Decoding The IB Mathematics Internal Assessment

27 Dec 2022

What is the purpose of the IB Internal Assessment

The IB Mathematics Internal Assessment comprises a 12 to 15-page report on an area of Mathematics which is of interest to students. The purpose of the IB Mathematics internal Assessment is to give students the opportunity to apply Mathematics to the real world. 

The primary goal of the IB Programme is to help individuals develop into curious, knowledgeable, communicative, principled, open-minded, compassionate, risk-taking, reflective, and balanced learners. When you attempt the IB Maths Internal Assessment, students can further incorporate their traits as IB learners into their learning. 

Common misconceptions of the IB Mathematics Internal Assessment in Singapore

  • Students should explore Mathematical topics beyond IB Higher Level Mathematics in order to score a 7

This is not true. Unlike IB Mathematics Extended Essay, students doing IB Mathematics Internal Assessment are not required to explore beyond the IB Mathematics curriculum. In fact, some IB students are overly ambitious and write an exploration beyond what they can handle, such as Fourier series and Laplace transformations. Instead of impressing the IB examiner, students ended up with mediocre scores as they were unable to explain the mathematical thinking behind it well. 

  • The IB Mathematics Internal Assessment is an academic paper which involves regurgitating Maths concepts gleaned from Math journals, chapters from textbooks, and online resources such as Math journals and youtube videos.

The IB Maths IA is meant to help students appreciate Mathematics in a real-world context. Students need to apply Mathematics to any data collected or real-world scenarios and show how Mathematics solves problems in that setting. Rehashing information or maths problems from journals or textbooks will not help students to score high marks.

  • The IB Mathematics Internal Assessment requires students to come up with new Mathematical formulae.

Do not worry. Students are not required to produce new maths formulas or theories. It is unrealistic to expect high school students to do that as they are not Maths professors. Students are only required to apply the mathematics they know in real-world contexts.

What are the assessment criteria for the Math IA?

Students are assessed on five criteria; Communication, Mathematical presentation, Personal Engagement, Reflection and use of Mathematics.

Criterion A: Communication 

This criterion assesses the overall organisation and structure of the exploration. A well-organised exploration includes an introduction, a rationale and an aim. Additionally, the rationale explains why this topic was chosen. The rationale is the ‘fun’ part of the IA, as most students use ideas which connect to their childhood. The aim of the exploration shows what the exploration hopes to achieve. The exploration needs a conclusion to summarise the ideas presented.

A thorough investigative approach is developed with the aid of logic and should not be overly complicated. Any argument you make must be presented with efficiency, and all the terminology used should be well defined. Get your peers to review your IA to ensure the concepts utilised will suit the essay. Use simple and concise explanations for any written maths so that anyone reading it would be able to comprehend the argument. If they express any confusion or falter when trying to make sense of your argument, it is a sign that your presentation should be reviewed and amended accordingly.

Criterion B: Mathematical presentation

This criterion assesses how mathematical languages (symbols, terms, and notations, for example) are used in the IA. Individuals need to use the correct terminology, language, and representations (diagrams, formulae, charts, graphs, and tables.) Employing the proper ICT tools like spreadsheets, graphs, and screenshots of graphic display calculators will also be checked. 

Criterion C: Personal engagement

This criterion assesses “ownership of the exploration”. The student is required to show independent thinking and examine mathematical ideas through their own lens. Many of the maths formulae and explanations can be found in textbooks and online resources. By personalising mathematical ideas, students are able to present their own views and analysis.

Criterion D: Reflection 

This criterion assesses a student’s ability to analyse, review, and evaluate the investigation. Reflection is found throughout the investigation, along with its conclusion. It can also be exemplified by taking its limitations or expansions of maths concepts into account. Queries regarding the significance of your lessons and meditations on how they can be extended will then be addressed. 

Criterion E: Use of Mathematics

This criterion assesses how adeptly students utilised maths in their investigation. They should be able to do work that is comparable to the course’s depth and difficulty. The mathematical concepts employed should be of the syllabus or something approximately equivalent. If it doesn’t compare to the course’s contents, you will only receive a maximum of two marks for this criterion.

