• Revision
    • Numeracy
      • Add & Subtract
      • Number Bonds
      • Multiply & Divide
      • Ratio Tables
      • Connected
        Calculations
      • Fractions
      • Decimals
      • Percentages
      • Ratio
    • GCSE
      • Grade Levels
        • 1-4
        • 2-5
        • 3-6
        • 4-7
        • 5-8
        • 6-9
      • Formulae
      • Algebraic
        Manipulation
      • Solving Quadratics
      • Graphs
      • Geometry
      • Data
  • Number
    • Bidmas
      • 4 Operations
      • All
    • Decimals
      • Arithmetic:
        1 Digit
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • Mixed
      • Arithmetic:
        1 & 2 Digit
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • Multiplying & Dividing: 10, 100, 1000
        • Mixed
      • Equivalence
        • To Fractions
        • To Percentages
        • To Both
        • Recurring Decimals
          to Fractions
        • With Fractions
        • With Percentages
        • FDP
        • FDP Ordering
        • FDPR
      • Money
        • Calculator
        • Non-Calculator
        • Rates of Pay
      • Ordering
      • Place Value
      • Recurring
        • Ordering
        • Converting to
          Fractions
    • Directed Numbers
      • Arithmetic
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying & Dividing
        • Mixed
        • Complex
      • Ordering
    • Equivalence
      • Converting Fractions
        • To Decimals
        • To Decimals:
          Calculator
        • To Percentages
        • To Percentages: Calculator
        • To Ratios
        • To All
        • With Decimals
        • With Percentages
        • With Ratios
        • With All
      • Converting Decimals
        • To Fractions
        • To Percentages
        • To Both
        • Recurring Decimals
          to Fractions
        • With Fractions
        • With Percentages
        • With Both
      • Converting Percentages
        • To Fractions
        • To Decimals
        • To Ratios
        • To All
        • With Fractions
        • With Decimals
        • With Ratios
        • With All
      • Converting Ratios
        • To Fractions
        • To Percentages
        • To Both
        • With Fractions
        • With Percentages
        • With Both
      • FDP
      • FDP Ordering
      • FPR
      • FDPR
    • Estimating &
      Rounding
      • Approximating Calculations
      • Estimating Roots
      • Estimation with
        Scale Drawings
      • Limits of Accuracy
        • Error Intervals
        • Calculations
      • Rounding
        • Decimal Places
        • Significant Figures
        • Whole Numbers
        • Mixed
    • Factors, Multiples & Primes
      • Prime Numbers
      • Multiples
      • Factors
      • Mixed
      • Prime Factorisation
      • HCF & LCM:
        Listing
        • HCF
        • LCM
        • Mixed
      • HCF & LCM:
        Prime Factorisation
        • HCF
        • LCM
        • Mixed
    • Fractions
      • Introduction
      • Arithmetic:
        Unit Fractions
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • With Integers
        • Mixed
      • Arithmetic:
        Non-Unit Fractions
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • With Cancelling
        • With Integers
        • Mixed
      • Equivalence
        • To Decimals
        • To Decimals:
          Calculator
        • To Percentages
        • To Percentages: Calculator
        • To Ratios
        • To All
        • With Decimals
        • With Percentages
        • With Ratios
        • FDP
        • FDP Ordering
        • FPR
        • FDPR
      • Equivalent Fractions
        • Simplifying
        • Comparing &
          Ordering
        • Comparing with
          Inequality Symbols
      • Expressing
        • Quantity
        • Change
      • Fraction of a Quantity
        • Unit Fractions
        • Non-Unit Fractions
        • Reverse
        • Increasing & Decreasing
        • FPR: Calculator
        • FPR: Non-Calculator
        • FPR: With
          Frequency trees
      • Mixed Numbers & Improper Fractions
        • Converting
          Mixed Numbers
        • Converting
          Improper Fractions
        • Converting: Mixed
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • Mixed Arithmetic
      • Mixed
      • Reciprocals
      • With a Calculator
    • Indices & Surds
      • Indices
        • Introduction
        • Square Numbers
        • Cube Numbers
        • Multiplying & Dividing
        • Negative
        • Fractional
        • Negative Fractional
        • With Brackets
        • Mixed
        • Equations
          with Indices
        • Reciprocals
      • Evaluating Roots
        • Estimating Roots
        • Square
        • Square & Cube
      • Mixed:
        Integer Values
      • Surds
        • Simplifying
        • Multiplying & Dividing
        • Adding & Subtracting
        • Expanding Brackets
        • Rationalising Denominators
        • Mixed
        • With Pythagoras
      • Mixed
    • Integers
      • Arithmetic:
        1 & 2 Digit
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • Mixed
      • Arithmetic:
        2 & 3 Digit
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • Multiplying & Dividing: 10, 100, 1000
        • Mixed
      • Place Value &
        Ordering
      • Real-Life:
        Including Money
        • Calculator
        • Non-Calculator
    • Measures
      • Compound
        • Area & Volume
          Conversion
        • Density, Mass & Volume
        • Human-Hours
        • Population Density
        • Pressure, Force &
          Area
        • Rates of Pay
        • Speed, Distance &
          Time
      • Measuring Lines
      • Money
        • Calculator
        • Non-Calculator
        • Rates of Pay
      • Reading Scales
      • Scale Drawings
      • Estimation with
        Scale Drawings
      • Systems of Measurement
        • Imperial
        • Metric
        • Mixed
        • Conversion Factors
        • Area & Volume
          Conversion
      • Time
        • Calculations
        • Converting
    • Standard Form
      • Calculations with Powers of 10
      • Adding & Subtracting
