The Complete IB Math Syllabus SL / HL 2021 (updated)
NEW IB MATHEMATICS SYLLABUS 2021
Courses previously available in mathematics (last exam in November 2020):

Mathematical Studies Standard Level

Mathematics Standard Level

Mathematics Higher level

Further Mathematics Higher Level (Final exam May 2020)
From August 2019 the following courses were introduced (First assessment in May 2021):
Download Complete IB Maths Syllabus
Mathematics: Analysis and Approaches SL
Similar to?
Old Mathematics SL
Which Students should take this course?

Students who are interested in mathematics

Are fairly moderate at it

Keen to study courses involving mathematics after high school (Eg. Economics & Sciences)
Topics Covered in Math AA SL

Number and Algebra (19 Hours)

Functions (21 Hours)

Geometry and Trigonometry (25 Hours)

Probability and Statistics (27 Hours)

Calculus (28 Hours)

Toolkit and Exploration (30 hours)
Changes Occured From Previous SL
Addition of Syllabus 
Deduction of Syllabus 
Simple deductive proof 
Vectors 
z on y regression line 
Volume of revolution 
Regression 
Mathematics: Analysis and Approaches HL
Similar to?
Old Mathematics HL
Which Students should take this course?

Students who love Mathematics

Are very strong at it

Interested in studying courses that highly involve math after high school (Eg. Engineering)
Get Free IB Trial Session Download IB Math eBook
Topics Covered in Math AA HL

Number and Algebra (39 Hours)

Functions (32 Hours)

Geometry and Trigonometry (51 Hours)

Probability and Statistics (33 Hours)

Calculus (55 Hours)

Toolkit and Exploration (30 hours)
Changes Occured From Previous HL
Addition Of Syllabus 
Deduction Of syllabus 
Binomial Theorem 
Poisson Distribution 
Partial Fractions 

Graphs (more depth) 

Sampling and Statistics 

Correlation and regression 

L’Hospital’s rule and Applications 

Differential Equations 

Maclaurin Series 
Mathematics: Applications and Interpretation SL
Similar to?
Old Math Studies
Which Students should take this course?

Students who are not strong at math

Do not plan to study any mathematicsbased course after high school
Topics Covered in Math AI SL

Number and Algebra (16 Hours)

Functions (31 Hours)

Geometry and Trigonometry (18 Hours)

Probability and Statistics (36 Hours)

Calculus (19 Hours)

Toolkit and Exploration (30 hours)
Changes Occured From Previous SL
Addition of Syllabus 
Deduction of Syllabus 
Sigma notation 
Number sets 
Amortization and Annuities 
Currency conversion 
System of Equations 
Logic (All 20 hours) 
General probability distributions 
Most of Set theory 
Binomial Distribution 

Correlation coefficient 

Chi squared 

Equation of perpendicular bisectors 

Voronoi diagrams and Applications 

Function modelling 

Basic Integration 
Mathematics: Applications and Interpretation HL
Similar to?
Unlike old courses
Which Students should take this course?
 Students who are strong at math
 Enjoy it
 don’t plan on studying any mathematicsbased course after high school
Topics Covered in Math AI HL

Number and Algebra (29 Hours)

Functions (42 Hours)

Geometry and Trigonometry (46 Hours)

Probability and Statistics (52 Hours)

Calculus (41 Hours)

Toolkit and Exploration (30 hours)
Changes Occured From Previous HL
Addition HL Content 
Log and Exponent laws 
Sum of infinite geometric sequences 
Complex Numbers 
Matrices. Eigenvalues and Eigenvectors 
Composite Functions, Inverse, Transformations 
Function modelling 
Radians, Trig identities, Trig equations 
Geometry transformations using matrices 
Vectors 
Graph Theory 
Nonlinear regression 
More sophistication with random variables and distribution (Poisson) 
Steady state and long term probabilities (transition matrices, Markov Chains) 
Derivatives, Second derivatives 
Integration, Area, Volume 
Kinematics 
Differential Equations 
Slope fields 
Sampling and data collection methods 
University Acceptance of IB Math
Mathematics: Applications and Interpretation 
Mathematics: Analysis and Approaches 

UNIVERSITY 
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HL 
University Of Oxford 
Requiring Math 
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University Of Cambridge 
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University Of Edinburgh 
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University Of Bristol 
Requiring Math HL 
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University of Sussex 
Requiring Math 
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King’s College London 
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University Of British Columbia 
Engineering, Commerce, Economics 
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The Complete IB Maths Syllabus: SL & HL
If you are going through this syllabus, I suppose you are interested in taking this course or you are presently joined with this course.
Courses and Ebooks available for IB Students (MYP & DP HL SL) from Countries UAE, Singapore, Oman, Qatar, Bahrain, Kuwait, Saudi Arabia, Thailand, Malaysia etcc.
In this article, I am going to discuss every topic covered in the IB Maths Standard level and IB Maths higher level along with the number of hours dedicated to each topic.
You can download the Complete IB Math Syllabus & IB Maths Book from here.
Download Complete IB Maths Syllabus
IB (International Baccalaureate) Math HL Online Preparation:
For IB Maths AA/AI SL, dedicated hours are 140 hours and for IB Maths AA/AI HL, dedicated hours are 182 hours
The topics are listed below:
Topic 1: Algebra
Longer Notes

