KS3 & GCSE Maths

186 KS3 & GCSE explainers and guides.

• Column Vectors and Vector Notation: KS3 Maths Guide

  What is a column vector? KS3 guide to column notation, adding and subtracting vectors, and using column vectors to describe translations. Worked examples included.

• Converting Units of Area and Volume: GCSE Maths Guide

  GCSE guide to converting units of area and volume — why cm² to m² needs a factor of 10 000, and cm³ to m³ needs 1 000 000 — with worked examples and common mistakes.

• Estimated Mean from Grouped Data: GCSE Maths Guide

  How to find the estimated mean from grouped frequency tables at GCSE — use class midpoints, multiply by frequency, divide by total. Worked example included.

• Factorising by Grouping: GCSE Maths Explained

  Factorising by grouping at GCSE — split a four-term expression into two pairs, factorise each separately, then extract the common bracket. Fully worked examples.

• How to Draw a Pie Chart: Step-by-Step KS3 Maths Guide

  Learn to draw a pie chart at KS3: convert frequencies to angles using 360° ÷ total, then draw each sector with a protractor. Includes a full worked example.

• Imperial and Metric Unit Conversions: KS3 Maths Guide

  KS3 guide to converting between metric and imperial units — miles to km, kilograms to pounds, litres to pints — with key conversion facts and worked examples.

• Inequalities and Regions on a Graph: GCSE Maths Guide

  GCSE graphical inequalities guide — drawing solid and dashed boundary lines, shading the correct region, and identifying the solution region for multiple inequalities.

• Percentage Multipliers: GCSE Maths Method Explained

  GCSE percentage multipliers explained — use a single decimal to increase or decrease in one step, combine successive changes, and reverse a percentage change.

• Pictograms and Tally Charts: KS3 Maths Guide

  KS3 guide to tally charts and pictograms — recording data in groups of five, reading pictogram keys, drawing your own diagrams, and choosing the right chart.

• Properties of Quadrilaterals: KS3 Maths Complete Guide

  KS3 guide to six quadrilateral types — square, rectangle, rhombus, parallelogram, trapezium, and kite — with parallel sides, diagonals, and symmetry properties.

• Ratio Problems at GCSE Maths: Harder Applications

  GCSE ratio problems guide: combining ratios, finding unknowns from one given share, ratio with algebra, and ratio in real-life contexts. Worked examples throughout.

• Surface Area of a Cylinder: GCSE Maths Formula and Examples

  GCSE guide to the surface area of a cylinder — the formula 2πr² + 2πrh explained step by step, with worked examples for both closed and open cylinders.

• Types of Polygons: Names, Properties, and Angle Sums at KS3

  KS3 guide to polygon names from triangle to dodecagon, regular vs irregular, convex vs concave polygons, and interior angle sums — with a quick-reference table.

• Types of Triangles: Properties and Classification at KS3 Maths

  KS3 guide to the four types of triangle — equilateral, isosceles, scalene, and right-angled — with properties, angle facts, and worked examples.

• Volume of Prisms: KS3 Maths Formula and Worked Examples

  KS3 guide to the volume of any prism — triangular prisms, trapezoidal prisms, and L-shaped prisms — using volume = cross-sectional area × length. Worked examples.

• Writing Algebraic Expressions: KS3 Maths Guide

  KS3 guide to writing algebraic expressions from words — using letters for unknowns, forming perimeter expressions, and translating word problems into algebra.

• Area Under a Graph — Trapezium Rule: GCSE Maths

  Estimate the area under a graph at GCSE using the trapezium rule — split into strips, apply the formula, and judge whether your answer over- or under-estimates.

• Composite and Inverse Functions: GCSE Maths Explained

  Master composite and inverse functions at GCSE — learn to calculate fg(x), distinguish it from gf(x), and find f⁻¹(x) step by step.

• Cube Numbers and Cube Roots: KS3 Maths Explained

  Learn what cube numbers are and how to find cube roots at KS3 — recognise perfect cubes, use the cube root symbol, and solve exam problems.

• Currency Exchange Rates: KS3 Maths Explained

  Convert between currencies using exchange rates at KS3 — multiply to go from pounds, divide to return, and compare best-value holiday money deals.

• Enlargement with Fractional and Negative Scale Factors: GCSE Maths

  Enlarge shapes using fractional and negative scale factors at GCSE — find object images, describe enlargements fully, and locate the centre of enlargement.

• Fibonacci and Special Number Sequences: KS3 Maths

  Explore Fibonacci, triangular and other special number sequences at KS3 — spot the pattern, find any term, and know how to recognise each sequence type.

• Gradient of a Curve at a Point: GCSE Maths Explained

  Estimate the gradient of a curve at GCSE by drawing a tangent at a point — learn to calculate rise over run and interpret rate of change in context.