      • Multiplying & Dividing
        • Calculator
        • Non-Calculator
      • Converting
        • Ordinary to
          Standard Form
        • Standard Form to Ordinary
        • Mixed
    • Systematic Listing
    • Using a Calculator
      • Complex Calculations
      • Fractions
  • Proportion
    • Compound Measures
      • Area & Volume
        Conversion
      • Density, Mass & Volume
      • Human-Hours
      • Population Density
      • Pressure, Force &
        Area
      • Rates of Pay
      • Time
        • Calculations
        • Converting
      • Speed, Distance &
        Time
    • Direct & Inverse
      • Introduction
      • Direct
      • Inverse
      • Mixed
      • Identifying Graphs
    • Graphs
      • Identifying
        Proportional Graphs
      • Conversion Graphs
        • Reading
        • Plotting & Reading
      • Cost Relationships
        • Introduction
        • With Equations
      • Depth-Time
      • Distance-Time:
        Constant Speeds
        • Reading
        • Plotting & Reading
      • Distance-Time:
        Variable Speeds
      • Velocity-Time
        • Distance
        • Acceleration
        • Mixed
      • Mixed: Distance & Velocity
      • Volume-Time
    • Percentages:
      Calculator
      • Expressing
        • Fraction
        • Quantity
        • Change
      • Percentage of a
        Quantity
        • Integer
        • Decimal
        • Reverse
        • FPR of Quantities
      • Increase & Decrease
        • Increase
        • Decrease
        • Mixed
        • Simple Interest
        • Using a
          Multiplier
        • Reverse
      • Repeated
        Percentage Change
        • Increase &
          Compound Interest
        • Decrease
        • Increase & Decrease
        • Reverse
        • Mixed
      • Mixed
    • Percentages:
      Non-Calculator
      • Equivalence
        • To Fractions
        • To Decimals
        • To Ratios
        • To All
        • With Fractions
        • With Decimals
        • With Ratios
        • FDP
        • FDP Ordering
        • FPR
        • FDPR
      • Expressing
        • Fraction
        • Quantity
        • Change
      • Percentage of a Quantity
        • 10s
        • 5s
        • All
        • Reverse
        • FPR of Quantities
      • Increase & Decrease
        • Increase
        • Decrease
        • Mixed
        • Reverse
      • Mixed
    • Ratio
      • Equivalence
        • To Fractions
        • To Percentages
        • To Both
        • With Fractions
        • With Percentages
        • FPR
        • FDPR
      • Expressing
        • Division
        • Simplifying
      • Ratios & Quantities
        • Dividing Into a Ratio
        • Reverse
        • Mixed
        • With Line Segments
        • FPR: Calculator
        • FPR: Non-Calculator
        • FPR: With
          Frequency Trees
      • Manipulation
        • Comparing
        • Combining
        • Changing
      • Mixed
        • Foundation
        • Higher
    • Real-Life
      • Prices
        • Calculator
        • Non-Calculator
      • Best Buys
        • Calculator
        • Non-Calculator
      • Exchange Rates
      • Recipes
        • Calculator
        • Non-Calculator
  • Algebra
    • Introduction
      • Definitions
      • Notation
      • Forming Expressions
        • With Function Machines
        • Linear
      • Manipulating
        Formulae
    • Equations:
      Linear
      • Forming
        • Shapes, Angles
          & Real Life
        • With Function Machines
        • With Functions & Sequences
      • Variable on One Side: Calculator
        • 1-Step
        • 2-Step
        • 3-Step
        • Mixed
      • Variable on One Side: Non-Calculator
        • 1-Step
        • 2-Step
        • 3-Step
        • Mixed
      • With Brackets
        • Without Coefficients
        • With Coefficients
        • Multiple
      • Variable on Both Sides
        • Without Brackets
        • With Brackets
        • Graphical Intersections
        • With Parallel Lines
      • Rational
      • Mixed
      • Inequalities
      • With Functions
      • With Indices
    • Equations:
      Quadratic
      • Forming
      • Factorisation:
        Double Brackets
        • Without Coefficients
        • With Coefficients
      • b = 0
        • Rearranging
        • Difference of
          Two Squares
        • Mixed
      • c = 0
      • Completing the Square
      • Rational
        • Without Coefficients
        • With Coefficients
      • Quadratic Formula
      • Equations
        with No Solution
      • Mixed
      • Trial & Improvement
      • Iteration
      • By Intersection
      • Inequalities
    • Equations: Simultaneous
      • Forming
      • Elimination
        • Without Balancing
          Coefficients
        • With Balancing
          Coefficients
      • Substitution
      • Mixed
      • Graphically
      • Linear & Non-Linear
        • Algebraically
        • Graphically
    • Functions
      • Forming
        • Expressions
        • Simple Functions
        • Changing the Subject
          of a Formula
        • Composite
        • Inverse
        • Composite & Inverse
      • Evaluating
        • Simple Function Machines
        • Graphing
        • With Equations & Sequences
        • Linear
        • With Indices
        • Composite
        • Inverse
        • Composite & Inverse
        • Solving Equations
        • Iteration
    • Graphs: Abstract
      • Coordinates
        • Reading
        • Reading & Plotting
        • Midpoint & Endpoint
          of a Line
        • Line Segments & Ratio
        • Geometric Problems
        • With Pythagoras
      • Linear: Calculating
        • Functions & Graphs
        • Identifying
          Gradient & Intercept
        • Evaluating
          Coordinates
        • Evaluating
          Intersections
        • From Coordinates
        • Parallel
        • Perpendicular
        • Parallel & Perpendicular
        • Mixed
        • Identifying Graphs
      • Linear: Plotting
        • With Functions
        • With Sequences
        • Cover-Up Method
        • Gradient of a Line
        • Gradient-Intercept Method
        • Table of Values
