked examples, and practice questions for Foundation and Higher…
Solving Inequalities –
Learn how to solve linear inequalities for GCSE Maths with step-by-step methods, number line diagrams, and exam-style practice que…
Forming and Solving Equations –
Learn how to form and solve equations from word problems for GCSE Maths with worked examples, methods, and practice questions.
Sequences and Nth Term –
Master arithmetic sequences and the nth term rule for GCSE Maths with clear methods, worked examples, and practice questions.
Quadratic Sequences & Nth Term –
Learn how to find the nth term of a quadratic sequence for GCSE Maths Higher tier with step-by-step methods and worked examples.
Solving Quadratics by Factorising –
Learn how to solve quadratic equations by factorising for GCSE Maths with step-by-step methods, worked examples, and practice ques…
Quadratic Formula –
Master the quadratic formula for GCSE Maths Higher tier with clear steps, worked examples, discriminant explanation, and practice …
Completing the Square –
Learn completing the square for GCSE Maths Higher tier with step-by-step methods, turning points, worked examples, and practice qu…
Algebraic Fractions –
Master algebraic fractions for GCSE Maths Higher tier including simplifying, adding, subtracting, multiplying, and solving equatio…
Simultaneous Equations: Elimination –
Learn how to solve simultaneous equations using the elimination method for GCSE Maths with worked examples and practice questions.
Simultaneous Equations: Substitution –
Learn the substitution method for simultaneous equations at GCSE with step-by-step examples for linear and non-linear systems.
Linear Graphs & Equation of a Line –
Master linear graphs and the equation of a line for GCSE Maths. Learn y = mx + c, gradient, intercept, and parallel/perpendicular …
Quadratic Graphs
Learn how to plot quadratic graphs, find turning points, roots and the line of symmetry for GCSE Maths. Includes worked examples a…
Cubic, Reciprocal & Exponential Graphs –
Recognise and sketch cubic, reciprocal and exponential graphs for GCSE Maths Higher tier. Key features, shapes and worked examples…
Graph Transformations
Master graph transformations for GCSE Maths Higher tier. Learn translations, reflections, stretches with f(x) notation and worked …
Functions & Function Notation –
Understand functions and function notation for GCSE Maths Higher tier. Learn f(x), domain, range, inputs and outputs with clear wo…
Inverse & Composite Functions –
Learn inverse and composite functions for GCSE Maths Higher tier. Step-by-step methods for f⁻¹(x) and fg(x) with worked examples a…
Algebraic Proof
Master algebraic proof for GCSE Maths Higher tier. Learn how to prove statements about odd, even and consecutive numbers with work…
Iteration
Learn the iteration method for GCSE Maths Higher tier. Solve equations using iterative formulas with worked examples and exam tips…
Expanding Double Brackets –
Master expanding double brackets using FOIL and grid methods for GCSE Maths with worked examples, difference of two squares, and p…
Factorising Quadratics –
Learn how to factorise quadratic expressions of the form x² + bx + c for GCSE Maths with factor pairs, worked examples, and practi…
Equations with Unknowns on Both Sides –
Learn how to solve equations with unknowns on both sides for GCSE Maths with collecting terms, worked examples, and practice quest…
Nth Term of Linear Sequences –
Learn how to find the nth term of a linear sequence for GCSE Maths with step-by-step methods, worked examples, and practice questi…
Using the Quadratic Formula –
Master the quadratic formula for GCSE Maths Higher tier with identifying a, b, c, the discriminant, worked examples, and practice …
Completing the Square Method –
Master the completing the square method for GCSE Maths Higher tier with turning points, solving equations, worked examples, and pr…
Plotting Straight-Line Graphs –
Learn how to plot straight-line graphs using table of values and gradient-intercept methods for GCSE Maths with worked examples an…
Finding the Equation of a Line –
Learn how to find the equation of a straight line for GCSE Maths. Covers gradient and a point, two points, parallel and perpendicu…
Iteration Method –
Master the iteration method for GCSE Maths Higher tier. Learn to apply iterative formulas, show rearrangements, and find solutions…
Composite Functions –
Learn composite functions for GCSE Maths Higher tier. Understand fg(x), gf(x), ff(x) with clear worked examples, common mistakes a…
Inverse Functions –
Learn how to find inverse functions for GCSE Maths Higher tier. Step-by-step method for finding f inverse x algebraically and grap…
