Cambridge IGCSE Mathematics

Number Types and Sets

Lessons

1. Types of Numbers
2. Sets and Venn Diagrams

Simulations

• Factors and multiplesFreeFind the factors and multiples of two numbers, their highest common factor and their lowest common multiple.
• Venn regionsFreeName the regions of a Venn diagram in set notation, and count what is in each one.

Powers, Roots and Indices

Lessons

1. Powers and Roots
2. Laws of Indices

Simulations

• The number toolkitFreeSimplify with the index laws, give the bounds of a rounded value, share in a ratio and find the better value, checking each answer.

Fractions, Decimals and Percentages

Lessons

1. Fractions
2. Decimals
3. Percentages

Simulations

• Parts of a wholeSee how a fraction, a decimal and a percentage describe the same part of a whole.
• Percentage growth and decayCompare a repeated percentage change with a simple one, and find what the multiplier does.

Ordering, Approximation and Accuracy

Lessons

1. Ordering Numbers
2. Rounding and Estimation

Simulations

• The number toolkitFree

Ratio, Proportion and Rates

Lessons

1. Ratio
2. Direct and Inverse Proportion
3. Rates

Simulations

• The number toolkitFree
• Gradient and interceptFreeSee what m and c do to a line, then write the equation of any line you are given.
• Inverse proportionFind what stays the same when x and y are inversely proportional, and what k does to the curve.

Algebraic Language and Manipulation

Lessons

1. Algebraic Expressions
2. Algebraic Fractions

Simulations

• Factorise it, and see the rectangleFactorise an expression into two brackets, and see why it works as the area of a rectangle.

Indices and Surds

Lessons

1. Algebraic Indices
2. Surds

Simulations

• The number toolkitFree

Factorisation and Algebraic Fractions

Lessons

1. Common Factors
2. Quadratic Factorisation

Simulations

• Factorise it, and see the rectangle

Equations

Lessons

1. Linear Equations
2. Simultaneous Equations
3. Quadratic Equations
4. Equations with Powers and Roots

Simulations

• Solve it, one move at a timeSolve equations, inequalities and simultaneous equations by doing the same to both sides, and find what dividing by a negative does to an inequality.
• Gradient and interceptFree
• Solve it on the graphSolve equations and inequalities by reading where a graph crosses the x-axis, or where two graphs meet.
• Move a parabolaFind what h, k and a each do to a parabola, and when it crosses the x-axis twice, once or not at all.

Inequalities

Lessons

1. Linear Inequalities
2. Quadratic Inequalities

Simulations

• Solve it, one move at a time
• Solve it on the graph
• Move a parabola

Sequences

Lessons

1. Number Sequences
2. Non-linear Sequences

Simulations

• Find the nth termFind the rule for the nth term of a linear or quadratic sequence from its differences.
• Gradient and interceptFree

Functions

Lessons

1. Function Notation
2. Inverse Functions

Simulations

• Gradient and interceptFree

Graphs and Relationships

Lessons

1. Straight-Line Graphs
2. Graphical Solutions
3. Quadratic Graphs
4. Other Graphs
5. Graph Transformations

Simulations

• Gradient and interceptFree
• Solve it on the graph
• Move a parabola
• Inverse proportion
• Exponential relationshipsCompare exponential growth with decay, and find what the base does to the curve.

Coordinates and Distance

Lessons

1. Cartesian Coordinates
2. Distance and Midpoint

Simulations

• Coordinates, distance and midpointFreeFind the distance, the midpoint and the gradient between two points from their coordinates.

Straight Lines

Lessons

1. Gradient
2. Equation of a Line
3. Parallel and Perpendicular Lines

Simulations

• Coordinates, distance and midpointFree
• Gradient and interceptFree

Geometrical Terms and Properties

Lessons

1. Angles
2. Polygons

Simulations

• Regular polygon anglesFreeFind the interior and exterior angles of a regular polygon from its number of sides, and the number of sides from an angle.

Triangles and Quadrilaterals

Lessons

1. Triangle Properties
2. Congruence
3. Quadrilateral Properties

Simulations

• Triangle sides, angles and areaFreeFind how two sides and the angle between them fix the third side and the area of a triangle.

Similarity and Enlargement

Lessons

1. Similar Shapes
2. Enlargement

Simulations

• Transform a triangleDescribe a transformation completely: what kind it is, and exactly how it moves the shape.
• Cylinders, prisms and conesFind how the radius and the height change the volume and the surface area of a cylinder, and how a cuboid and a cone compare.

Circle Geometry

Lessons

1. Circle Vocabulary
2. Circle Theorems
3. Geometrical Proof

Simulations

• Circle sectorsFind the arc length and the area of a sector as a fraction of the whole circle.
• Circle theorems, and the reasonFind the angle facts that hold wherever the points are on a circle, and give a reason with every answer.

