KS3 & GCSE Maths

301 KS3 & GCSE explainers and guides.

• Adding and Subtracting Mixed Numbers: KS3 Maths

  Master adding and subtracting mixed numbers at KS3 — convert to improper fractions, find a common denominator, then convert back and simplify clearly.

• Area and Perimeter of a Semicircle: GCSE Maths with Worked Examples

  Find the area and perimeter of a semicircle in GCSE maths using half-circle formulas, with worked examples and questions involving composite shapes.

• Area of a Kite: KS3 Maths Formula, Proof and Worked Examples

  Find the area of a kite using the diagonal formula — half the product of the two diagonals. This KS3 guide covers the formula, the proof, and worked examples.

• Back-to-Back Stem and Leaf Diagrams: GCSE Maths Guide

  Back-to-back stem and leaf diagrams compare two data sets side by side. Learn to draw them, find medians and ranges, and compare distributions in GCSE maths.

• Constructing Regular Polygons with Compass and Ruler: KS3 Maths

  Learn how to construct a regular hexagon and equilateral triangle using only compasses and a ruler in KS3 maths, with clear step-by-step instructions.

• How to Bisect an Angle: KS3 Compass and Ruler Construction

  Learn how to bisect an angle accurately with a compass and ruler. This KS3 construction guide gives clear steps, explains the locus reasoning, and exam tips.

• Multiplying Fractions by Integers: KS3 Maths Guide

  Multiplying a fraction by an integer is a key KS3 skill. Learn to cancel before multiplying, use worked examples, and solve word problems confidently.

• Percentage Error in KS3 Maths: Formula, Examples and Mistakes to Avoid

  Percentage error measures how accurate an estimate is compared to the true value. Learn the formula with clear KS3 worked examples and common mistakes avoided.

• Perfect Square Identities: (a+b)² and (a−b)² Explained for KS3 Maths

  The perfect square identities (a+b)² and (a−b)² let you expand or evaluate squared expressions instantly. Learn the patterns, the proof, and GCSE uses.

• Population and Sample in Statistics: KS3 Maths Explained

  Understand the difference between a population and a sample in KS3 statistics — why we sample, what makes a sample representative, and how bias is avoided.

• Proof of Pythagoras' Theorem: GCSE Maths — Three Methods Explained

  Three proofs of Pythagoras' theorem for GCSE — the four-triangle dissection, similar triangles, and an area rearrangement — explained with clear written working.

• Sum of an Arithmetic Series: GCSE Maths Formula and Examples

  The sum formula for arithmetic series lets you add long sequences without listing every term. Learn both forms with step-by-step GCSE maths worked examples.

• Surface Area of Compound 3D Shapes: GCSE Maths Guide

  Calculate the surface area of compound 3D shapes in GCSE maths by identifying exposed faces. Step-by-step examples combine cylinders, cones and hemispheres.

• The Complement Rule in Probability: KS3 Maths Guide

  The complement rule P(not A) = 1 − P(A) is an essential KS3 probability shortcut. Learn when to use it, see worked examples, and avoid common mistakes.

• The Factor Theorem: GCSE Higher Maths Explained with Examples

  The factor theorem states that if f(a) = 0 then (x − a) is a factor. Learn how to use it to factorise cubic expressions in GCSE Higher maths with examples.

• Truncation in GCSE Maths: How to Truncate and Find Error Intervals

  Learn what truncation means in GCSE maths, how to truncate to decimal places and significant figures, and find the correct error interval every time.

• Area and Perimeter of Compound Shapes with Circles — GCSE Maths

  Calculate area and perimeter of GCSE compound shapes involving circles — combine rectangles, triangles and sectors using exact answers in terms of π.

• Average and Instantaneous Rate of Change — GCSE Maths

  Understand average and instantaneous rate of change at GCSE — use chord gradients for average rates and tangent gradients for the instantaneous rate at a point.

• Calculating with Time — KS3 Maths

  Learn to add and subtract hours and minutes without a calculator at KS3 — convert between time units, bridge through clock boundaries and check with estimation.

• Collecting Data — Primary and Secondary — KS3 Maths

  Understand how to collect primary and secondary data at KS3 — design data collection sheets, choose an appropriate sampling method and identify sources of bias.

• Combined Transformations: GCSE Maths Guide

  Learn how to perform combined transformations at GCSE — apply two successive reflections, rotations or translations and find the single equivalent transformation.

• Constructions and Loci — GCSE Maths

  Master GCSE loci and constructions — draw perpendicular bisectors, angle bisectors and solve harder region problems that satisfy two or more conditions at once.