Inequalities on a Number Line –
Learn how to represent inequalities on a number line for GCSE Maths. Covers open and closed circles, single and double inequalitie…
Difference of Two Squares –
Master the difference of two squares at GCSE. Learn the a²−b² = (a+b)(a−b) identity with worked examples, numerical tricks, and pr…
Factorising Harder Quadratics –
Learn how to factorise quadratics where the coefficient of x² is not 1. Step-by-step ac method with worked examples and practice q…
Solving Equations with Fractions –
Learn how to solve equations containing fractions at GCSE. Multiply through by the LCD, cross-multiply, and practise with worked e…
Forming Equations from Shapes –
Learn how to form and solve equations from geometric diagrams at GCSE. Uses angle facts, perimeter, and area with worked examples …
Geometric Sequences –
Master geometric sequences at GCSE. Learn the common ratio, nth term formula ar^(n-1), and how to find missing terms with worked e…
Quadratic Inequalities –
Learn how to solve quadratic inequalities at GCSE. Factorise, sketch the parabola, and identify solution intervals with worked exa…
Inequalities on a Graph –
Learn how to represent inequalities on a graph at GCSE. Draw boundary lines, use solid or dashed lines, and shade the correct regi…
Simplifying Algebraic Fractions –
Learn how to simplify algebraic fractions at GCSE by factorising the numerator and denominator, then cancelling common factors. Wo…
Adding Algebraic Fractions –
Learn how to add and subtract algebraic fractions at GCSE. Find common denominators with algebraic expressions, combine, and simpl…
Parallel and Perpendicular Lines –
Learn parallel and perpendicular line rules at GCSE. Same gradient means parallel, product of gradients = −1 means perpendicular. …
Midpoint and Distance Between Points –
Learn the midpoint and distance formulas at GCSE. Find the midpoint of two coordinates and the distance between them with worked e…
Sketching Quadratic Graphs –
Learn how to sketch quadratic graphs at GCSE. Find the roots, y-intercept, turning point, and determine the shape of the parabola …
Cubic and Reciprocal Graphs –
Learn the shapes of cubic, reciprocal, and exponential graphs at GCSE. Recognise y = x³, y = 1/x, and y = aˣ with worked examples …
Graph Transformations: Translations and Reflections –
Learn graph transformations at GCSE: f(x)+a, f(x+a), −f(x), and f(−x). Understand translations and reflections with worked example…
Rearranging Formulae –
Learn how to rearrange formulae in GCSE Maths by changing the subject using inverse operations, with worked examples and practice …
Substitution into Expressions –
Master substitution into algebraic expressions and formulae for GCSE Maths with BIDMAS rules, negative values, and fully worked pr…
Expanding Triple Brackets –
Step-by-step guide to expanding triple brackets in GCSE Maths Higher tier, including worked examples of (x+a)(x+b)(x+c) and practi…
Solving Equations with Brackets –
Learn how to solve equations with brackets in GCSE Maths, including expanding first, brackets on both sides, and step-by-step work…
Real-Life Graphs –
Understand real-life graphs for GCSE Maths including conversion graphs, container filling graphs, and interpreting gradient in con…
Simultaneous Equations Graphically –
Solve simultaneous equations graphically in GCSE Maths by plotting two lines and finding their intersection, with step-by-step wor…
Equation of a Circle –
Learn the equation of a circle x² + y² = r² for GCSE Maths Higher tier, including finding the radius, centre at the origin, and ta…
Function Machines –
Understand function machines for GCSE Maths with input-output diagrams, finding outputs, working backwards to find inputs, and wri…
Rearranging Complex Formulae –
Rearranging complex formulae for GCSE Higher Maths: subject appears twice, formulae with powers and roots, factorising out the sub…
Quadratic Formula and Discriminant –
Quadratic formula and discriminant for GCSE Maths Higher: use b²-4ac to find how many solutions, then solve quadratics with worked…
Proof and Counter-Examples –
Proof and counter-examples for GCSE Maths Higher tier: prove algebraic statements, disprove with counter-examples, and even/odd nu…
Coordinates and Plotting –
Coordinates and plotting for GCSE Maths: read and plot points in all four quadrants, find midpoints, and understand x-y axes with …
Solving Simultaneous Equations from Context –
Solve simultaneous equations from word problems in GCSE Maths: set up equations from real-life contexts like tickets, ages, and sh…
Ratio, Proportion & Rates of Change
Speed, density, compound measures, growth and decay, scale, conversions.
