IB Math AA Paper 3 - Mastering the Final Challenge
As a Higher Level student, when taking the course of Mathematics Analysis and Approaches, you will have to face a total of three exams. The last one is Paper 3, which is often referred to as a mathematical investigation. As paper 3 is different from the other two exams you have to take to complete the mathematics course (paper 1 and paper 2), many students are not sure how to properly and effectively prepare for this paper. In this article, you will find details on the structure of the exam, as well as tips on how to get ready for its completion.
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Time and worth
This exam consists of two long-answer questions, which are worth 55 points in total. The resulting grade accounts for 20% of your final result for the Math AA course. The time allocated for this exam is 1 hour, and you are allowed to use a graphic display calculator when solving the problems. There are no sections in the structure of the exam, and it is expected that both questions will be completed.
Wondering how much Paper 3 really matters? Let’s break down the structure, timing, and scoring - so you know exactly what’s at stake and how to prepare smart.
General exam tips
The Paper 3 exam is a big leap compared to the other two you have to take, therefore, you may find yourself unsure how to even approach studying to do well in this exam. As always in mathematics, the best way to prepare is to do practice questions! The purpose of this paper is to test how well you understand and apply the theoretical concepts taught during classes, as well as test your problem-solving abilities. Since this exam is exclusively taken by HL students, you should expect to encounter problems revolving around the HL-only syllabus sections. Examples of these topics include:
Complex numbers - Euler and polar forms, working with Argand diagrams, finding roots of complex polynomials, application of De Moivre’s theorem.
Functions - Viete’s formulas for the sum and product of roots, odd and even functions, graphing modulus functions, solving inequalities numerically and graphically.
Vectors - equations of lines and planes, scalar and vector products, intersections of lines and planes.
Trigonometry - reciprocal ratios and general relationships between trigonometric functions, compound angle identities.
Probability - Bayes’ theorem, discrete and continuous random variable analyses.
Calculus - L’Hopital’s rule for limits, related rates, optimisation, integration (by parts, substitution and repeated), volumes of revolution through the x and y axes, Maclaurin series.
Many questions in the past years have included the concepts of modelling, problem solving, in-depth analysis of optimisation, and mathematical puzzles. As there are only two questions in the entire exam, you may expect each of them to require a combination of different topics.
For example, you may be asked to complete an analysis of a geometric sequence/series and later connect that to a probability distribution table - find the expected value and the variance. Therefore, when studying mathematics, it is crucial to realise just how closely connected many of the concepts are to each other. What you learned alongside topic 2, based on the analysis of different functions, you later used to understand the basic concepts found in topic 5 - calculus.
During the exam, you will be given 5 minutes of reading time - make use of them! Make a mental note of which sub-questions seem easy, read every problem as thoroughly as possible, and try to think which mathematical concepts or formulas you are expected to use to solve the problem at hand. As the paper is supposed to last 1 hour, it is expected that you will spend no more than 30 minutes on each of the two assigned questions. Make sure that when doing practice paper 3 questions, you have a timer set to check whether you fit within the allocated time frame for the exam. Even if one of the questions looks scary and complicated, the first two or three sub-questions it contains should be ‘free points’ - easy to solve problems that do not require much in-depth thinking or calculations.
Try not to panic if you find yourself stuck or confused by what the problem is asking of you. Write down clearly all of the information or data provided by the text - keep in mind that sometimes it may not be given as a numerical value, but as a term or a phrase.
For example, you may be told that ‘The function f(x) has a horizontal tangent when x = 2’. Here, you are expected to recognise that a horizontal tangent implies that the gradient is equal to zero, meaning that the derivative f’(x) at this point must be equal to zero. If the problem is based on trigonometry or calculus and no supporting diagram or graph is provided, make one yourself. This will help visualise the problem at hand and potentially point in the direction you are supposed to take to find the final answer to a sub-question.
The questions often include a general analysis and derivation of new formulas based on the ones you have seen throughout your mathematics classes for the past two years. It is important to show as much of your work as possible, so make sure to write down even the smallest steps or assumptions you may be making. The examiner checking your answers may not be able to give you full points if there are inexplicable leaps in calculations or proofs. The point is to demonstrate clear understanding, as well as the ability to apply previously found information to later sub-questions.
Same as in the previous exams, unless stated otherwise, it is expected that your answers are provided rounded to three significant figures. Aside from correct notation, it is expected that appropriate units will be used. If the question provides values of angles in radians, it is expected that your answer will be in radians as well. If you find it easier to complete the analysis and calculations using other units, you are more than welcome to do so. However, keep in mind that your final answer must later be converted to the units specified in the text of the question you are solving. Not following these rules can lead to reduced points for the final answer, which later can result in an overall lower grade for the entire exam.
Make sure to use your calculator and formula booklet!
The use of a calculator and a formula booklet is allowed throughout Paper 3; therefore, do not be afraid to make use of these tools. Both of them can help make the solving process easier when used correctly. Before you enter the exam, you should be familiar with the contents of the formula booklet for Math AA, as well as feel comfortable with using your calculator. Knowing where to find different modes and options in your calculator in advance can save you a lot of time during the exam itself. Rather than losing time looking for a numerical solve operation, you should know where to find it in your GDC beforehand. Therefore, make sure that you know what your calculator is capable of, as well as where you can find certain functions it possesses.
As paper 3 includes an exploration of in-depth mathematical problems, one of the best ways to prepare is to do regular practice on mathematical puzzles. Whether that means taking part in competitions, completing past paper questions from older paper 3 examinations, or simply searching up mathematical puzzles is up to you! As long as you understand and can apply the concepts taught in class, completing problems should not pose much of a problem. Make sure that you truly understand the underlying concepts for each of the topics, rather than remember their definitions by heart. A great way to test whether you understand a math concept is to explain it to a friend or a sibling. If you can clearly and effectively describe an idea, then you are ready to go!
Feeling worried and unprepared?
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