HL course

Mathematics: Analysis and Approaches HL

HL algebra, functions, calculus, proof, probability, and exam reasoning for students aiming at demanding STEM pathways.

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 and algebra

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

  1. Use proof by mathematical induction Build · 20 variants · visual · AI feedback
  2. Analyse recurrence relations Build · 15 variants · visual · AI feedback
  3. Analyse divisibility proofs Build · 15 variants · visual · AI feedback
  4. Analyse eigenvector geometry Exam stretch · 15 variants · visual · AI feedback

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

Start pathway
Maths route

Functions

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

  1. Analyse advanced function transformations Build · 15 variants · visual · AI feedback
  2. Use technology to solve nonlinear equations Build · 15 variants · visual · AI feedback
  3. Analyse inverse trigonometric domains Exam stretch · 15 variants · visual · AI feedback
  4. Model periodic phenomena with phase parameters Build · 15 variants · visual · AI feedback

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

Start pathway
Maths route

Geometry and trigonometry

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

  1. Use reciprocal and Pythagorean identities Build · 15 variants · visual · AI feedback
  2. Find distances from points to planes Build · 15 variants · visual · AI feedback
  3. Analyse spherical trigonometry contexts Exam stretch · 15 variants · visual · AI feedback
  4. Analyse vector motion in three dimensions Exam stretch · 15 variants · visual · AI feedback

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

Start pathway
Maths route

Calculus

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

  1. Differentiate with product quotient and chain rules Build · 20 variants · visual · AI feedback
  2. Use volumes of revolution Exam stretch · 20 variants · visual · AI feedback
  3. Use differential equations in motion models Exam stretch · 15 variants · visual · AI feedback
  4. Analyse curvature in parametric models Exam stretch · 15 variants · visual · AI feedback

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

Start pathway
Maths route

Statistics and probability

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

  1. Use Bayes theorem and conditional probability Build · 20 variants · visual · AI feedback
  2. Use conditional expectation Exam stretch · 15 variants · visual · AI feedback
  3. Use covariance matrices Exam stretch · 15 variants · visual · AI feedback
  4. Analyse sampling distribution approximations 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 and algebra Proof, complex numbers, polynomials, partial fractions, inequalities, and advanced sequences for Mathematics AA HL. Functions Advanced function behaviour, transformations, inverses, composites, polynomial/rational/exponential/logarithmic models, and parametric representations. Geometry and trigonometry Higher-level trigonometric identities, extended equations, and vector geometry. Calculus Higher-level differentiation, integration, optimization, rates, concavity, and differential equations. Statistics and probability Higher-level probability reasoning, Bayes theorem, and continuous random variables.