• Dividing Algebraic Expressions by a Single Term — KS3

  Learn to divide an algebraic expression by a single term at KS3 — split each term in the numerator over the same denominator and cancel common factors.

• Mental Maths Strategies — KS3

  Build speed and confidence with key mental arithmetic strategies for KS3 — learn doubling, halving, near-number adjustments and partitioning step by step.

• Misleading Statistics and Graphs — GCSE Maths

  Spot misleading statistics and graphs at GCSE — truncated axes, biased samples and cherry-picked averages explained with real examples and exam question tips.

• Reading Scales — KS3 Maths

  Practise reading scales accurately at KS3 — work out the interval between divisions on rulers, weighing scales, thermometers and measuring cylinders.

• Simultaneous Equations — Substitution Method GCSE

  Learn the substitution method for GCSE simultaneous equations — rearrange one equation for a variable, substitute into the second and solve step by step.

• Tree Diagrams: GCSE Maths Probability

  Master GCSE tree diagram probability — draw two-stage and three-stage trees, multiply along branches and add outcomes to solve combined event problems.

• Types of Numbers — KS3 Maths

  Understand the different types of numbers at KS3 — natural numbers, integers, rational numbers and square numbers, and how each set contains the previous.

• Using Algebra to Find Angles — KS3 Maths

  Use algebra to find missing angles at KS3 — set up equations from angle-sum facts in triangles, on straight lines and around a point, then solve for x.

• Writing Algebraic Expressions for Perimeter — KS3 Maths

  Write and simplify algebraic expressions for the perimeter and area of shapes at KS3 — form expressions from side lengths, collect like terms and evaluate.

• Written Column Addition and Subtraction — KS3 Maths

  Master written column addition and subtraction at KS3 — align digits by place value, carry into the next column and always check your answer by estimation.

• Algebraic Long Division: GCSE Higher Step-by-Step

  Divide a polynomial by a linear expression at GCSE Higher using algebraic long division: step-by-step method with fully worked examples and guidance on spotting factors.

• Bearings and Trigonometry: GCSE Maths Combined Problems

  Solve GCSE bearings problems that require trigonometry: find back bearings, form non-right-angled triangles from bearing data and apply the sine rule or cosine rule.

• Converse of Pythagoras' Theorem: GCSE Maths Guide

  Test whether a triangle is right-angled at GCSE using the converse of Pythagoras: if a² + b² = c², the triangle has a right angle opposite the longest side.

• Density, Mass and Volume Problems: GCSE Maths Guide

  Solve GCSE density, mass and volume problems using D = M ÷ V: rearrange the formula triangle, work with g/cm³ and kg/m³, and apply it with cylinders, spheres and prisms.

• Exponential Growth and Decay: GCSE Maths Guide

  Understand exponential growth and decay at GCSE: use the model y = abˣ to represent bacteria, population and radioactive decay, and read or sketch the exponential graph.

• Forming Quadratic Equations from Geometry: GCSE Step-by-Step

  Set up and solve GCSE quadratic equations from geometry: write sides as expressions in x, use area or Pythagoras, rearrange to ax² + bx + c = 0 and solve.

• Magnitude and Resultant Vectors: GCSE Maths Guide

  Calculate the magnitude of a vector and find resultant vectors at GCSE: use |a| = √(x² + y²), add and subtract column vectors, and apply scalar multiplication.

• Midpoint of a Line Segment — KS3 Maths

  Find the midpoint of a line segment at KS3 by averaging the x- and y-coordinates: M = ((x₁+x₂)/2, (y₁+y₂)/2) — with examples and finding a missing endpoint.

• Mortgages and Loans: GCSE Maths Financial Problems

  Solve GCSE mortgage and loan problems: calculate total repayment, total interest paid and monthly payments, and compare two loan deals with worked examples.

• Power Proportion (y ∝ xⁿ): GCSE Maths Step-by-Step

  Solve power proportion problems at GCSE: if y ∝ xⁿ, write y = kxⁿ, find k from a known pair, then calculate unknowns. Covers y ∝ x², y ∝ x³, y ∝ √x and y ∝ 1/x².

• Scatter Graphs and Correlation: GCSE Maths Guide

  How to draw and interpret scatter graphs at GCSE: identify correlation type and strength, draw a line of best fit, interpolate, extrapolate and spot causation errors.

• Solving Trigonometric Equations: GCSE Maths Step-by-Step

  Find all solutions of sinθ = k, cosθ = k and tanθ = k in a given range at GCSE: use inverse trig to find the first solution, then apply symmetry to find all others.

• Successive Percentage Changes: GCSE Maths Step-by-Step

  Find the result of two or more different percentage changes in sequence at GCSE: multiply the decimal multipliers together to find the equivalent single change.

