**Introduction**

The latest IBDP Mathematics syllabus (from May 2021 examinations) features a new and unique Paper 3 component for Analysis & Approaches (AA) and Applications & Interpretation (AI) Higher Level subjects. This paper accounts for a total of 55 marks out of 300, or approximately 20% of the overall grade.

Importantly, the paper consists of two compulsory extended-response problem solving questions to be completed within one hour. Usually, the first part of the question will be on syllabus content leading to the problem-solving context. This means that **knowledge of all topics is required** for this paper, as the examiner may test on any topic(s). A Graphic Display Calculator (GDC) is allowed for the paper, but not every question or sub-question requires it.

**The Extended-Response Problem Solving Question**

The Paper 3 questions require extended responses involving sustained reasoning. Individual questions will develop from a single theme where the emphasis is on problem solving leading to a generalization or the interpretation of a context.

These questions may be presented in the form of words, symbols, diagrams or tables, or combinations of these. Normally, each question reflects an incline in difficulty, from relatively easy at the start of a question to relatively difficult tasks at the end of the question. The emphasis is on problem solving.

**General Approach to AAHL Paper 3**

Full marks are not necessarily awarded for a correct answer with no working. Answers **must be supported by working and/or explanations**. Solutions found from a graphic display calculator should be supported by suitable working. For example, if graphs are used to find a solution, **you should sketch these** as part of your answer. Where an answer is incorrect, some marks may be given for a correct method, provided this is shown by written working. You are therefore advised to **show all working**.

In this article, we focus on how to approach AAHL Paper 3 questions. The November 2021 Paper 3 is used as a reference.

**Breakdown & Analysis of Math HLAA Paper 3 November 2021**

**Question 1**

Figure 1: Question 1- IBDP Math HLAA Nov 21 Paper 3

Although a broad introduction is provided by sharing that trigonometric functions and special functions are tested at the start of the question, a quick glance through this question will reveal deeper insights; this question attempts to examine the student’s understanding and application of **second-order differentials, conversion of complex numbers from polar to cis form, graphical interpretation of hyperbolas and unit circle**. Before you begin attempting the question, have a **quick browse of the whole question and their sub-questions** to quickly get a feel of what’s coming and prepare your mind with the necessary concepts.

Next, by being **very familiar with all the topics in the syllabus**, it is clear that the entire lengthy question can be divided into 3 parts: differentiation and proofing, complex numbers and proofing, followed by graph sketching and finding roots. I have dissected the question as such below.

**Question 1 Part 1- “Differentiation & Proofing”**

**Question 1 Part 2- “Complex Numbers & Proofing”**

**Question 1 Part 3- “Graph Sketching & Finding Roots”**

**Question 2**

Figure 2: Question 2- IBDP Math HLAA Nov 21 Paper 3

The question is introduced as an exploration of different strategies of solving a system of linear equations. A quick glance through this question will reveal that indeed the entire question is based on calculus and in particular, first order differential equations. Hence, students who are

**very familiar with all the topics in the syllabus **will have ready in mind the standard techniques required to solve linear differential equations: separation of variables, integrating factor, substitution and Euler’s method. This question is dissected based on the techniques required.

**Question 2 Part 1- “Separation of Variables, Integrating Factor”**

**Question 2 Part 2- “Differentiation, Separation of Variables, Substitution”**

**Question 2 Part 3- “Implicit Differentiation, Substitution”**

**Conclusion**

From the analysis above, the extended response questions in Paper 3 do not seem to be very tricky or conceptually challenging as compared to the Section Bs of Paper 1 and 2. Instead, they require a good understanding of all topics in the syllabus, followed by the logical, step-by-step guided problem-solving based on a certain context.

This article was written by Dr (PhD) Boon, a graduate from Imperial College London with a Masters in Nuclear Engineering and a PhD in Materials Science from National University of Singapore. He is also a highly sought after Mathematics tutor who has taught around the world and helped hundreds of students score a perfect 7 in IB Mathematics.

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