This course is designed for IB Diploma Programme students taking Mathematics: Analysis and Approaches HL who need both deep syllabus mastery and practical preparation for assessed work. It combines topic-by-topic instruction with explicit training in IB command terms, markscheme expectations, timed-paper technique, and mathematical communication.
Students begin with a diagnostic process to identify strengths, weaknesses, and realistic grade targets. From there, the course develops the full HL toolkit through structured lessons in algebra, functions, sequences and series, trigonometry, geometry, vectors, complex numbers, differential calculus, integral calculus, applications of calculus, and statistics and probability.
Each part of the program is built to teach the underlying mathematics rather than shortcuts alone. Lessons focus on what students must be able to understand, calculate, justify, interpret, and communicate in IB-style tasks, including unfamiliar questions that require several ideas to be linked together.
- Foundations and reasoning: algebraic manipulation, equations and inequalities, notation, logical structure, conjectures, and proof by induction
- Functions and graphs: domain and range, composite and inverse functions, transformations, polynomial and rational behaviour, and exponential and logarithmic models
- Sequences and series: arithmetic and geometric forms, sigma notation, recurrence, and binomial expansion including validity conditions and approximation
- Trigonometry and geometry: radians, identities, equations, circular functions, coordinate geometry, loci, and vector methods
- Complex numbers: Argand diagrams, modulus and argument, polar form, powers, roots, loci, and polynomial connections
- Calculus: first principles, differentiation rules, implicit differentiation, integration techniques, numerical methods, optimization, kinematics, area, volume, and differential equations
- Statistics and probability: sampling, descriptive statistics, probability structure, distributions, regression, and hypothesis testing
- Assessment readiness: command terms, paper formats, calculator expectations, mark allocation, error analysis, revision planning, and timed exam performance
- Internal Assessment support: topic selection, research focus, mathematical depth, structure, reflection, and final quality control
The course also includes a strong revision and performance component. Students learn how to use mistake logs, spaced review, cumulative practice, timed drills, and markscheme analysis to turn weak areas into secure scoring areas. This is especially useful for students aiming to improve from partial understanding to consistent high-level performance.
By the end of the program, students should be able to solve advanced HL problems accurately, explain methods clearly, apply concepts to new situations, meet assessment criteria with confidence, and prepare strategically for examinations and coursework.