International Baccalaureate · IB Diploma
Mathematics: Analysis and Approaches · HL
Papers, samples and curriculum documents for this course. · Papers, amostras e documentos curriculares deste curso.
Handouts, exercise sheets and slides
Shared topic documents retain their source course and topic titles. Use your chosen board’s specification for coverage, tier and exam requirements.
Handouts · Material de apoio · A-Level Mathematics · Matemática do A-Level (5)
Exercise sheets · Folhas de exercícios · A-Level Mathematics · Matemática do A-Level (33)
- 1.1 Quadratics · 1.1 Quadráticas
- 1.2 Functions · 1.2 Funções
- 1.3 Coordinate geometry · 1.3 Geometria analítica
- 1.4 Circular measure · 1.4 Medida circular
- 1.5 Trigonometry · 1.5 Trigonometria
- 1.6 Series · 1.6 Séries
- 1.7 Differentiation · 1.7 Diferenciação
- 1.8 Integration · 1.8 Integração
- 2.1 Algebra · 2.1 Álgebra
- 2.2 Logarithmic and exponential functions · 2.2 Funções logarítmicas e exponenciais
- 2.3 Trigonometry · 2.3 Trigonometria
- 2.4 Differentiation · 2.4 Diferenciação
- 2.5 Integration · 2.5 Integração
- 2.6 Numerical solution of equations · 2.6 Solução numérica de equações
- 3.1 Algebra · 3.1 Álgebra
- 3.2 Logarithmic and exponential functions · 3.2 Funções logarítmicas e exponenciais
- 3.3 Trigonometry · 3.3 Trigonometria
- 3.4 Differentiation · 3.4 Diferenciação
- 3.5 Integration · 3.5 Integração
- 3.6 Numerical solution of equations · 3.6 Solução numérica de equações
- 3.7 Vectors · 3.7 Vetores
- 3.8 Differential equations · 3.8 Equações diferenciais
- 3.9 Complex numbers · 3.9 Números complexos
- 5.1 Representation of data · 5.1 Representação de dados
- 5.2 Permutations and combinations · 5.2 Permutações e combinações
- 5.3 Probability · 5.3 Probabilidade
- 5.4 Discrete random variables · 5.4 Variáveis aleatórias discretas
- 5.5 The normal distribution · 5.5 A distribuição normal
- 6.1 The Poisson distribution · 6.1 A distribuição de Poisson
- 6.2 Linear combinations of random variables · 6.2 Combinações lineares de variáveis aleatórias
- 6.3 Continuous random variables · 6.3 Variáveis aleatórias contínuas
- 6.4 Sampling and estimation · 6.4 Amostragem e estimação
- 6.5 Hypothesis tests · 6.5 Testes de hipótese
Presentation slides · Slides de apresentação · A-Level Mathematics · Matemática do A-Level (5)
Course units and learning goals · Unidades do curso e objetivos de aprendizagem
These lessons teach selected course objectives. Check the remaining coverage gaps; the material is not a complete preparation programme. · Estas aulas ensinam objetivos selecionados do curso. Verifique as lacunas de cobertura restantes; o material não é um programa completo de preparação.
1 · Number and algebra · Números e álgebra
- Exact arithmetic and estimation: A prime number that divides the integer exactly.
- Indices, surds and standard form: The power to which a base is raised.
- Sequences, series and recurrence: The constant multiplier between consecutive terms of a geometric sequence.
- Percentages, ratio and proportional reasoning: A factor that performs a percentage change in one multiplication.
- Complex numbers and roots: The number obtained by reversing the sign of the imaginary part.
- Binomial expansion and valid approximations: The number of ways to choose a specified number of objects from a set.
- Series, finite differences and Taylor expansions: A polynomial formed from a function's derivatives at a chosen centre.
- prime factor
- A prime number that divides the integer exactly.
- index
- The power to which a base is raised.
- common ratio
- The constant multiplier between consecutive terms of a geometric sequence.
- multiplier
- A factor that performs a percentage change in one multiplication.
- complex conjugate
- The number obtained by reversing the sign of the imaginary part.
- binomial coefficient
- The number of ways to choose a specified number of objects from a set.
- Taylor polynomial
- A polynomial formed from a function's derivatives at a chosen centre.
2 · Functions · Funções
- Domains, inverses and composition: The set of allowed inputs to a function.
- Exponentials, logarithms and modelling: The time for a decaying quantity to fall to half its initial value.
