IB HL Maths

Here is the link: HL Maths notes

If you take the statistics option, here are some example ‘trick’ questions that should interest you (there aren’t many, but I hope they are of high quality):

Statistics worked examples

Contents

1. Algebra
   1. Sequences and series
   2. Summation
   3. Permutations and combinations
   4. The Binomial Theorem
   5. Mathematical induction
2. Functions and equations
   1. Graphs
   2. Polynomials
   3. Circular functions and trigonometry
   4. Systems of equations
3. Vectors
   1. Scalar products
   2. Vector products
   3. Projections and resolving vectors
   4. Straight lines
   5. Planes
4. Calculus
   1. Differentiation
   2. Integration
   3. Definite integrals
5. Probability and Statistics
   1. Probability
   2. Discrete random variables
   3. Discrete distributions
   4. Continuous random variables
   5. The Normal distribution
   6. Sampling
   7. Estimators
   8. Confidence intervals
   9. Hypothesis testing
   10. PGFs
   11. Bivariate data and correlations
6. Complex numbers
   1. Forms of complex numbers
   2. Operations on complex numbers
   3. Relation to trigonometry
   4. Polynomials
   5. Roots of complex numbers
7. Miscellaneous

About the notes

• The notes are organised mostly according to the syllabus, but I’ve reordered some things (e.g. putting complex numbers at the end).
• These notes were made specially for the statistics option. You’ll notice that Chapter 5 is quite big; this is because I felt it was better to put all the stats stuff together – both the core and the option. For students of other options, you may have to avoid chapter 5 all together because of the way I’ve linked it together. However, I think it would be productive for you to read it anyway, and just be clear on which topics are core and which are option.
• I do not claim that these are comprehensive, because I’ve left out some facts that either seem obvious to me or are ingrained in my memory. That being said, I have made them fairly detailed and there has been a generally positive response among those who have used the notes.
• Not that you care, but I actually spent a lot of time on these making them aesthetically pleasing, by typing them in $\LaTeX$.

How one should study maths

Here’s an interesting quote, which is of some relevance to HL maths:

Be as the bird, and wing it - Anon

‘Winging it’ is an expression used by students to signify that they have done no preparation for a test and are instead hoping they come up with something on the spot. When I say that HL maths involves ‘winging it’, I don’t mean to say that there’s no preparation, but that it involves a lot of improvisation. These notes are what should be remembered going into the exam: useful facts or relationships that will save you time. I think that’s how maths should be done: make sure you have all of the concepts in your head, but when it comes down to it, it’s all about applying these concepts. Obviously, to practice this, you ought to do past papers. But do them actively, making sure you understand what you are doing.