IBDP Maths – MAA and MAI Resources- Syllabus, Practice Questions and Notes

## IBDP Maths MAA and MAI

Maths in IBDP is required at either standard level or higher level. You can take two courses: Analysis & Approaches (AA) or Applications & Interpretations (AI). Each course covers the same 5 topics (Number & Algebra, Functions, Geometry & Trig, Statistics, and Calculus), with different focus and weightage. Higher level courses in both AI and AA cover content in-depth, and also harder topics.

Whereas Math AI focuses more on the practical applications of math, with emphasis on functions and statistics, Math AA is a more traditional course, with more emphasis on number & algebra, geometry & trig, and calculus. As for the actual content, you can refer to the subject guides for each course.

# Exam Style Practice Questions, Notes and Past Paper for IBDP Maths - MAA and MAI 2025

**IBDP Maths Analysis and Approaches**

**IBDP Maths Analysis and Approaches HL**

- Higher Level (HL) IB Style Question Banks with Solution
- Math AA : Syllabus and Study Guide
- IB Maths AA HL – Past Papers
- Mock Exams MAA HL

**IBDP Maths Analysis and Approaches SL**

- Standard Level (SL) IB Style Question Banks with Solution
- Math AA: Syllabus and Study Guide
- IB Maths AA SL – Past Papers
- Mock Exams MAA SL

**IBDP Maths Applications and Interpretation**

**IBDP Maths Applications and Interpretation HL**

- HL IB Style Question Banks with Solution
- Math AI : Syllabus and Study Guide
- Mock Exams MAI HL
- IB Maths AI HL – Past Papers

**IBDP Maths Applications and Interpretation SL**

- SL IB Style Question Banks with Solution
- Math AI: Syllabus and Study Guide
- IB Maths AI SL – Past Papers
- Mock Exams MAI SL

#### What is Maths AA and AI?

Maths AA and AI are the two new IB mathematics courses introduced which replaced the old IB mathematics curricula for first assessment in May 2021. Maths AA stands for Mathematics: Analysis and Approaches and Maths AI stands for Mathematics: Applications and Interpretations. If you are an IB Diploma, it is compulsory to take one of these two courses at either Standard Level or Higher Level.

#### What are the differences between Maths AA and Maths AI?

Oh, this is the big one, so I’ll cut to the chase. The most prominent differences are found in **the teaching hours for each of the courses’ components**, in this next table. If you can’t understand it, don’t worry, as I’ve explained it after the table.

COMPONENT NAME | AA SL | AI SL | AA HL | AI HL |
---|---|---|---|---|

Number and Algebra | 19 | 16 | 39 | 29 |

Functions | 21 | 31 | 32 | 42 |

Geometry and Trigonometry | 25 | 18 | 51 | 46 |

Statistics and Probability | 27 | 39 | 33 | 52 |

Calculus | 28 | 19 | 55 | 41 |

The table shows that there are significant differences between the two courses in terms of content weightage. In essence:

**Maths AA**gives more emphasis on**Number & Algebra, Geometry & Trigonometry**and**Calculus**.**Maths AI**gives more emphasis on**Functions**and**Statistics & Probability**.

The subject brief also describes the nature of the two courses’ syllabi:

**Maths AA:**Develops important mathematical concepts in a rigorous way

Solves abstract problems as well as ones set in a meaningful context

Emphasizes on construction, communication and justification of correct mathematical arguments

Teaches students to have insights into mathematical form and structure

**Maths AI:**Emphasises on mathematics used in applications or mathematical modelling

Includes traditional components such as calculus and statistics

Develops strong technology skills

Encourages students to solve real world problems, construct and communicate them mathematically and interpret conclusions or generalisations

There is also a difference in their **assessments**.

**Maths AA** has one paper which prohibits the use of a calculator, Paper 1. Paper 2 and HL Paper 3 permit calculator use. **Maths AI** permits calculator use in all papers.

**Maths AA** paper 1 and paper 2 each are divided into two sections. Section A has short response questions, and Section B has extended-response questions. **Maths AI** paper 1 is exclusively short response questions, and paper 2 is exclusively extended response questions.

Note that HL paper 3 for both AI and AA are extended-response problem solving questions, and both of them share the same format, but have differing questions due to their differing syllabi.

**Maths AA** is the ‘analytical’ based, heavy on calculus and geometry/trigonometry. You cannot use a calculator in one paper. **Maths AI** is more ‘application’ based, heavy on functions and probability/statistics. You must use a calculator in all papers.