          Method
        • Inequalities
        • Simultaneous Equations
      • Linear: Reading
        • Horizontal & Vertical
        • Gradient of a Line
        • Equation of a Line
        • Evaluating
          Intersections
        • Identifying
      • Linear: Mixed
      • Quadratic
        • Plotting
        • Significant Points
        • Turning Points by
          Completing the Square
        • Solving
          by Intersection
        • Simultaneous Equations
      • Circles
        • Equation
        • Tangent
      • Other Non-Linear
        • Plotting
        • Identifying:
          Non-Linear
        • Identifying: Proportional
        • Estimating Gradient
        • Exponential Functions
        • Trigonometric Functions
      • Transformations
    • Graphs: Real-Life
      • Conversion Graphs
        • Reading
        • Plotting & Reading
      • Cost Relationships
        • Introduction
        • With Equations
      • Depth-Time
      • Distance-Time:
        Constant Speeds
        • Reading
        • Plotting & Reading
      • Distance-Time:
        Variable Speeds
      • Velocity-Time
        • Distance
        • Acceleration
        • Mixed
      • Mixed: Distance & Velocity
      • Volume-Time
    • Inequalities
      • Linear
        • Forming
        • Evaluating
        • Representing
        • Solving :
          Single
        • Solving:
          Single & Double
        • Mixed
      • Graphical
      • Quadratic
      • Trial &
        Improvement
    • Manipulation
      • Notation
      • Algebraic Fractions
        • Adding & Subtracting
        • Multiplying & Dividing
        • Simplifying
        • Simplifying:
          With Factorisation
        • Rational: Difference
          of Two Squares
      • Changing the Subject
        of a Formula
        • Manipulating
          Formulae
        • Using a Function Machine
        • Without Factorisation
        • With Factorisation
      • Expanding Single Brackets
        • Without Coefficients
        • With Coefficients
        • With Indices
        • Multiple
        • Mixed
        • With Factorisation:
          Without Indices
        • With Factorisation:
          With Indices
      • Expanding Double & Triple Brackets
        • Double: Without Coefficients
        • Double: With Coefficients
        • With Factorisation
        • Squares
        • Triple
        • Mixed
        • With Surds
      • Factorising into
        Single Brackets
        • Without Indices
        • With Indices
        • With Expanding:
          Without Indices
        • With Expanding:
          With Indices
      • Factorising into
        Double Brackets
        • Quadratic
          Without Coefficients
        • Quadratic:
          With Coefficients
        • With Expanding
        • Completing the Square
        • Difference of Two Squares
        • Mixed
      • Forming
        Expressions
        • With Function Machines
        • Linear
        • Quadratic
      • Proofs
      • Simplifying
        Expressions
        • Adding
        • Adding:
          With Brackets
        • Adding:
          With Indices
        • Multiplying
        • Multiplying & Adding
        • Dividing
        • Multiplying & Dividing
        • Squared & Cubed
        • Mixed Arithmetic
        • With Negative &
          Fractional Indices
        • Rational:
          With Factorisation
        • Rational: Difference
          of Two Squares
        • Mixed: All
      • Mixed
        • Foundation
        • Higher
    • Sequences
      • Introduction
      • With Graphs
      • With Equations & Functions
      • Linear
      • Linear:
        Evaluating Terms
      • Quadratic
      • Linear & Quadratic
      • Geometric
      • Special
      • Mixed
    • Substitution
      • Using Symbols
        • Positive
        • Negative
        • Mixed
      • Without Indices
        • Positive
        • Negative
        • Mixed
      • With Indices
        • Positive
        • Negative
        • Mixed
      • With a Calculator
      • Vectors
  • Geometry
    • Angles
      • Angle Facts
        • Vocabulary
        • Around a Point
        • On Straight Lines
        • Vertically Opposite
        • Triangles
        • Mixed
      • Drawing & Measuring
        • Drawing
        • Measuring
        • Drawing & Measuring
        • Estimating
      • Circle Theorems
        • Vocabulary
        • Alternate Segment
        • At the Circumference
        • Cyclic Quadrilaterals
        • Tangents & Chords
        • With Pythagoras
        • Combined
        • Mixed
      • Parallel Lines
        • Introduction
        • Solving Equations
      • Polygons
        • Triangles
        • Regular
        • Irregular
        • Special Quadrilaterals
        • Mixed
      • Mixed
        • Without
          Circle Theorems
        • With
          Circle Theorems
    • Area & Perimeter
      • Circles
        • Vocabulary
        • Area
        • Area In Terms of π
        • Circumference
        • Area & Circumference
        • Arc Length
        • Sector Area
        • Arcs & Sectors
        • Mixed
      • Compound Shapes: Rectilinear
        • Area
        • Perimeter
        • Mixed
      • Compound Shapes:
        Polygonal
        • Area
        • Perimeter
        • Perimeter:
          With Pythagoras
      • Compound Shapes:
        With Circles
        • Area
        • Perimeter
        • Mixed
      • Quadrilaterals
        • Vocabulary
        • Rectangle:
          Area
        • Rectangle:
          Perimeter
        • Rectangle:
          Area & Perimeter
        • Parallelogram
        • Trapezium
      • Triangles
        • Area
        • Area Using Sine Rule
      • Mixed
        • Polygons
        • Polygons & Circles
    • Bearings
      • Cardinal Points
      • Measuring
      • Scale Drawings & Bearings
      • Calculating
      • With Trigonometry
    • Classifying &
      Vocabulary
      • Classifying Shapes
        • Diagonals
        • Symmetry
        • Quadrilaterals
        • 2D Shapes
      • Vocabulary
        • Angles
        • Circles
        • 2D Shapes
        • 3D Shapes
        • Sketching Diagrams
