IB Maths is often thought of as daunting and so is left to the bottom of the revision pile. But, fear not, below we outline what to expect and how you can best prepare for your IB Maths exams!
Please note: This is a guide to the Maths syllabus for candidates taking the 2019/20 examinations. After this, the Maths syllabus will change.
What to expect
Knowing the topics that could come up in the paper is key. As you can see in the tables above, almost all of the syllabus can come up in every paper (apart from Maths Higher Level paper 3, but even this may still have some core content). This means it is crucial to revise each and every topic that you cover. Below we have listed all of the topics for each Maths level for you to tick off during your revision:
- Number and algebra
- Descriptive statistics
- Logic, sets and probability
- Statistical applications
- Geometry and trigonometry
- Mathematical models
- Introduction to differential calculus
Standard Level and Higher Level
- Functions and equations
- Circular functions and trigonometry
- Statistics and probability
- Optional modules (HL only): Statistics and probability; Sets, relations and groups; Calculus; Discrete mathematics
Before you start
Before you begin your study or revision, it is important to make sure you have a strong grasp on basic skills and techniques that you will need to succeed. These include cross-multiplication, fractions and basic algebra. Being comfortable using these skills will help you to approach all of the examination questions confidently and eliminate any small errors. If you are looking to revise one of these topics, GCSE Mathematics revision is often helpful; for example, you could use a website such as BBC Bitesize for this.
In addition, make sure you have the required equipment for your course and the exam. A ruler, pen, pencil, protractor and pair of compasses are essential. Similarly, please ensure that you purchase a graphical calculator, such as the TI-84 plus. Check with your school to see if they are able to sell these at a cheaper price to students.
Focusing your revision
Once you are equipped with the tools you will need, several key pieces of advice are worth bearing in mind as you approach revision.
Try to focus on areas that you find most difficult. Common areas are functions and calculus as these contain a variety of different topics and approaches. It is useful to focus your efforts here, building on what you do already know, so that you feel confident in these areas. This will also build your confidence in the exam allowing you to answer quicker.
If you need help revising a specific topic area, in Maths or any other subject, why not use the help of our tutors? Our tutors, who average 43 points in the Diploma, offer online and in-person tutoring. Please feel free to contact us if you are interested.
Once you have identified the areas you find most tricky, a good source of practice are past papers. To being with, I find completing and marking each question individually is more effective than completing the entire past paper and then marking it. By doing this you can isolate each topic and spend some time identifying where you picked up or missed marks in the question. This will help you set targets for your work going forward. For example, I created a ‘crib sheet’ which had reminders of what I had learnt from doing the past papers that I read before I did the final exam.
Understand why, not just how
The way previous exams (for example, GCSEs) may have been structured meant that learning a process enabled students to answer many questions without understanding why they were doing what they were doing. However, the IB will include scenarios and frame questions in ways that may not, at first glance, have an obvious solution. Therefore, it is crucial that you understand why you are performing a particular transformation or operation, as well as how to perform it. This spans from calculating the dot-product to inverting a matrix to taking the second derivative – understanding why, as well as how, is key.
Know how to use your calculator
A graphical calculator can seem daunting when you first use it; I know I definitely found the jump from using the GCSE Casio calculator to the IB’s graphical version quite difficult. However, with practice comes skill, and with skill comes success! Getting to grips with a graphical calculator takes time, yet after 2 to 3 weeks using it during your revision you will definitely know the key tools. Trigonometry, logarithms and graphing are 3 key tools to know how to use, as these will form a considerable component of paper 2 at standard and higher level. Solving calculator questions with fellow students or your teacher can often help you to pick these skills up quickly as you can see how others do it.
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Practice your radians and know your formulas
One of the pieces of help that the IB give you comes in the shape of your formula booklet – your pass to all of the mathematical formulae you need to know. However, this can be as much of a hindrance as a help. It is important that you become swift looking up formulae in here as, during the exam, this is time you could spend completing the answer. When using past papers, practice using the formula booklet and get to know the formulae in here. For example, knowing that cos^2(θ)+sin^2(θ)=1 or that dy/dx (e^x)=e^x will save you time during the exam as you will not need to consult the formula booklet.