**Which one is more useful in university?**

Also one of the most common questions. Unfortunately, it is a very vague one. Neither is inherently ‘more’ useful, as it is entirely dependent on the region and your ambition in college or university.

If there is a preference for AA or AI in terms of courses, it exists for engineering or mathematics-heavy courses such as Physics or Math degrees. In these cases, AA is preferred or even required, but it only applies to countries that even differentiate between AA or AI.

I have made a very brief summary for certain popular countries for further studies and their trends for preferring AA or AI. But there exists so many exceptions that it is unjustifiable to even call it a ‘trend’ so please take this with a grain of salt and rely more on your own research.

**United States:**No AA/AI differentiation, but may require/prefer HL over SL for math heavy degrees**Canada:**No AA/AI differentiation, but may require/prefer HL over SL for math heavy degrees**Australia:**No AA/AI differentiation**United Kingdom:**There are cases of differentiation in a considerable number of universities. Generally, AA HL is the course which opens the most doors, as nearly all engineering and math heavy degrees require AA HL. Many competitive economics programs even prefer or require AA HL. Of course, there are major exceptions, most notably being Oxbridge which has no preference between the two, as they already have their own entrance exams which include maths. Unfortunately, I have personally never seen any case where AI is preferred over AA, but the other way round is very common. Do correct me in the comments if you come by any exception.

**So, which course should I select?**

Honestly, this depends on a variety of factors. Most notably, your performance and attitude in studying mathematics, and your individual strengths or weaknesses in individual components that may lead you to choose one course or another. If you are one of those all-rounders in mathematics, then perhaps you could choose based on university plans. If you are not confident in mathematics skills but still want to pursue math-related degrees, it is also an important factor to consider.Overall, remember that you are going to spend 2 years with this subject, so make sure you like what you’re doing, and have confidence in doing well in the subject in your IB exams. Do remember to consult your teachers, school, friends and family for advice on subject selection.

So that pretty much is the end. I may have missed out certain points, maybe even have some inaccuracies, but it is the least I could do for future IB students. I hope you found this useful, and do feel free to comment with your own perspectives!

Two new courses became part of the Diploma Programme (DP) in 2019, both taught at the Higher level (HL) and Standard level (SL). The first is **Mathematics: analysis and approaches** and the second is **Mathematics: applications and interpretation**.

From August 2019 the following courses, with first assessment in May 2021, are available:

- Mathematics: analysis and approaches SL
- Mathematics: analysis and approaches HL
- Mathematics: applications and interpretation SL
- Mathematics: applications and interpretation HL

**Students can only study one course in mathematics as part of their diploma.**

Each course approaches topics at varying levels of teaching hours. This guide will provide some insights into which course will be the best fit for your school and students.

The courses are separated by how they approach mathematics, described generally by the table below:

#### Mathematics: analysis and approaches

- Emphasis on algebraic methods
- Develop strong skills in mathematical thinking
- Real and abstract mathematical problem solving
- For students interested in mathematics, engineering physical sciences, and some economics

#### Mathematics: applications and interpretation

- Emphasis on modelling and statistics
- Develops strong skills in applying mathematics to the real-world
- Real mathematical problem solving using technology
- For students interested in social sciences, natural sciences, medicine, statistics, business, engineering, some economics, psychology and design

All of these courses (SL and HL in each) cover the same 5 topics within mathematics but with varying emphasis in each area: number and algebra, functions, geometry and trigonometry, statics and probability, and calculus. The chart below may help you select the right course based on the amount of time dedicated to a given topic.

#### New IB Math courses for the IB Class of 2021 Onward

Please see below the program documentation for a discussion of the math curriculum changes effective September 2019 for the IB Class of 2021.

The following chart summarizes the new courses and provides guidance in course selection:

New math course started in September 2019 for IB Class of 2021 | Course description from IB | Approximate current equivalent | Recommended prior math background |

Mathematics: Applications and interpretation | This course is designed for students who enjoy describing the real world and solving practical problems using mathematics, those who are interested in harnessing the power of technology alongside exploring mathematical models and enjoy the more practical side of mathematics. | STANDARD LEVEL (SL): This class is most similar to the current Mathematical Studies SL course. HIGHER LEVEL (HL): This course will include new content, including statistics. It is intended to meet the needs of students whose interest in mathematics is more practical than theoretical but seek more challenging content. | STANDARD LEVEL (SL): Strong Algebra 1 skills HIGHER LEVEL (HL): Strong Algebra 2 skills |

Mathematics: Analysis and approaches | This course is intended for students who wish to pursue studies in mathematics at university or subjects that have a large mathematical content; it is for students who enjoy developing mathematical arguments, problem solving and exploring real and abstract applications, with and without technology. | STANDARD LEVEL (SL): This class is most similar to the current Mathematics SL course. HIGHER LEVEL (HL): This class is most similar to the current Mathematics HL course. | STANDARD LEVEL (SL): Strong Algebra 2H skills HIGHER LEVEL (HL): Very strong Algebra 2H skills |

The following pages summarize the content of the new courses.