    • Construction
      • Angles
        • Drawing
        • Measuring
        • Drawing & Measuring
        • Estimating
      • Triangles
      • Bisectors
        • Line
        • Angle
        • Mixed
      • Loci
      • Bisectors & Loci
      • Nets
      • Plans & Elevations
      • Isometric Grids
      • Measuring Lines
      • Scale Drawings
      • Estimation with
        Scale Drawings
      • Scale Drawings & Bearings
      • Sketching Diagrams
    • Coordinates
      • Reading
      • Reading & Plotting
      • Midpoint & Endpoint
        of a Line
      • Line Segments & Ratio
      • Geometric Problems
      • With Pythagoras
    • Measures
      • Compound
        • Area & Volume
          Conversion
        • Density, Mass & Volume
        • Human-Hours
        • Population Density
        • Pressure, Force &
          Area
        • Rates of Pay
        • Speed, Distance &
          Time
      • Measuring Lines
      • Money
        • Calculator
        • Non-Calculator
        • Rates of Pay
      • Reading Scales
      • Scale Drawings
      • Estimation with
        Scale Drawings
      • Systems of Measurement
        • Imperial
        • Metric
        • Mixed
        • Conversion Factors
        • Area & Volume
          Conversion
      • Time
        • Calculations
        • Converting
    • Pythagoras
      • Introduction
      • Finding A or B
      • Finding A, B or C
      • Isosceles Triangles
      • Real-Life
      • 3D
      • Coordinates
      • Mixed
      • Shape Perimeters
      • With Surds
      • With Trigonometry
        • Trig. OR Pythag.
        • Trig. AND Pythag.
      • With Circle Theorems
    • Similarity
      • Area & Volume
        Conversion
      • Similar 2D Shapes
      • Similar Triangles
        • Abstract
        • Real-Life
      • Congruent Triangles
      • Length, Area & Volume
        Scale Factors
        • Length & Area
        • Length & Volume
        • Length, Area &
          Volume
      • Rotational Symmetry
    • Transformations
      • Enlargement
        • Positive
        • Negative
        • Fractional
        • Negative Fractional
        • Ray Method
        • Mixed: Foundation
        • Mixed: Higher
      • Reflection
      • Rotation
      • Symmetry
      • Rotational Symmetry
      • Translation
      • Invariant Points
      • Combined
      • Mixed
        • Foundation
        • Higher
    • Trigonometry
      • Introduction
      • Angles Between
        0° & 360°
      • Area of a Triangle
      • Choosing a Ratio
      • Sine & Cosine Ratios
        • Lengths
        • Angles
        • Mixed
      • Tangent Ratio
        • Lengths
        • Angles
        • Mixed
      • All Ratios
        • Lengths
        • Angles
        • Mixed
      • Isosceles Triangles
      • Real-Life
        • Elevation &
          Depression
        • Practical Problems
        • 3D
        • With Bearings
      • Sine & Cosine Rules
        • Sine Rule
        • Cosine Rule: Lengths
        • Cosine Rule: Angles
        • Cosine Rule: Mixed
        • Mixed
        • Solving Any Triangle
      • Without a Calculator
      • With Pythagoras
        • Trig. OR Pythag.
        • Trig. AND Pythag.
    • Vectors
      • Translation
      • Expressing
      • Substitution
      • Around Shapes
      • Proofs
    • Volume &
      Surface Area
      • Vocabulary
      • Introduction to
        Volume
      • Cone
        • Volume
        • Surface Area
        • Mixed
      • Cuboid
        • Volume
        • Surface Area
        • Mixed
      • Cylinder
        • Volume
        • Surface Area
        • Mixed
      • Prism
        • Volume
        • Surface Area
        • Mixed
      • Cylinder & Prism
        • Volume
        • Surface Area
        • Mixed
      • Pyramid: Volume
      • Sphere
        • Volume
        • Surface Area
        • Mixed
      • Mixed
        • Foundation
        • Higher
  • Data
    • Analysing
      • Mean
        • From a List
        • Reverse
      • Median
      • Range & Mode
      • Mixed
      • From a Bar Chart
    • Collecting
      • Collecting
      • Sampling
    • Frequency Tables
      • Ungrouped Data
        • Creating & Reading
        • Calculating Averages
      • Grouped Data
        • Creating & Reading
        • Calculating Averages
      • Two Way Tables
        • Creating & Reading
        • With Probability
        • With Bar Charts
    • Representing
      • Bar Charts
        • Single
        • Dual
        • Composite
        • Vertical Line Charts
        • Mixed
        • Calculating Averages
        • With Two-Way Tables
      • Box Plots
      • Cumulative Frequency Graphs
      • Box Plots
        with Graphs
      • Frequency Polygons
      • Frequency Trees
        • Introduction
        • With FPR
        • With Probability Trees
      • Histograms
      • Line Graphs
      • Pictograms
      • Pie Charts
        • Reading
        • Scaling Method
        • Proportional Method
        • Mixed
      • Scatter Graphs
      • Stem & Leaf
        Diagrams
      • Two-Way Tables
        • Creating & Reading
        • With Probability
        • With Bar Charts
      • Venn Diagrams
        • Creating & Reading
        • With Probability
        • Sets with Notation
        • Notation & Probability
  • Probability
    • Calculating
      Probabilities
      • Probability Scale
      • Single Event
      • An Event Will Not Happen
      • Mutually Exclusive & Exhaustive
      • Multiple Events
      • Sample Space
        Diagrams
      • Systematic Listing
      • Mixed
      • With Equations
    • Experiment & Expectation
      • Experimental Probability
      • Expectation
    • Frequency
      Tree Diagrams
      • Introduction
      • With FPR
      • With Probability Trees
    • Probability
      Tree Diagrams
      • Unconditional
      • Conditional
      • Mixed
      • With Frequency Trees
    • Two-Way Tables
      • Creating & Reading
      • With Probability
      • With Bar Charts
    • Venn Diagrams
      • Creating & Reading
      • With Probability
      • Sets with Notation
      • Notation & Probability
custom gray background around logo