• Midpoint and Distance Between Two Points: GCSE Maths

  Find the midpoint and distance between two coordinate pairs at GCSE — apply the midpoint formula and Pythagoras with step-by-step worked examples.

• Pressure, Force and Area: GCSE Maths Explained

  Use the pressure, force and area formula triangle at GCSE — calculate any one of the three quantities given the other two, with compound measure examples.

• Rationalising the Denominator: GCSE Maths Explained

  Rationalise surd denominators at GCSE — use multiplication by the surd or its conjugate to produce a rational denominator, with worked examples.

• Solving Equations with Fractions: GCSE Maths Step by Step

  Solve equations containing fractions at GCSE — multiply through by the LCM to clear denominators, then solve step by step with worked examples.

• The AND and OR Rules of Probability: GCSE Maths

  Apply the AND and OR rules of probability at GCSE — know when to multiply or add, handle dependent events, and avoid the most common exam errors.

• The Quadratic Formula: GCSE Maths Explained

  Use the quadratic formula at GCSE to solve any quadratic equation — master the discriminant, avoid calculator errors, and check answers efficiently.

• Types of Data — Discrete, Continuous and Categorical: KS3 Maths

  Understand the difference between discrete, continuous and categorical data at KS3 — and learn how data type determines which chart you should draw.

• Volume of a Frustum: GCSE Maths Higher Explained

  Find the volume of a frustum at GCSE Higher — reconstruct the full cone, remove the smaller cone using similar triangles, and subtract the volumes.

• Volume of a Sphere: GCSE Maths Explained

  Calculate the volume of a sphere at GCSE using V = 4/3πr³ — identify the radius, answer in terms of π, and find the volume of hemispheres too.

• 3D Shapes: Vertices, Edges, and Faces — KS3 Maths Guide

  How to count vertices, edges, and faces of common 3D shapes at KS3. Includes Euler's formula, a complete reference table, and exam-style examples.

• Adding and Subtracting Decimals: KS3 Maths Step-by-Step Guide

  How to add and subtract decimal numbers at KS3 maths using the column method. Includes lining up decimal points, worked examples, and common mistakes.

• Area and Circumference of Circles: KS3 Maths Guide

  How to calculate the area and circumference of a circle at KS3 maths. Step-by-step worked examples, formulae using pi, and exam tips for Year 7–9.

• Area of a Trapezium and Parallelogram: KS3 Maths Guide

  How to find the area of a trapezium and a parallelogram at KS3 maths. Formulae, step-by-step worked examples, and common mistakes for Year 7–9 pupils.

• Comparing and Ordering Fractions: KS3 Maths Step-by-Step Guide

  How to compare and order fractions at KS3 maths using common denominators. Covers mixed numbers, negative fractions, and worked examples for Year 7–9.

• Exact Trigonometric Values: GCSE Maths Guide (30°, 45°, 60°)

  The exact values of sin, cos, and tan for 0°, 30°, 45°, 60°, and 90° at GCSE maths. Derivations, a memory table, and exam-style worked examples.

• Forming and Solving Equations from Word Problems: KS3 Maths

  How to translate word problems into equations and solve them at KS3 maths. Step-by-step strategy with worked examples for Year 7, 8, and 9 students.

• Grouped Frequency Tables: KS3 Maths Guide with Worked Examples

  How to read, complete, and analyse grouped frequency tables at KS3 maths. Includes modal class, estimated mean, and step-by-step worked examples.

• Number Machines and Function Machines: KS3 Maths Guide

  What number machines and function machines are, how to work forwards and backwards, and how they link to algebra in KS3 maths. With worked examples.

• Percentage of an Amount, VAT, and Profit: KS3 Maths Guide

  How to find a percentage of an amount and apply it to real-life VAT and profit problems at KS3 maths. Worked examples with money for Year 7–9.

• Percentage Profit and Loss: KS3 Maths with Worked Examples

  How to calculate percentage profit and loss at KS3 maths. Step-by-step worked examples with money contexts, formulae, and exam tips for Year 8 and 9.

• Scale Drawings and Maps: KS3 Maths Step-by-Step Guide

  How to read and create scale drawings and interpret map scales at KS3 maths. Worked examples, unit conversions, and exam tips for Year 7–9 students.

• Speed, Distance, and Time: KS3 Maths Formulae and Worked Examples

  How to use the speed, distance, and time formulae at KS3 maths. The SDT triangle, unit conversions, and step-by-step worked examples for Year 7–9.

• Stem and Leaf Diagrams: KS3 Maths Step-by-Step Guide

  How to draw and interpret stem and leaf diagrams at KS3 maths. Includes back-to-back diagrams, finding the median, and worked examples for Year 7–9.

