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International Baccalaureate IB Diploma Programme Mathematics: Analysis and Approaches

Syllabus DP Mathematics: Analysis and Approaches · First assessment 2021 · sourced from International Baccalaureate Organization, Diploma Programme, Mathematics: analysis and approaches guide, first assessment 2021 (published February 2019, updated August 2019/May 2020/August 2020/November 2020), verified 2026-09-08.

  1. 1. Number and algebra

    • 1.1 Operations with numbers in the form a × 10^k
    • 1.2 Arithmetic sequences and series
    • 1.3 Geometric sequences and series
    • 1.4 Financial applications of geometric sequences and series
    • 1.5 Laws of exponents and introduction to logarithms
    • 1.6 Simple deductive proof
    • 1.7 Laws of exponents and laws of logarithms
    • 1.8 Sum of infinite convergent geometric sequences
    • 1.9 The binomial theorem
    • 1.10 Counting principles and extension of the binomial theorem (AHL only)
    • 1.11 Partial fractions (AHL only)
    • 1.12 Complex numbers: Cartesian form and the complex plane (AHL only)
    • 1.13 Complex numbers: modulus-argument (polar) and Euler form (AHL only)
    • 1.14 Complex conjugate roots and De Moivre’s theorem (AHL only)
    • 1.15 Proof by mathematical induction, contradiction and counterexample (AHL only)
    • 1.16 Solutions of systems of linear equations (AHL only)

  2. 2. Functions

    • 2.1 Equations of a straight line
    • 2.2 Concept of a function, domain, range and inverse
    • 2.3 The graph of a function
    • 2.4 Key features of graphs and points of intersection
    • 2.5 Composite functions and inverse functions
    • 2.6 The quadratic function
    • 2.7 Solving quadratic equations and inequalities; the discriminant
    • 2.8 The reciprocal function and rational functions
    • 2.9 Exponential and logarithmic functions
    • 2.10 Solving equations graphically and analytically
    • 2.11 Transformations of graphs
    • 2.12 Polynomial functions, zeros, roots and factors (AHL only)
    • 2.13 Rational functions of higher degree (AHL only)
    • 2.14 Odd and even functions; self-inverse functions (AHL only)
    • 2.15 Solutions of inequalities g(x) ≥ f(x) (AHL only)
    • 2.16 Graphs of |f(x)|, f(|x|) and related functions; modulus equations (AHL only)

  3. 3. Geometry and trigonometry

    • 3.1 3D geometry: distance, midpoint, volume and surface area
    • 3.2 The sine rule, cosine rule and area of a triangle
    • 3.3 Applications of right and non-right-angled trigonometry
    • 3.4 The circle: radian measure, arc length and area of a sector
    • 3.5 Definitions of cosθ, sinθ and tanθ using the unit circle
    • 3.6 The Pythagorean identity and double angle identities
    • 3.7 The circular functions sin x, cos x and tan x
    • 3.8 Solving trigonometric equations
    • 3.9 Reciprocal trigonometric ratios and inverse circular functions (AHL only)
    • 3.10 Compound angle identities (AHL only)
    • 3.11 Relationships between trigonometric functions and symmetry of their graphs (AHL only)
    • 3.12 Vectors: concept, components and algebraic/geometric operations (AHL only)
    • 3.13 The scalar product of two vectors (AHL only)
    • 3.14 Vector equation of a line in two and three dimensions (AHL only)
    • 3.15 Coincident, parallel, intersecting and skew lines (AHL only)
    • 3.16 The vector product of two vectors (AHL only)
    • 3.17 Vector equations of a plane (AHL only)
    • 3.18 Intersections of lines and planes (AHL only)

  4. 4. Statistics and probability

    • 4.1 Concepts of population, sample, sampling techniques and outliers
    • 4.2 Presentation of data: frequency distributions, histograms and box-and-whisker diagrams
    • 4.3 Measures of central tendency and measures of dispersion
    • 4.4 Linear correlation of bivariate data and the regression line of y on x
    • 4.5 Concepts of trial, outcome, sample space, event and probability
    • 4.6 Combined, mutually exclusive, conditional and independent events
    • 4.7 Discrete random variables and their probability distributions
    • 4.8 The binomial distribution
    • 4.9 The normal distribution
    • 4.10 The regression line of x on y
    • 4.11 Formal definition of conditional probability and independence
    • 4.12 Standardization of normal variables (z-values)
    • 4.13 Bayes’ theorem (AHL only)
    • 4.14 Variance of discrete and continuous random variables (AHL only)

  5. 5. Calculus

    • 5.1 Introduction to the concept of a limit; derivative as gradient function
    • 5.2 Increasing and decreasing functions
    • 5.3 Derivative of f(x) = ax^n
    • 5.4 Tangents and normals at a given point
    • 5.5 Introduction to integration as anti-differentiation
    • 5.6 Derivatives of x^n, sin x, cos x, e^x and ln x; chain, product and quotient rules
    • 5.7 The second derivative and graphical behaviour of functions
    • 5.8 Local maximum and minimum points, optimization and points of inflexion
    • 5.9 Kinematic problems: displacement, velocity, acceleration and distance
    • 5.10 Indefinite integration by inspection or substitution
    • 5.11 Definite integrals and areas between curves
    • 5.12 Continuity, differentiability and derivative from first principles (AHL only)
    • 5.13 Evaluation of limits using l’Hôpital’s rule or Maclaurin series (AHL only)
    • 5.14 Implicit differentiation, related rates of change and optimisation (AHL only)
    • 5.15 Derivatives and indefinite integrals of further functions (AHL only)
    • 5.16 Integration by substitution and by parts (AHL only)
    • 5.17 Areas enclosed with the y-axis and volumes of revolution (AHL only)
    • 5.18 First order differential equations (AHL only)
    • 5.19 The Maclaurin series (AHL only)