IB Maths: Analysis and Approaches HL Revision notes
Clear notes for every subtopic, with key terms and exam tips.
Number and algebra16 subtopics
- 1.1 Scientific notation
- 1.2 Arithmetic sequences and series
- 1.3 Geometric sequences and series
- 1.4 Financial applications of geometric sequences
- 1.5 Laws of exponents and introduction to logarithms
- 1.6 Simple deductive proof
- 1.7 Rational exponents, laws of logarithms and exponential equations
- 1.8 Infinite geometric series
- 1.9 The binomial theorem
- 1.10 Counting principles and extended binomial theorem
- 1.11 Partial fractions
- 1.12 Complex numbers in Cartesian form
- 1.13 Modulus–argument and Euler form
- 1.14 Polynomial roots, De Moivre's theorem, powers and roots
- 1.15 Proof by induction, contradiction and counterexample
- 1.16 Systems of linear equations
Functions16 subtopics
- 2.1 Equations of straight lines
- 2.2 Functions, domain, range and inverse
- 2.3 The graph of a function
- 2.4 Key features of graphs
- 2.5 Composite and inverse functions
- 2.6 The quadratic function
- 2.7 Quadratic equations, inequalities and the discriminant
- 2.8 Reciprocal and simple rational functions
- 2.9 Exponential and logarithmic functions
- 2.10 Solving equations graphically and analytically
- 2.11 Transformations of graphs
- 2.12 Polynomial functions
- 2.13 Further rational functions
- 2.14 Odd and even functions; inverse with domain restriction
- 2.15 Solving inequalities
- 2.16 Modulus and further transformed graphs
Geometry and trigonometry18 subtopics
- 3.1 Three-dimensional geometry
- 3.2 Right-angled and non-right-angled trigonometry
- 3.3 Applications of trigonometry
- 3.4 Radians, arcs and sectors
- 3.5 The unit circle and exact values
- 3.6 Trigonometric identities
- 3.7 Circular functions and their graphs
- 3.8 Solving trigonometric equations
- 3.9 Reciprocal and inverse trigonometric functions
- 3.10 Compound angle identities
- 3.11 Symmetry properties of trigonometric graphs
- 3.12 Vectors: concepts and algebra
- 3.13 The scalar product
- 3.14 Vector equation of a line
- 3.15 Relationships between lines
- 3.16 The vector product
- 3.17 Equations of a plane
- 3.18 Intersections and angles of lines and planes
Statistics and probability14 subtopics
- 4.1 Populations, samples and data collection
- 4.2 Presentation of data
- 4.3 Measures of central tendency and dispersion
- 4.4 Correlation and regression of y on x
- 4.5 Basic probability
- 4.6 Combined, conditional and independent events
- 4.7 Discrete random variables
- 4.8 The binomial distribution
- 4.9 The normal distribution
- 4.10 Regression line of x on y
- 4.11 Formal conditional probability and independence
- 4.12 Standardisation and inverse normal with unknown parameters
- 4.13 Bayes' theorem
- 4.14 Discrete and continuous random variables
Calculus19 subtopics
- 5.1 Limits and the derivative
- 5.2 Increasing and decreasing functions
- 5.3 Differentiating polynomials
- 5.4 Tangents and normals
- 5.5 Introduction to integration
- 5.6 Further differentiation rules
- 5.7 The second derivative
- 5.8 Stationary points, optimisation and inflexion
- 5.9 Kinematics
- 5.10 Indefinite integrals and substitution
- 5.11 Definite integrals and areas
- 5.12 Continuity, differentiability and first principles
- 5.13 Limits and l'Hôpital's rule
- 5.14 Implicit differentiation, related rates and optimisation
- 5.15 Further derivatives and integrals
- 5.16 Integration by substitution and by parts
- 5.17 Areas with the y-axis and volumes of revolution
- 5.18 Differential equations
- 5.19 Maclaurin series