• Three-Way Ratios: Dividing Into a:b:c at KS3 Maths

  Divide a quantity into three parts using ratio a:b:c at KS3: add the parts, find the value of one part, then multiply to find each share — with worked examples.

• Trigonometric Identities: GCSE Maths — sin²θ + cos²θ = 1

  Learn the two key GCSE trigonometric identities — sin²θ + cos²θ = 1 and tanθ = sinθ/cosθ — with proofs, worked simplification examples and exam tips.

• Types of Mathematical Proof: GCSE Maths Comparison Guide

  Compare the GCSE proof methods — deductive algebraic proof, proof by exhaustion and disproof by counter-example — and learn when to apply each, with worked examples.

• Area of a Circular Segment GCSE: Sector Minus Triangle

  Calculate the area of a circular segment at GCSE by subtracting the triangle area from the sector area, using ½r² sin θ for the triangle with worked examples.

• Capture-Recapture GCSE: Estimating Population Size

  Learn how to estimate population size using the mark-recapture method at GCSE, with the Lincoln-Petersen formula, worked examples, and exam tips.

• Congruence Criteria KS3: SSS, SAS, ASA, and RHS

  Understand and apply the four congruence criteria — SSS, SAS, ASA, and RHS — to decide whether two triangles are congruent at KS3 maths.

• Constructing Triangles KS3: Ruler and Compasses

  Learn to construct accurate triangles using a ruler and compasses at KS3, covering SSS, SAS, and ASA methods with step-by-step instructions and diagrams.

• Coordinate Geometry Proofs GCSE: Shapes on a Grid

  Use coordinates, gradients, midpoints, and distances to prove geometric facts at GCSE Higher — squares, rectangles, and parallel lines with worked examples.

• Cross-Sections of 3D Solids GCSE: What Slicing Reveals

  Identify cross-sections of 3D solids at GCSE — prisms, pyramids, cylinders, and cones — and understand how slicing affects shape, area, and volume reasoning.

• Describing Transformations GCSE: Full Marks Every Time

  Learn how to fully describe any transformation in GCSE maths — translation, reflection, rotation, and enlargement — with every defining feature included.

• Domain and Range of Functions GCSE Higher

  Understand domain and range for GCSE Higher maths: what inputs a function accepts, what outputs it produces, with mapping diagrams and worked examples.

• Income Tax and Personal Finance GCSE Maths

  Understand gross pay, net pay, income tax bands, and National Insurance at GCSE maths, with step-by-step worked examples for all personal finance questions.

• Moving Averages GCSE: Smoothing Time Series Data

  Learn how to calculate and plot three-point moving averages at GCSE, smooth out seasonal variation in time series data, and identify underlying trends.

• Proof by Exhaustion GCSE: Checking Every Case

  Master proof by exhaustion in GCSE maths: cover every possible case to prove a statement, with worked examples on last digits, remainders, and parity.

• Recognising Graph Types GCSE: Six Families Explained

  Recognise the six key graph types at GCSE — linear, quadratic, cubic, reciprocal, exponential, and trigonometric — from their equations and characteristic shapes.

• Simultaneous Equations from Word Problems GCSE

  Form and solve simultaneous equations from GCSE word problems: translate sentences into algebra, choose an efficient method, and interpret the solution in context.

• Solving Equations Graphically KS3: Reading Off Intersections

  Solve equations graphically at KS3 by drawing two functions and finding where they intersect, with worked examples for linear, quadratic, and cubic equations.

• Surface Area of Pyramids GCSE: Square and Triangular Bases

  Calculate the surface area of square-based and triangular pyramids at GCSE by summing the base and slant-face triangles, with net diagrams and worked examples.

• Vector Geometry Proofs GCSE: Collinearity and Parallel Lines

  Use position vectors at GCSE Higher to prove geometric facts: collinearity, parallel lines, and midpoints — with step-by-step vector algebra proofs.

• Angle of Elevation and Depression — GCSE Maths

  Calculate angles of elevation and depression at GCSE using trigonometry — with labelled diagrams, worked examples, and tips for setting up the right-angled triangle.

• Angles in Regular Polygons — GCSE Maths

  Calculate interior and exterior angles of regular polygons at GCSE using the formulas for n-sided shapes — with worked examples for hexagons, octagons, and beyond.

• Area of a Triangle Using Sine — GCSE Maths

  Use the formula Area = ½ab sin C to find the area of any triangle at GCSE — including obtuse-angled triangles — with worked examples and exam tips.

