How to Write a Level 7 IB Maths IA: Structure, Examples & Tips

The IB Mathematics Internal Assessment (IA) is worth 20% of your final IB Maths grade, making it a valuable opportunity to boost your results outside your final exams.

But unlike a typical maths exam, your IA isn't just about finding the correct answer. You need to choose an interesting problem, investigate it using mathematics and clearly explain your thinking.

So, what does a high-scoring IB Maths IA actually look like?

In this guide, we'll break down the IB Maths IA structure, marking criteria and worked examples to help you create a mathematical exploration that targets the highest mark bands.

Table of Content

• What Is the IB Maths Internal Assessment?
• How to Choose a Strong IB Maths IA Topic
• How to Write Each Section
• Understanding the IB Maths IA Marking Criteria

What Is the IB Maths Internal Assessment?

The IB Maths IA, officially called the Mathematical Exploration, is an individual written investigation of a mathematical topic of your choice.

It applies to all four IB Mathematics courses:

• Mathematics: Analysis and Approaches (AA SL and HL)
• Mathematics: Applications and Interpretation (AI SL and HL)

Your exploration is assessed against five criteria:

Key things to know:

• Weighting: 20% of your final IB Mathematics grade.
• Length: Approximately 12–20 pages is suggested by the IB, although this is not a strict page limit.
• Assessment: Marked by your teacher and externally moderated by the IB.
• HL vs SL: Both use the same five criteria, but the expectations for the use of mathematics differ.

Remember, your IA is marked out of 20, not given a separate grade of 7. A strong IA contributes to your overall subject grade alongside your examinations.

1. How to Choose a Strong IB Maths IA Topic

One of the hardest parts of the Maths IA is choosing what to investigate.

The best topics combine three things:

1. Personal interest: Something you're genuinely curious about.
2. Mathematical depth: Enough mathematics to support meaningful exploration.
3. A focused aim: A clear mathematical question you can investigate and answer.

For example:

Weak topic: "The mathematics of basketball."

This is far too broad. It doesn't tell the examiner what you're actually investigating.

Stronger topic:

"How accurately can a quadratic function model the trajectory of a basketball shot, and what does the model suggest about the ball's path through the hoop?"

This is better because it identifies a clear mathematical problem, involves modelling with quadratic functions and provides opportunities for calculations, graphical analysis and reflection.

IB Maths IA Topic Ideas

Need inspiration? Here are some ideas to get you started.

For Maths AA, topics involving algebraic reasoning, calculus, functions or mathematical proofs can work particularly well.

For Maths AI, modelling, statistics, real-world data and appropriate use of technology can provide strong starting points.

However, both courses allow a broad range of mathematical investigations. The most important thing is choosing mathematics appropriate to your course and demonstrating your understanding.

Our tip: Don't choose the most complicated topic you can find. A straightforward investigation with original reasoning, thorough analysis and meaningful reflection can be more successful than advanced mathematics you don't fully understand.

2. IB Maths IA Structure: How to Write Each Section

Unlike the sciences, the Maths IA doesn't follow a rigid experimental-report format.

However, a strong mathematical exploration generally has four main sections:

Introduction and Aim

Your introduction should explain:

• What you're investigating.
• Why you chose the topic.
• Your mathematical aim or research question.
• The approach you intend to use.

Example introduction:

As a basketball player, I've always been interested in how the trajectory of a shot influences whether it reaches the basket. In this exploration, I will investigate whether a quadratic function can accurately model the path of a basketball. By analysing the coordinates of a shot, I aim to develop a mathematical model, determine its maximum height and examine whether the predicted trajectory passes through the hoop.

Why does this work?

The student establishes a clear aim, explains their interest and identifies the mathematics they intend to explore.

Mathematical Exploration and Calculations

This is the most important part of your IA.

You need to demonstrate the mathematics behind your investigation, explain your calculations and interpret your results.

Let's continue with our basketball example.

A quadratic function can be written as:

y = ax² + bx + c

Where:

• x: Horizontal distance travelled by the basketball (m).
• y: Height of the basketball above the ground (m).
• a, b, c: Constants describing the trajectory.

Suppose we obtain the following illustrative measurements.

Using these three points, we can solve for the coefficients and obtain:

y = −0.20x² + 1.21x + 2.00

Now, let's determine the maximum height of the basketball.

For a quadratic function, the x-coordinate of the vertex is:

x = −b / (2a)

Substituting our values:

x = −1.21 / (2 × −0.20) = 3.025 m

Substituting this back into the function gives:

Maximum height ≈ 3.83 m

Therefore, the model predicts that the basketball reaches its maximum height approximately 3.03 metres horizontally from the release point.

But don't stop here!

A strong exploration would go further by comparing predictions with actual measurements, investigating how changes in the model affect the trajectory and considering whether the mathematical assumptions are reasonable.

For instance, the model predicts a height of 3.05 m at a horizontal distance of 5.0 m. Although this matches the standard basketball hoop height, it doesn't automatically guarantee a successful shot. The ball's size, entry angle and position relative to the rim also matter.

Key takeaway: Showing the correct formula isn't enough. Explain why you're using it, what your answer means and how it helps answer your investigation's aim.