Maths can be seen as accurate even if there are discrepancies, provided it doesn’t impede the flow of the maths. Optimising mathematical applications will involve the utilisation of difficult maths ideas, finding a different angle to view the problem, and identifying underlying structures that would connect to different mathematical concepts.

How do you structure your IB Maths IA?

Let us show you a template to help you write your Math IA.

Step 1: Research a suitable topic.

This is the most challenging step. Students are required to find a suitable topic with an appropriate level of maths and real-world application. It is not uncommon for students to face countless rejections from their teacher before a Math IA topic finally gets approved.

Spend some time searching for a topic and reading outside of your school textbook. Many students may not have read Math academic journals before. However, it is good to get into the habit of doing so. These academic journals are a rich source of ideas for students. Some of our students obtained many good ideas from these journals and aced their Math Internal Assessment.

Some topics to avoid:

  1. a typical textbook solution 
  2. Topics commonly attempted by previous students (for example, the Monty Hall game, the spread of Covid)

Step 2: Submit a proposal to your teacher

Before commencing your Internal Assessment, submit a detailed proposal to your teacher. In your proposal, you should outline the type of Mathematics formulas and working used. Explain to your teacher how your IA can be applied in the real world.

Step 3: Writing your IA

As soon as your teacher approves your IA, you should start writing! The IB program is like a marathon, and students are inundated with many assignments. Starting early leaves you more time to make amendments or even change your topic if the topic does not work out. 

The best way to write an IA is in the first person’s point of view. This is because personal engagement is one of the criteria for Math IA, and writing in the first person makes it easier for the reader to connect with you.

Most students I know find writing an essay for Math daunting. Many students have not had the experience of writing a Math essay throughout their student life, so they do not know how to get started!

Don’t worry. We’ve got you covered. Through our esteemed IB Maths tuition, we have a step-by-step approach to help you through the Math Internal assessment in a stress-free manner. 

Refer to the table below for a quick overview of the sections to include in your IA.

IB Mathematics Internal Assessment Topic Ideas

For students who are facing a dearth of Math Internal Assessment topic ideas, our IB Maths tutors in Singapore have thought of a list of possible ideas to help you begin.


  • Why this topic? (Rationale and significance)
  • To write an effective introduction, you should make use of keywords that are relevant to your topic. You should also provide a brief overview of your section so that readers can get a better idea about what they will be reading.

  • WHY do you want to investigate this? Because…… (consider the pointers under “personal engagement”)


  • What do you hope to find at the end of this exploration



  • Mathematical ideas are investigated in this section
  • This is where you use suitable Mathematical tools to do your Mathematical calculations
Mathematical Analysis

  • Define key Mathematical terms
  • Use Mathematical language and representation to explain
  • Include graphs, tables and diagrams at appropriate places
  • All diagrams, charts and tables need to be labelled clearly



  • Evaluate your approaches throughout your IA. A common misconception students have is that reflection should be left to the end. This is not true at all! To demonstrate critical thinking, evaluation should be demonstrated throughout the IA.
  • Discuss any limitations and/or extensions
  • Discuss the implications of the results
  • Link to different fields and other areas of Mathematics
  • Recognise and explain patterns where possible
  • Relate mathematical ideas to personal/previous knowledge

  • Show your findings
  • Discuss the results obtained (Are the results realistic/practical?)
  • Generalize and justify the conclusions


Annotated Bibliography:

  • This should be a record of relevant information you have found from books or the internet. It will include correctly formatted references with a brief synopsis of the articles









Some possible ideas for Math IA include:

  • Calculus: Finding the volume or surface area of an odd-shaped object
  • Graph theory: Finding the shortest distance between two cities
  • Differential equations: Tumour growth prediction
  • Statistics: Modelling data using statistical tools
  • Voronoi Diagrams: Finding the best location to open a restaurant
  • Calculus: Topology
  • Trigonometry: Applications to music
  • Statistics: How much to price each game at a school fun fair
  • Permutations and Combinations: Winning at Tic Tac Toe
  • Trigonometry: Dissonance in music
  • Differential equations: Newton’s Law of cooling

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