Diploma del Bachillerato Internacional · IB Diploma
Mathematics: Analysis and Approaches · 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.
- 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
- 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
- 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
- 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 · 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.
5 · Calculus
- 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
- 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: 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 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: 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 · 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 →