Reflection and Discussion

Reflection is one of the most overlooked parts of a Maths IA.

You should evaluate your mathematical approach rather than simply describing your results.

Weak reflection:

The quadratic model worked well and helped me understand basketball trajectories.

Stronger reflection:

Although the quadratic function provides a useful approximation of the basketball's trajectory, the model assumes that the ball travels along a parabolic path. This ignores factors such as air resistance and spin, which may influence the actual trajectory. Additionally, using only three measured points produces an exact quadratic fit to those points, but does not establish whether the model accurately predicts the rest of the shot. Collecting more measurements and comparing residual errors would provide a stronger assessment of its accuracy.

Notice how the stronger example identifies limitations, explains their mathematical significance and suggests ways to improve the model.

Our tip: Don't save all your reflection for the conclusion. Include meaningful observations throughout your exploration, particularly when you make decisions, encounter limitations or refine your mathematical approach.

Conclusion

Your conclusion should return to your original aim and explain what your mathematical investigation revealed.

Example conclusion:

This exploration demonstrated how quadratic functions can be used to approximate the trajectory of a basketball. The model predicted a maximum height of approximately 3.83 m and a height of 3.05 m at the horizontal position of the hoop. However, because the model was constructed using only three points, further measurements are required to assess its predictive accuracy. Extending the investigation to compare multiple shots could reveal how consistent the quadratic model is across different trajectories.

A strong conclusion provides a clear answer, supports it with mathematical findings and recognises the limits of those findings.

3. Understanding the IB Maths IA Marking Criteria

Now that we've covered the structure, how do you maximise your marks?

Criterion A: Presentation (4 Marks)

Your exploration should be coherent, organised and concise.

Make sure your introduction, calculations, graphs, discussion and conclusion follow a logical sequence.

Top tip: Put important graphs and calculations near the paragraphs discussing them rather than sending everything to the appendix.

Criterion B: Mathematical Communication (4 Marks)

Use correct mathematical notation, terminology and representations throughout your investigation.

This means:

• Define important variables.
• Label graph axes and include units where relevant.
• Present equations consistently.
• Explain your mathematical working clearly.

Avoid dumping calculator screenshots into your report without explaining them.

Criterion C: Personal Engagement (3 Marks)

Personal engagement isn't simply writing about your hobbies.

Examiners want evidence that you've taken ownership of the mathematics through independent thinking, creative approaches, personal decisions or original exploration.

For example, collecting your own basketball data and comparing alternative mathematical models demonstrates more engagement than reproducing a ready-made solution from the internet.

Criterion D: Reflection (3 Marks)

Reflect on your mathematical findings and decisions throughout the investigation.

Ask yourself:

• What does this result actually tell me?
• Are my assumptions reasonable?
• How reliable is my model?
• Could another mathematical approach work better?

Strong reflection involves evaluating the mathematics, not just commenting that the investigation was interesting.

Criterion E: Use of Mathematics (6 Marks)

This criterion considers whether your mathematics is relevant, appropriately challenging and correctly understood.

For HL students, there are higher expectations for mathematical sophistication and rigour.

However, using advanced formulas doesn't automatically earn more marks. You must show genuine understanding of the mathematics you apply.

4. Common IB Maths IA Mistakes That Cost Marks

Even a promising topic can lose marks through avoidable mistakes.

1. Choosing a topic that's too broad

A focused investigation with a clear aim is easier to develop into a coherent exploration.

2. Including complicated mathematics you don't understand

Examiners reward mathematical understanding, not just impressive-looking equations.

3. Using technology without explaining the mathematics

Tools such as Desmos, GeoGebra, Excel and graphing calculators can be useful, but you still need to explain what you did and interpret the results.

4. Forgetting personal engagement

Don't simply reproduce a mathematical investigation you found online. Make meaningful decisions and develop your own approach.

5. Describing results instead of reflecting on them

Explain the limitations, implications and reliability of your findings.

6. Including unnecessary calculations

Every calculation should contribute to the aim of your exploration. More pages don't automatically mean more marks.

5. Final IB Maths IA Checklist

Before submitting your mathematical exploration, make sure you can tick off the following:

• My investigation has a clear mathematical aim.
• My chosen topic allows for meaningful mathematical exploration.
• I've explained why I chose my topic and demonstrated independent thinking.
• My mathematical calculations are accurate and clearly explained.
• I've used appropriate graphs, diagrams and mathematical notation.
• My exploration follows a logical structure without unnecessary content.
• I've interpreted results in the context of my investigation.
• I've critically reflected on assumptions, limitations and improvements.
• My conclusion directly addresses my original aim.
• I've referenced any external sources, data and mathematical methods appropriately.

Need Help With Your IB Maths IA?

Struggling to find an interesting Maths IA topic? Unsure whether your mathematics is challenging enough or how to improve your reflection?

At KIS Academics, our experienced IB Maths tutors can help you build confidence in your mathematical skills, understand the IA marking criteria and develop the knowledge needed to complete your own exploration.

Explore KIS Academics IB Maths tutoring and get personalised support to aim for your best possible result!

Frequently Asked Questions About the IB Maths IA

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