HL course

Mathematics: Applications and Interpretation HL

HL modelling, statistics, networks, calculus, technology use, and written interpretation for AI HL.

Guided practice pathways

Assessment routes built from the live skills in this course. Each pathway moves from the first decision students need to make toward the kind of source use, calculation, writing, or judgement that costs marks in real assessment.

Maths route

Number, finance, and discrete models

Build from recognition to method choice, representation, calculation, and interpretation.

  1. Model amortised loans Build · 15 variants · visual · AI feedback
  2. Use recurrence relations in finance Build · 15 variants · visual · AI feedback
  3. Apply shortest path reasoning Build · 15 variants · visual · AI feedback
  4. Interpret linear programming shadow values Build · 15 variants · visual · AI feedback

A complete route checks both the result and the reasoning used to get there.

Start pathway
Maths route

Functions, modelling, and geometry

Build from recognition to method choice, representation, calculation, and interpretation.

  1. Analyse logistic models Build · 15 variants · visual · AI feedback
  2. Fit and compare regression models Build · 15 variants · visual · AI feedback
  3. Interpret sinusoidal models Build · 15 variants · visual · AI feedback
  4. Use Voronoi diagrams in context Build · 15 variants · visual · AI feedback

A complete route checks both the result and the reasoning used to get there.

Start pathway
Maths route

Statistics, probability, and inference

Build from recognition to method choice, representation, calculation, and interpretation.

  1. Use Spearman rank correlation Build · 15 variants · visual · AI feedback
  2. Use chi-square tests for independence Build · 15 variants · visual · AI feedback
  3. Use hypothesis tests with normal and t models Build · 15 variants · visual · AI feedback
  4. Use Markov chains and steady states Build · 15 variants · visual · AI feedback

A complete route checks both the result and the reasoning used to get there.

Start pathway
Maths route

Calculus and numerical methods

Build from recognition to method choice, representation, calculation, and interpretation.

  1. Optimise models using derivatives Build · 15 variants · visual · AI feedback
  2. Solve separable differential equations Build · 15 variants · visual · AI feedback
  3. Integrate rates for accumulated change Build · 15 variants · visual · AI feedback
  4. Estimate logistic half-capacity time Build · 15 variants · visual · AI feedback

A complete route checks both the result and the reasoning used to get there.

Start pathway
Maths route

Probability distributions and decision models

Build from recognition to method choice, representation, calculation, and interpretation.

  1. Use discrete probability distributions Build · 15 variants · visual · AI feedback
  2. Use normal approximations to binomial models Build · 15 variants · visual · AI feedback
  3. Use Bayes theorem in decision contexts Build · 15 variants · visual · AI feedback
  4. Use continuous random variables Build · 15 variants · visual · AI feedback

A complete route checks both the result and the reasoning used to get there.

Start pathway
Maths route

Technology, diagnostics, and model choice

Build from recognition to method choice, representation, calculation, and interpretation.

  1. Interpret residual plots Build · 20 variants · visual · AI feedback
  2. Evaluate piecewise models Build · 15 variants · visual · AI feedback
  3. Use moving averages in time series Build · 15 variants · visual · AI feedback
  4. Interpret residual standard deviation Build · 15 variants · visual · AI feedback

A complete route checks both the result and the reasoning used to get there.

Start pathway

Topics

Choose a topic to see the skills you can practise. Start with the area your class is studying now, or use the list to find weaker topics before a test or exam.

Number, finance, and discrete models Financial mathematics, matrices, recurrence, graph theory, and constrained decision models for IB Mathematics AI HL. Functions, modelling, and geometry Model selection, transformations, logistic and sinusoidal models, and diagram-based applied reasoning. Statistics, probability, and inference Rank correlation, chi-square testing, confidence intervals, hypothesis tests, and Markov-style probability models. Calculus and numerical methods AI HL calculus, accumulated change, optimisation, differential equations, numerical methods, and technology-supported interpretation. Probability distributions and decision models Discrete and continuous probability models, Bayes reasoning, expectation, variance, and risk decisions for AI HL. Technology, diagnostics, and model choice Technology output, residual diagnostics, regression interpretation, numerical solving, and model-choice reasoning for AI HL. Advanced inference and statistical decisions Standardisation, p-values, errors, two-sample inference, paired tests, and interval interpretation for AI HL. Advanced calculus and dynamic models Graph-based calculus, numerical methods, slope fields, phase lines, logistic rates, and constrained optimisation. Applied probability and decision analysis Binomial, geometric, expected value, decision-tree, and payoff reasoning for AI HL. Continuous distributions and technology output Density functions, CDFs, inverse normal outputs, percentile interpretation, and calculator-supported distribution reasoning. Applied calculus in economics and science Marginal analysis, elasticity, area between rates, implicit rates, and optimisation in applied AI HL settings. Extended statistics and risk modelling Sample-size planning, risk comparison, conditional expectation, and transformed random variables for AI HL. Extended networks and discrete systems Graph walks, Markov extensions, Voronoi boundaries, recurrence closed forms, and optimisation sensitivity. Finance, inference, and network extensions Net present value, amortisation detail, proportions, chi-square reasoning, and network decision methods for AI HL. Official HL update coverage Complex numbers, vector product, Poisson models, and HL hypothesis tests aligned to the latest IB AI HL emphasis.