Try to also spot common patterns amongst formulas and questions. For instance, difficult integration questions will often integrate to give the arc tan or arc sin formulae. Knowing this in advance will help you to spot this quicker in the exam and know where to go. Speaking of the exam…
In the exam
Here are a few more hints and tips for you to use during the exam itself:
Don’t be afraid to go wrong
Perseverance is key during all of your IB examinations, especially so in your maths exam. Some questions will take time to break down, and you may need to try 3 or 4 different methods in order to find the one that works. Here, practice is key. Spotting which of the formulae to use when proving an identity such as sin 2θ/(1+cos 2θ) =tan(θ) takes time and effort, but persevere and you will choose the right path! (P.S. you need to cancel to leave sinθ/cosθ)
Estimating the answer
Try to have a rough idea of what the answer may be before you start the question, as this will be especially useful during calculator papers. If asked to graph a function, consider whether it is linear or parabolic, and note down where its roots should be. Similarly, if asked a question on probability, consider what a sensible probability may be. This is a good guide to test your answer against.
Read the question twice
Many mistakes during IB Maths exams come from not reading the question properly. Please make sure that you take the time to read, and re-read, the question! You could also underline the key points here, acting like a checklist, making sure you have included all of these in your answer. Moreover, you could use the first read of the question to gain an understanding of the question as a whole, and the second re-read to note down the key points. I found this to be very useful as I had a chance to understand the question first and then re-read to find the key parts I needed for the final answer.
Number of marks
In addition to re-reading the question, noting how many marks the question is worth will guide you as to how much to write. For a 1-mark question, the answer will be somewhere already in your working or a simple extension of it, and will often be accompanied by command terms such as “give” or “state”. This also acts as a useful guide regarding how much time to spend on a question. It may be worth setting a time limit of 2 minutes on a question worth 1 mark, or 10 minutes on a 5-mark question, so that you do not run over time. Remember the timings for Maths studies and SL are 1.5 hours for both papers and for HL are 2 hours for papers 1 and 2 and 1 hour for paper 3.
Integers and fractions
A small but useful piece of advice for HL/SL paper 1 is that an integer or fraction as an answer is often a good sign. Without a calculator to use in the exam, the IB often construct paper 1 questions so that they give a whole number or fraction. Therefore, remember to look for opportunities to cancel and simplify your answer, as this could get you the mark that tips you over the grade boundary!
Simplify at the end of your working
For both studies papers, and SL/HL paper 2, try to store the answers you have on your graphical calculator until the end of your working and then round your final answer to 3 significant figures. This will minimise any discrepancies caused by rounding during your working and will give you a final answer that matches with that on the examiner’s sheet.
(Higher Level specific) Score highly on paper 3
Your optional module will normally have been picked by your school to give you the best chance of scoring highly on this paper. Moreover, this is the paper where common themes appear most; for example, Fermat’s little theorem and Kruskal’s or Dijkstra’s algorithm are frequent questions on the Discrete optional paper. Therefore, revising these and other key topics that appear in past papers is a must and will definitely allow you to score highly here.
Firstly, ensure that you know what is in the syllabus. As you can see above, there are 7 topic areas for each tier, so make sure you are ticking off which areas you have covered during your revision. The contents pages of maths textbooks are often organised to address each of these areas so they are a good point of reference.
Secondly, make sure you have everything you need for the exam – writing materials and a graphical calculator. This are essential to succeed. Practice using your calculator as much as possible so, come the final exam, it will be much simpler to remember where the relevant operators are.
Finally, make use of past paper questions! They are incredibly helpful for honing your mathematical skills, practising your formula book swiftness and noticing which topics frequently come up. Start by doing questions individually and then build to doing the entire past paper under timed conditions to mimic the structure of the final exam.