LemmaraFree lessonsIGCSE & O Level maths, one topic at a time
314 short lessons with worked examples, the mistakes examiners see most, and the real past-paper questions on each topic. Free, no account needed.
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Number
Number and Language
- Natural Numbers
- Written Methods of Multiplication
- Written Methods of Division
- Integers
- Directed Numbers
- What Is a Fraction?
- Rational Numbers
- Irrational Numbers
- Real Numbers
- Factors and Multiples
- Prime Numbers
- Prime Factorization
- HCF and LCM
- Square Numbers
- Square Roots
- Cube Numbers
- Cube Roots
- Further Powers and Roots
- Reciprocals
- Using a Calculator
- Number Review: Mixed Practice
Approximation and Bounds
Ordering and Order of Operations
Fractions, Decimals and Percentages
- Fractions of an Amount
- Mixed Numbers and Improper Fractions
- Equivalent Fractions
- Introduction to Percentages
- Addition and Subtraction of Fractions
- Multiplication and Division of Fractions
- Understanding Decimal Place Value
- Adding, Subtracting, Multiplying and Dividing Decimals
- Converting Fractions to Decimals
- Converting Decimals to Fractions
- Recurring Decimals
Percentages
Ratio and Proportion
Indices, Standard Form and Surds
Money and Finance
Sets and Venn Diagrams
Algebra & graphs
Algebraic Manipulation
Algebraic Indices
Equations and Simultaneous Equations
- Solving Linear Equations
- Constructing Equations
- Simultaneous Equations by Elimination
- Solving by Substitution
- Solving Quadratics by Factorising
- The Quadratic Formula and Completing the Square
- Equations That Become Quadratics
- Simultaneous Equations with a Curve
- Linear Inequalities
- Quadratic Inequalities
- Hidden Quadratics and Harder Simultaneous Equations
Inequalities and Regions
Sequences
Travel and Conversion Graphs
Curved Graphs
- Plotting Curves from a Table of Values
- Quadratic Graphs and the Parabola
- Completed Square Form and Turning Points
- Solving Quadratics from a Graph
- Reciprocal Functions
- Exponential Functions
- Recognising and Sketching Graph Shapes
- Solving Equations by Graphical Methods
- Sketching Cubics and Cubic Inequalities
- Rational Functions and Asymptotes
Differentiation
- Differentiating Polynomials
- Gradient of a Curve at a Point
- Equation of the Tangent Line
- Stationary Points and Turning Points
- The Second Derivative
- Derivatives of Powers, eˣ, ln x and Trig
- The Chain Rule
- The Product and Quotient Rules
- Tangents, Normals and Stationary Points (Further)
- Connected Rates of Change and Small Changes
Functions
Quadratic Theory
Modulus Functions
Logarithms and Exponentials
Binomial Expansion
Coordinate geometry
Coordinate Geometry
- Coordinates and Plotting Points
- The Gradient of a Straight Line
- The Equation y = mx + c
- Equation of a Line Through Two Points
- Equation in the Form ax + by + c = 0
- Parallel Lines and Their Equations
- Drawing Straight-Line Graphs
- Graphical Solution of Simultaneous Equations
- Length of a Line Segment
- Area from Coordinates
- Perpendicular Lines
- Finding the Equation From a Graph
- The Perpendicular Bisector
- Coordinate Geometry of Shapes
- The Point Dividing a Line in a Ratio
Geometry
Geometrical Vocabulary and Construction
Similarity and Congruence
Symmetry
Angles and Circle Theorems
Mensuration
Units and Conversions
Mensuration
- Perimeter and Area of a Rectangle
- Area of a Triangle
- Area of a Parallelogram and Trapezium
- Circumference and Area of a Circle
- Surface Area of a Cuboid and Cylinder
- Volume of a Prism
- Arc Length
- Area of a Sector
- Volume and Surface Area of a Sphere
- Volume of a Pyramid
- Surface Area of a Pyramid
- Volume and Surface Area of a Cone
- Composite Perimeter, Area and Volume
- Equating Volumes: Melting and Recasting
- Frustum of a Cone
Trigonometry
Pythagoras and Trigonometry
- Labelling Sides of a Right-Angled Triangle
- The Tangent Ratio
- Choosing the Right Trigonometric Ratio
- The Sine Ratio
- The Cosine Ratio
- Pythagoras' Theorem
- Using Trigonometry and Pythagoras Together
- Angles of Elevation and Depression
- Special Angles and Exact Ratios
- Trigonometric Graphs and Equations
- Bearings and Trigonometry
Further Trigonometry
- The Sine Rule
- The Ambiguous Case of the Sine Rule
- The Cosine Rule
- Area of a Triangle Using Sine
- Trigonometry in 3D: Cuboids
- Trigonometry in 3D: Pyramids and Cones
- Angle Between a Line and a Plane
- Shortest Distance from a Point to a Line
- Choosing Between Sine and Cosine Rules
- Bearings with Sine and Cosine Rules
Radians
Trigonometric Identities and Equations
Transformations & vectors
Vectors
Probability
Probability
Combined Probability
Permutations and Combinations
Statistics
Averages and Range
Statistical Diagrams
Other
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