• Tessellations: KS3 Maths Guide to Tiling Patterns

  What tessellations are and how to identify regular, semi-regular, and irregular tessellations at KS3 maths. Includes why some shapes tile and others do not.

• Volume of Cones and Pyramids: GCSE Maths Formulae and Worked Examples

  How to calculate the volume of cones and pyramids at GCSE maths. Formulae, step-by-step worked examples, and common exam mistakes for Year 10–11.

• Best Buy Problems: GCSE Maths Value for Money Guide

  Solve best buy problems GCSE maths sets using unit pricing, with a clear method and worked examples comparing pack sizes to find the best value option.

• Congruent Triangle Proofs: SSS, SAS, ASA, RHS (GCSE)

  Congruent triangle proofs GCSE explained: use SSS, SAS, ASA or RHS to prove two triangles congruent, with a worked geometric proof and exam-style layout.

• Converting Recurring Decimals to Fractions: GCSE Maths

  Learn converting recurring decimals to fractions GCSE style, using the algebraic method with fully worked examples for single, double and mixed repeats.

• Difference of Two Squares: GCSE Maths Explained

  Difference of two squares GCSE explained: spot a² − b² instantly and factorise it into (a + b)(a − b), with worked examples and common exam traps.

• Expanding Triple Brackets: GCSE Maths Step-by-Step

  Master expanding triple brackets GCSE style: multiply three linear brackets into a cubic expression, with fully worked examples and a checking method.

• Frequency Trees: GCSE Maths Explained

  Frequency trees GCSE maths explained: how to draw, label and read a frequency tree from raw data, with a fully worked example and common exam pitfalls.

• Function Notation f(x): GCSE Maths Explained

  Function notation GCSE maths made clear: what f(x) means, how function machines work, and how to evaluate and combine functions with worked examples.

• Geometric Sequences: GCSE Maths Explained

  Learn geometric sequences GCSE maths: spot the common ratio, apply the nth term formula ar^(n-1), and compare geometric with arithmetic sequences.

• Mixed Numbers and Improper Fractions: KS3 Maths Guide

  Mixed numbers and improper fractions KS3 explained, with clear steps and worked examples for converting between the two forms in either direction.

• Negative and Fractional Indices: GCSE Maths

  A step-by-step guide to negative and fractional indices GCSE questions, covering reciprocal and root rules with fully worked higher-tier examples.

• Nets of 3D Shapes: KS3 Maths Guide

  Nets of 3D shapes KS3 guide: what a net is, how to identify valid nets of cubes, cuboids, cylinders and prisms, with a worked surface area example.

• Parallel and Perpendicular Lines: GCSE Maths Gradients

  Master parallel and perpendicular lines GCSE maths: same gradient for parallel lines, negative reciprocal for perpendicular ones, with worked steps.

• Rational and Irrational Numbers: GCSE Maths Explained

  Rational and irrational numbers GCSE explained: clear definitions, how to tell them apart, and worked examples involving fractions, decimals and surds.

• Relative Frequency and Experimental Probability (GCSE)

  Relative frequency and experimental probability GCSE explained: the formula, how it estimates true probability from trials, and a worked dice-bias example.

• Sample Space Diagrams: KS3 Maths Guide

  Sample space diagrams KS3 maths, explained with a two-dice grid: how to list every possible outcome of combined events and use the grid to find probabilities.

• Similar Shapes: Area and Volume Scale Factors (GCSE)

  Learn similar shapes area and volume scale factor GCSE rules: square the linear factor for area, cube it for volume, with worked examples and a summary table.

• Simultaneous Equations: Linear and Quadratic (GCSE)

  Solve simultaneous equations linear and quadratic GCSE style using substitution, with fully worked examples, a circle case, and a check on solution count.

• Sine Rule and Cosine Rule: GCSE Maths Explained

  Sine rule and cosine rule GCSE explained: how to solve non-right-angled triangles, find sides and angles, and calculate area, with worked examples.

• Stratified Sampling: GCSE Maths Explained

  Learn stratified sampling GCSE maths with the formula, step-by-step method and a fully worked example, so every group in a population is fairly represented.

• Time Series Graphs: GCSE Maths Explained

  Understand time series graphs GCSE maths: how to plot data over time, spot the trend, calculate moving averages and interpret patterns with a worked example.

• Trigonometric Graphs: GCSE Maths Sin, Cos and Tan

  Trigonometric graphs GCSE maths guide: the shape, period and key points of y = sin x, y = cos x and y = tan x, with a value table and worked examples.

• 3D Pythagoras and Trigonometry GCSE: Finding Lengths and Angles in Solids

  Extend Pythagoras' theorem and SOHCAHTOA into three dimensions at GCSE: find diagonals of cuboids and angles in 3D solids using right-angled triangles step by step.

