International Baccalaureate · IB Diploma

Mathematics: Analysis and Approaches · HL

Papers, samples and curriculum documents for this course.

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 · A-Level Mathematics (5)

Exercise sheets · A-Level Mathematics (33)

Presentation slides · A-Level Mathematics (5)

These lessons teach selected course objectives. Check the remaining coverage gaps; the material is not a complete preparation programme.

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: 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.

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.

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.