All worksheets GCSE

Free GCSE Higher maths worksheets

Higher tier. One worksheet for each chapter of the course. Pick a chapter to find its worksheet.

Chapter 1Basic number

Decimals, estimates, primes and factorsMultiplying and dividing decimals, estimating with rounded numbers, prime factors, HCF and LCM, and negative numbers in calculations.Grades 4–9 · about 80 minutes · 89 marks

Chapter 2Fractions, ratio and proportion

Fraction arithmetic and percentage changeAdding, subtracting, multiplying and dividing fractions and mixed numbers, one quantity as a fraction or percentage of another, and percentage increase, decrease and change.Grades 4–9 · about 80 minutes · 87 marks

Chapter 3Statistical diagrams and averages

Charts, averages from tables and scatter graphsReading and drawing pictograms, bar charts, pie charts and stem-and-leaf diagrams, averages and spread from frequency tables, and scatter graphs with a line of best fit.Grades 4–9 · about 85 minutes · 84 marks

Chapter 4Number and sequences

Linear, special and quadratic sequencesFinding and using the nth term of linear sequences, square, cube, triangular and Fibonacci-type sequences, rules from growing patterns, and the nth term of quadratic sequences.Grades 4–9 · about 80 minutes · 87 marks

Chapter 5Ratio and proportion

Ratio, rates and repeated percentagesSharing in a ratio, the unitary method and best buys, speed, density and pressure, and repeated and reverse percentage change.Grades 4–9 · about 85 minutes · 83 marks

Chapter 6Angles

Angle facts, polygons and bearingsAngles on lines, in triangles and across parallel lines, interior and exterior angles of polygons, and bearings and scale drawings.Grades 4–9 · about 80 minutes · 90 marks

Chapter 7Transformations, constructions and loci

Congruence, transformations, constructions and lociCongruent triangles, the four transformations and combinations of them, ruler-and-compass constructions, loci, and plans and elevations.Grades 4–9 · about 85 minutes · 90 marks

Chapter 8Algebraic manipulation

Simplifying, expanding, factorising and rearrangingSubstituting, simplifying and taking out common factors, expanding two and three brackets, factorising quadratics, and changing the subject of a formula.Grades 4–9 · about 80 minutes · 92 marks

Chapter 9Length, area and volume

Circles, sectors, areas, prisms and solidsCircumference and area of circles and sectors, parallelograms and trapezia, prisms and cylinders, and the volume and surface area of pyramids, cones and spheres.Grades 4–9 · about 85 minutes · 94 marks

Chapter 10Linear graphs

Gradients, equations of lines and real-life graphsGradients and intercepts, finding the equation of a line, parallel and perpendicular lines, conversion and rate graphs, and solving simultaneous equations from a graph.Grades 4–9 · about 80 minutes · 91 marks

Chapter 11Right-angled triangles

Pythagoras' theorem and trigonometry in right-angled trianglesPythagoras' theorem in two and three dimensions, sine, cosine and tangent, and right-angled triangles inside real problems.Grades 4–9 · about 85 minutes · 93 marks

Chapter 12Similarity

Similar triangles, and the area and volume of similar shapesFinding lengths in similar triangles, and using length, area and volume scale factors between similar shapes and solids.Grades 4–9 · about 80 minutes · 90 marks

Chapter 13Exploring and applying probability

Relative frequency, expected outcomes, two-way tables and Venn diagramsEstimating probabilities from experiments, working out expected numbers, and finding probabilities from probability tables, two-way tables and Venn diagrams.Grades 4–9 · about 80 minutes · 90 marks

Chapter 14Powers and standard form

Index laws, zero and negative powers, and standard formUsing the index laws with numbers and letters, zero and negative indices, and writing and calculating with numbers in standard form.Grades 4–9 · about 80 minutes · 91 marks

Chapter 15Equations and inequalities

Linear and simultaneous equations, inequalities and trial and improvementSolving linear equations with brackets and fractions, simultaneous equations, linear inequalities and regions, and finding a root by trial and improvement.Grades 4–9 · about 90 minutes · 94 marks

Chapter 16Counting, accuracy, powers and surds

Recurring decimals, fractional powers, surds, bounds and countingRecurring decimals as fractions, negative and fractional indices, exact work with surds, upper and lower bounds, and counting outcomes with the product rule.Grades 4–9 · about 85 minutes · 90 marks

Chapter 17Quadratic equations

Chapter 18Sampling and more complex diagrams

Sampling, frequency polygons, cumulative frequency, box plots and histogramsTaking a fair sample, then reading and comparing grouped data on frequency polygons, cumulative frequency graphs, box plots and histograms.Grades 4–9 · about 85 minutes · 90 marks

Chapter 19Combined events

The addition rule, tree diagrams and conditional probabilityAdding probabilities when events cannot both happen, taking the overlap back off when they can, tree diagrams with and without replacement, and conditional probability.Grades 4–9 · about 80 minutes · 90 marks

Chapter 20Properties of circles

Circle theorems, tangents, chords and the alternate segmentFinding angles with the circle theorems, using tangents and chords, and giving a reason for every step.Grades 4–9 · about 85 minutes · 90 marks

Chapter 21Variation

Direct and inverse proportion: formulae, graphs and changesWriting a proportion as a formula with a constant k, including squares, cubes, square roots and inverses, recognising the graphs, and working out what a change in one quantity does to the other.Grades 4–9 · about 75 minutes · 88 marks

Chapter 22Triangles

Trigonometry in 2D and 3D, trigonometric graphs, and the sine and cosine rulesMulti-step trigonometry in two and three dimensions, the graphs of sine and cosine with their second solutions, and solving any triangle with the sine rule, the cosine rule and the area formula.Grades 4–9 · about 90 minutes · 90 marks

Chapter 23Graphs

Distance-time and velocity-time graphs, areas under curves, circles, other graphs and transformationsReading speed and acceleration from graphs, estimating the area under a curve with trapezia, the circle x² + y² = r² and its tangents, recognising cubic, reciprocal and exponential graphs, and translating and reflecting y = f(x).Grades 4–9 · about 90 minutes · 96 marks

Chapter 24Algebraic fractions and functions

Algebraic fractions, rearranging formulae, composite and inverse functions, and iterationSimplifying, adding and dividing algebraic fractions, making a letter the subject when it appears twice, using composite and inverse functions, and finding a solution by iteration.Grades 4–9 · about 85 minutes · 92 marks

Chapter 25Vectors

Column vectors, vector arithmetic and vector proofs in geometryAdding, subtracting and scaling column vectors, finding the length of a vector, writing a path round a shape in terms of given vectors, and using vectors to show that lines are parallel or that points lie on a straight line.Grades 4–9 · about 85 minutes · 92 marks