• Algebraic Proof GCSE: How to Prove Statements Always True

  Master algebraic proof for GCSE: use algebra to prove results about integers, consecutive numbers, odd and even expressions, with worked examples and common techniques.

• Bounds and Error Intervals GCSE: Upper and Lower Bounds Explained

  Understand bounds and error intervals for GCSE: find upper and lower bounds, write error intervals with inequality notation, and tackle compound measure problems.

• Common GCSE Maths Exam Mistakes (and How to Avoid Them)

  Common GCSE Maths exam mistakes examiners see every year — from rounding errors to skipped working — and practical steps to avoid losing marks.

• Conditional Probability GCSE: P(A|B), Without Replacement and Tree Diagrams

  Understand conditional probability at GCSE: find P(A|B), use tree diagrams for events without replacement, and apply the multiplication rule with worked examples.

• Cubic Graphs KS3: Plotting y = x³ and Recognising the S-Shape

  Understand cubic graphs at KS3: plot y = x³ and related curves, identify key features like the point of inflection, and interpret cubic graphs in context.

• Equation of a Circle GCSE: Centre and Radius Explained

  Learn to write and use the equation of a circle at GCSE: x² + y² = r² and (x − a)² + (y − b)² = r², with worked examples and exam tips.

• Exponential Graphs GCSE: Sketching y = aˣ and Recognising Growth and Decay

  Explore exponential graphs at GCSE: sketch y = aˣ curves, recognise growth and decay, find key features, and interpret them in real-life modelling contexts.

• GCSE Maths Foundation vs Higher: Which Tier to Choose?

  GCSE Maths Foundation vs Higher tier: which to choose based on grade cap, current attainment, and how to know if switching tier is the right move.

• Graph Transformations GCSE: Translations, Reflections and Stretches

  Master graph transformations for GCSE: translate, reflect and stretch any curve using f(x) notation, with step-by-step worked examples and key rules.

• How to Revise A-Level Maths

  How to revise A-level Maths: a subject-specific technique covering Pure, Statistics and Mechanics, past-paper strategy, and how to sequence revision by topic weighting.

• How to Tackle GCSE Maths Problem-Solving Questions

  A gcse maths problem solving question technique for multi-step, wordy exam questions: decode the question, choose a method, show working, and check the answer.

• How to Use the GCSE Maths Formula Sheet

  Using the GCSE maths formula sheet: which formulas are given in the exam, which ones students must memorise, and how to use the sheet efficiently.

• Inverse Proportion GCSE: y ∝ 1/x and y ∝ 1/x² Explained

  Explore inverse proportion at GCSE: recognise y ∝ 1/x and y ∝ 1/x² relationships, find the constant of proportionality, and solve problems with worked examples.

• Iteration GCSE Maths: How to Use Iterative Formulas

  Learn iteration for GCSE maths: use iterative formulas to find approximate solutions to equations that cannot be solved algebraically, with step-by-step examples.

• Long Division and Long Multiplication KS3: Step-by-Step Column Methods

  Learn long division and long multiplication at KS3: follow the column methods step by step, avoid common errors, and build confidence with large-number calculations.

• Place Value and Decimals KS3: Understanding Digit Values and Ordering Numbers

  Master place value and decimals at KS3: understand digit values in whole numbers and decimals, compare and order numbers, and multiply or divide by powers of 10.

• Proportion Equations GCSE: Direct and Inverse Proportion Using k

  Form and use proportion equations at GCSE: write direct and inverse proportion using the constant k, find k from a table of values, and solve problems with full working.

• Quadratic Inequalities GCSE: Finding Ranges Where ax² + bx + c > 0

  Solve quadratic inequalities at GCSE: find where a quadratic expression is positive or negative, write the solution on a number line, and use set notation correctly.

• Reciprocal Graphs KS3: Plotting and Understanding y = k/x

  Learn about reciprocal graphs at KS3: understand the shape of y = k/x, plot a hyperbola, identify asymptotes, and recognise inverse proportion from a graph.

• Simultaneous Equations Graphically GCSE: Finding Intersections of Lines and Curves

  Solve simultaneous equations graphically at GCSE: draw two lines or curves, find their intersection, and check your answer algebraically — with worked examples.

• What Is A-Level Maths Really Like? A Student's Guide

  What is A-level Maths really like? A guide to the topics covered, the jump in difficulty from GCSE, and how to decide if it's right for you.

• Factorising and Solving Quadratic Equations: GCSE Maths

  Factorise and solve quadratic equations at GCSE — from simple expressions like x² + 5x + 6 to the difference of two squares, with step-by-step worked examples.

• Gradient and Equation of a Straight Line: GCSE Maths

  Go beyond basic plotting — master gradient and y = mx + c at GCSE, find equations from two points, and interpret parallel and perpendicular lines with examples.