Constructions and Loci

Lessons

1. Geometrical Constructions
2. Loci

Simulations

• Ruler, compass and lociConstruct bisectors, perpendiculars and loci with a ruler and compasses, and check what your construction really makes.

Units and Measurement

Lessons

1. Measurement Systems
2. Compound Measures

Perimeter and Area

Lessons

1. Perimeter
2. Area
3. Circular Area

Simulations

• Circle sectors
• Triangle sides, angles and areaFree

Surface Area and Volume

Lessons

1. Prisms
2. Cuboids and Cylinders
3. Pyramids, Cones and Spheres

Simulations

• Cylinders, prisms and cones

Arc Length and Sector Area

Lessons

1. Circular Arcs
2. Sectors

Simulations

• Circle sectors

Right-Angled Triangles

Lessons

1. Pythagoras' Theorem
2. Basic Trigonometric Ratios
3. Trigonometric Applications

Simulations

• Triangle sides, angles and areaFree

Exact and Special-Angle Relationships

Lessons

1. Special Triangles
2. Trigonometric Relationships

Simulations

• Triangle sides, angles and areaFree

Non-Right-Angled Triangles

Lessons

1. Sine Rule
2. Cosine Rule
3. Area of a Triangle

Simulations

• Triangle sides, angles and areaFree

Three-Dimensional Trigonometry

Lessons

1. 3D Geometry

Transformations

Lessons

1. Reflection
2. Rotation
3. Translation
4. Enlargement

Simulations

• Transform a triangle

Vectors

Lessons

1. Vector Representation
2. Vector Operations
3. Vector Geometry

Simulations

• Vectors as journeysUse vectors as journeys: reach a point, divide a line in a ratio, and show that three points lie on a line.
• Coordinates, distance and midpointFree

Basic Probability

Lessons

1. Probability Concepts
2. Probability of Events

Simulations

• Parts of a whole
• Two-draw probability treeWork out the probabilities of two draws on a tree diagram, with and without replacement.

Probability Diagrams

Lessons

1. Sample Space
2. Venn Diagrams
3. Tree Diagrams

Simulations

• What should happen, and what doesFreeWork out what should happen from the sample space, then see how close real throws of two dice get, and when.
• Venn regionsFree
• Two-draw probability tree

Expected Frequency and Relative Frequency

Lessons

1. Relative Frequency
2. Expected Frequency

Simulations

• What should happen, and what doesFree
• Two-draw probability tree

Conditional Probability

Lessons

1. Dependent Events

Simulations

• Two-draw probability tree

Types of Data and Sampling

Lessons

1. Data Types
2. Sampling

Simulations

• What should happen, and what doesFree

Tables and Frequency

Lessons

1. Frequency Tables
2. Frequency Density

Simulations

• Build the diagramDraw a bar chart, a pie chart, a stem-and-leaf diagram or a time series from the data, and check it against the data.
• Explore a datasetFind how the mean, the median and the range respond when one value changes or an outlier arrives.
• Why a histogram needs frequency densityFind out why a histogram with unequal classes plots frequency density rather than frequency.

Averages and Measures of Spread

Lessons

1. Mean, Median and Mode
2. Range and Spread
3. Quartiles and Interquartile Range

Simulations

• Explore a dataset

Statistical Charts and Diagrams

Lessons

1. Bar Charts and Pie Charts
2. Line and Time-Series Graphs
3. Stem-and-Leaf Diagrams
4. Histograms

Simulations

• Build the diagram
• Why a histogram needs frequency density

Cumulative Frequency

Lessons

1. Cumulative Frequency Tables
2. Cumulative Frequency Curves
3. Comparing Distributions

Simulations

• Cumulative frequency, end to endBuild a cumulative frequency curve from a table, read the median, the quartiles and the spread off it, and compare two groups.
• Explore a dataset

Scatter Diagrams and Correlation

Lessons

1. Scatter Diagrams
2. Lines of Best Fit

Simulations

• Correlation and a line you place yourselfDecide how two quantities are related, place your own line of best fit, and use it to make an estimate.

Mathematical Communication

Lessons

1. Mathematical Notation
2. Interpretation

Calculator and Non-Calculator Skills

Lessons

1. Non-Calculator Techniques
2. Calculator Techniques

Problem-Solving Strategies

Lessons

1. Multi-Step Problems
2. Reasoning and Checking

Accuracy and Estimation

Lessons

1. Accuracy

Simulations

• The number toolkitFree

Algebraic and Graphical Reasoning

Lessons

1. Relationships

Simulations

• Gradient and interceptFree

Geometry and Measurement

Lessons

1. Geometrical Accuracy

Simulations

• Ruler, compass and loci

Data Handling

Lessons

1. Statistical Reasoning

Simulations

• Explore a dataset