Packet: Series, Complex Numbers, Differentiation FP

Packet: Complex Numbers, Theorem of Algebra, Modulus, Exponential Form, Nth Roots of Unit

Packet: De Moivre's Theorem, Expansions for Trig Functions, Derivative of sin x
Quick Overview

Algebraic Sequences

Sequences

Arithmetic Sequences and Series

Geometric Sequences and Series

Complex Numbers

Arithmetics with Complex Numbers

Addition / Subtraction

Multiplication

Division

Argand Diagrams

Modulus of a Complex Number

Polar Form

Multiplication / Division in Polar Form

De Moivre's Theorem

Applications of the Theorem

Roots of Equations

Complex Roots

Long Division

References
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Topic 2: Functions and Equations
Longer Notes

Packet: Indices, Surds, Linear, Quadratics, Cubics, Inequalities

Packet: Functions, Graphs, Polynomials
Quick Overview

Concept of Functions

Functional Limits

Domain

Range

Number Sets

Integers

Real Numbers

Natural Numbers

Combined Functions

Graphs of Functions

Inverse Function

Modulus Functions

Logarithms and Exponents

Natural Logs

Natural Exponent

Polynomial Functions

Quadratic Formulas and Graphs

Graph Transformations

Translation

Horizontal

Vertical

Stretch

Horizontal

Vertical

Reflection

Horizontal

Vertical

Modulus Transformations

Inverse Transformations

Four Things Graph Sketching
Intercepts
Asymptotes
Millionaire Theory
Table
Calculator
Topic 3: Circular Functions and Trigonometry
Longer Notes

Packet: Trigonometry

Packet: De Moivre's Theorem, Expansions for Trig Functions, Derivative of sin x
Quick Overview

Radians

Length of Arc

Area of a Sector

Definitions of Trigonometric Ratios

Special Angles

Definition of Reciprocal Trigonometric Ratios
Secant
Cosecant
Cotangent

Pythagorean Identities

Compound Angle Identities

Double Angle Identities

Manipulation of Trigonometric Functions

Inverse Trigonometric Functions
Arcsin
Arccos
Arctan

Solving Trigonometric Equations

Cosine Rule

Sine Rule

Area of a Triangle
Topic 4: Vectors
Longer Notes

Packet: Matrices, Vectors
Quick Overview

Concept of a Vector

Representation of Vectors Using Directed Line Segments

Unit Vectors and Base Vectors

Algebraic and Geometric Vector Calculations

Sum and Difference of Two Vectors

Special Vectors

Scalar Multiplication

Magnitude of a Vector

Position Vectors

Scalar Product of Two Vectors

Properties of the Scalar Product

The angle between two vectors

Perpendicular and Parallel Vectors

Vector Equation of a Line

The Angle Between Two Lines

Distinguishing Between Geometric Cases of Lines Using Vectors

Coincident Lines

Parallel Lines

Intersecting Lines

Skew Lines

Points of Intersection

Vector Product of Two Vectors

Properties of the Vector Product

Vector Equation of a Plane

Vector Equation Normal Form

Cartesian Equation of a Plane

Intersections With Planes

A Line With a Plane

Two Planes

Angle of Intersections with Planes

Line and Plane

Plane and Plane
Topic 5: Statistics and Probability
Longer Notes

Packet: Statistics Definitions, Charts and Graphs, Representing data, Standard Deviation

Packet: Sets and Probability, Permutations and Combinations, Distributions
Quick Overview

Measures of Central Tendency (Year 5 Maths)

Mean

Median

Mode

Measures of Spread

Range

Interquartile Range

Variance

Standard Deviation

Adding and Subtracting Mean/Variance

Discrete Distributions

Uniform / Stick

Binomial

Geometric

Poisson

Negative Binomial

Continuous Distributions

Normal

Zvalue

Probability Density Functions

Central Limit Theorem

Confidence Limits

Hypothesis Testing  Known Variance

Type I and Type II Errors

Unknown Variance

Confidence Limits  Unknown Variance

Hypothesis Testing  Unknown Variance

Matched Pairs

Bivariate Data

Probability Generating Functions (PGF)
Topic 6: Calculus
Longer Notes

Packet: Differentiation, Max/Min, Parametrics, Kinematics

Packet: Integration, Differentials, Even/Odd Functions, Induction

Packet: Harder Integration Questions
Quick Overview

Differentiation

Differentiation by First Principle

Exploring the Gradient Function

Equations of Tangents and Normals

Maximums and Minimums

Points of Inflection

Rates of Change

Kinematics

Parametric Equations

Integration

Exploring the Integral Function

Integration Basics

Finding Areas from Integrals

Volumes of Revolution

Separable Differential Equations

The Trapezium Rule
Options  HL Only 48 hours
IB Math HL students have to study one of the following from the four options:
Topic 7: Statistics and Probability
Topic 8: Sets, Relations, and Groups
Topic 9: Calculus
Topic 10: Discrete Mathematics
Useful Links
IB Mathematics Analysis and Approaches HL Preparation Guide