• Gradient and Equation of a Straight Line: GCSE Maths

  Find the gradient and equation of a straight line at GCSE: use y = mx + c, calculate gradient from two points, and write equations in different forms.

• Histograms with Unequal Class Widths: GCSE Maths Explained

  Understand frequency density, draw histograms with unequal class widths at GCSE, and interpret histogram area as frequency with worked exam examples.

• Plans and Elevations KS3 Maths: Drawing 2D Views of 3D Shapes

  Learn to draw and interpret plans and elevations at KS3: front, side, and top views of 3D shapes, with a step-by-step method and common shape examples.

• Quadratic Equations: GCSE Maths Methods Explained

  Solve quadratic equations at GCSE using factorisation, the quadratic formula, and completing the square, with worked examples and common exam mistakes explained.

• Quadratic Sequences and nth Term: GCSE Maths

  Find the nth term of a quadratic sequence at GCSE: identify second differences, use the standard method, and build fluency with fully worked examples.

• Real-Life Graphs at KS3: Conversion, Depth, and More

  Interpret real-life graphs at KS3 maths — from conversion graphs to water depth and cooling curves — learning what gradient and shape tell you about a situation.

• Rotation, Reflection, and Translation: KS3 Maths

  Understand rotation, reflection, and translation at KS3: how to describe and perform each transformation fully, with worked examples on coordinate grids.

• Surface Area of Spheres and Cones: GCSE Maths

  Calculate the surface area of spheres and cones at GCSE: use the correct formulae, understand curved and total surface area, with fully worked examples.

• Trial and Improvement: KS3 Maths Step-by-Step

  Learn the trial and improvement method at KS3 maths: narrow down a solution to an equation by systematic substitution, with worked examples and a clear table.

• Algebraic Fractions: GCSE Maths Step-by-Step

  Master algebraic fractions at GCSE: simplify by cancelling common factors, add and subtract by finding a common denominator, and multiply and divide with clear examples.

• Arc Length and Sector Area: GCSE Maths Guide

  Master arc length and sector area at GCSE maths: use the angle as a fraction of 360° to find arc lengths and sector areas, with clear worked examples and formula cards.

• Circle Theorems GCSE: All 8 Rules Explained

  Master all 8 circle theorems for GCSE maths: angle at the centre, cyclic quadrilateral, tangent-radius, angles in the same segment, and more — with worked examples.

• Completing the Square: GCSE Maths Step-by-Step

  Master completing the square at GCSE maths: write a quadratic in the form (x + p)² + q, find the vertex of a parabola, and solve quadratic equations with clear examples.

• Congruence and Similarity: KS3 Maths Explained

  Understand congruent and similar shapes at KS3 maths: congruent shapes are identical in size and shape; similar shapes have equal angles and proportional sides.

• Cumulative Frequency and Box Plots: GCSE Maths Guide

  Learn to draw cumulative frequency graphs and box plots at GCSE maths: find median, quartiles, and interquartile range from grouped data with step-by-step examples.

• Frequency Polygons: KS3 Maths Explained

  Learn to draw and interpret frequency polygons at KS3 maths: plot midpoints from a grouped frequency table, join them in order, and compare two distributions.

• Gradient and Rate of Change: KS3 Maths Explained

  Learn to find the gradient of a straight line at KS3 maths: use rise over run from a graph or two coordinates, and interpret gradient as a real-world rate of change.

• Histograms and Frequency Density: GCSE Maths Guide

  Master histograms at GCSE maths: calculate frequency density using frequency ÷ class width, draw and read histograms with unequal class widths, and find frequencies.

• Linear Inequalities on a Number Line: KS3 Maths

  Learn to solve linear inequalities and show solutions on a number line at KS3 maths: use open and closed circles, solve multi-step inequalities, and handle negatives.

• Loci and Constructions: KS3 Maths Guide

  Learn compass constructions and loci at KS3 maths: perpendicular bisector, angle bisector, and drawing the locus of points with clear step-by-step examples.

• Prime Factor Decomposition: KS3 Maths Step-by-Step

  Learn prime factor decomposition at KS3 maths: use factor trees or repeated division to write any integer as a product of prime factors, then find HCF and LCM.

• Quadratic Graphs: How to Plot and Interpret Parabolas

  Learn to plot quadratic graphs at GCSE maths: build a table of values, identify roots, vertex, and line of symmetry, and read solutions to equations from the graph.

• Solving Quadratic Equations by Factorising: GCSE Guide

  Learn to solve quadratic equations by factorising at GCSE maths: factor pairs, double brackets, difference of two squares — with clear step-by-step worked examples.

