IB Math AI Paper 3 - Everything You Wish Someone Told You
At the end of IB, as a Higher Level student taking Mathematics Applications and Interpretations, you will have to take three final exams that will dictate 80% of your total course grade. The remaining 20% of the grade lies in the Internal Assessment, which you need to have completed and submitted before attending the exams.
To best prepare for Paper 3, we have created a summary of what you can expect when taking the exam, as well as our best tips on how to ace it. For the previous two exams and our tips on how to best prepare, check out paper 1 and paper 2!
Struggling to prepare for your IB Math AI Paper 3? Our expert IB tutors can help you master exam techniques, understand mark schemes, and boost your score with confidence.
Time and worth
You will have a time of 1 hour to solve two long-answer questions, worth a total of 55 points. This exam is only taken by students doing Math AI at a Higher Level. The Paper 3 examination accounts for 20% of your final grade for the mathematics course, therefore, it is important to prepare for it as best as possible. You will be allowed to use your graphic-display calculator, and you will be provided with a formula booklet, the same as in the other two exams you have to face.
General exam tips
Paper 3, when set side by side with the other two papers, is almost a different form of examination.
Its purpose is to provide a sort of mathematical puzzle or an investigation, which is supposed to test your skills in applying concepts learned in class to more general real-life modelling problems.
Many students, maybe including you, find themselves stumped when having to start preparing and studying for this exam. Of course, the most effective way to study mathematics and make sure that you understand it is by doing practice questions. Firstly, you have to make sure that you have gone over the entire Math AI syllabus, paying a lot of attention to the HL-only topics covered. Some of these topics include, but are not limited to:
Algebraic concepts - laws of logarithms, sum of infinite geometric sequences, complex numbers (Cartesian, polar and Euler forms), eigenvalues and eigenvectors.
Functions - graph transformations, modelling functions, log-based graphs, and solving for inverse functions with domain restrictions.
Trigonometry - radians, unit circle, solving trigonometric equations numerically and graphically.
Geometry - vector equations of lines in 2D and 3D, vector and scalar products of vectors, adjacency matrices and tables, cycle algorithms.
Statistics - validity tests, non-linear regression, central limit theorem, Poisson distribution, Markov chains, type I and II errors in different statistical tests.
Calculus - derivative rules, indefinite integration (reverse chain rule, u-substitution), volumes of revolutions about the x and y axes, slope fields, Euler’s method for first and second order differential equations, kinematics problems.
Although usually you see these topics in questions separately, in Paper 3, you can expect a combination of many of them.
For example, you may first be asked to complete an analysis based on an arithmetic sequence/series, then apply it to vector notation to describe the kinematics behind the problem. Therefore, a key point when studying for this exam is understanding that all of the topics covered during the Math AI course are intertwined and can be used to solve a number of different real-life problems.
Paper 3 includes only two problems to be solved, and it is supposed to test most (if not all) of your mathematical knowledge from the past two years of studying. You should be prepared to work with a combination of different topics that you may have previously deemed as separate.
Before starting the actual problem-solving part of the exam, you will be given 5 minutes of reading time. This is the perfect moment to take a deep breath, open the exam and try not to panic. Read every problem and its sub-questions as carefully as possible and make a mental note of which mathematical concepts or equations you may have to use to solve a particular question.
You are expected to allocate the two halves of your total time to the two problems assigned. This means that you should be spending no more than 30 minutes on a single question. When practising for the exam or doing past papers of paper 3, make sure to check whether you can solve it in the expected timeframe.
Solving complicated problems under time pressure can be extremely stressful, which may lead to clouded thinking when taking the exam. If you find yourself clueless about what the sub-question requires from you, do not panic just yet!
Make sure that you have read the text of the question properly, taken notes of the information given and created a diagram/graph if one was not provided in the exam. You must take into account that some information may not be given as a number or an equation, but rather as a phrase. As an example, let us assume that a question is based on kinematics. You are given a formula for the velocity of a moving particle dependent on time, and the sub-question is asking you to state the initial velocity. Initial implies that no time has passed, therefore, you would solve the equation for when the time is equal to zero.
Usually, the first two or three sub-questions are considered ‘free points’ as they do not require complicated calculations or extensive derivations. If a question states ‘write down’, the answer is already provided somewhere, either in a diagram or in the text; you are only asked to interpret its meaning in the context of the problem.
Points Matter!
More often than not, the number of points that you can score for a sub-question hints at what may be expected of you. If a question is worth one point, only the final answer is expected. When a question is worth three points, you may be expected to provide a more detailed answer - show the intermediate steps, and only then provide the final answer. If you do not provide the examiner with the steps you took and any assumptions made to get to the final answer, you will not be given any points (even if it’s a correct one!).
The point of the exam is to show a clear understanding of the underlying concepts, equations, as well as how they can be applied to different problems. Remember to write all of your answers to three significant figures, unless the text of the problem states otherwise. Although it may seem insignificant, not doing so may cost you points, leading to a lower grade for the entire exam.
Use GDC and formula booklet
Keep in mind that you are allowed to use your GDC and the formula booklet during the exam. Make sure that you know where you can find all of the important functions in your calculator, as well as how to change its settings between radians and degrees. The perfect time to become comfortable using both of these tools is when doing practice questions - make sure that you know your way around and understand all of the symbols used in the formulas provided.
Aside from doing past paper questions from old paper 3 examinations, another great way to prepare is to do mathematical puzzles. You can find many great problems in your course textbook, online forums, or in math/logic competitions. Try to start doing such practice as early as possible - this will ensure that you will be more comfortable with the format of paper 3 questions. If you would like to first test whether you understand a mathematical topic before jumping into questions, a great method to test your knowledge is to try to explain it to a friend. If you can present a concept clearly and concisely, you are good to go! It may take more than one try to get it right, however, learning is a process of both failures and successes - don’t be afraid of making mistakes. Better to make them now and learn from them, rather than during the exam.
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