High School / IB

IB Mathematics (AA & AI)

In-depth education at HL/SL levels for both the Analysis & Approaches (AA) and Applications & Interpretation (AI) curricula of the International Baccalaureate (IB) program.

Curriculum / Syllabus

  1. Number and Algebra
  2. Functions
  3. Geometry and Trigonometry
  4. Statistics and Probability
  5. Calculus
  6. Internal Assessment (IA) Project Support

Exam & Course Strategy

IB Math exams (Paper 1, 2, and Paper 3 for HL) strictly evaluate Graphic Display Calculator (GDC) proficiency and step-by-step logical deduction (method marks).

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Lesson-by-Lesson Curriculum Plan

IB Mathematics AA (SL & HL): 25-Lesson Curriculum Plan

This program follows the five topics of the IB Mathematics: Analysis and Approaches guide (first assessment 2021): Number and Algebra, Functions, Geometry and Trigonometry, Statistics and Probability, and Calculus. Lessons marked HL only cover the additional higher level content.

Each topic ends with practice on past-paper style questions for Paper 1 (no calculator) and Paper 2 (calculator).

  • Total lessons: 25
  • Lesson duration: 90 minutes

Flow of a standard 90-minute lesson

  • 0–10 minutes Warm-up, quick review of the previous lesson, or a mini-quiz.
  • 10–55 minutes Lecture, analysis, and theoretical review of the new topic.
  • 55–85 minutes Guided problem solving: the student works exam-style questions under my direct supervision and receives instant feedback.
  • 85–90 minutes Summary, homework, and wrap-up.
Part 1: Number and Algebra, Functions Lessons 1 - 7

Covers Topic 1 (Number and Algebra) and Topic 2 (Functions).

  1. Lesson 1
    Core 1 / Topic 1 Arithmetic and geometric sequences and series, sigma notation, financial applications, sum to infinity.
  2. Lesson 2
    Core 2 / Topic 1 Exponents and logarithms, laws of logarithms, the binomial theorem, simple deductive proof.
  3. Lesson 3
    Core 3 / Topic 1 (HL only) Counting principles, proof by induction and by contradiction, complex numbers, systems of linear equations.
  4. Lesson 4
    Core 4 / Topic 2 Functions: domain and range, composite and inverse functions, graphs and their key features, transformations.
  5. Lesson 5
    Core 5 / Topic 2 Quadratic, rational, exponential, and logarithmic functions; solving equations graphically and analytically.
  6. Lesson 6
    Core 6 / Topic 2 (HL only) Polynomial functions, the factor and remainder theorems, further rational functions, odd and even functions, inequalities, the modulus function.
  7. Lesson 7
    Paper Practice 1 Past-paper style questions on Topics 1 and 2: Paper 1 and Paper 2 technique.
Part 2: Geometry and Trigonometry Lessons 8 - 12

Covers Topic 3 (Geometry and Trigonometry).

  1. Lesson 8
    Core 7 / Topic 3 Three-dimensional geometry, right-angled and non-right-angled trigonometry, the sine and cosine rules, radians, arcs and sectors.
  2. Lesson 9
    Core 8 / Topic 3 The unit circle, trigonometric identities, trigonometric functions and their graphs, solving trigonometric equations.
  3. Lesson 10
    Core 9 / Topic 3 (HL only) Reciprocal and inverse trigonometric functions, compound angle identities.
  4. Lesson 11
    Core 10 / Topic 3 (HL only) Vectors: scalar and vector products, equations of lines and planes, intersections and angles.
  5. Lesson 12
    Paper Practice 2 Past-paper style questions on Topic 3.
Part 3: Statistics and Probability Lessons 13 - 16

Covers Topic 4 (Statistics and Probability).

  1. Lesson 13
    Core 11 / Topic 4 Sampling, presenting data, measures of central tendency and dispersion, correlation and linear regression.
  2. Lesson 14
    Core 12 / Topic 4 Probability, conditional probability, and independent events; discrete random variables and expected value.
  3. Lesson 15
    Core 13 / Topic 4 The binomial and normal distributions; standardization and inverse normal calculations. HL only: Bayes' theorem and continuous random variables.
  4. Lesson 16
    Paper Practice 3 Past-paper style questions on Topic 4, with efficient use of the graphic display calculator.
Part 4: Calculus Lessons 17 - 22

Covers Topic 5 (Calculus).

  1. Lesson 17
    Core 14 / Topic 5 Limits and the derivative, rules of differentiation: power, chain, product, and quotient rules.
  2. Lesson 18
    Core 15 / Topic 5 Tangents and normals, stationary points, the second derivative, points of inflexion, optimization.
  3. Lesson 19
    Core 16 / Topic 5 Integration as anti-differentiation, definite integrals, areas under and between curves, integration by substitution; kinematics: displacement, velocity, acceleration, and total distance travelled.
  4. Lesson 20
    Core 17 / Topic 5 (HL only) Continuity and differentiability, L'Hôpital's rule, implicit differentiation, related rates.
  5. Lesson 21
    Core 18 / Topic 5 (HL only) Integration by parts and partial fractions, volumes of revolution, differential equations, Maclaurin series.
  6. Lesson 22
    Paper Practice 4 Past-paper style questions on Topic 5.
Part 5: Exam Practice and Simulation Lessons 23 - 25

Comprehensive exam practice on full papers.

  1. Lesson 23
    Exam Simulation Full Paper 1 simulation (no calculator), with time management and marking according to the markscheme.
  2. Lesson 24
    Exam Simulation Full Paper 2 simulation (calculator). HL only: Paper 3 extended problem-solving questions.
  3. Lesson 25
    Evaluation Simulation analysis, addressing common mistakes, and course wrap-up.
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