Handcrafted resources for maths teachers.

  • Number
    • Bidmas
      • 4 Operations
      • All
    • Decimals
      • Arithmetic:
        1 Digit
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • Mixed
      • Arithmetic:
        1 & 2 Digit
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • Multiplying & Dividing: 10, 100, 1000
        • Mixed
      • Equivalence
        • To Fractions
        • To Percentages
        • To Both
        • Recurring Decimals
          to Fractions
        • With Fractions
        • With Percentages
        • FDP
        • FDP Ordering
        • FDPR
      • Money
        • Calculator
        • Non-Calculator
        • Rates of Pay
      • Ordering
      • Place Value
      • Recurring
        • Ordering
        • Converting to
          Fractions
    • Directed Numbers
      • Arithmetic
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying & Dividing
        • Mixed
        • Complex
      • Ordering
    • Equivalence
      • Converting Fractions
        • To Decimals
        • To Decimals:
          Calculator
        • To Percentages
        • To Percentages: Calculator
        • To Ratios
        • To All
        • With Decimals
        • With Percentages
        • With Ratios
        • With All
      • Converting Decimals
        • To Fractions
        • To Percentages
        • To Both
        • Recurring Decimals
          to Fractions
        • With Fractions
        • With Percentages
        • With Both
      • Converting Percentages
        • To Fractions
        • To Decimals
        • To Ratios
        • To All
        • With Fractions
        • With Decimals
        • With Ratios
        • With All
      • Converting Ratios
        • To Fractions
        • To Percentages
        • To Both
        • With Fractions
        • With Percentages
        • With Both
      • FDP
      • FDP Ordering
      • FPR
      • FDPR
    • Estimating &
      Rounding
      • Approximating Calculations
      • Estimating Roots
      • Estimation with
        Scale Drawings
      • Limits of Accuracy
        • Error Intervals
        • Calculations
      • Rounding
        • Decimal Places
        • Significant Figures
        • Whole Numbers
        • Mixed
    • Factors, Multiples & Primes
      • Prime Numbers
      • Multiples
      • Factors
      • Mixed
      • Prime Factorisation
      • HCF & LCM:
        Listing
        • HCF
        • LCM
        • Mixed
      • HCF & LCM:
        Prime Factorisation
        • HCF
        • LCM
        • Mixed
    • Fractions
      • Introduction
      • Arithmetic:
        Unit Fractions
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • With Integers
        • Mixed
      • Arithmetic:
        Non-Unit Fractions
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • With Cancelling
        • With Integers
        • Mixed
      • Equivalence
        • To Decimals
        • To Decimals:
          Calculator
        • To Percentages
        • To Percentages: Calculator
        • To Ratios
        • To All
        • With Decimals
        • With Percentages
        • With Ratios
        • FDP
        • FDP Ordering
        • FPR
        • FDPR
      • Equivalent Fractions
        • Simplifying
        • Comparing &
          Ordering
        • Comparing with
          Inequality Symbols
      • Expressing
        • Quantity
        • Change
      • Fraction of a Quantity
        • Unit Fractions
        • Non-Unit Fractions
        • Reverse
        • Increasing & Decreasing
        • FPR: Calculator
        • FPR: Non-Calculator
        • FPR: With
          Frequency trees
      • Mixed Numbers & Improper Fractions
        • Converting
          Mixed Numbers
        • Converting
          Improper Fractions
        • Converting: Mixed
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • Mixed Arithmetic
      • Mixed
      • Reciprocals
      • With a Calculator
    • Indices & Surds
      • Indices
        • Introduction
        • Square Numbers
        • Cube Numbers
        • Multiplying & Dividing
        • Negative
        • Fractional
        • Negative Fractional
        • With Brackets
        • Mixed
        • Equations
          with Indices
        • Reciprocals
      • Evaluating Roots
        • Estimating Roots
        • Square
        • Square & Cube
      • Mixed:
        Integer Values
      • Surds
        • Simplifying
        • Multiplying & Dividing
        • Adding & Subtracting
        • Expanding Brackets
        • Rationalising Denominators
        • Mixed
        • With Pythagoras
      • Mixed
    • Integers
      • Arithmetic:
        1 & 2 Digit
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • Mixed
      • Arithmetic:
        2 & 3 Digit
        • Adding
        • Subtracting
        • Adding & Subtracting
        • Multiplying
        • Dividing
        • Multiplying & Dividing
        • Multiplying & Dividing: 10, 100, 1000
        • Mixed
      • Place Value &
        Ordering
      • Real-Life:
        Including Money
        • Calculator
        • Non-Calculator
    • Measures
      • Compound
        • Area & Volume
          Conversion
        • Density, Mass & Volume
        • Human-Hours
        • Population Density
        • Pressure, Force &
          Area
        • Rates of Pay
        • Speed, Distance &
          Time
      • Measuring Lines
      • Money
        • Calculator
        • Non-Calculator
        • Rates of Pay
      • Reading Scales
      • Scale Drawings
      • Estimation with
        Scale Drawings
      • Systems of Measurement
        • Imperial
        • Metric
        • Mixed
        • Conversion Factors
        • Area & Volume
          Conversion
      • Time
        • Calculations
        • Converting
    • Standard Form
      • Calculations with Powers of 10
      • Adding & Subtracting
      • Multiplying & Dividing
        • Calculator
        • Non-Calculator
      • Converting
        • Ordinary to
          Standard Form
        • Standard Form to Ordinary
        • Mixed
    • Systematic Listing
    • Using a Calculator
      • Complex Calculations
      • Fractions
  • Proportion
    • Compound Measures
      • Area & Volume
        Conversion
      • Density, Mass & Volume
      • Human-Hours