#### Mathematics: Analysis and approaches

The number and algebra SL looks at: scientific notation, arithmetic and geometric sequences and series and their applications including financial applications, laws of logarithms and exponentials, solving exponential equations, simple proof, approximations and errors, and the binomial theorem. The number and algebra HL looks at: permutations and combinations, partial fractions, complex numbers, proof by induction, contradiction and counter-example, and solution of systems of linear equations.

The functions SL looks at: equations of straight lines, concepts and properties of functions and their graphs, including composite, inverse, the identity, rational, exponential, logarithmic and quadratic functions. Solving equations both analytically and graphically, and transformation of graphs. The functions HL looks at: the factor and remainder theorems, sums and products of roots of polynomials, rational functions, odd and even functions, self-inverse functions, solving function inequalities and the modulus function.

The geometry and trigonometry SL looks at: volume and surface area of 3d solids, right angled and non -right -angled trigonometry including bearings and angles o f elevation and depression, radian measure, the unit circle and Pythagorean identity, double angle identities for sine and cosine, composite trigonometric functions, solving trigonometric equations. The geometry and trigonometry HL looks at: reciprocal trigonometric ratios, inverse trigonometric function s, compound angle identities ,double angle identity for tangent, symmetry properties of trigonometric graphs, vector theory, applications with lines and planes, and vector algebra.

The statistics and probability SL looks at: collecting data and using sampling techniques, presenting data in graphical form, measures of central tendency and spread, correlation, regression, calculating probabilities, probability diagrams, the normal distribution with standardization of variables, and the binomial distribution. The statistics and probability HL looks at: Bayes theorem, probability distributions, probability density functions, expectation algebra.

The calculus SL looks at: informal ideas of limits and convergence, differentiation including analysing graphical behaviour of functions, finding equations of normals and tangents, optimization, kinematics involving displacement, velocity, acceleration and total distance travelled, the chain, product and quotient rules, definite and indefinite integration. The calculus HL looks at: introduction to continuity and differentiability, convergence and divergence, differentiation from first principles, limits and L’Hopital’s rule, implicit differentiation, derivatives of inverse and reciprocal trigonometric functions, integration by substitution and parts, volumes o f revolution, solution of first order differential equations using Euler’s method, by separating variables and using the integrating factor, Maclaurin series.

**Mathematics: Applications and interpretation**

The number and algebra SL looks at: scientific notation, arithmetic and geometric sequences and series and their applications in finance including loan repayments, simple treatment of logarithms and exponentials, simple proof, approximations and errors. The number and algebra HL looks at: laws of logarithms, complex numbers and their practical applications, matrices and their applications for solving systems of equations, for geometric transformations, and their applications to probability.

The functions SL looks at: creating, fitting and using models with linear, exponential, natural logarithm, cubic and simple trigonometric functions. The functions HL looks at: use of log-log graphs, graph transformations, creating, fitting and using models with further trigonometric, logarithmic, rational, logistic and piecewise functions.

The geometry and trigonometry SL looks at: volume and surface area of 3d solids, right angled and non -right-angled trigonometry including bearings, surface area and volume of composite 3d solids, establishing optimum positions and paths using Voronoi diagrams.

The geometry and trigonometry HL looks at: vector concepts and their applications in kinematics, applications o f adjacency matrices, and tree and cycle algorithms.

The statistics and probability SL looks at: collecting data and using sampling techniques, presenting data in graphical form, measures of central tendency and spread, correlation using Pearson’s pro duct-moment and Spearman’s rank correlation coefficients, regression, calculating probabilities, probability diagrams, the normal distribution, Chi-squared test for independence and goodness of fit. The statistics and probability HL looks at: the binomial and Poisson distributions, designing data collection methods, tests for reliability and validity, hypothesis testing and confidence intervals.

The calculus SL looks at: differentiation including analyzing graphical behavior of functions and optimization , using simple integration and the trapezium/ trapezoidal rule to calculate areas of irregular shapes. The calculus HL looks at: kinematics and practical problems involving rates of change, volumes of revolution, setting up and solving models involving differential equations using numerical and analytic methods, slope fields, coupled and second-order differential equations in context.