Since the May 2021 examinations, the International Baccalaureate Organisation (IBO) has revised its Mathematics syllabus and now offers two types of Mathematics: Analysis & Approaches (AA) or Applications and Interpretation (AI), both offering two difficulty levels; Standard or Higher Level. Prior to this, only one main Mathematics was offered at the IBDP level at three different difficulty levels: Mathematical Studies, Mathematics Standard Level and Higher Level.

An in-depth review comparing the former syllabus and the new syllabus of Mathematics reveals significant revision, modification and enhancement to the scope and content, topical emphasis, teaching hours and assessment approach. Before we begin to decide on which Mathematics we should choose, a good understanding of the difference between both subject offerings is required.

## Key Points for Consideration

**1. The essential difference between Analysis & Approaches (AA) and Applications & Interpretation (AI) **

The main difference between the Mathematics subjects is that AA takes a more classical, conceptual and abstract learning approach to Mathematics. A significant level amount of higher-order thinking and understanding is required for abstract concepts like Vectors (Lines, Planes), Complex Numbers (Real and Imaginary Components) and solving Calculus problems like optimization, rate of change, volumes of revolution and differential equations.

On the contrary, a significant level of high-order application and know-how learning is required for AI Mathematics. Topics like Matrices (Adjacent matrices,

transformations), Algorithms (Tree & Cycle, Hamiltonian paths), Statistical distributions (Poisson) and testing (Hypothesis) require nimble application techniques on the Graphic Display Calculator (GDC).

Both types of Mathematics require different Mathematical skillsets, and it can be said that they are challenging and unique in their own ways. A student who graduates from AA can be said to have gained a better understanding of how to understand difficult Mathematical concepts. A student who graduates from AI can be said to be proficient in applying real-world techniques to solve current Mathematical problems.

**2. Begin with the End in Mind**

If you fail to plan, you plan to fail. A key consideration that most students take is the post-IBDP university programmes that they plan and hope to embark on. Generally, the Analysis & Approaches is suitable for future mathematicians, engineers, scientists and economists. The Applications & Interpretation are for those more passionate about social sciences, natural sciences, medicine, statistics, business, psychology and design.

Do check on the various university course requirements on their website and prospectus to be sure of their entry requirements, which could change yearly.

**3. Leverage on Your Strength**

An important factor to consider is your current aptitude and strengths in Mathematics during your time in middle school or secondary school. For those who have been strong in mental calculations for topics like algebra, solving linear and quadratic equations, completing the square, trigonometry and pre-calculus, perhaps Mathematics AA can be considered as you will have an edge over the rest. For students who have been strong in probability & statistics, game theory, tree diagrams, dice and coin summation, perhaps Math AI will be more suitable for you.

**4. Pursue Your Passion and Interests**

More importantly, it is key to pursue what you love. Even if you do not have a strong background in certain Mathematical skills, pursue it fervently. If you truly are passionate about the subject and its topics and take a keen interest in it, I am sure it will drive you to put in the hours and excel in it.

## Prior Learning Topics

The Prior Learning Topics are the same for both AA & AI Mathematics. We strongly encourage all students embarking on IBDP Mathematics to develop a strong foundation in these topics before your programme starts. They include Number & Algebra concepts like prime numbers, factors and multiples, standard form, solving linear and quadratic equations. Functions concepts like Mapping and Graphing Using Technology. Geometry & Trigonometry concepts including Pythagoras Theorem, Bearings, Transformations, Circular Measure and

Mensuration. Statistics & Probability visual aid tools like Histograms, Venn and Tree diagrams. Calculus concepts for kinematics like distance, speed and time formula and graphs.

## Teaching Hours

The cumulative teaching hours are 150 hours and 240 hours for Standard Level and Higher Level respectively. The HL option is significantly more rigorous across all topics compared to SL, with the additional 90 hours spread across all topics. It is important to note that more emphasis is placed on calculus for AA and statistics for AI.

## Assessment Format, Weightage & Details

## The Additional HL (AHL) Content

The topics listed below are the additional Higher Level topics required for each type of Mathematics.
**Analysis & Approaches**
• Permutations & Combinations
• Extension Of Binomial Theorem to Fractional And Negative Indices
• Partial Fractions
• Complex Numbers
• Proofing By Mathematical Induction
• Proofing By Contradiction
• Remainder & Factor Theorem
• Sum And Product of Roots
• Odd & Even Functions
• Inverse And Self-Inverse Functions
• Reciprocal Trigonometric Ratios
• Compound And Double Angle Identities
• Vectors
• Lines & Planes
• Bayes’ Theorem
• Discrete And Continuous Random Variables
• L’opital’s Rule & Maclaurin’s Series
• Implicit Differentiation
• Rate Of Change
• Optimisation
• Trigonometric Differentiation
• Integration By Substitution
• Integration By Parts
• Volume Of Revolution
• First Order Ordinary Differential Equations

**Applications & Interpretation**
• Laws Of Logarithms
• Complex Numbers
• Matrices
• Composite Functions
• Graph Transformation
• Sinusoidal, Logistic and Piecewise Models
• Circular Measure
• Trigonometric Identities
• Matrix Transformations
• Vectors
• Adjacency Matrices
• Tree & Cycle Algorithms
• Eulerian Trails and Circuits
• Hamiltonian Paths and Cycles
• Minimum Spanning Tree
• Chinese Postman and Travelling Salesman
• Chi^Squared Test
• Linear & Non-Linear Regression
• Coefficient Of Determination
• Unbiased Estimators
• Independent Normal Variables
• Poisson Distribution
• Hypothesis Testing
• Markov Chains
• Trigonometric Differentiation
• Stationery Points
• Integration By Substitution
• Volume Of Revolution
• Kinematics
• Separation Of Independent Variables
• Slope Fields
• Euler’s Method
• Phase Portrait of Differential Equations & Solutions
• 2nd Order Differential Equations by Euler’s Method

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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