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Group 5 · Mathematics · 2025 syllabus

IB Mathematics: Analysis and Approaches

5

Units

49

Topics

150h

SL hours

240h

HL hours

1

Number and algebra

19h SL · 39h HL
  • SL 1.1

    Partial Fractions, Indices & Standard Form

  • SL 1.2

    Exponentials & Logs

  • SL 1.3

    Sequences & Series

  • SL 1.4

    Simple Proof & Reasoning

  • SL 1.5

    Proof by Induction & Contradiction

  • SL 1.6

    Binomial Theorem

  • SL 1.7

    Permutations & Combinations

  • SL 1.8

    Complex Numbers

  • SL 1.9

    Further Complex Numbers

  • SL 1.10

    Systems of Linear Equations

2

Functions

21h SL · 32h HL
  • SL 2.1

    Linear Functions & Graphs

  • SL 2.2

    Quadratic Functions & Graphs

  • SL 2.3

    Functions Toolkit

  • SL 2.4

    Other Functions & Graphs

  • SL 2.5

    Reciprocal & Rational Functions

  • SL 2.6

    Transformations of Graphs

  • SL 2.7

    Polynomial Functions

  • SL 2.8

    Inequalities

  • SL 2.9

    Modulus Functions & Further Transformations

3

Geometry and trigonometry

25h SL · 51h HL
  • SL 3.1

    Geometry Toolkit

  • SL 3.2

    Geometry of 3D Shapes

  • SL 3.3

    Trigonometry

  • SL 3.4

    The Unit Circle & Exact Values

  • SL 3.5

    Trigonometric Functions & Graphs

  • SL 3.6

    Trigonometric Equations & Identities

  • SL 3.7

    Inverse & Reciprocal Trigonometric Functions

  • SL 3.8

    Trigonometric Proof & Equation Strategies

  • SL 3.9

    Vector Properties

  • SL 3.10

    Vector Equations of Lines

  • SL 3.11

    Vector Planes

4

Statistics and probability

27h SL · 33h HL
  • SL 4.1

    Statistics Toolkit

  • SL 4.2

    Correlation & Regression

  • SL 4.3

    Probability

  • SL 4.4

    Discrete Random Variables

  • SL 4.5

    Binomial Distribution

  • SL 4.6

    Normal Distribution

  • SL 4.7

    Continuous Random Variables

5

Calculus

28h SL · 55h HL
  • SL 5.1

    Differentiation

  • SL 5.2

    Techniques & Applications of Differentiation

  • SL 5.3

    Integration

  • SL 5.4

    Techniques & Applications of Integration

  • SL 5.5

    Optimisation

  • SL 5.6

    Kinematics

  • SL 5.7

    Basic Limits & Continuity

  • SL 5.8

    Further Differentiation

  • SL 5.9

    Further Integration

  • SL 5.10

    Differential Equations

  • SL 5.11

    Maclaurin Series

  • SL 5.12

    Limits using l'Hopital's Rule & Maclaurin Series

Track your progress through this syllabus

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