• Vectors: GCSE Maths Introduction

  Understand vectors at GCSE maths: column vector notation, adding and subtracting vectors, multiplying by a scalar, and finding vector paths in geometry questions.

• Venn Diagrams and Set Notation: KS3 Maths Guide

  Learn Venn diagrams and set notation at KS3 maths: understand union, intersection, and complement, sort data into sets, and use Venn diagrams to calculate probabilities.

• Compound Interest and Depreciation: GCSE Maths

  Master compound interest and depreciation for GCSE maths — learn the multiplier method with step-by-step worked examples and exam tips.

• How to Find Averages from a Frequency Table: KS3 Maths

  Step-by-step guide to finding the mean, median, and mode from a frequency table — with worked examples and common mistakes to avoid for KS3 maths.

• How to Simplify Ratios: KS3 Maths (Step by Step)

  A step-by-step KS3 guide to simplifying ratios — find the HCF, divide both parts, and handle ratios with different units or three parts.

• How to Simplify Surds: GCSE Maths

  A clear GCSE guide to simplifying surds — find the largest square factor, rationalise the denominator, and add or subtract like surds with worked examples.

• How to Use Two-Way Tables: KS3 Maths

  A clear KS3 guide to reading and completing two-way tables — find missing values, calculate totals, and use tables to find fractions and probabilities.

• Interior and Exterior Angles of Polygons: KS3 Maths

  Learn how to find interior and exterior angles of any polygon using simple formulas — with worked examples for KS3 maths students.

• Significant Figures and Decimal Places: KS3 Maths

  Understand the difference between significant figures and decimal places — with clear rules for rounding and worked examples for KS3 maths students.

• Volume and Surface Area of a Cylinder: KS3 Maths

  Learn how to calculate the volume and surface area of a cylinder using π — with step-by-step worked examples and common mistakes for KS3 maths students.

• Compound Measures: Speed and Density at KS3 Maths

  Master compound measures at KS3 maths: speed, density, and pressure formulas with worked examples, unit conversions, and formula triangles for Year 8 and 9.

• Distance-Time Graphs Explained: KS3 Maths

  Understand distance-time graphs at KS3: what the gradient means, how to read speed, and how to spot stationary periods — with a worked interpretation.

• Enlargement and Scale Factor: KS3 Maths Guide

  Understand enlargement and scale factor at KS3: how to enlarge shapes, find missing lengths, and use centres of enlargement with worked examples for Year 7–9.

• Factorising Expressions: KS3 Maths Guide

  Learn how to factorise algebraic expressions at KS3 maths: finding common factors, factorising into single brackets, and checking answers with worked examples.

• How to Rearrange Formulae (Change the Subject): KS3 Maths

  Learn how to rearrange formulae and change the subject at KS3 — inverse operations, step-by-step method and worked examples including multi-step rearrangements.

• How to Share an Amount in a Given Ratio: KS3 Maths

  Step-by-step guide to sharing amounts in a given ratio at KS3 — find the total parts, find the value of one part, then multiply. Includes worked examples.

• How to Solve Simultaneous Equations: KS3 and GCSE Maths

  Step-by-step guide to solving simultaneous equations by elimination and substitution — with worked examples for KS3 and GCSE maths students.

• How to Work Out Bearings: KS3 Maths (Step by Step)

  A step-by-step KS3 guide to working out and measuring bearings — three-figure notation, how to draw them, and common bearing problems explained clearly.

• Reverse Percentages: Finding the Original Amount (GCSE Maths)

  Learn how to find the original amount before a percentage change using reverse percentages — a GCSE maths method with clear worked examples included.

• Solving Equations with Unknowns on Both Sides: KS3 Maths

  Step-by-step guide to solving linear equations with unknowns on both sides at KS3 maths, with worked examples, bracket equations, and tips for Year 8 and 9.

• Surface Area of Prisms and Cuboids: KS3 Maths

  How to find the surface area of prisms and cuboids at KS3 — unfolding into nets, adding face areas, with full worked examples for triangular and rectangular prisms.

• Trigonometry SOHCAHTOA Explained: KS3 and GCSE Maths

  Understand trigonometry SOHCAHTOA at KS3 and GCSE — labelling sides, choosing the right ratio, and finding missing sides and angles with worked examples.

• Angles in Triangles and Quadrilaterals: KS3 Maths Guide

  Learn the angle sum rules for triangles and quadrilaterals at KS3, with worked examples for finding missing angles in Year 7, 8, and 9 maths.

• Angles on Parallel Lines — KS3 Maths

  Angles on parallel lines for KS3 maths: alternate, co-interior, and corresponding angle rules explained with worked examples and geometric reasons for Year 8 and 9.

• Angles: Rules and Types Explained for KS3 Maths

  Learn the main angle types and key angle rules at KS3, including angles on a straight line, around a point, and vertically opposite angles, with worked examples.

