IB Math Higher Level Syllabus
For Examinations beginning in May 2000
Part I: Core (195 hours)
All topics in the core are compulsory. Candidates are required to study all the sub-topics in each of the six topics in this part of the syllabus.
- Number and Algebra (20 hours)
- Arithmetic and Geometric Sequences and Series
- Exponents and Logarithms
- BInomial Theorem
- Mathematical Induction
- Complex Number Algebra, DeMoivre's Theorem, and Conjugate Roots of Polynomials
- Functions and Equations (25 hours)
- Domain, Range, Function Notation, Inverse Functions
- Graphing and Use of Graphic Calculators to Estimate Solutions
- Transformations of Graphs including Absolute Value and Recipricol
- Treatment of Following Functions
- Linear
- Quadratic in all forms
- Reciprocal
- Exponential including base e
- Logarithmic including natural log
- Polynomial Functions including Remainder and Factor Theorems
- Graphic Solution of f(x)=g(x) and f(x)>g(x)
- Circular Functions and Trigonometry (25 hours)
- Radian Measure, Arc Length and Sector Area
- Unit Circle Definition of Sine, Cosine and Pythagorean Identities
- Six Circular Functions and the Inverses, Domains, Ranges and Graphs also Changes in Amplitude, Period and Phase Shifts
- Addition, Double-Angle and Half Angle Formula
- Sine and Cosine Rule and Area of a Triangle for Non-Right Triangles
- Vector Geometry (25 hours)
- Column Representation of Vectors in two or three Dimensions, Sums, Scalar Multiplication, Magnitutde, Position Vectors and Unit Vectors
- Dot (Scalar) Product - Properties and Relation to Slopes and Angles
- Cross Product and Area of a Triangle
- Vector Representation of a Line and Plane
- Intersections and Distances between Lines, Points and Planes in two and three Dimensions
- Matrices and Transformations (20 hours)
- Matrix Algebra through Inverse, Inverse of Compounds and Determinants
- Transformations in the Plane through Composition, Inverse and Isometries
- Vector and Matrix Representations of Transformations and Linear Combinations
- Solutions of Linear Equations up to three Variables including Conditions for Number of Solutions
- Statistics (10 hours)
- Treatment of Discrete, Continuous, Grouped and Simple Data
- Methods of Display
- Frequency Tables and Histograms
- Cumulative Frequency Tables and Graphs
- Measures of Central Tendencies, Dispersion, Percentiles
- Probability (20 hours)
- Probability through Conditional Probability including Bayes' Theorem for two Events
- Use of Venn Diagrams and Tree Diagrams to Solve Problems
- Counting Methods
- DIscrete and Continuous Probability Distributions - expectation, mode, median, variance and standard deviation
- Binomial and Normal Distributions
- Calculus (50 hours)
- Informal Idea of Limit and Convergence
- Differentiation from First Principles
- Derivatives of Polynomials, Sine, Cosine, Tangent, Natural Logarithms and Exponentials base e through sums and chain rule
- Application of First Derivative - Tangents, Minima and Maxima, Velocity an Acceleration
- Product and Quotient Rule for Differentiation, Differentiation of general Logarithmic and Exponential Functions
- Graphing Functions including Use of Second Derivative and Behavior for large x to Find Asymptotes
- Indefinite Integration as Anti-differential then with Boundary Condition to Determine Constant
- Definite Integration and Area under Curve
- Integration using u substitutions, and by Parts
- Solution of First Order Differential Equations by Separation of Variables
Part II: Options (35 hours)
Candidates are required to study all the sub-topics in one of the following options.
Ed. Note: When I have time, I will fill in the details of the higher level options,
- Statistics
- Sets, Relations and Groups
- Discrete Mathematics
- Analysis and Approximation
- Euclidean Geometry and Conic Sections
Portfolio (10 hours)
Five assignments, based on different areas of the syllabus, representing the following three activities:
- Mathematical Investigation
- Extended Closed-Problem Solving
- Mathematical Modelling
- Mathematical Research
