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IB Diploma Mathematics

IB DP Mathematics: Applications & Interpretation HL

A demanding applied mathematics route for students who want modelling, statistics, technology, and real-world problem solving at HL depth.

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AI HL
TrackApplications & Interpretation
LevelHigher Level
FocusModelling confidence
Papers & IA
Paper 1 2 hr · 110 marks · 30% GDC required
Paper 2 2 hr · 110 marks · 30% GDC required
Paper 3 1 hr · 55 marks · 20% HL modelling
IA 20 marks · 20% Applied exploration
Number & Algebra Functions Geometry & Trigonometry Statistics & Probability Calculus
Route Navigator

Choose the right IB Math pathway

One clean page template for all IB DP mathematics routes, so students can compare without feeling lost.

AA SL Analysis & Approaches SL Standard Level AA HL Analysis & Approaches HL Higher Level AI SL Applications & Interpretation SL Standard Level AI HL Applications & Interpretation HL Higher Level
Student Fit

Who should take AI HL?

Applications & Interpretation HL works best when the student's university goals, mathematical confidence, and preferred problem style match the course route.

Students who need Higher Level mathematics for data-oriented economics, business analytics, psychology, biology, environmental science, social sciences, or applied quantitative degrees.

Learners who are strong with technology, statistics, modelling, interpretation, and written judgement, and who want HL depth without choosing the pure AA HL route.

Students who want a serious applied-maths profile: not an easier shortcut, but a different HL route built around real data, assumptions, and model quality.

Syllabus Map

AI HL syllabus, organized for scoring

The five IB topic families stay visible, while lessons adapt to the exact AA/AI and SL/HL demand.

01

Applied Algebra & Technology

Use algebra, numerical methods, and technology to build, test, and refine models.

02

Functions & Modelling

Explore families of models, transformations, regression, parameter meaning, and domain limitations.

03

Geometry, Vectors & Trigonometry

Handle HL spatial and vector ideas through practical contexts and interpretation.

04

Statistics Depth

Develop stronger distribution, inference, probability, regression, and data-analysis skills.

05

Calculus & Change

Use calculus, rates, optimization, and accumulated change to explain behaviour in applied situations.

SL + HL Syllabus Map

AI HL topics: SL foundation and HL extension

HL includes the complete SL foundation. The right column shows the extra HL-only extension added on top for higher-level papers and Paper 3.

01

Number & Algebra

SL Foundation

Fully included in AI HL

Approximation, estimation and percentage change Units, error and technology-supported calculation Arithmetic and geometric sequences and series Financial mathematics Loans, annuities, depreciation and growth Applied algebraic modelling
HL Extension

Extra depth beyond SL

Complex numbers Matrices, determinants and inverses Systems of linear equations Eigenvalues and eigenvectors
02

Functions

SL Foundation

Fully included in AI HL

Linear equations and graphs Quadratic, exponential and sinusoidal models Applications of functions in context Domain, range, composite and inverse functions Transformations Regression, residuals and model reliability Interpreting parameters with a GDC
HL Extension

Extra depth beyond SL

Non-linear regression and model comparison Logistic, sinusoidal and piecewise modelling Technology-led parameter interpretation
03

Geometry & Trigonometry

SL Foundation

Fully included in AI HL

Perimeter, area, volume and surface area Similarity, scale and geometry of 3D shapes Right and non-right triangle trigonometry Bearings and practical measurement problems Voronoi diagrams Technology-supported diagrams and checks
HL Extension

Extra depth beyond SL

Trigonometric functions and identities Geometric transformations using matrices Vectors and kinematics applications Graph theory
04

Statistics & Probability

SL Foundation

Fully included in AI HL

Sampling, bias and data presentation Descriptive statistics and spread Bivariate statistics and regression Probability diagrams and conditional probability Discrete random variables and expected value Binomial and normal distributions GDC probability and distribution workflows
HL Extension

Extra depth beyond SL

Transition matrices and Markov chains Random variable combinations Hypothesis testing Estimation and confidence intervals
05

Calculus

SL Foundation

Fully included in AI HL

Gradient and derivative as rate of change Differentiation rules in context Increasing/decreasing behaviour and optimization Integration as area and accumulation Kinematics basics Interpreting calculus results in real contexts
HL Extension

Extra depth beyond SL

Product, chain and quotient rules Second derivative tests and related rates Volumes of revolution and trapezoidal rule Differential equations and Euler's method
Assessment

Exam and IA preparation

1

Paper 1 and Paper 2: calculator-supported applied and extended-response work.

2

Paper 3: technology-rich extended problem solving with interpretation and modelling.

3

Internal Assessment: an exploration that can connect data, modelling, and a personal real-world question.

How Classes Run

Teaching plan

  • Build a modelling-first study plan that still protects algebra, functions, and calculus fundamentals.
  • Practise Paper 3 style thinking: assumptions, model testing, interpretation, and written judgement.
  • GDC tutorial for regression, distributions, matrices/statistics, graphing, numerical methods, and checking reasonableness.
  • IA mentoring focused on reliable data, useful models, and a convincing conclusion.
Outcome Focus

What students build in AI HL

Modelling confidence Paper 3 control Data interpretation Applied HL depth
Next Step

Start with a route check, not guesswork.

Bring the student's current syllabus, recent test, or university target. The demo class can confirm whether AI HL is the right path and where to begin.

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