Maths IA basic structure:
For HL Maths, the IA will be marked by the following criteria:
- Communication (maximum mark: 4)
- Mathematical Presentation (maximum mark: 3)
- Personal Engagement (maximum mark: 4)
- Reflection (maximum mark: 3)
- Use of mathematics (maximum mark: 6)
The IA as shown will be marked out of 20 in total. There is no actual word limit, but the suggested page limit is 12 because this is the range where students can achieve the best communication level. To start, it is helpful to open the HL maths book and view all the chapters and think about some real life applications or situations that utilises the maths in the course.
The maths IA is also called a mathematics exploration. Just like its name, the IB wants you to dig deep down into a specific area of maths. Although it requires an unconventional mathematical investigation, it is not asking the student to come up with a new equation or prove the unsolved equation (if you do, you might get a high mark, but it will be extremely difficult). The mathematics of your exploration could be on the Internet. What they really want from the exploration is where you apply the ‘conventional maths’. For example, using implicit differentiation – (HL maths course) on an ellipsoidal equation (Not in the course but it is an easy question that can be learnt from online sources).
Out of these 5 criteria, your focus should be on:
- Fluidity (communication). It is best for you to write it like a formal diary where you explain all the thought process that you went through during the exploration and what/why your findings were interesting to you. Your reflection eventually follows. Most importantly, you do not have to have the entire IA planned before you start. You should start by looking into one interesting feature, and you should keep digging deeper from that feature. This is why a structure like a diary works the best.
- Use of mathematics. For SL students, it you want to get a high score in the mathematics section, all you need to do is use a mathematics that is in the HL course (or can be things outside of your course). Here are the list of subjects that HL teaches that SL does not:
- Quadratics:
- Even & Odd functions
- Inequalities
- The modulus function
- Rational Function
- Finding where graphs meet
- Transforming functions:
- Simple rational function
- The reciprocal function
- Modulus function
- All of chapter: Complex Number / Advanced Complex Number
- All of chapter: Counting and the binomial expansion
- All of chapter: Mathematic induction
- Unit circle and radian measure
- Negative and complementary angle formulae
- Trigonometric function
- Reciprocal trigonometric function
- Inverse trigonometric function
- Transforming equations and identities
- Compound angle formulae
- Trigonometric series and products
- Vectors
- Vector products
- Vector applications
- Area
- Planes
- Angles in space
- Intersecting planes
- Introduction to differential calculus
- Trigonometric limits
- Rules of differentiation
- Implicit differentiation
- Derivatives of inverse trigonometric functions
- Applications of differentiation
- Related rates
- Integration
- Integration by parts
- Applications of integration
- Problem solving by integration
- Probability
- Probabilities using permutations and combination
- Bayes’ theorem
- Discrete random variables
- Properties of E(x) and Var(x)
- The Poisson distribution
- Continuous random variables
For HL students, it is a good idea to use at least 3 of HL course mathematics and apply it to a slightly complex maths. You can also guarantee the mathematic utility marks by using the maths from your option booklets.
- Personal Engagement. Personal engagement is something that will make your IA original, and this is what the IB likes. Therefore it is a good idea to study about something you are interested in personally. Real life situation (examples and usage of specific mathematical theory) will be a great topic to investigate as you can do physical experiments, which will guarantee the personal engagement mark.
Fresh Questions & Good Talks 