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 using 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 one 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 3 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.

## How To Use This Guide During the School Year

Take advantage of this guide throughout the year to help you prepare for your in-class tests. Look at this article if you need extra help or if you didn’t fully understand your teacher’s explanation. **Make sure you master each topic during the school year and don’t wait to cram until the week before the exam.**

## The Best Study Practices for IB Math HL

Practice related IB Math past paper questions as you learn each subject. You can find out how to access **FREE IB Math SL/HL past papers in our other article**. If you’re having a hard time understanding your teacher’s lectures, you should be reviewing the corresponding chapter in a textbook or in this study guide.

## 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:

## 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 & 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 4 options:

### Topic #7: Statistics and Probability

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

### Topic #9: Calculus

### Topic #10: Discrete Mathematics

## 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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As an SAT/ACT tutor, Dora has guided many students to test prep success. She loves watching students succeed and is committed to helping you get there. Dora received a full-tuition merit based scholarship to University of Southern California. She graduated magna cum laude and scored in the 99th percentile on the ACT. She is also passionate about acting, writing, and photography.

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