Ratio Basics & Sharing in a Ratio –
Learn ratio basics and how to share amounts in a given ratio for GCSE Maths. Simplifying ratios, sharing and worked examples for F…
Ratio Problem Solving in Context –
Solve ratio problems in real-life contexts for GCSE Maths. Recipes, best buys, scaling and multi-step ratio questions with worked …
Direct & Inverse Proportion –
Learn direct and inverse proportion for GCSE Maths. Formulas, graphs, worked examples and practice questions for Foundation and Hi…
Percentages: Increase & Decrease –
Master percentage increase and decrease for GCSE Maths. Multipliers, compound interest, repeated change and worked examples for al…
Reverse Percentages
Master reverse percentages for GCSE Maths. Learn how to find the original amount before a percentage increase or decrease with wor…
Compound Interest & Depreciation –
Master compound interest and depreciation for GCSE Maths with step-by-step methods, worked examples, and practice questions.
Speed, Distance and Time –
Learn speed, distance and time calculations for GCSE Maths with the formula triangle, worked examples and practice questions.
Compound Measures: Density & Pressure –
Master density and pressure for GCSE Maths with formula triangles, worked examples at Foundation and Higher, and practice question…
Unit Conversions –
Master metric and imperial unit conversions for GCSE Maths with step-by-step methods, worked examples and practice questions.
Scale Drawings and Maps –
Master scale drawings and maps for GCSE Maths with step-by-step methods, worked examples and practice questions for all exam board…
Growth and Decay –
Master exponential growth and decay for GCSE Higher Maths with formulas, worked examples and practice questions for AQA, Edexcel a…
Sharing in a Ratio –
Master sharing in a ratio for GCSE Maths. Learn to divide amounts, find one share, and solve ratio problems when given a total or …
Speed, Distance & Time Calculations –
Master speed, distance and time calculations for GCSE Maths. S=D/T formula triangle, unit conversions, average speed and worked ex…
Direct Proportion Equations –
Learn direct proportion equations for GCSE Maths Higher. Covers y is proportional to x, x squared, and square root with constant k…
Compound Interest Calculations –
Master compound interest calculations for GCSE Maths. A = P(1 + r/100)^n, multiplier method, simple vs compound interest and depre…
Density, Mass & Volume –
Master density, mass and volume calculations for GCSE Maths. D = M/V formula triangle, unit conversions, worked examples and pract…
Simplifying Ratios –
Learn how to simplify ratios by dividing by the HCF, handle fractions and decimals in ratios, and convert to the 1:n form for GCSE…
Best Buy Problems –
Learn how to solve best buy problems by comparing unit prices, with real-world shopping examples, worked solutions and GCSE practi…
Inverse Proportion –
Master inverse proportion at GCSE: y is proportional to 1/x, finding the constant k, graphs, tables and worked Higher tier example…
Distance–Time Graphs –
Learn how to read and interpret distance-time graphs: gradient equals speed, horizontal lines mean stationary, with worked example…
Simple Interest –
Learn how to calculate simple interest using I = PRT/100, compare with compound interest, and find total amounts after n years at …
Metric and Imperial Conversions –
Learn key metric conversions (km, m, cm, mm, kg, g, l, ml) and imperial approximations (miles, inches, pints) with worked examples…
Velocity-Time Graphs –
Master velocity-time graphs for GCSE Maths: find acceleration from the gradient, distance from the area under the graph, with work…
Direct Proportion Graphs –
Direct proportion graphs for GCSE Maths: recognise y = kx lines through the origin, find the constant k from a graph, and solve pr…
