IB Math SL and IB Math HL are two of the toughest classes in the IB curriculum. It’s no surprise if you need a little extra help in either class.

**I’ve compiled this article of the best free online materials for IB Math SL/HL** so you can get all the IB Math notes you need in one place. For convenience, I ordered the resources following the IB Math SL/HL syllabus.

## How To Use This IB Math Guide

If you’re in search of information on one topic, **use the Command + F function on your computer to search this guide for that specific topic. **For instance, if you want to read about Algebraic Sequences, use Command + F to bring up the search function. Type “Algebraic Sequences,” and you’re computer will show you all of the study materials for Algebraic Sequences.

I split the material into three categories:

**Longer Notes:**notes (generally 3-10 pages) that provide a more detailed review.**Quick Reference:**brief (typically one-page) summary of a subject if you only need a quick refresher.**Video:**demonstration videos of how to solve past paper problems related to the subject.

## Common Study Errors IB Math SL/HL Students Make

IB Math SL/HL cover a lot of material. With so much material, you can’t afford to fall behind because you won’t be able to catch back up. You need to master the subjects during the school year in order to excel on the IB Math SL/HL papers. Common errors are:

**Ignoring the material you don’t understand.**If you didn’t understand it from your teacher, you need to look for outside help, possibly in this IB Math study guide or for even more help consider tutoring.**Only studying right before the IB Math SL/HL papers.**As I said before, there are too many topics for both courses to master in only a couple weeks (that’s why these courses are spread over a couple years). Master the subjects when you’re learning them in class. Use this study guide or hire a tutor if you need extra help:

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## Core Topics - 140 Hours for SL and 182 Hours for HL

For IB Math SL and HL, all students study the topics listed below. Here are a complete set of IB Math notes.

### Topic 1: Algebra

- Longer Notes:
- Quick References:
- 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

### Topic 2: Functions and Equations

- Longer Notes:
- Quick References:
- 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

### Topic 3: Circular Functions and Trigonometry

- Longer Notes:
- Quick References:
- 3.1.1 Radians
- 3.1.2 Length of Arc
- 3.1.3 Area of a Sector
- 3.2.1 Definitions of Trigonometric Ratios
- 3.2.2 Special Angles
- 3.2.3 Definition of Reciprocal Trigonometric Ratios
- Secant
- Cosecant
- Cotangent
- 3.2.4 Pythagorean Identities
- 3.3.1 Compound Angle Identities
- 3.3.2 Double Angle Identities
- 3.4.1 Manipulation of Trigonometric Functions
- 3.5.1 Inverse Trigonometric Functions
- Arcsin
- Arccos
- Arctan
- 3.6.1 Solving Trigonometric Equations
- 3.7.1 Cosine Rule
- 3.7.2 Sine Rule
- 3.7.3 Area of a Triangle

### Topic 4: Vectors

- Longer Notes:
- Packet: Matrices, Vectors

- Quick References:
- 4.1.1 Concept of a Vector
- 4.1.2 Representation of Vectors Using Directed Line Segments
- 4.1.3-4 Unit Vectors and Base Vectors
- 4.1.5 Algebraic and Geometric Vector Calculations
- Sum and Difference of Two Vectors
- Special Vectors
- Scalar Multiplication
- Magnitude of a Vector
- Position Vectors
- 4.2.1 Scalar Product of Two Vectors
- 4.2.2 Properties of the Scalar Product
- 4.2.3 The angle between two vectors
- 4.2.4 Perpendicular and Parallel Vectors
- 4.3.1 Vector Equation of a Line
- 4.3.2 The Angle Between Two Lines
- 4.4.1 Distinguishing Between Geometric Cases of Lines Using Vectors
- Coincident Lines
- Parallel Lines
- Intersecting Lines
- Skew Lines
- 4.4.2 Points of Intersection
- 4.5.1 Vector Product of Two Vectors
- 4.5.2 Properties of the Vector Product
- 4.6.1 Vector Equation of a Plane
- 4.6.2 Vector Equation Normal Form
- 4.6.3 Cartesian Equation of a Plane
- 4.7.1 Intersections With Planes
- 4.7.1.1 A Line With a Plane
- 4.7.1.2 Two Planes
- 4.7.2 Angle of Intersections with Planes
- 4.7.2.1 Line and Plane
- 4.7.2.2 Plane and Plane

### Topic 5: Statistics and Probability

- Longer Notes:
- Quick References:
- 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
- Z-value
- 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:
- Quick References:
- 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 - 48 Hours for HL Only

IB Math HL students study one of the following four options:

### Topic 7: Statistics and Probability

### Topic 8: Sets, Relations, and Groups

### Topic 9: Calculus

### Topic 10: Discrete Mathematics

## Summary: The Best IB Math Study Materials

IB Math has six Core Topics that both SL and HL students study, as well as one of four Options that HL students will also study. There are many free IB Math notes and study resources available online, especially when compared to other IB classes, which often have few high-quality online resources. **This makes it easier to keep up with what you're learning in IB Math and be prepared for all the exams for the class.**

There are multiple types of IB Math study resources, including general study guides, in-depth notes, and videos you can watch. Try out each of them to see which ones work best with your study style. Remember, you want to study **early and consistently** in order to be well prepared throughout the school year.

## What’s Next?

Learn more about IB Math:

Learn more about other IB classes:

- Every IB History Past Paper Available: Free and Official
- Every IB Economics Past Paper Available: Free and Official
- Every IB English Past Paper Available: Free and Official

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