Maths — Year 3 to GCSE

79 lessons, each with practice questions, a printable worksheet and an end-of-chapter test. Free to browse.

• Functions: Composite & Inverse Years 10–11 · Evaluate functions, build composite functions fg(x), and find inverses by rearranging.
• Sine & Cosine Rules Years 10–11 · Solve non-right triangles with the sine rule, cosine rule and the ½ab·sinC area formula.
• Introduction to Differentiation Year 11 · Differentiate polynomials, find the gradient at a point, a tangent equation, and…
• Bounds & Accuracy Years 10–11 · Find upper and lower bounds of rounded measurements and calculate correctly with them.
• Set Notation & Venn Diagrams Years 9–11 · Use set notation and two- and three-set Venn diagrams to organise and solve problems.
• Direct & Inverse Variation Years 10–11 · Model direct and inverse proportion with y = kx and y = k/x, find k, then solve.
• Exponential, Cubic & Reciprocal Graphs Years 10–11 · Recognise and sketch y = aˣ, y = x³ and y = a/x, and read gradients and values from them.
• Matrices & Matrix Transformations Years 10–11 · Matrix notation, addition and multiplication, determinants and inverses of 2×2 matrices,…
• Trigonometric Functions & Graphs Years 10–11 · Degrees and radians, the unit circle definition of sine and cosine, the graphs of…
• Sampling & Statistical Inference Years 9–11 · Population vs sample, random/systematic/stratified sampling, sources of bias, and…
• Place Value & Ordering Years 6–8 · Read, write, order and round whole numbers and decimals.
• The Four Operations Years 6–8 · Add, subtract, multiply and divide whole numbers and decimals using written methods.
• Factors, Multiples & Primes Years 6–9 · Find factors, multiples, primes, HCF and LCM using prime factorisation.
• Fractions Years 6–11 · Simplify, compare, and carry out the four operations with fractions.
• Decimals & Rounding Years 6–10 · Round to decimal places and significant figures; convert between fractions and decimals.
• Percentages Years 6–11 · Find percentages, percentage change, and reverse percentages.
• Indices & Standard Form Years 8–11 · Apply index laws and write large/small numbers in standard form.
• Surds Years 10–11 · Simplify surds, and rationalise denominators (Higher).
• Negative Numbers Years 6–9 · Order, add, subtract, multiply and divide positive and negative numbers (integers).
• Notation & Simplifying Years 6–9 · Use algebraic notation and collect like terms.
• Expanding & Factorising Years 8–11 · Expand single & double brackets and factorise expressions.
• Solving Linear Equations Years 7–11 · Solve equations including those with brackets and unknowns on both sides.
• Inequalities Years 8–11 · Solve linear inequalities and show solutions on a number line.
• Sequences & nth Term Years 7–11 · Continue sequences and find the nth term of a linear sequence.
• Straight-Line Graphs Years 8–11 · Use y = mx + c: gradient, intercept, and plotting lines.
• Simultaneous Equations Years 9–11 · Solve a pair of linear equations by elimination or substitution.
• Quadratics Years 9–11 · Factorise and solve quadratic equations of the form x² + bx + c = 0.
• The Coordinate Plane & Functions Years 7–11 · Plot and read points on the grid, and understand relations, functions and their graphs.
• Rearranging Formulae Years 8–11 · Substitute values into a formula and change its subject.
• The Quadratic Formula Years 10–11 · Solve any quadratic with the formula, and complete the square (Higher).
• Introduction to Ratio Years 6–8 · Write, simplify and use ratios.
• Sharing in a Ratio Years 7–11 · Divide a quantity in a given ratio and use part:whole reasoning.
• Direct & Inverse Proportion Years 8–11 · Use the unitary method; recognise direct and inverse proportion.
• Percentage Change & Interest Years 7–11 · Use multipliers for change, reverse percentages, and compound interest.
• Units & Compound Measures Years 7–11 · Convert between metric units and use compound measures like speed and density.
• Angles & Lines Years 6–9 · Use angle facts on lines, at points and with parallel lines.
• Triangles & Polygons Years 7–11 · Interior and exterior angles of polygons; types of triangle.
• Area & Perimeter Years 6–9 · Find area and perimeter of rectangles, triangles, parallelograms and trapezia.
• Circles Years 7–11 · Circumference and area of circles; arcs and sectors.
• Volume & Surface Area Years 8–11 · Volume and surface area of prisms, cylinders and other solids.
• Pythagoras' Theorem Years 8–11 · Find missing sides in right-angled triangles.
• Trigonometry (SOHCAHTOA) Years 9–11 · Find missing sides and angles in right-angled triangles.