Exchange Rate Problems –
Master exchange rate problems for GCSE Maths. Learn to convert currencies, handle buying and selling rates, and solve multi-step c…
Recipe and Scaling Problems –
Learn how to solve recipe and scaling problems in GCSE Maths. Scale ingredients up or down using the unitary method with worked ex…
Pressure, Force and Area –
Learn the pressure formula P = F/A for GCSE Maths. Rearranging, unit conversions between N/m² and Pa, and real-world pressure prob…
Ratio and Fractions –
Convert between ratios and fractions for GCSE Maths. Find the fraction of a total from a ratio with clear methods, worked examples…
Percentage Profit and Loss –
Master percentage profit and loss for GCSE Maths. Calculate profit or loss as a percentage of cost price, find selling prices and …
Ratio Given the Difference –
Solve ratio problems when given the difference between parts, not the total. Step-by-step method, worked examples and practice for…
Proportional Reasoning –
Master proportional reasoning for GCSE Maths. Learn the unitary method, scaling, and how to recognise proportional relationships w…
Reverse Compound Interest –
Learn reverse compound interest for GCSE Maths Higher tier. Find the original value, interest rate or number of years with worked …
Converting Area and Volume Units –
Learn how to convert area and volume units for GCSE Maths. Understand why cm² to m² uses 10,000 and cm³ to litres uses 1,000 with …
Rates of Change –
Understand rates of change for GCSE Maths Higher tier. Learn to draw tangents, estimate gradients of curves and interpret rate in …
Exponential Growth and Decay –
Learn exponential growth and decay for GCSE Maths Higher tier. Understand y = ab^x models, population growth, radioactive decay, h…
Percentage Increase and Decrease Multipliers –
Master percentage multipliers for GCSE Maths. Use multipliers for increase and decrease, handle repeated changes, and find origina…
Geometry & Measures
Angles, polygons, circles, Pythagoras, trigonometry, vectors, transformations.
Area of 2D Shapes
Master area formulas for all 2D shapes at GCSE including rectangles, triangles, circles, trapeziums and composite shapes.
Perimeter –
Learn how to calculate perimeters of all shapes for GCSE Maths with methods, worked examples and practice questions.
Volume of 3D Shapes –
Master volume formulas for cubes, prisms, cylinders, cones, spheres and pyramids with worked examples and GCSE practice questions.
Surface Area –
Master surface area of 3D shapes for GCSE Maths including cuboids, cylinders, cones and spheres with worked examples.
Pythagoras' Theorem
Master Pythagoras' theorem for GCSE Maths with step-by-step methods, 2D and 3D examples, and practice questions for all tiers.
Trigonometry SOHCAHTOA –
Master SOHCAHTOA trigonometry for GCSE Maths with step-by-step methods, worked examples and practice questions for Foundation and …
Sine & Cosine Rules –
Master the sine rule and cosine rule for GCSE Higher Maths with step-by-step methods, worked examples and practice questions.
Trigonometry in 3D –
Master 3D trigonometry for GCSE Maths Higher tier with step-by-step methods, worked examples, and practice questions.
Circle Theorems –
Learn all circle theorems for GCSE Maths Higher tier with clear diagrams, worked examples, and exam-style practice questions.
Arc Length and Sector Area –
Master arc length and sector area for GCSE Maths with clear formulas, worked examples at Foundation and Higher, and practice quest…
Angles: Basic Rules & Parallel Lines –
Learn angle rules and parallel line angles for GCSE Maths with step-by-step methods, worked examples, and practice questions.
Angles in Polygons –
Learn interior and exterior angles in polygons for GCSE Maths with formulas, worked examples, and practice questions.
