Lesson 0
GCSE Maths is a toolkit, not a memory test
Learn how to read GCSE Maths questions, spot command words, choose a method and show clear working.
Free Lessons → GCSE / Key Stage 4 → Maths
GCSE Maths
Build the GCSE Maths skills one calm step at a time.
GCSE Maths feels easier when the basics are secure and each new method has a clear purpose. These lessons use clear working, quick checks and realistic practice across the full GCSE Maths course.
Number
Algebra
Ratio
Geometry
Probability
Statistics
All GCSE Maths lessons
Study skills
Start here if GCSE Maths feels broad or unfamiliar.
Number
Build arithmetic, place value, fractions, percentages, powers, exact values and bounds.
Lesson 1
Factors, Multiples and Divisibility
Understand factors and multiples, use divisibility tests, and build a prime factor tree.
Lesson 2
Highest Common Factor and Lowest Common Multiple
Find shared factors, shared multiples, and decide which one a word problem needs.
Lesson 3
Prime Factorisation
Break numbers into prime factors using factor trees, ladders and powers.
Lesson 4
Squares, Cubes and Roots
Understand square numbers, cube numbers and roots before later indices and algebra work.
Lesson 5
Powers and Indices
Use index notation and the core index laws for powers, division, zero indices and negative indices.
Lesson 6
Standard Form
Write very large and very small numbers using powers of 10, then interpret calculator notation safely.
Lesson 7
Equivalent Fractions and Simplifying
Make equivalent fractions, simplify confidently and recognise when a fraction is in its simplest form.
Lesson 8
Fractions: Four Operations
Add, subtract, multiply and divide fractions using the right method for each operation.
Lesson 9
Decimals and Place Value
Read, compare and round decimal numbers using place value and zero placeholders.
Lesson 10
Negative Numbers, Ordering and Inequality Symbols
Use number-line thinking to compare negative values and write clear inequality statements.
Lesson 11
Order of Operations and Inverse Operations
Choose the correct calculation order, then use inverse operations to check and work backwards.
Lesson 12
Rounding, Estimation and Bounds
Round accurately, estimate sensibly and write error intervals for rounded measurements.
Lesson 13
Percentages: Finding and Comparing
Convert percentages, find percentages of amounts and compare quantities fairly.
Lesson 14
Percentages: Increase, Decrease, Reverse Percentages and Interest
Use percentage multipliers for growth, discounts, originals and interest.
Ratio, proportion and rates
Use scaling, unit rates, compound measures and proportional relationships.
Lesson 15
Ratio: Simplifying and Equivalent Ratios
Read ratio notation, simplify ratios and build equivalent ratios by scaling every part.
Lesson 16
Ratio: Sharing Into Parts
Divide a total into unequal shares using total parts, one part and a final check.
Lesson 17
Ratio and Fractions
Connect ratio parts to fractions of the whole and avoid the common denominator trap.
Lesson 18
Proportion Problems and Best Buys
Use unit prices, scaling and rate comparisons to choose fair best buys.
Lesson 19
Direct Proportion
Recognise direct proportion, find the constant and use equations, tables and graphs.
Lesson 20
Inverse Proportion
Use constant products, equations and curved graphs when one quantity falls as another rises.
Lesson 21
Scale Drawings and Map Scales
Read scale notation, convert distances and use map scales without losing the units.
Lesson 22
Compound Measures: Speed, Density and Pressure
Use formulae and units for journeys, materials and forces.
Lesson 23
Rates of Change and Units
Interpret rates, graph gradients and per-units in practical contexts.
Lesson 24
Growth, Decay and Iteration Problems
Use repeated multipliers and step-by-step rules in GCSE contexts.
Algebra
Move from notation and equations into graphs, functions, quadratics and algebraic fractions.
Lesson 25
Algebra Notation and Substitution
Read variables, terms and formulae, then substitute values accurately.
Lesson 26
Simplifying Expressions
Collect like terms, simplify algebraic products and check expressions by substitution.
Lesson 27
Expanding Brackets
Multiply into brackets, simplify the result and keep signs under control.
Lesson 28
Factorising Expressions
Put expressions back into brackets using common factors and simple quadratic patterns.
Lesson 29
Linear Equations
Solve equations using inverse operations, brackets and unknowns on both sides.
Lesson 30
Inequalities
Read, draw and solve inequalities, including number-line notation and integer solutions.
Lesson 31
Formulae and Changing the Subject
Substitute into formulae and rearrange them so the letter you need is on its own.
Lesson 32
Sequences and the nth Term
Continue patterns, find nth terms and check whether a value belongs to a sequence.
Lesson 33
Coordinates and Straight-Line Graphs
Plot coordinates, draw straight-line graphs and connect gradient and intercept to equations.
