Download IB Math Higher Level Curriculum

IB Math Higher Level Curriculum
Year 1
Sequences and Series
 Set Notation
 Arithmetic Sequence
 Geometric Sequence
 Sigma Notation
 Arithmetic Series
 Geometric Series
 Infinite Series
Triangle Trigonometry (Trig 1)
 The Right Triangle
 Special Angles
 Area of a Triangle
 Sine Law
 Cosine Law
Logarithms and Exponents
 Log Laws
 ax = b
 Change of Base
 Growth and Decay
Functions
 Definition
 The Linear Function
 The Absolute Value Function
 The Quadratic Function
 Polynomials
 Compositions
 Inverses
 The Reciprocal Function
 Transformations
 Inequalities
Combinatorics
 Sum rule
 Product Rule
 Permutations
 Combinations
 Pascal's Triangle
 Binomial Theorem
Circular Functions (Trig 2)
 Unit Circle definitions
 Pythagorean Identities
 Related Angles
 Radian Measure
 Trigonometric Equations
 Angle Formulae
 Trigonometric Identities
 Arcs, Sectors, Segments
 Trigonometric Graphs
Calculus 1
 Elementary Limits
 Definition of Derivative
 Tangents and Normals
 Linear Rule
 Product Rule
 Quotient Rule
 Trig and Reciprocal Trig Derivatives
 Chain Rule
 Critical Points
 Inflection Points
 Sign Analysis
 Optimization Problems
 Related Rates
Complex Numbers 1
 Definition of a Complex Number
 Polar Form
 Operations with Complex Numbers
 Square roots of complex numbers
 DeMoivre
 nth roots
 The quadratic equation
Calculus 2
 Fundamental Theorem of Integral Calculus
 The Definite Integral
 Reimman Sums
 Trapezium
 Area
 Antiderivatives
 Integration by U- Substitution
 Integration by Parts – Tabular and Cyclic
Calculus 3
 Implicit Differentiation
 Derivatives of exponential and logarithmic functions
 Logarithmic Differentiation
 Integration of transcendental functions
 Integration by Trigonometric Substitution
 Partial Fractions
 Volumes of Revolved Solids
 Volumes of Solids with Known Cross-Sections
Year 2
Stats & Prob Intro
 Concept of population and sample
 Discrete and Continuous Data
 Frequency tables
 Box and Whisker Plots
 Grouped Data
 Measures of Central Tendency: Mean, Median, Mode
 Measures of Spread: Range, Interquartile range,
variance, standard deviation
 Unbiased vs. Biased estimates for the mean and
standard deviation
 Cumulative Frequency Graphs, Ogives
 Transformations of data
 Sample Space, event
 Probability of an event
 Complementary events
 Combined events (intersection or union)
 Mutually exclusive events
 Conditional Probability
 Independent Events
 Bayes Theorem
 Venn Diagrams, Tree Diagrams
 Probability using Combinations
Prob & Stats 2
 Discrete Probability Distributions
 Expected Value, mode, median, variance and standard
deviation
 Binomial Distribution
 Mean and Variance of Binomial Distribution
 Poisson Distribution
 Mean and Variance of Poisson Distribution
 Continuous Probability Distributions
 Expeced value, mean, median, mode
 Normal Distribution
 Standardization of a normal distribution
 Using the statistics tables
Calculus Review
 Limits
 All derivatives inc. implicit and logarithmic
differentiation
 Sign analysis
 Optimization and Related Rates
 Antiderivatives, area, trapezium
 Integration by inspection, u-sub, partial fractions, parts,
tabular, cyclic, trig sub
 Volumes of Revolved Solids and solids with known
cross-sections
Series and Differential Equations
 Infinite Series
 Ratio Test
 Limit Comparison Test
 Integral Test
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Alternating Series
Power Series
Radius of Convergence
Maclaurin series
Taylor Series and polynomials
Error
L’Hopital
Slope fields
Homogenious Differential Equations
Euler’s Method
Vectors in 2-D
 Vectors as displacement in the plane and in three
dimensions
 Components of a vector, column representation
 Sum of two vectors,; Zero, inverse, position and unit
vectors
 Multiplication by a scalar
 Magnitude of a vector
 Angle between vectors
 Vector Equation of a Line
 Parametric and Cartesian Equations of a line
 Scalar product of two vectors
 Perpendicular and Parallel Vectors
 Angle between two lines
 Distance between a point and a line
Matrices
 Element Row column Order
 Algebra with Matrices
 Multiplication of Matrices
 Identity and Zero Matrices
 Determinants
 Inverses of Matrices
 Systems of Linear Equations with Matrices
Vectors in 3-D
 Parametric and Cartesian Equations for a line in 3-D
 Vector Product
 Applications of Vector Product (area of parallelogram
or triangle, shortest distance between two skew lines)
 Vector equations of planes
 Cartesian equations of planes
 Equation of a plane passing through a point containing
two lines
 Distance between a parallel line and a plane
 Distance from a point to a plane
 Intersection of a line and plane
 Angle between planes
 Intersection of 2 planes
 Intersection of 3 planes; inverse matrix method and
Gaussian elimination
Induction