Vectors –
Master vectors for GCSE Maths Higher tier with clear notation, worked examples, and exam-style practice questions.
Transformations: Reflection, Rotation, Translation
Master reflections, rotations, and translations for GCSE Maths with step-by-step methods, worked examples, and practice questions.
Enlargement & Scale Factor –
Learn enlargement and scale factor for GCSE Maths with step-by-step methods, fractional and negative scale factors, and practice q…
Congruence and Similarity –
Master congruence and similarity for GCSE Maths with congruence conditions, similar shapes, area and volume scale factors, and pra…
Constructions and Loci –
Learn constructions and loci for GCSE Maths with step-by-step compass and ruler methods, worked examples, and practice questions.
Bearings –
Master bearings for GCSE Maths with three-figure notation, step-by-step methods, worked examples, and practice questions.
Plans and Elevations –
Learn plans and elevations for GCSE Maths Foundation with step-by-step methods, worked examples, and practice questions.
Area of a Trapezium –
Learn how to calculate the area of a trapezium using the formula A = half(a+b)h, with worked examples, exam tips and GCSE practice…
Area of a Circle –
Master the area of a circle formula A = pi r squared for GCSE Maths, including semicircles, quarter circles and finding the radius…
Area of Compound Shapes –
Learn how to find the area of compound shapes by splitting into rectangles, triangles, trapeziums and semicircles with GCSE worked…
Volume of a Prism –
Master the volume of a prism formula (cross-section area times length) for GCSE Maths with triangular prism examples and practice …
Volume of a Cylinder –
Learn the volume of a cylinder formula V = pi r squared h for GCSE Maths with worked examples, reverse problems and real-world con…
Volume of a Cone –
Master the volume of a cone formula V = one-third pi r squared h for GCSE Higher, including frustums and finding missing dimension…
Volume of a Sphere –
Master the volume of a sphere formula V = four-thirds pi r cubed for GCSE Higher, including hemispheres and finding the radius fro…
Surface Area of a Cylinder –
Learn the surface area of a cylinder formula SA = 2 pi r squared + 2 pi rh for GCSE Maths, including open cylinders and net diagra…
Finding the Hypotenuse –
Learn how to find the hypotenuse using Pythagoras' theorem with step-by-step methods, Pythagorean triples, worked examples and pra…
Finding a Shorter Side (Pythagoras) –
Learn how to find a shorter side using Pythagoras' theorem by rearranging the formula, with worked examples and practice questions…
SOHCAHTOA Finding Missing Sides –
Master finding missing sides using SOHCAHTOA trigonometry with step-by-step methods, calculator tips, worked examples and GCSE pra…
SOHCAHTOA Finding Missing Angles –
Learn how to find missing angles using inverse trig functions sin⁻¹, cos⁻¹ and tan⁻¹ with worked examples and GCSE Maths practice …
Sine Rule –
Master the sine rule for GCSE Higher Maths with step-by-step methods for finding sides and angles, worked examples and exam practi…
Cosine Rule –
Master the cosine rule for GCSE Higher Maths — learn to find sides and angles in non-right-angled triangles with worked examples a…
Angles on a Straight Line and at a Point –
Master angles on a straight line (180°), angles at a point (360°), and vertically opposite angles with worked examples and exam pr…
Alternate, Corresponding and Co-interior Angles –
Learn alternate (Z), corresponding (F), and co-interior (C/U) angles in parallel lines with clear rules, worked examples, and prac…
Interior and Exterior Angles of Polygons –
Learn how to calculate interior and exterior angles of regular and irregular polygons with formulas, worked examples, and practice…
Arc Length –
Learn how to calculate arc length using the formula (theta/360) x 2 pi r, with step-by-step worked examples and GCSE exam practice…
Sector Area –
Master sector area with the formula (theta/360) x pi r squared, perimeter of a sector, worked examples, and GCSE exam-style practi…
Congruent Triangles –
Learn the four congruence conditions SSS, SAS, ASA, and RHS for GCSE Maths with formal proof structure, worked examples, and pract…
Similar Shapes and Scale Factors –
Understand similar shapes, linear scale factors, area scale factor (k squared), and volume scale factor (k cubed) with GCSE worked…
Reflections –
