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IB Mathematics: Analysis and Approaches HL

Topics follow the official College Board structure: 5 units, 42 topics. The first unit is open to everyone, the rest is for members.

IB Mathematics: Analysis and Approaches HL: what membership unlocks

  • 33 topic lessons
  • 330 quiz questions
  • Unit quizzes and skipping a unit
  • 1 practice exams a month with progress reports
See membership

Unit 1

Number and Algebra

9 topicsFree
  1. 1.1Arithmetic and Geometric Sequences and Series
  2. 1.2Exponents and Logarithms
  3. 1.3The Binomial Theorem
  4. 1.4Simple Proof, Approximation, and Errors
  5. 1.5Counting Principles and the Extended Binomial Theorem
  6. 1.6Complex Numbers in Cartesian Form
  7. 1.7Polar and Exponential Form, De Moivre's Theorem, and Roots
  8. 1.8Proof by Induction, Contradiction, and Counterexample
  9. 1.9Systems of Linear Equations

Unit 2

Functions

7 topicsMembers
  1. 2.1Functions: Domain, Range, Composite, and Inverse
  2. 2.2Quadratic Functions and the Discriminant
  3. 2.3Rational Functions and Asymptotes
  4. 2.4Exponential and Logarithmic Functions
  5. 2.5Transformations of Graphs
  6. 2.6Polynomial Functions: Factor and Remainder Theorems, Sums and Products of Roots
  7. 2.7Odd and Even Functions, Modulus, and Inequalities

Unit 3

Geometry and Trigonometry

8 topicsMembers
  1. 3.1Volume, Surface Area, and Distance in 3D
  2. 3.2Right-Angled and Non-Right-Angled Triangles
  3. 3.3Radian Measure, Arcs, and Sectors
  4. 3.4The Unit Circle and Trigonometric Identities
  5. 3.5Trigonometric Functions and Equations
  6. 3.6Reciprocal and Inverse Trigonometric Functions, Compound Angle Identities
  7. 3.7Vectors, Scalar Product, and Lines
  8. 3.8Vector Product, Planes, and Intersections

Unit 4

Statistics and Probability

7 topicsMembers
  1. 4.1Sampling and Descriptive Statistics
  2. 4.2Correlation and Regression
  3. 4.3Probability: Venn Diagrams, Trees, and Conditional Probability
  4. 4.4Discrete Random Variables and the Binomial Distribution
  5. 4.5The Normal Distribution
  6. 4.6Bayes' Theorem
  7. 4.7Continuous Random Variables

Unit 5

Calculus

11 topicsMembers
  1. 5.1Limits and the Derivative
  2. 5.2Differentiation Rules
  3. 5.3Applications of Differentiation
  4. 5.4Integration and the Fundamental Theorem
  5. 5.5Areas and Kinematics
  6. 5.6Continuity, Differentiability, and L'Hôpital's Rule
  7. 5.7Implicit Differentiation, Related Rates, and Further Derivatives
  8. 5.8Integration by Parts, Substitution, and Partial Fractions
  9. 5.9Volumes of Revolution
  10. 5.10Differential Equations
  11. 5.11Maclaurin Series