      • Population Density
      • Pressure, Force &
        Area
      • Rates of Pay
      • Time
        • Calculations
        • Converting
      • Speed, Distance &
        Time
    • Direct & Inverse
      • Introduction
      • Direct
      • Inverse
      • Mixed
      • Identifying Graphs
    • Graphs
      • Identifying
        Proportional Graphs
      • Conversion Graphs
        • Reading
        • Plotting & Reading
      • Cost Relationships
        • Introduction
        • With Equations
      • Depth-Time
      • Distance-Time:
        Constant Speeds
        • Reading
        • Plotting & Reading
      • Distance-Time:
        Variable Speeds
      • Velocity-Time
        • Distance
        • Acceleration
        • Mixed
      • Mixed: Distance & Velocity
      • Volume-Time
    • Percentages:
      Calculator
      • Expressing
        • Fraction
        • Quantity
        • Change
      • Percentage of a
        Quantity
        • Integer
        • Decimal
        • Reverse
        • FPR of Quantities
      • Increase & Decrease
        • Increase
        • Decrease
        • Mixed
        • Simple Interest
        • Using a
          Multiplier
        • Reverse
      • Repeated
        Percentage Change
        • Increase &
          Compound Interest
        • Decrease
        • Increase & Decrease
        • Reverse
        • Mixed
      • Mixed
    • Percentages:
      Non-Calculator
      • Equivalence
        • To Fractions
        • To Decimals
        • To Ratios
        • To All
        • With Fractions
        • With Decimals
        • With Ratios
        • FDP
        • FDP Ordering
        • FPR
        • FDPR
      • Expressing
        • Fraction
        • Quantity
        • Change
      • Percentage of a Quantity
        • 10s
        • 5s
        • All
        • Reverse
        • FPR of Quantities
      • Increase & Decrease
        • Increase
        • Decrease
        • Mixed
        • Reverse
      • Mixed
    • Ratio
      • Equivalence
        • To Fractions
        • To Percentages
        • To Both
        • With Fractions
        • With Percentages
        • FPR
        • FDPR
      • Expressing
        • Division
        • Simplifying
      • Ratios & Quantities
        • Dividing Into a Ratio
        • Reverse
        • Mixed
        • With Line Segments
        • FPR: Calculator
        • FPR: Non-Calculator
        • FPR: With
          Frequency Trees
      • Manipulation
        • Comparing
        • Combining
        • Changing
      • Mixed
        • Foundation
        • Higher
    • Real-Life
      • Prices
        • Calculator
        • Non-Calculator
      • Best Buys
        • Calculator
        • Non-Calculator
      • Exchange Rates
      • Recipes
        • Calculator
        • Non-Calculator
  • Algebra
    • Introduction
      • Definitions
      • Notation
      • Forming Expressions
        • With Function Machines
        • Linear
      • Manipulating
        Formulae
    • Equations:
      Linear
      • Forming
        • Shapes, Angles
          & Real Life
        • With Function Machines
        • With Functions & Sequences
      • Variable on One Side: Calculator
        • 1-Step
        • 2-Step
        • 3-Step
        • Mixed
      • Variable on One Side: Non-Calculator
        • 1-Step
        • 2-Step
        • 3-Step
        • Mixed
      • With Brackets
        • Without Coefficients
        • With Coefficients
        • Multiple
      • Variable on Both Sides
        • Without Brackets
        • With Brackets
        • Graphical Intersections
        • With Parallel Lines
      • Rational
      • Mixed
      • Inequalities
      • With Functions
      • With Indices
    • Equations:
      Quadratic
      • Forming
      • Factorisation:
        Double Brackets
        • Without Coefficients
        • With Coefficients
      • b = 0
        • Rearranging
        • Difference of
          Two Squares
        • Mixed
      • c = 0
      • Completing the Square
      • Rational
        • Without Coefficients
        • With Coefficients
      • Quadratic Formula
      • Equations
        with No Solution
      • Mixed
      • Trial & Improvement
      • Iteration
      • By Intersection
      • Inequalities
    • Equations: Simultaneous
      • Forming
      • Elimination
        • Without Balancing
          Coefficients
        • With Balancing
          Coefficients
      • Substitution
      • Mixed
      • Graphically
      • Linear & Non-Linear
        • Algebraically
        • Graphically
    • Functions
      • Forming
        • Expressions
        • Simple Functions
        • Changing the Subject
          of a Formula
        • Composite
        • Inverse
        • Composite & Inverse
      • Evaluating
        • Simple Function Machines
        • Graphing
        • With Equations & Sequences
        • Linear
        • With Indices
        • Composite
        • Inverse
        • Composite & Inverse
        • Solving Equations
        • Iteration
    • Graphs: Abstract
      • Coordinates
        • Reading
        • Reading & Plotting
        • Midpoint & Endpoint
          of a Line
        • Line Segments & Ratio
        • Geometric Problems
        • With Pythagoras
      • Linear: Calculating
        • Functions & Graphs
        • Identifying
          Gradient & Intercept
        • Evaluating
          Coordinates
        • Evaluating
          Intersections
        • From Coordinates
        • Parallel
        • Perpendicular
        • Parallel & Perpendicular
        • Mixed
        • Identifying Graphs
      • Linear: Plotting
        • With Functions
        • With Sequences
        • Cover-Up Method
        • Gradient of a Line
        • Gradient-Intercept Method
        • Table of Values
          Method
        • Inequalities
        • Simultaneous Equations
      • Linear: Reading
        • Horizontal & Vertical
        • Gradient of a Line
        • Equation of a Line
        • Evaluating
          Intersections
        • Identifying
      • Linear: Mixed
      • Quadratic
        • Plotting
        • Significant Points
        • Turning Points by
          Completing the Square
        • Solving
          by Intersection
        • Simultaneous Equations
