Biblioteca de cursos

Números e aritmética

The Integers

Commutative, Associative and Distributive LawsEm breve
Order of OperationsEm breve
The Number LineEm breve
Arithmetic with Negative NumbersEm breve
Properties of ZeroEm breve
Absolute ValueEm breve
Place ValueEm breve

Fractions

IntroductionEm breve
Fraction ArithmeticEm breve
Mixed NumbersEm breve
Dividing FractionsEm breve

Decimals

IntroductionEm breve
Adding and Subtracting DecimalsEm breve
Ordering DecimalsEm breve
Multiplying and Dividing DecimalsEm breve
Converting Decimals and FractionsEm breve
RoundingEm breve

Rates, Percentages and Ratios

Ratios and MixturesEm breve
PercentagesEm breve
Percentage Increase and DecreaseEm breve
InterestEm breve
Ratios and RatesEm breve

Roots and Exponents

Square and Cube RootsEm breve
Rational and Irrational NumbersEm breve
Powers and ExponentsEm breve
Large and Small NumbersEm breve
Scientific NotationEm breve

Equações e Funções

Introduction to Algebra

IntroductionEm breve
Constants and VariablesEm breve
Manipulating ExpressionsEm breve
ModellingEm breve

Proportional Relationships

IntroductionEm breve
Direct and Inverse ProportionEm breve
Graphing Proportional RelationshipsEm breve
Constant of ProportionalityEm breve

Linear Equations

Reasoning with Tape DiagramsEm breve
Weighing and BalancingEm breve
Manipulating EquationsEm breve
Solving Linear EquationsEm breve
InequalitiesEm breve

Linear Functions

Input and OutputEm breve
Graphing FunctionsEm breve
Slope and InterceptEm breve
Parallel and Perpendicular LinesEm breve
Linear FunctionsEm breve
Piecewise Functions and Systems of EquationsEm breve

Geometria

Area and Shapes

IntroductionEm breve
Parallelograms and TrianglesEm breve
PolygonsEm breve
Circles and CircumferencesEm breve
Area of CirclesEm breve

Angles and Polygons

AnglesEm breve
Angles in PolygonsEm breve
Drawing Triangles
Pythagoras’ TheoremEm breve
The Coordinate PlaneEm breve
Transformations and CongruenceEm breve

3D Solids

IntroductionEm breve
Nets and Surface AreaEm breve
Prisms and PyramidsEm breve
Cylinders and ConesEm breve
SpheresEm breve

Units and Measuring

MeasuringEm breve
Units and ConversionEm breve
Scale DrawingsEm breve
Scaling and DimensionsEm breve
EstimationEm breve

Probabilidade e Estatística

Introduction to Probability

IntroductionEm breve
Computing ProbabilitiesEm breve
Probability TreesEm breve
Venn DiagramsEm breve

Data and Statistics

IntroductionEm breve
Center and SpreadEm breve
Visualising DataEm breve
SamplingEm breve
Scatter Plots and Linear ModelsEm breve

Geometria

Euclidean Geometry

IntroductionEuclid’s AxiomsRuler and Compass Construction
Even More ConstructionsEm breve
Angles and ProofsEm breve
Origami and Paper Folding

Triangles and Trigonometry

IntroductionProperties of Triangles
Midsegments and SimilarityEm breve
Triangle CongruencePythagoras’ Theorem
Isosceles and Equilateral TrianglesEm breve
TrigonometrySine and Cosine Rules

Polígonos e Poliedros

PolígonosQuadriláterosPavimentaçõesPoliedros
Redes e Seções TransversaisEm breve
Prismas e pirâmidesEm breve
Escalando formas e sólidosEm breve
Sólidos platônicos

Círculos e Pi

IntroduçãoGraus e radianosTangentes, acordes e arcos
Os Teoremas do CírculoEm breve
Polígonos CíclicosEm breve
Esferas, cones e cilindrosSeções cônicas

Álgebra

Functions

Relations and FunctionsEm breve
Graphing and Interpreting FunctionsEm breve
Linear Functions and EquationsEm breve
Piecewise FunctionsEm breve
Absolute Value FunctionsEm breve
Inverse FunctionsEm breve
Rates of ChangeEm breve

Quadratic Equations

Introduction
Binomial ExpressionsEm breve
Solving Quadratic EquationsEm breve
The Quadratic FormulaEm breve
Graphing QuadraticsEm breve
Projectile MotionEm breve
More ApplicationsEm breve

Inequalities and Systems of Equations

Systems of Linear EquationsEm breve
Row Operations and EliminationEm breve
Linear InequalitiesEm breve
Systems of InequalitiesEm breve
Quadratic InequalitiesEm breve

Exponential Functions

Carbon Dating
Exponential Growth and DecayEm breve
Comparing ModelsEm breve
Compound InterestEm breve
Population DynamicsEm breve

Probabilidade e Matemática Discreta

Probability

Introduction
Probability Trees and Venn DiagramsEm breve
Conditional ProbabilityEm breve
The Monty Hall Problem
The Birthday ProblemEm breve
True Randomness