Learn how to reflect shapes in the x-axis, y-axis, y = x, y = -x, and other mirror lines with worked examples and GCSE practice qu…
Rotations –
Master rotations for GCSE Maths including centre, angle, and direction of rotation with 90, 180, and 270 degree worked examples an…
Translations and Column Vectors –
Learn how to translate shapes using column vectors, apply translations on a grid, and describe translations as vectors for GCSE Ma…
Enlargement and Centre of Enlargement –
Learn how to draw enlargements from a centre, use integer, fractional, and negative scale factors, and find the centre of enlargem…
Perpendicular Bisector and Angle Bisector –
Step-by-step compass and ruler constructions for the perpendicular bisector and angle bisector with accuracy tips and GCSE practic…
Loci and Regions –
Learn the four standard loci for GCSE Maths — from a point, from a line, equidistant from two points and two lines — with shading …
Pythagoras in 3D –
Learn how to apply Pythagoras' theorem in three dimensions to find space diagonals in cuboids and longest diagonals in 3D shapes f…
Exact Trigonometric Values –
Memorise the exact values of sin, cos, and tan for 0, 30, 45, 60, and 90 degrees with derivations from special triangles and GCSE …
Area of a Triangle –
Master the area of a triangle using A = ½ × base × height and A = ½ab sin C for Higher tier, with worked examples and GCSE practic…
Area of a Parallelogram –
Learn how to calculate the area of a parallelogram using A = base × perpendicular height, with worked examples and GCSE practice q…
Circumference of a Circle –
Learn how to calculate the circumference of a circle using C = πd and C = 2πr, with worked examples, exam tips and GCSE practice q…
Volume of a Pyramid –
Learn how to calculate the volume of a pyramid using V = one-third × base area × height, with worked examples and GCSE practice qu…
Surface Area of a Cone –
Learn how to calculate the surface area of a cone using SA = πrl + πr², including finding slant height with Pythagoras, with worke…
Surface Area of a Sphere –
Learn how to calculate the surface area of a sphere using SA = 4πr² and hemispheres using 3πr², with worked examples and GCSE prac…
Bearings and Trigonometry –
Master bearings with trigonometry: three-figure bearings, calculating distances and angles using SOHCAHTOA, and finding return bea…
Describing Transformations –
Learn how to fully describe each of the four transformations — reflection, rotation, translation and enlargement — with worked exa…
Properties of Quadrilaterals –
Properties of quadrilaterals for GCSE Maths — sides, angles, diagonals and symmetry of squares, rectangles, parallelograms, rhombu…
Symmetry: Lines and Rotational –
Symmetry revision for GCSE Maths — learn lines of symmetry, rotational symmetry order, and how to identify both in 2D shapes and p…
Nets of 3D Shapes –
Nets of 3D shapes for GCSE Maths — learn to identify and draw nets of cubes, cuboids, prisms, pyramids, cylinders and cones with e…
3D Shapes: Faces, Edges and Vertices –
3D shapes faces edges and vertices for GCSE Maths — Euler's formula, naming solids, properties, and cross-sections with worked exa…
Perimeter of Compound Shapes –
Perimeter of compound shapes for GCSE Maths — find missing lengths, add outer edges, and handle semicircles and quarter circles st…
Surface Area of a Cuboid –
Surface area of a cuboid for GCSE Maths — use SA = 2(lw + lh + wh), identify three pairs of faces, and solve open-top box problems…
Volume of a Hemisphere –
Volume of a hemisphere for GCSE Maths Higher — V = two-thirds pi r cubed, relationship to sphere volume, and surface area with wor…
Angles in a Triangle –
Angles in a triangle for GCSE Maths — angle sum of 180 degrees, isosceles base angles, equilateral triangles, and the exterior ang…
Parts of a Circle –
Parts of a circle for GCSE Maths — radius, diameter, chord, tangent, arc, sector and segment definitions with diagrams, examples a…
Vectors: Proving Parallel and Collinear –
Vectors proving parallel and collinear for GCSE Maths Higher — scalar multiples for parallel lines, collinear points, and ratio pr…
Area Using ½ab sin C –
Area using half ab sin C for GCSE Maths Higher — formula for any triangle, when to use it, and combining with sine and cosine rule…
Properties of Triangles –
Properties of triangles for GCSE Maths — scalene, isosceles, equilateral and right-angled triangle identification, angle rules and…