• Comparing Statistical Distributions — GCSE Maths

  Compare statistical distributions at GCSE using median and IQR — interpret box plots and cumulative frequency curves and write full exam-style comparison answers.

• Conversion Graphs — KS3 Maths

  Read and draw conversion graphs at KS3 — use straight-line graphs to convert between units such as miles and kilometres, degrees Celsius and Fahrenheit, and currencies.

• Geometric Proofs Using Angle Facts — GCSE Maths

  Write geometric proofs using angle facts at GCSE: chain angle reasons step by step, prove angles are equal or supplementary, and present working that earns full marks.

• Isometric Drawings — KS3 Maths

  Learn to draw 3D shapes on isometric dot paper at KS3: position the grid correctly, represent cuboids and compound solids, and interpret existing isometric drawings.

• Leaving Answers in Exact Form — GCSE Maths Guide

  Know when and how to leave GCSE maths answers in exact form — as surds, fractions, or multiples of pi — rather than rounding to a decimal, with worked examples.

• Multiplying and Dividing Surds — GCSE Maths

  Multiply and divide surds at GCSE using the product and quotient laws, expand surd brackets, and simplify results to exact form — with fully worked examples.

• Position Vectors — GCSE Maths

  Understand and use position vectors at GCSE: describe points relative to an origin, find the vector between two points, and calculate midpoints using column vectors.

• Probability With and Without Replacement — GCSE Maths

  Calculate probabilities for events with and without replacement at GCSE using tree diagrams — understand how removing an item changes the sample space and fractions.

• Questionnaire Design and Bias — GCSE Maths Statistics

  Identify and fix bias in GCSE statistics questionnaires: leading questions, overlapping options, sampling bias, and how to run a pilot study — with worked examples.

• Simultaneous Equations: Elimination and Substitution — GCSE Maths

  Solve simultaneous linear equations at GCSE using elimination and substitution with step-by-step worked examples, including equations that need scaling first.

• Standard Form Calculations — GCSE Maths

  Multiply, divide, and add numbers in standard form at GCSE — with step-by-step worked examples, common pitfalls, and non-calculator tips.

• Using a Scientific Calculator — GCSE Maths

  Master your scientific calculator for GCSE maths: enter fractions, powers, roots, trigonometry, and standard form correctly — with Casio fx tips and common mistake fixes.

• Venn Diagrams for Probability — GCSE Maths

  Use Venn diagrams to calculate GCSE probability — fill in regions from given information, find union and intersection probabilities, and use conditional probability.

• Adding and Subtracting Surds: GCSE Maths Step-by-Step

  Learn how to add and subtract surds at GCSE by collecting like surd terms — including cases where you must simplify first — with clear worked examples and exam tips.

• Bounds in Calculations: Upper and Lower Bounds GCSE

  Use upper and lower bounds correctly in GCSE maths — learn which bounds to combine for the maximum or minimum value of a sum, difference, product or quotient.

• Comparing Data Sets at KS3 Maths: Mean, Median and Range

  Learn how to compare two data sets at KS3 maths using the mean or median for average and the range for spread, then write a conclusion that links back to the context.

• Constructing Formulae from Words: KS3 Algebra Guide

  Learn how to write algebraic formulae from word descriptions at KS3 maths — turning real-life rules into equations with variables, operations and constants, step by step.

• Divisibility Rules KS3: Quick Tests for 2, 3, 4, 5, 6, 8, 9 and 10

  Learn the divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10 at KS3 maths — quick tests to tell whether a number divides exactly, without doing the full division.

• Equation of a Tangent to a Circle: GCSE Maths Higher

  Find the equation of a tangent to a circle at any point — a GCSE Higher skill using the perpendicular radius rule and the straight-line equation, with worked examples.

• Expressing One Quantity as a Percentage of Another: KS3

  Learn how to express one quantity as a percentage of another at KS3 — divide the part by the whole, multiply by 100, and use the skill for test scores and comparisons.

• Exterior Angle of a Triangle: KS3 Theorem Explained

  Understand the exterior angle theorem at KS3 maths: the exterior angle equals the sum of the two non-adjacent interior angles, with a short proof and worked examples.

• Four Operations with Negative Numbers: KS3 Maths Rules

  Master adding, subtracting, multiplying, and dividing with negative numbers at KS3 maths — clear sign rules, a worked example for each operation, and common mistakes.

• Gradient and Intercept in Real-Life Contexts: GCSE Maths

  Learn how to interpret the gradient and y-intercept of a straight-line graph in real-life contexts at GCSE maths — rates of change, starting values, and units explained.

• Multiplying and Dividing by Powers of 10 at KS3 Maths

  Learn how multiplying or dividing by 10, 100, and 1000 shifts digits in the place-value system at KS3 maths, with worked examples for whole numbers and decimals.