      • Circles
        • Equation
        • Tangent
      • Other Non-Linear
        • Plotting
        • Identifying:
          Non-Linear
        • Identifying: Proportional
        • Estimating Gradient
        • Exponential Functions
        • Trigonometric Functions
      • Transformations
    • Graphs: Real-Life
      • Conversion Graphs
        • Reading
        • Plotting & Reading
      • Cost Relationships
        • Introduction
        • With Equations
      • Depth-Time
      • Distance-Time:
        Constant Speeds
        • Reading
        • Plotting & Reading
      • Distance-Time:
        Variable Speeds
      • Velocity-Time
        • Distance
        • Acceleration
        • Mixed
      • Mixed: Distance & Velocity
      • Volume-Time
    • Inequalities
      • Linear
        • Forming
        • Evaluating
        • Representing
        • Solving :
          Single
        • Solving:
          Single & Double
        • Mixed
      • Graphical
      • Quadratic
      • Trial &
        Improvement
    • Manipulation
      • Notation
      • Algebraic Fractions
        • Adding & Subtracting
        • Multiplying & Dividing
        • Simplifying
        • Simplifying:
          With Factorisation
        • Rational: Difference
          of Two Squares
      • Changing the Subject
        of a Formula
        • Manipulating
          Formulae
        • Using a Function Machine
        • Without Factorisation
        • With Factorisation
      • Expanding Single Brackets
        • Without Coefficients
        • With Coefficients
        • With Indices
        • Multiple
        • Mixed
        • With Factorisation:
          Without Indices
        • With Factorisation:
          With Indices
      • Expanding Double & Triple Brackets
        • Double: Without Coefficients
        • Double: With Coefficients
        • With Factorisation
        • Squares
        • Triple
        • Mixed
        • With Surds
      • Factorising into
        Single Brackets
        • Without Indices
        • With Indices
        • With Expanding:
          Without Indices
        • With Expanding:
          With Indices
      • Factorising into
        Double Brackets
        • Quadratic
          Without Coefficients
        • Quadratic:
          With Coefficients
        • With Expanding
        • Completing the Square
        • Difference of Two Squares
        • Mixed
      • Forming
        Expressions
        • With Function Machines
        • Linear
        • Quadratic
      • Proofs
      • Simplifying
        Expressions
        • Adding
        • Adding:
          With Brackets
        • Adding:
          With Indices
        • Multiplying
        • Multiplying & Adding
        • Dividing
        • Multiplying & Dividing
        • Squared & Cubed
        • Mixed Arithmetic
        • With Negative &
          Fractional Indices
        • Rational:
          With Factorisation
        • Rational: Difference
          of Two Squares
        • Mixed: All
      • Mixed
        • Foundation
        • Higher
    • Sequences
      • Introduction
      • With Graphs
      • With Equations & Functions
      • Linear
      • Linear:
        Evaluating Terms
      • Quadratic
      • Linear & Quadratic
      • Geometric
      • Special
      • Mixed
    • Substitution
      • Using Symbols
        • Positive
        • Negative
        • Mixed
      • Without Indices
        • Positive
        • Negative
        • Mixed
      • With Indices
        • Positive
        • Negative
        • Mixed
      • With a Calculator
      • Vectors
  • Geometry
    • Angles
      • Angle Facts
        • Vocabulary
        • Around a Point
        • On Straight Lines
        • Vertically Opposite
        • Triangles
        • Mixed
      • Drawing & Measuring
        • Drawing
        • Measuring
        • Drawing & Measuring
        • Estimating
      • Circle Theorems
        • Vocabulary
        • Alternate Segment
        • At the Circumference
        • Cyclic Quadrilaterals
        • Tangents & Chords
        • With Pythagoras
        • Combined
        • Mixed
      • Parallel Lines
        • Introduction
        • Solving Equations
      • Polygons
        • Triangles
        • Regular
        • Irregular
        • Special Quadrilaterals
        • Mixed
      • Mixed
        • Without
          Circle Theorems
        • With
          Circle Theorems
    • Area & Perimeter
      • Circles
        • Vocabulary
        • Area
        • Area In Terms of π
        • Circumference
        • Area & Circumference
        • Arc Length
        • Sector Area
        • Arcs & Sectors
        • Mixed
      • Compound Shapes: Rectilinear
        • Area
        • Perimeter
        • Mixed
      • Compound Shapes:
        Polygonal
        • Area
        • Perimeter
        • Perimeter:
          With Pythagoras
      • Compound Shapes:
        With Circles
        • Area
        • Perimeter
        • Mixed
      • Quadrilaterals
        • Vocabulary
        • Rectangle:
          Area
        • Rectangle:
          Perimeter
        • Rectangle:
          Area & Perimeter
        • Parallelogram
        • Trapezium
      • Triangles
        • Area
        • Area Using Sine Rule
      • Mixed
        • Polygons
        • Polygons & Circles
    • Bearings
      • Cardinal Points
      • Measuring
      • Scale Drawings & Bearings
      • Calculating
      • With Trigonometry
    • Classifying &
      Vocabulary
      • Classifying Shapes
        • Diagonals
        • Symmetry
        • Quadrilaterals
        • 2D Shapes
      • Vocabulary
        • Angles
        • Circles
        • 2D Shapes
        • 3D Shapes
        • Sketching Diagrams
    • Construction
      • Angles
        • Drawing
        • Measuring
        • Drawing & Measuring
        • Estimating
      • Triangles
      • Bisectors
        • Line
        • Angle
        • Mixed
      • Loci
      • Bisectors & Loci
      • Nets
      • Plans & Elevations
      • Isometric Grids
      • Measuring Lines
      • Scale Drawings
      • Estimation with
        Scale Drawings
      • Scale Drawings & Bearings
      • Sketching Diagrams
    • Coordinates
      • Reading
      • Reading & Plotting
      • Midpoint & Endpoint
        of a Line