Negative Scale Factor Enlargement –
Negative scale factor enlargement for GCSE Maths Higher — inverted images, drawing step by step from a centre of enlargement with …
Isometric Drawings –
Isometric drawings for GCSE Maths — learn to draw 3D shapes on isometric paper and convert between plans, elevations and isometric…
Exterior Angle Theorem –
Exterior angle theorem for GCSE Maths — the exterior angle of a triangle equals the sum of the two opposite interior angles, with …
Surface Area of a Triangular Prism –
Surface area of a triangular prism for GCSE Maths — calculate two triangular faces plus three rectangular faces with step-by-step …
Area of a Sector and Segment –
Area of a sector and segment for GCSE Maths Higher — sector area formula, segment area equals sector minus triangle, with worked e…
Statistics & Probability
Averages, cumulative frequency, histograms, tree diagrams, Venn diagrams.
Mean Median Mode and Range –
Learn how to calculate the mean, median, mode and range for GCSE Maths with worked examples, exam tips and practice questions.
Frequency Tables and Grouped Data –
Master frequency tables and grouped data for GCSE Maths with step-by-step methods, worked examples and practice questions.
Bar Charts Pie Charts and Pictograms –
Master bar charts, pie charts and pictograms for GCSE Maths Foundation with clear methods, worked examples and practice questions.
Histograms –
Learn how to draw and interpret histograms for GCSE Maths Higher with frequency density, worked examples and practice questions.
Cumulative Frequency and Box Plots –
Master cumulative frequency diagrams and box plots for GCSE Maths Higher with step-by-step methods, worked examples and practice q…
Scatter Graphs and Correlation –
Learn scatter graphs and correlation for GCSE Maths with lines of best fit, worked examples and practice questions for Foundation …
Probability Basics and Relative Frequency –
Master probability basics and relative frequency for GCSE Maths with clear methods, worked examples and practice questions.
Probability Tree Diagrams –
Learn how to draw and use probability tree diagrams for GCSE Maths with worked examples, exam tips and practice questions.
Venn Diagrams –
Master Venn diagrams for GCSE Maths with set notation, worked examples and practice questions for Foundation and Higher tiers.
Conditional Probability –
Master conditional probability for GCSE Maths Higher with tree diagrams, Venn diagrams, worked examples and practice questions.
Sampling Methods –
Learn sampling methods for GCSE Maths including random, systematic and stratified sampling with worked examples and practice quest…
Mean from a Frequency Table –
Learn how to calculate the mean from frequency tables for GCSE Maths. Ungrouped and grouped data, estimated mean, modal class and …
Drawing & Reading Histograms –
Learn how to draw and read histograms for GCSE Maths Higher. Frequency density, unequal class widths, estimating frequencies and w…
Cumulative Frequency Diagrams –
Master cumulative frequency diagrams for GCSE Maths Higher. Plotting, reading median, quartiles, IQR and comparing distributions s…
Probability Tree Diagrams –
Master probability tree diagrams for GCSE Maths. Independent and dependent events, AND/OR rules, without replacement and worked ex…
Conditional Probability & Venn Diagrams –
Master conditional probability and Venn diagrams for GCSE Maths Higher. P(A|B) formula, set notation, two-way tables and worked ex…
Finding the Mean –
Master finding the mean for GCSE Maths with step-by-step methods, worked examples and practice questions for Foundation and Higher…
Finding the Median –
Learn how to find the median for GCSE Maths including ordering data, the position rule, and median from frequency tables with work…
Mode and Range –
Master the mode and range for GCSE Maths including modal class for grouped data, comparing distributions, worked examples and prac…
Estimated Mean from Grouped Data –
Learn how to calculate the estimated mean from grouped data for GCSE Maths using midpoints, worked examples and practice questions…
Drawing Pie Charts –
Learn how to draw and read pie charts for GCSE Maths with angle calculations, protractor use, worked examples and practice questio…
Reading and Drawing Bar Charts –
Master bar charts for GCSE Maths including single, dual and composite bar charts, choosing scales, and spotting misleading graphs.