- domain
- The set of allowed inputs to a function.
- half-life
- The time for a decaying quantity to fall to half its initial value.
3 · Geometry and trigonometry · Geometria e trigonometria
- Angle reasoning, similarity and mensuration: The multiplier that relates corresponding lengths in similar shapes.
- Right triangles and non-right triangles: The side opposite the right angle in a right-angled triangle.
- Radians, identities and trigonometric equations: The angle subtended by an arc whose length equals the radius.
- Vectors and transformation geometry: The vector sum representing the combined displacement or force.
- scale factor
- The multiplier that relates corresponding lengths in similar shapes.
- hypotenuse
- The side opposite the right angle in a right-angled triangle.
- radian
- The angle subtended by an arc whose length equals the radius.
- resultant
- The vector sum representing the combined displacement or force.
4 · Statistics and probability · Estatística e probabilidade
- Data summaries, histograms and interpretation: Frequency divided by class width, used as histogram height.
- Probability, trees and conditional reasoning: The probability of an event after restricting the sample space to a stated condition.
- Binomial, normal and Poisson models: The probability-weighted mean of a random variable.
- frequency density · densidade de frequência
- Frequency divided by class width, used as histogram height.
- conditional probability
- The probability of an event after restricting the sample space to a stated condition.
- expected value
- The probability-weighted mean of a random variable.
5 · Calculus · Cálculo
- Derivatives and stationary points: The instantaneous rate of change, also the gradient of a tangent.
- Integrals, area and accumulation: A function whose derivative equals the given integrand.
- Chain, product, quotient and implicit differentiation: The rule that multiplies the outer derivative by the inner derivative for a composite function.
- Substitution, parts and partial fractions: An integration method based on the derivative of a product.
- Differential equations and numerical solutions: A specified value that selects a particular solution from a family.
- derivative
- The instantaneous rate of change, also the gradient of a tangent.
- antiderivative
- A function whose derivative equals the given integrand.
- chain rule
- The rule that multiplies the outer derivative by the inner derivative for a composite function.
- integration by parts
- An integration method based on the derivative of a product.
- initial condition
- A specified value that selects a particular solution from a family.
IA · School-supervised mathematical exploration · Exploração matemática supervisionada pela escola
- Planning a mathematical exploration: A condition adopted to make a mathematical model possible and whose effect should be evaluated.
- assumption
- A condition adopted to make a mathematical model possible and whose effect should be evaluated.
Preparing for this qualification · Preparação para esta qualificação
- Current first-assessment-2021 course: AA Paper 1 prohibits technology; Paper 2 allows it. HL Paper 3 permits technology and tests extended problem solving.
- External examination contributes 80%; the school-supervised mathematical exploration contributes 20%. SL papers are 40% each; HL Papers 1/2 are 30% each and Paper 3 is 20%.
- Public briefs establish structure, not full official learning objectives. School access to the current full guide, formula booklet and calculator policy is required to certify complete parity.
- Do not apply the revised 2029 marks, paper timing or exploration criteria to current cohorts.
Teaching coverage still needed · Cobertura do ensino ainda necessária
- Official question-bank boundaries, scheme alignment and all objective-level teaching coverage require the recorded review; no practice registry promotion.
- The authored diagnostic assessments are not full-length qualification mocks.
- The complete current IB guide, formula booklet, authenticated exploration criteria and full SL/HL objective codes are unavailable in the public archive.
Specifications and sample documents · Especificações e documentos de exemplo
- Mathematics: Analysis and Approaches — Specimen papers · 2021 ↗
First assessment: 2021
- Mathematics: Analysis and Approaches — Subject brief · 2029 ↗
First assessment: 2029
- Calculator guidance (2020) ↗
- Mathematics: Analysis and Approaches — Subject brief · 2021 ↗
First assessment: 2021
Course materials · Materiais do curso
- Study notes · Notas de estudo →
- Teaching guidance · Orientações de ensino · Teacher access · Acesso do professor →
- Teacher diagnostics · Diagnósticos do professor · Teacher access · Acesso do professor →
- Teacher solutions · Soluções do professor · Teacher access · Acesso do professor →
Course preparation · Preparação do curso
Documents are available. Board-specific notes, assessments and interactive past-paper practice are not yet available for every course. · Os documentos estão disponíveis. Notas específicas da banca, avaliações e prática interativa de provas anteriores ainda não estão disponíveis para todos os cursos.
Lessons · Lições →