International Baccalaureate · IB Diploma
Mathematics: Applications and Interpretation · HL
Papers, samples and curriculum documents for this course. · Papers, amostras e documentos curriculares deste curso.
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.
- Percentages, ratio and proportional reasoning: A factor that performs a percentage change in one multiplication.
- Sequences, series and recurrence: The constant multiplier between consecutive terms of a geometric sequence.
- Regression, financial models and residuals: The observed value minus the value predicted by a fitted model.
- Matrix transformations, inverses and eigenvalues: A scalar that determines whether a square matrix is invertible and, in two dimensions, its signed area factor.
- Complex numbers and roots: The number obtained by reversing the sign of the imaginary part.
- prime factor
- A prime number that divides the integer exactly.
- multiplier
- A factor that performs a percentage change in one multiplication.
- common ratio
- The constant multiplier between consecutive terms of a geometric sequence.
- residual
- The observed value minus the value predicted by a fitted model.
- determinant
- A scalar that determines whether a square matrix is invertible and, in two dimensions, its signed area factor.
- complex conjugate
- The number obtained by reversing the sign of the imaginary part.
2 · Functions · Funções
- Domains, inverses and composition: The set of allowed inputs to a function.
- Regression, financial models and residuals: The observed value minus the value predicted by a fitted model.
- 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.
- residual
- The observed value minus the value predicted by a fitted model.
- 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.
- 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.
- 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.
- Hypothesis testing and contextual conclusions: The chosen probability threshold for rejecting a null hypothesis.
- Confidence intervals, chi-square and regression: An interval calculated by a procedure designed to cover the population parameter at a stated long-run rate.
- 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.
- significance level
- The chosen probability threshold for rejecting a null hypothesis.
- confidence interval
- An interval calculated by a procedure designed to cover the population parameter at a stated long-run rate.
5 · Calculus · Cálculo
- Derivatives and stationary points: The instantaneous rate of change, also the gradient of a tangent.
- Root finding and numerical integration: A repeated update in which each new approximation is calculated from the previous one.
- 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.
- iteration
- A repeated update in which each new approximation is calculated from the previous one.
- 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: AI permits technology on both papers. 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: Applications and Interpretation — Specimen papers · 2021 ↗
First assessment: 2021
- Mathematics: Applications and Interpretation — Subject brief · 2021 ↗
First assessment: 2021
- Calculator guidance (2020) ↗
- Mathematics: Applications and Interpretation — Subject brief · 2029 ↗
First assessment: 2029
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 →