Statistics and Data

Casino Mathematics
Data VisualisationEm breve
Center and Spread of DataEm breve
Sampling and EstimationEm breve
Spreadsheets and Frequency TablesEm breve
Linear ModelsEm breve

Codes and Ciphers

Introduction
Binary NumbersEm breve
Error DetectionEm breve
Secret CodesEm breve
The EnigmaEm breve
Public Key CryptographyEm breve

Game Theory

The Prisoners’ Dilemma
Cards, Coins and DiceEm breve
The Winning Move
Random WalksEm breve

Álgebra e Análise

Polynomials

IntroductionEm breve
Zeros of PolynomialsEm breve
Sketching Polynomial FunctionsEm breve
The Factor and Remainder TheoremsEm breve
Systems of EquationsEm breve

Function Transformations

Combining and Composing FunctionsEm breve
Translating FunctionsEm breve
Reflecting FunctionsEm breve
Scaling FunctionsEm breve
Inverse functionsEm breve

Rationals and Radicals

Rational and Irrational NumbersEm breve
Rational Functions and ExpressionsEm breve
Solving Rational EquationsEm breve
Exponent LawsEm breve
Radical FunctionsEm breve
Solving Radical EquationsEm breve

Exponentials and Logarithms

Exponential Growth and DecayEm breve
Exponential FunctionsEm breve
Introduction to LogarithmsEm breve
Laws of LogarithmsEm breve
The Number eEm breve
Logarithmic FunctionsEm breve

Sequences and Series

SequencesEm breve
Series and Sigma NotationEm breve
Arithmetic and Geometric SeriesEm breve
The Binomial TheoremEm breve

Geometria e Álgebra Linear

Coordinate Geometry

Equations of LinesEm breve
Parallel and Perpendicular LinesEm breve
Equations of CirclesEm breve
Properties of PolygonsEm breve
TransformationsEm breve

Trigonometry

The Unit Circle DefinitionEm breve
Graphs of Trigonometric FunctionsEm breve
Amplitude, Frequency and TransformationsEm breve
Pythagorean IdentitiesEm breve
More Trigonometric IdentitiesEm breve
Inverse Trigonometric FunctionsEm breve
Circular MotionEm breve

Conic Sections and Polar Coordinates

Parametric CurvesEm breve
Circles and EllipsesEm breve
ParabolaeEm breve
HyperbolaeEm breve
Polar CoordinatesEm breve

Vectors

IntroductionEm breve
Vector ArithmeticEm breve
Scalar Products and Equations of PlanesEm breve
Cross Products and Equations of LinesEm breve
Geometry ProblemsEm breve

Matrices

Matrices as TransformationsEm breve
Matrix ArithmeticEm breve
DeterminantsEm breve
Matrix InversesEm breve
Cramer’s Rule and Gaussian EliminationEm breve
Eigenvalues and EigenvectorsEm breve

Complex Numbers

IntroductionEm breve
Complex ArithmeticEm breve
Quadratic, Cubic and Quartic EquationsEm breve
Euler’s IdentityEm breve
De Moivre’s Theorem and Roots of UnityEm breve

Fractais

IntroduçãoO Triângulo de SierpinskiO Conjunto de Mandelbrot
Curvas de preenchimento de espaçoEm breve

Cálculo

Differentiation

IntroductionEm breve
Limits and GradientsEm breve
Differentiation Rules IEm breve
Differentiation Rules IIEm breve
Optimisation problemsEm breve

Integration

IntroductionEm breve
Integration RulesEm breve
Definite Integrals and Areas under a CurveEm breve
Improper IntegralsEm breve
Solids of RevolutionEm breve

Numerical Methods

Solving Equations NumericallyEm breve
The Newton­-Raphson MethodEm breve
Numerical IntegrationEm breve
Maclaurin and Taylor seriesEm breve

Differential Equations

Simple Differential EquationsEm breve
First Order Separable EquationsEm breve
Second Order Differential EquationsEm breve
Homogenous Equations and Particular IntegralsEm breve
Simple Harmonic MotionEm breve
Coupled Differential EquationsEm breve

Chaos Theory

Introduction
Mathematical BilliardEm breve
The Three Body ProblemEm breve
Phase Space and Strange AttractorsEm breve
The Logistic MapEm breve

Probabilidade e Estatística

Random Variables

IntroductionEm breve
Discrete Random VariablesEm breve
Binomial and Poisson DistributionEm breve
Continuous Random VariablesEm breve
The Normal DistributionEm breve
The Central Limit TheoremEm breve

Statistics and Hypothesis Tests

Sampling and EstimationEm breve
Hypothesis Tests and Confidence IntervalsEm breve
Linear Models and Correlation CoefficientsEm breve
Contingency tables and Chi Squared TestsEm breve
Bayesian StatisticsEm breve

Algorithms

Introduction to ComputingEm breve
Complexity and O NotationEm breve
Sorting AlgorithmsEm breve
Linear Programming and the Simplex AlgorithmEm breve
Graphs, Trees and NetworksEm breve

Machine Learning

IntroductionEm breve
Linear RegressionEm breve
Support Vector MachinesEm breve
Neural NetworksEm breve
Unsupervised LearningEm breve