• Area of Rectangles and Triangles: KS3 Maths Guide with Worked Examples

  How to find the area of rectangles and triangles at KS3 maths. Clear formulae, step-by-step worked examples, and compound shape problems for Year 7 and 8 pupils.

• Converting Fractions, Decimals and Percentages: KS3 Maths Guide

  Master converting between fractions, decimals and percentages at KS3. Step-by-step methods with worked examples, a conversion table, and common mistakes to avoid.

• Coordinates and the Four Quadrants: KS3 Maths Guide

  Understand coordinates and the four quadrants for KS3 maths. Covers plotting points, negative coordinates, midpoints and common mistakes for Year 7 and Year 8.

• Direct Proportion and the Unitary Method — KS3 Maths

  Understand direct proportion and the unitary method for KS3 maths: what direct proportion means, how to use the unitary method, and worked examples for Year 8 and Year 9.

• Fractions of an Amount — KS3 Maths Explained

  Learn how to find fractions of an amount at KS3 with two clear methods, worked examples, and common mistakes to avoid in Year 7, 8, and 9 maths.

• HCF and LCM Explained — KS3 Maths

  Clear explanation of highest common factor (HCF) and lowest common multiple (LCM) for KS3 maths, with prime factor trees, Venn diagrams, and worked examples.

• How to Add and Subtract Fractions: KS3 Maths Step-by-Step Guide

  Learn how to add and subtract fractions at KS3 with clear step-by-step worked examples, common mistakes, and tips for finding common denominators in Year 7 and 8.

• How to Convert Metric Units — KS3 Maths

  Step-by-step guide to converting metric units at KS3: length, mass, and capacity conversions with worked examples for Year 7, Year 8, and Year 9 maths pupils.

• How to Draw and Interpret Scatter Graphs — KS3 Maths

  How to draw and interpret scatter graphs at KS3 maths: correlation types, lines of best fit, and making predictions — worked examples for Year 8 and Year 9 pupils.

• How to Expand Double Brackets (FOIL) — KS3 Maths

  Learn how to expand double brackets in KS3 maths using FOIL — First, Outer, Inner, Last — with worked examples, negative terms and how to simplify.

• How to Expand Single Brackets in KS3 Maths (Step by Step)

  Learn how to expand single brackets in KS3 maths step by step, using the distributive law — with worked examples, negative terms and common mistakes.

• How to Find a Percentage of an Amount — KS3 Maths

  How to find a percentage of an amount at KS3: two reliable methods with worked examples, percentage increase and decrease, and reverse percentage explained.

• How to Interpret Pie Charts — KS3 Maths

  How to read and interpret pie charts at KS3 maths: calculate sector angles, find frequencies from sectors, and draw your own — with worked examples for Year 7 to 9.

• How to Multiply and Divide Fractions — KS3 Maths

  Step-by-step guide to multiplying and dividing fractions at KS3: worked examples, the keep-change-flip rule for division, and common mistakes to avoid.

• How to Plot Straight Line Graphs — KS3 Maths

  Step-by-step guide to plotting straight line graphs at KS3: table of values, gradient, y-intercept, and reading equations in y = mx + c form for Year 8 and 9.

• How to Read and Draw Bar Charts: KS3 Maths Guide

  Learn how to read and draw bar charts at KS3, including frequency bar charts and comparative bar charts, with step-by-step examples for Year 7 and 8 maths.

• How to Round Numbers and Estimate: KS3 Maths Guide

  Master rounding to decimal places and significant figures at KS3, plus estimation strategies for checking answers in Year 7, 8, and 9 maths.

• How to Simplify Fractions: KS3 Maths Step-by-Step Guide

  Learn how to simplify fractions at KS3 with clear worked examples, the highest common factor method, and tips for Year 7 and 8 maths.

• How to Solve Equations with Brackets at KS3: Step-by-Step Guide

  Learn how to solve equations with brackets at KS3 maths. Expand, simplify, and balance equations with clear worked examples for Year 8 and Year 9 pupils.

• How to Solve Two-Step Equations — KS3 Maths

  Learn how to solve two-step equations at KS3 using inverse operations and the balance method, with worked examples, negative numbers and checking answers.

• How to Substitute into Formulae: KS3 Maths Step-by-Step Guide

  Learn how to substitute values into formulae at KS3. Step-by-step worked examples covering positive numbers, negatives, and squared terms for Year 7, 8 and 9 pupils.

• How to Use a Protractor to Measure Angles — KS3 Maths

  Step-by-step guide to using a protractor to measure and draw angles at KS3. Covers acute, obtuse, and reflex angles with common errors for Year 7 and Year 8.