• Transformations Years 7–11 · Translate, reflect, rotate and enlarge shapes.
• Symmetry Years 6–9 · Recognise line symmetry and rotational symmetry in shapes.
• Similar & Congruent Triangles Years 8–11 · Tell congruent shapes (identical) from similar shapes (same shape, scaled).
• Circle Theorems Years 10–11 · Angle rules inside circles: centre, semicircle, same segment, cyclic quadrilaterals,…
• Vectors Years 10–11 · Describe movement with column vectors and add, subtract and scale them.
• Bearings & Scale Drawings Years 8–11 · Use three-figure bearings, find back bearings, and convert with a map scale.
• Constructions & Loci Years 9–11 · Use compasses and a ruler for accurate constructions, and find loci (paths of points).
• Averages & Range Years 6–9 · Find the mean, median, mode and range of a data set.
• Frequency Tables & Grouped Data Years 7–11 · Find averages from frequency tables and estimate the mean of grouped data.
• Charts & Diagrams Years 6–9 · Read and draw bar charts, pictograms and pie charts.
• Scatter Graphs & Correlation Years 8–11 · Describe correlation and use a line of best fit.
• Histograms & Cumulative Frequency Years 10–11 · Frequency density, histograms, and cumulative frequency (median, quartiles, IQR).
• Basic Probability Years 6–9 · Measure likelihood on a 0–1 scale and use equally likely outcomes.
• Combined Events & Tree Diagrams Years 8–11 · Use AND/OR rules and tree diagrams for two events.
• Venn Diagrams & Sets Years 8–11 · Use Venn diagrams and set notation (∪, ∩, complement).
• Conditional Probability Years 10–11 · Probability when one event affects the next — picking without replacement.
• Place Value to 1,000 (Year 3) Year 3 · Learn how the place of each digit in a 3-digit number tells you its real value.
• Column Add & Subtract (Year 3–4) Years 3–4 · Add and subtract 3-digit numbers neatly using columns, with carrying and exchanging.
• Times Tables & Multiplication (Year 3–4) Years 3–4 · Learn the 2, 3, 4, 5, 8 and 10 times tables and multiply a 2-digit number by 1 digit.
• Division & Sharing (Year 3–4) Years 3–4 · Divide by sharing and grouping, use times tables, and handle simple remainders.
• Fractions: Halves, Quarters & Thirds (Year 3) Year 3 · A fraction is a fair share of one whole, like a half or a quarter.
• Bigger Numbers & Rounding (Year 4–5) Years 4–5 · Read big numbers using place value, then round them to make them tidy.
• Introducing Decimals (Year 4–5) Years 4–5 · Decimals show parts of a whole, like the pence in a pound.
• Money: Pounds & Pence (Year 3–4) Years 3–4 · Count coins, write amounts in pounds and pence, and work out change.
• 2D Shapes & Their Properties (Year 3) Year 3 · Meet flat shapes like squares, triangles and hexagons. Learn to count their sides and…
• 3D Shapes (Year 3–4) Years 3–4 · Explore solid shapes like cubes, spheres and cylinders. Count their faces, edges and…
• Measuring Length, Mass & Capacity (Year 3–5) Years 3–5 · Learn the units for length, mass and capacity. Read rulers and scales, pick the right…
• Telling the Time (Year 3–4) Years 3–4 · Read clocks to o'clock, half past and quarters. Learn minutes past the hour, am and pm,…
• Perimeter (Year 4–5) Years 4–5 · Perimeter is the distance all the way around a shape. Add up every side to find it, in…
• Area by Counting Squares (Year 4–5) Years 4–5 · Area is the space inside a flat shape. Count the square units, or for a rectangle…
• Angles & Symmetry (Year 4–5) Years 4–5 · An angle measures a turn. Learn right, acute and obtuse angles, quarter and half turns,…
• Tables & Tally Charts (Year 3–4) Years 3–4 · Collect data, make tally marks in gates of five, turn tallies into a frequency table and…
• Pictograms & Bar Charts (Year 3–5) Years 3–5 · Read pictograms with a key where one picture stands for 2 or 5, read and draw bar…
• Line Graphs (Year 5) Year 5 · Read line graphs that show change over time, read off points, and spot the biggest rise…
• Fractions of a Quantity (Year 4–5) Years 4–5 · Find a half, third, quarter and three-quarters of a number by sharing into equal parts,…
• Scaling & Simple Ratio (Year 5) Year 5 · Scale recipes up and down, use 'for every' language, and read simple ratios like 1 adult…
• Function Machines & Missing Numbers (Year 5) Year 5 · Use number machines to find the output, work backwards to find the input, and solve…