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. Operate with scientific notation Free Exam stretch · 20 variants · visual · AI feedback
  2. Combine expressions using logarithm laws Exam stretch · 15 variants · visual · AI feedback
  3. Count arrangements with restrictions Exam stretch · 15 variants · visual · AI feedback
  4. Classify linear systems using row reduction 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. Use equations and gradients of straight lines Free Exam stretch · 15 variants · visual · AI feedback
  2. Solve exponential equations using technology Exam stretch · 15 variants · visual · AI feedback
  3. Find oblique asymptotes of rational functions Exam stretch · 15 variants · visual · AI feedback
  4. Solve lower-bound modulus inequalities 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

Geometry and trigonometry

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

  1. Calculate reciprocal trigonometric ratios Exam stretch · 15 variants · visual · AI feedback
  2. Calculate vector products Exam stretch · 15 variants · visual · AI feedback
  3. Find angles between lines and planes Exam stretch · 15 variants · visual · AI feedback
  4. Recover parameters from points on vector lines Exam stretch · 15 variants · visual · AI feedback

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

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Maths route

Calculus

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

  1. Differentiate products of linear functions Exam stretch · 20 variants · visual · AI feedback
  2. Calculate volumes of revolution about the x-axis Exam stretch · 20 variants · visual · AI feedback
  3. Model Newton cooling with differential equations Exam stretch · 15 variants · visual · AI feedback
  4. Calculate washer volumes about the x-axis 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. Apply Bayes theorem to three sources Exam stretch · 20 variants · visual · AI feedback
  2. Calculate variances of continuous uniform densities Exam stretch · 15 variants · visual · AI feedback
  3. Find medians of linear continuous densities Exam stretch · 15 variants · visual · AI feedback
  4. Compare variance after scaling and shifting Exam stretch · 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.