Types of Correlation –
Understand positive, negative and no correlation for GCSE Maths with line of best fit, interpolation vs extrapolation, and worked …
Probability Scale and Basic Probability –
Master the probability scale and basic probability for GCSE Maths with clear methods, worked examples and practice questions for a…
Expected Frequency –
Learn expected frequency for GCSE Maths with step-by-step methods, comparing expected vs actual results, fairness, and worked exam…
Relative Frequency –
Master relative frequency (experimental probability) for GCSE Maths with step-by-step methods, worked examples and practice questi…
Mutually Exclusive Events –
Learn mutually exclusive events for GCSE Maths with the addition rule, complement rule, exhaustive events, worked examples and pra…
Independent and Dependent Events –
Master independent and dependent events for GCSE Maths with the multiplication rule, tree diagrams, without replacement, and worke…
Stratified Sampling –
Master stratified sampling for GCSE Maths Higher with proportional representation, sample size calculations, worked examples and p…
Box Plots and Comparing Distributions –
Learn box plots for GCSE Maths Higher with the five-number summary, IQR, comparing distributions, skewness, worked examples and pr…
Two-Way Tables –
Two-way tables GCSE Maths revision: learn to read, complete and use two-way tables to find totals, missing values and probabilitie…
Frequency Polygons –
Frequency polygons GCSE Maths revision: plot midpoints against frequency, compare distributions and read values with step-by-step …
Time Series Graphs –
Time series graphs GCSE Maths revision: plot data over time, identify trends and seasonal variation, and calculate moving averages…
Sample Space Diagrams –
Sample space diagrams GCSE Maths revision: list all outcomes for combined events using two-way grids, then calculate probabilities…
Set Notation and Venn Diagrams –
Set notation and Venn diagrams GCSE Maths revision: master union, intersection, complement and formal notation with worked example…
Systematic Listing and Product Rule –
Systematic listing and product rule for counting GCSE Maths: list outcomes methodically and use the product rule to find total com…
Stem-and-Leaf Diagrams –
Stem-and-leaf diagrams GCSE Maths revision: draw ordered stem-and-leaf plots, read median, mode and range, and compare back-to-bac…
Comparing Data Sets –
Comparing data sets GCSE Maths revision: use mean, median, range and IQR to compare distributions and write full comparison senten…
Misleading Graphs and Data –
Misleading graphs and data GCSE Maths revision: identify truncated axes, misleading scales, cherry-picked data and bias in data pr…
Probability from Two-Way Tables –
Probability from two-way tables GCSE Maths revision: calculate simple and conditional probabilities from tables with step-by-step …
Combined Events Probability –
Combined events probability GCSE Maths revision: calculate P(A and B) and P(A or B) for independent and dependent events with work…
Interpreting Data from Tables and Charts –
Interpreting data from tables and charts GCSE Maths revision: read values, calculate totals and percentages, draw conclusions and …
Random and Systematic Sampling –
Random and systematic sampling GCSE Maths revision: understand random, systematic and stratified sampling methods with advantages,…
Quartiles and Interquartile Range –
Quartiles and interquartile range GCSE Maths revision: find Q1, Q2, Q3 from listed data and cumulative frequency, calculate IQR an…
Print one. Stick it on your wall.
Every sheet is print-optimised. Open one, click the Print / Save as PDF button, and you have a clean A4 reference.
Master PDF (free) →