Lesson 34
Simultaneous Equations
Solve pairs of equations by elimination, substitution and graph intersections.
Lesson 35
Quadratic Expressions and Equations
Expand, factorise and solve quadratic equations using clear bracket methods.
Lesson 36
Quadratic Graphs
Plot quadratic curves, then read roots, intercepts and turning points accurately.
Lesson 37
Functions and Composite/Inverse Functions
Use function notation, combine functions in order and find inverse functions.
Lesson 38
Algebraic Fractions
Simplify, multiply, add and solve with fractions that contain algebra.
Geometry and measures
Cover angle facts, area and volume, units, trigonometry, constructions, transformations and vectors.
Lesson 39
Angles, Lines and Parallel Lines
Use angle facts, parallel-line rules and clear reasons to solve missing-angle problems.
Lesson 40
Polygons and Interior/Exterior Angles
Find angle sums, regular polygon angles and exterior-angle routes through shape questions.
Lesson 41
Perimeter and Area
Find outside lengths, space inside shapes, compound areas and the correct units for each answer.
Lesson 42
Circles: Circumference and Area
Use radius, diameter and pi to find circle circumference, area, exact answers and rounded answers.
Lesson 43
3D Shapes, Surface Area and Volume
Find volumes, surface areas, prism cross-sections and the correct square or cubic units.
Lesson 44
Units, Metric Conversions and Measures
Convert metric units, handle square and cubic units, and choose sensible units for measured answers.
Lesson 45
Time, Money and Real-Life Measures
Calculate with clock times, intervals, money, wages, exchange rates and everyday measure contexts.
Lesson 46
Pythagoras' Theorem
Use right-angled triangles to find hypotenuses, shorter sides, diagonals and practical distances.
Lesson 47
Trigonometry in Right-Angled Triangles
Use sine, cosine and tangent to find missing sides, missing angles and practical heights or distances.
Lesson 48
Bearings, Loci and Constructions
Draw three-figure bearings, describe loci and use compass constructions with clear method marks.
Lesson 49
Transformations
Translate, reflect, rotate and enlarge shapes, then describe each transformation completely.
Lesson 50
Congruence and Similarity
Compare exact matching shapes with scaled copies, then use length, area and volume scale factors.
Lesson 51
Vectors
Use directed line segments, column vectors and vector journeys in GCSE geometry.
Lesson 52
Circle Theorems
Use angle facts in circles and give clear theorem reasons.
Lesson 53
Sine Rule, Cosine Rule and Area of a Triangle
Solve non-right-angled triangles using the sine rule, cosine rule and area formula.
Probability
Practise probability scales, outcome listing, diagrams, trees, dependence and conditional probability.
Lesson 54
Probability Language and Scales
Use probability words, fractions, decimals and percentages on the 0 to 1 scale.
Lesson 55
Listing Outcomes and Sample Space Diagrams
List outcomes systematically so none are missed or counted twice.
Lesson 56
Frequency Trees and Two-Way Tables
Organise grouped counts and use totals to answer probability questions.
Lesson 57
Probability Trees
Use tree diagrams for multi-stage probability problems.
Lesson 58
Independent and Dependent Events
Decide whether one event changes the probability of another.
Lesson 59
Conditional Probability
Find probabilities when extra information is already known.
Lesson 60
Product Rule for Counting
Count combinations by multiplying the number of choices at each stage.
Statistics
Plan data collection, calculate summaries and interpret charts, graphs and distributions.
Lesson 61
Collecting and Classifying Data
Plan fair data collection and recognise types of data.
Lesson 62
Averages and Range
Find and compare mean, median, mode and range.
Lesson 63
Tables, Charts and Diagrams
Read and draw common statistical diagrams accurately.
Lesson 64
Scatter Graphs and Correlation
Use scatter graphs to describe relationships and estimate values.
Lesson 65
Cumulative Frequency
Build cumulative frequency tables and read medians and quartiles from curves.
Lesson 66
Box Plots
Draw and compare box plots using medians, quartiles and range.
Lesson 67
Histograms
Use frequency density to draw and read histograms with unequal class widths.
Lesson 68
Place Value, Ordering and Comparing Numbers
Read, order and compare integers, decimals and large numbers using place value.
Lesson 69
Four Operations and Calculator Checks
Choose efficient methods for addition, subtraction, multiplication and division, then check answers sensibly.
Lesson 70
Surds and Exact Values
Simplify surds, use exact forms and avoid rounding too early.
Lesson 71
Recurring Decimals and Fractions
Convert recurring decimals to fractions using simple algebra.
Lesson 72
Error Intervals and Limits of Accuracy
Write the possible range of values behind rounded measurements.