      • Line Segments & Ratio
      • Geometric Problems
      • With Pythagoras
    • Measures
      • Compound
        • Area & Volume
          Conversion
        • Density, Mass & Volume
        • Human-Hours
        • Population Density
        • Pressure, Force &
          Area
        • Rates of Pay
        • Speed, Distance &
          Time
      • Measuring Lines
      • Money
        • Calculator
        • Non-Calculator
        • Rates of Pay
      • Reading Scales
      • Scale Drawings
      • Estimation with
        Scale Drawings
      • Systems of Measurement
        • Imperial
        • Metric
        • Mixed
        • Conversion Factors
        • Area & Volume
          Conversion
      • Time
        • Calculations
        • Converting
    • Pythagoras
      • Introduction
      • Finding A or B
      • Finding A, B or C
      • Isosceles Triangles
      • Real-Life
      • 3D
      • Coordinates
      • Mixed
      • Shape Perimeters
      • With Surds
      • With Trigonometry
        • Trig. OR Pythag.
        • Trig. AND Pythag.
      • With Circle Theorems
    • Similarity
      • Area & Volume
        Conversion
      • Similar 2D Shapes
      • Similar Triangles
        • Abstract
        • Real-Life
      • Congruent Triangles
      • Length, Area & Volume
        Scale Factors
        • Length & Area
        • Length & Volume
        • Length, Area &
          Volume
      • Rotational Symmetry
    • Transformations
      • Enlargement
        • Positive
        • Negative
        • Fractional
        • Negative Fractional
        • Ray Method
        • Mixed: Foundation
        • Mixed: Higher
      • Reflection
      • Rotation
      • Symmetry
      • Rotational Symmetry
      • Translation
      • Invariant Points
      • Combined
      • Mixed
        • Foundation
        • Higher
    • Trigonometry
      • Introduction
      • Angles Between
        0° & 360°
      • Area of a Triangle
      • Choosing a Ratio
      • Sine & Cosine Ratios
        • Lengths
        • Angles
        • Mixed
      • Tangent Ratio
        • Lengths
        • Angles
        • Mixed
      • All Ratios
        • Lengths
        • Angles
        • Mixed
      • Isosceles Triangles
      • Real-Life
        • Elevation &
          Depression
        • Practical Problems
        • 3D
        • With Bearings
      • Sine & Cosine Rules
        • Sine Rule
        • Cosine Rule: Lengths
        • Cosine Rule: Angles
        • Cosine Rule: Mixed
        • Mixed
        • Solving Any Triangle
      • Without a Calculator
      • With Pythagoras
        • Trig. OR Pythag.
        • Trig. AND Pythag.
    • Vectors
      • Translation
      • Expressing
      • Substitution
      • Around Shapes
      • Proofs
    • Volume &
      Surface Area
      • Vocabulary
      • Introduction to
        Volume
      • Cone
        • Volume
        • Surface Area
        • Mixed
      • Cuboid
        • Volume
        • Surface Area
        • Mixed
      • Cylinder
        • Volume
        • Surface Area
        • Mixed
      • Prism
        • Volume
        • Surface Area
        • Mixed
      • Cylinder & Prism
        • Volume
        • Surface Area
        • Mixed
      • Pyramid: Volume
      • Sphere
        • Volume
        • Surface Area
        • Mixed
      • Mixed
        • Foundation
        • Higher
  • Data
    • Analysing
      • Mean
        • From a List
        • Reverse
      • Median
      • Range & Mode
      • Mixed
      • From a Bar Chart
    • Collecting
      • Collecting
      • Sampling
    • Frequency Tables
      • Ungrouped Data
        • Creating & Reading
        • Calculating Averages
      • Grouped Data
        • Creating & Reading
        • Calculating Averages
      • Two Way Tables
        • Creating & Reading
        • With Probability
        • With Bar Charts
    • Representing
      • Bar Charts
        • Single
        • Dual
        • Composite
        • Vertical Line Charts
        • Mixed
        • Calculating Averages
        • With Two-Way Tables
      • Box Plots
      • Cumulative Frequency Graphs
      • Box Plots
        with Graphs
      • Frequency Polygons
      • Frequency Trees
        • Introduction
        • With FPR
        • With Probability Trees
      • Histograms
      • Line Graphs
      • Pictograms
      • Pie Charts
        • Reading
        • Scaling Method
        • Proportional Method
        • Mixed
      • Scatter Graphs
      • Stem & Leaf
        Diagrams
      • Two-Way Tables
        • Creating & Reading
        • With Probability
        • With Bar Charts
      • Venn Diagrams
        • Creating & Reading
        • With Probability
        • Sets with Notation
        • Notation & Probability
  • Probability
    • Calculating
      Probabilities
      • Probability Scale
      • Single Event
      • An Event Will Not Happen
      • Mutually Exclusive & Exhaustive
      • Multiple Events
      • Sample Space
        Diagrams
      • Systematic Listing
      • Mixed
      • With Equations
    • Experiment & Expectation
      • Experimental Probability
      • Expectation
    • Frequency
      Tree Diagrams
      • Introduction
      • With FPR
      • With Probability Trees
    • Probability
      Tree Diagrams
      • Unconditional
      • Conditional
      • Mixed
      • With Frequency Trees
    • Two-Way Tables
      • Creating & Reading
      • With Probability
      • With Bar Charts
    • Venn Diagrams
      • Creating & Reading
      • With Probability
      • Sets with Notation
      • Notation & Probability

What’s New?

  • Tips & Tricks
  • What’s New?
  • About Go Teach Maths
  • What Do Teachers Say About GTM?
  • Legal

Help us help you 🙂

If you have 30 seconds to spare… Online Feedback Form

If you would like to donate… Patreon

© goteachmaths

Contact us:

tom@goteachmaths.co.uk

Go Teach Maths uses cookies. Click here for more information.
Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these cookies, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may have an effect on your browsing experience.
Necessary
Always Enabled

Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.

Non-necessary

Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.

SAVE & ACCEPT