International Baccalaureate · IB Diploma

Mathematics: Applications and Interpretation · 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.
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: 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.

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.

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.