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Paper 3 is the final exam for IB Mathematics Analysis and Approaches (AA) HL students, marking the last challenge in your IB Math AA assessment. In this post, we’ll provide a thorough breakdown of IB Math AA Paper 3, ensuring you are familiarised with the structure of the exam and know what type of questions to expect.
IB Math AA Paper 3
- Accounts for 20% of the student's subject grade.
- Students have 1 hour 15 minutes to complete Paper 3.
- Students can score up to 55 marks.
- Paper 3 is made up of 2 questions. Students must answer both questions.
- A GDC calculator is required for this paper.
- Paper 3 focuses on the HL content of the Math AA syllabus.
A typical Math AA Paper 3 question may look the following way:
This question asks you to investigate some properties of the sequence of functions of the form fn(x) = cos(n arccosx), -1 ≤ x ≤ 1 and n ∈ Z+
Important: When sketching graphs in this question, you are not required to find the coordinates of any axes intercepts or the coordinates of any stationary points unless requested.
(a) On the same set of axes, sketch the graphs of y = f1(x) and y = f3(x) for -1 ≤ x ≤ 1. [2]
(b) For odd values of n > 2, use your graphic display calculator to systematically vary the value of n. Hence suggest an expression for odd values of n describing, in terms of n, the number of (i) local maximum points; (ii) local minimum points. [4]
(c) On a new set of axes, sketch the graphs of y = f2(x) and y = f4(x) for -1 ≤ x ≤ 1. [2]
(d) For even values of n > 2, use your graphic display calculator to systematically vary the value of n. Hence suggest an expression for even values of n describing, in terms of n, the number of (i) local maximum points; (ii) local minimum points. [4]
(e) Solve the equation fn'(x) = 0 and hence show that the stationary points on the graph of y = fn(x) occur at x = cos kπ/n where k ∈ Z+ and 0 < k < n. [4]
The sequence of functions, fn(x) , defined above can be expressed as a sequence of polynomials of degree n.
(f) Use an appropriate trigonometric identity to show that f2(x) = 2x2 - 1. [2]
Consider fn+1(x) = cos((n + 1)arccosx).
(g) Use an appropriate trigonometric identity to show that fn+1(x) = cos(narccosx)cos(arccosx) - sin(narccosx)sin(arccosx). [2]
(h) Hence (i) show that fn+1 (x) + fn-1(x) = 2xfn(x), n ∈ Z+; (ii) express f3(x) as a cubic polynomial. [5]
How to succeed in Math AA Paper 3?
Solving numerous past papers is one of the best ways to prepare for IB Math AA Paper 3, as it helps you get used to the style of questions and improves your ability to apply mathematical techniques effectively. It is important to do this under exam conditions to master your time management skills and get used to the exam format.
It is also crucial you master the GDC. It is a tool that can save you time on complex calculations, graphing, and statistical analysis while reducing the risk of human error. However, mastering its use is critical because it isn’t always intuitive to operate. We highly recommend you spend a considerable amount of time learning and practicing with your GDC as this will ensure that you can use its functions confidently during the exam.
We hope you found this post helpful. For more useful materials associated with the IB check out the wide variety of IA, EE and TOK exemplars available at Clastify.
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