• Indices and Powers Explained — KS3 Maths

  Plain-English guide to indices and powers for KS3 maths: index notation, the laws of indices, zero and negative powers, with worked examples for Year 8 and Year 9.

• Inequalities Explained: KS3 Maths Guide with Worked Examples

  A clear KS3 guide to inequalities: reading inequality symbols, solving linear inequalities, representing solutions on a number line, and common exam mistakes.

• KS3 Maths Topics by Year: Year 7, 8 and 9 Breakdown

  A year-by-year breakdown of KS3 maths topics for Years 7, 8 and 9 — number, algebra, geometry, ratio and statistics — mapped to the national curriculum.

• Mean, Median, Mode and Range: KS3 Maths Guide

  Understand mean, median, mode, and range at KS3 with clear definitions, worked examples, and tips for choosing the right average in Year 7, 8, and 9 maths.

• Multiplying and Dividing Decimals — KS3 Maths

  How to multiply and divide decimals at KS3 using integer methods and powers of ten. Worked examples for Year 7, 8, and 9 with common mistakes to avoid.

• Negative Numbers Explained — KS3 Maths

  Negative numbers explained for KS3: how to add, subtract, multiply and divide with negatives, number line tips, and common sign-error mistakes to avoid.

• Order of Operations: BIDMAS Explained for KS3 Maths

  What is BIDMAS and why does order of operations matter? KS3 guide with worked examples, common mistakes, and why 2 + 3 × 4 equals 14, not 20.

• Percentage Increase and Decrease — KS3 Maths Guide

  How to calculate percentage increase and decrease at KS3: two methods, multiplier shortcut, worked examples for Year 7, 8, and 9, plus reverse percentage.

• Perimeter and Area of Compound Shapes — KS3 Maths

  How to find the perimeter and area of compound shapes at KS3 by splitting into rectangles and triangles. Worked examples for Year 7, 8, and 9 maths pupils.

• Prime Numbers, Factors and Multiples Explained for KS3 Maths

  What are prime numbers, factors and multiples? KS3 guide with worked examples, factor trees, and HCF and LCM methods for Year 7 and Year 8 maths pupils.

• Probability Basics: KS3 Maths Guide with Worked Examples

  A complete KS3 guide to probability basics: the probability scale, calculating simple probabilities, listing outcomes, and complementary events for Year 7 to Year 9.

• Probability Tree Diagrams — KS3 Maths

  How to draw probability tree diagrams at KS3 maths: multiply along branches, add between branches, with and without replacement — worked examples for Year 8 and 9.

• Pythagoras' Theorem: KS3 Introduction with Worked Examples

  A clear KS3 introduction to Pythagoras' theorem: what a²+b²=c² means, finding the hypotenuse or a shorter side, and common exam mistakes explained with worked steps.

• Sequences and the nth Term: KS3 Maths Guide

  Learn how to find the nth term of a linear sequence at KS3, continue sequences, and use the formula to find any term, with worked examples for Year 8 and 9.

• Solving One-Step Linear Equations: A KS3 Maths Guide

  A KS3 guide to solving one-step linear equations using inverse operations — with worked examples for addition, subtraction, multiplication and division.

• Square Numbers and Square Roots — KS3 Maths

  Clear guide to square numbers and square roots for KS3: what they are, how to calculate them, the first 15 perfect squares, and worked examples for Year 7 and 8 pupils.

• Standard Form Explained: KS3 Maths Guide

  Understand standard form at KS3: how to convert large and small numbers, multiply and divide in standard form, with worked examples for Year 8 and 9 maths.

• Symmetry and Transformations — KS3 Maths Explained

  Clear guide to symmetry and transformations at KS3: reflections, rotations, translations, and enlargements explained with worked examples for Year 7, 8, and 9.

• Volume of Cuboids: KS3 Maths Guide with Worked Examples

  How to find the volume of a cuboid at KS3. Covers the formula, worked examples with whole numbers and decimals, unit conversion, and exam tips for Year 7 and 8.

• What Are Like Terms? Collecting Terms in KS3 Algebra

  Learn what like terms are in KS3 algebra, how to identify them, and how to collect them to simplify expressions — with worked examples and practice.

• What Is Algebra? A KS3 Introduction for Year 7 and 8 Students

  What is algebra and why does it matter at KS3? This Year 7 guide explains variables, expressions, equations and terms with clear examples and no assumed knowledge.

• What Is Pi? Circles and Circumference Explained — KS3 Maths

  What is pi, and how do you use it to find the circumference and area of a circle? KS3 guide with worked examples, the key formulas and common mistakes.

• What Is Ratio and Proportion? KS3 Maths Explained

  What is ratio and proportion in KS3 maths? Clear definitions, worked examples, simplifying ratios, sharing in a ratio, and direct proportion explained.