Diploma del Bachillerato Internacional · IB Diploma
Mathematics: Applications and Interpretation · HL
Papers, samples and curriculum documents for this course. · Papeles, muestras y documentos curriculares para este 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 apoyo · A-Level Mathematics · A-Level Matemáticas (5)
Exercise sheets · Hojas de ejercicios · A-Level Mathematics · A-Level Matemáticas (33)
- 1.1 Quadratics · 1.1 Cuaráticas
- 1.2 Functions · 1.2 Funciones
- 1.3 Coordinate geometry · 1.3 Geometría analítica
- 1.4 Circular measure · 1.4 Medida circular
- 1.5 Trigonometry · 1.5 Trigonometría
- 1.6 Series
- 1.7 Differentiation · 1.7 Diferenciación
- 1.8 Integration · 1.8 Integración
- 2.1 Algebra · 2.1 Álgebra
- 2.2 Logarithmic and exponential functions · 2.2 Funciones logarítmicas y exponenciales
- 2.3 Trigonometry · 2.3 Trigonometría
- 2.4 Differentiation · 2.4 Diferenciación
- 2.5 Integration · 2.5 Integración
- 2.6 Numerical solution of equations · 2.6 Solución numérica de ecuaciones
- 3.1 Algebra · 3.1 Álgebra
- 3.2 Logarithmic and exponential functions · 3.2 Funciones logarítmicas y exponenciales
- 3.3 Trigonometry · 3.3 Trigonometría
- 3.4 Differentiation · 3.4 Diferenciación
- 3.5 Integration · 3.5 Integración
- 3.6 Numerical solution of equations · 3.6 Solución numérica de ecuaciones
- 3.7 Vectors · 3.7 Vectores
- 3.8 Differential equations · 3.8 Ecuaciones diferenciales
- 3.9 Complex numbers · 3.9 Números complejos
- 5.1 Representation of data · 5.1 Representación de datos
- 5.2 Permutations and combinations · 5.2 Permutaciones y combinaciones
- 5.3 Probability · 5.3 Probabilidad
- 5.4 Discrete random variables · 5.4 Variables aleatorias discretas
- 5.5 The normal distribution · 5.5 La distribución normal
- 6.1 The Poisson distribution · 6.1 La distribución de Poisson
- 6.2 Linear combinations of random variables · 6.2 Combinaciones lineales de variables aleatorias
- 6.3 Continuous random variables · 6.3 Variables aleatorias continuas
- 6.4 Sampling and estimation · 6.4 Muestreo y estimación
- 6.5 Hypothesis tests · 6.5 Pruebas de hipótesis
Presentation slides · Diapositivas de presentación · A-Level Mathematics · A-Level Matemáticas (5)
Course units and learning goals · Unidades del curso y objetivos de aprendizaje
These lessons teach selected course objectives. Check the remaining coverage gaps; the material is not a complete preparation programme. · Estas lecciones enseñan objetivos del curso seleccionados. Revisa los vacíos de cobertura restantes; el material no es un programa completo de preparación.
1 · Number and algebra
- 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
- 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
- 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
- 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 · densidad de frecuencia
- 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
- 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
- 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 · Preparación para esta cualificación
- 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 docente aún necesaria
- 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 · Especificaciones y documentos de muestra
- 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 · Materiales del curso
Course preparation · Preparación del curso
Documents are available. Board-specific notes, assessments and interactive past-paper practice are not yet available for every course. · Los documentos están disponibles. Las notas específicas de la entidad evaluadora, las evaluaciones y la práctica interactiva deantiguos exámenes no están disponibles aún para todos los cursos.
Lessons · Lecciones →