• Proof by Counter-Example: GCSE Maths Guide

  Learn how to disprove mathematical conjectures at GCSE using a single counter-example — what counts as valid, how to find one efficiently, and exam question types.

• Sampling Methods KS3: Random, Systematic and Convenience

  Learn the three main sampling methods at KS3 maths — random, systematic, and convenience — what bias is, and how to choose an appropriate sample for your enquiry.

• Systematic Listing Strategies: KS3 Maths Counting Guide

  List all possible outcomes systematically at KS3 maths using organised tables and ordered lists — essential for probability, combinations, and counting problems.

• The Statistical Enquiry Cycle: KS3 Data Handling Guide

  Understand the statistical enquiry cycle at KS3 maths: how to pose a question, plan data collection, process results, draw conclusions, and evaluate your investigation.

• Turning Points of Quadratic Graphs: GCSE Maths Explained

  Find the turning point, axis of symmetry and minimum or maximum of a quadratic graph at GCSE maths — using completing the square or the vertex formula.

• 3D Coordinates — KS3 Maths

  Understand 3D coordinates for KS3 maths: how to plot and read points in three dimensions using (x, y, z) notation, with worked examples and grid diagrams.

• Collecting Like Terms — KS3 Maths Algebra

  How to collect like terms and simplify algebraic expressions at KS3 maths — group terms with the same letter and power, then add or subtract the coefficients.

• Expected Frequency — KS3 Maths Probability

  How to find expected frequency in KS3 maths probability: multiply the theoretical probability of an event by the number of trials to predict how often it should occur.

• Finding Percentage Change — KS3 Maths

  How to find percentage change in KS3 maths: use the formula (change ÷ original) × 100 to calculate the percentage increase or decrease between two values.

• Index Laws — GCSE Maths

  Understand the three index laws for GCSE maths — multiplying, dividing and raising powers — with worked examples and exam tips for AQA and Edexcel.

• Interquartile Range — KS3 Maths Statistics

  How to find the interquartile range at KS3 maths: locate the lower and upper quartiles from ordered data, then subtract to measure the spread of the middle half.

• Multiplying Algebraic Terms — KS3 Maths

  How to multiply algebraic terms at KS3 maths: multiply coefficients together and add indices on matching letters — with worked examples from simple to harder expressions.

• Parts of a Circle — KS3 Maths

  Learn the key parts of a circle for KS3 maths — radius, diameter, chord, arc, tangent, sector and segment — with clear diagrams and definitions.

• Perimeter with Arcs — GCSE Maths

  How to find the perimeter of composite shapes with curved edges at GCSE maths — combine arc lengths with straight sides using the formula arc = (θ/360) × 2πr.

• Quadratic Graphs — KS3 Maths Introduction

  How to plot and read quadratic graphs at KS3 maths — complete a table of values for y = x², identify the vertex and line of symmetry, with worked examples.

• Rearranging Harder Formulae — GCSE Maths

  How to rearrange harder formulae for GCSE maths: make the subject appear twice, collect and factorise, or deal with squares and square roots — step by step.

• Simple Interest — KS3 Maths

  How to calculate simple interest in KS3 maths: use the formula I = PRT ÷ 100 to find interest on savings or loans — with worked examples and exam tips.

• Time and Timetables — KS3 Maths

  Understand time problems for KS3 maths: convert between 12-hour and 24-hour clock, calculate time intervals and read bus or train timetables — with worked examples.

• Velocity-Time Graphs — GCSE Maths

  Learn to read velocity-time graphs at GCSE maths: find acceleration from gradient, calculate distance from area under the graph, with worked examples.

• Volume of Composite Solids — GCSE Maths

  How to find the volume of composite solids at GCSE maths — break compound 3D shapes into simpler parts, calculate each volume and add or subtract them.

• Which Average to Use — KS3 Maths Statistics

  Understand when to use the mean, median or mode as an average in KS3 maths — compare each measure's strengths and weaknesses with real-life examples and exam tips.

• How to Find a Missing Value from the Mean (KS3)

  Work backwards from an average at KS3: multiply the mean by how many values there are to get the total, then find the missing number, combined means and removed values.

• Product Rule for Counting: GCSE Maths Explained

  How to use the product rule for counting at GCSE maths: multiply the choices at each stage, handle repeats and restrictions, with worked PIN and menu examples.

• The Discriminant: How Many Roots Does a Quadratic Have?

  Use the discriminant b² − 4ac to find how many real roots a quadratic has at GCSE higher tier, with worked examples, equal-roots questions and tangent problems.

• 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.