Number and algebra
HL-only depth: counting principles, complex numbers in Cartesian and polar forms, proof, and linear systems.
- Advanced algebra and proof
- Complex numbers
- Polynomial behaviour
- Series and convergence
- HL problem-solving chains
Practice betaThis is unofficial practice, not certified exam-board material.
MATH AA HL · Learning hub
Mathematics AA: Higher Level
About this subject
Extend SL technique to HL-only content: complex numbers, further calculus and deeper proof. Selected topics only, not full syllabus coverage.
Topics & subtopics
Calculus
HL-only depth: product rule, quotient rule and integration by substitution.
- Advanced differentiation
- Advanced integration techniques
- Differential equations
- Maclaurin series
- HL optimisation and modelling
Functions
HL-only depth: polynomial division, the factor theorem and rational functions.
- Function transformations
- Inverse and composite functions
- Polynomial and rational functions
- Exponential and logarithmic functions
- HL function proof and modelling
Statistics and probability
Extends SL probability with Bayes' theorem, the general variance formula for a discrete random variable, and continuous random variables.
- Discrete and continuous distributions
- Conditional probability
- Hypothesis testing
- Normal and binomial modelling
- HL interpretation of results
Geometry and trigonometry
HL-only depth: the vector cross and scalar triple products, the geometry of lines and planes in three dimensions, and compound and double angle identities.
- Trigonometric equations and identities
- Vectors in two and three dimensions
- Lines and planes
- Geometric proof
- HL spatial reasoning
Structured progression
Revision Ladder
Start with foundations, then move through application and challenge. Stages use activity marks and complexity.
Stage 1
Start stage Foundation
Recall core ideas and establish reliable methods.
14 questions available0/14 completedStage 2
Start stage Apply
Connect concepts and apply them in exam-style contexts.
55 questions available0/55 completedStage 3
Start stage Challenge
Tackle advanced reasoning and multi-step questions.
6 questions available0/6 completedProgress dashboard
Topic practice
Recommended next: Number and algebra
01
Number and algebra
Not startedHL-only depth: counting principles, complex numbers in Cartesian and polar forms, proof, and linear systems.
0%0/30 complete
02Calculus
Not startedHL-only depth: product rule, quotient rule and integration by substitution.
0%0/30 complete
03Functions
Not startedHL-only depth: polynomial division, the factor theorem and rational functions.
0%0/30 complete
04Statistics and probability
Not startedExtends SL probability with Bayes' theorem, the general variance formula for a discrete random variable, and continuous random variables.
0%0/30 complete
05Geometry and trigonometry
Not startedHL-only depth: the vector cross and scalar triple products, the geometry of lines and planes in three dimensions, and compound and double angle identities.
0%0/30 complete
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This is unofficial practice under accuracy, provenance, and rights review. Use the latest official subject guide to confirm syllabus coverage and examination requirements.