How to Choose a Winning IB HL IA Topic
- James Quarrington
- Jun 10
- 4 min read
✅ Need help planning, structuring, or refining your IA? Work with me to get expert feedback and support.
Choosing the right topic for your IB Maths Internal Assessment (IA) can feel overwhelming — especially at Higher Level (HL) where you are expected to demonstrate rigour and sophistication in your Mathematics. It's really important to choose an original topic which is personal to you, written at the right level and also manageable!
You don't need to reinvent the wheel. It is however very important that you write a focused question, showing clear mathematical methods, and genuine interest in what you're exploring.
I’ll guide you through how to choose a winning IA topic, with examples from three of the most successful IA styles from my past students (shared with their permission), all who scored 16 or higher on their IA:
📈 Mathematical Modelling
🔁 Volumes of Revolution
🔗 Graph Theory
What Makes a Great IA?
Referring to the IB assessment criteria, a high-scoring IA shows:
✅ Clear personal engagement
✅ Sophisticated mathematical techniques
✅ Logical structure and well-communicated reasoning
✅ Reflection on limitations and validity
If your topic is mathematically rich and personally meaningful — and you explore it well — you're already on the right track.
Next, lets look at some past IAs. However, here is an important disclaimer:
These examples are for learning and inspiration only.The IB uses Turnitin and other plagiarism-detection software.If your IA is found to be copied, you will fail the entire IB Diploma. Use these exemplars to: 1. See what top-level mathematical reasoning looks like 2. Understand structure and flow 3. Get inspired to make your own IA unique and meaningful
Modelling IA Topic Ideas
Mathematical modelling allows you to take real-world situations and apply mathematical functions to describe or predict behaviour. These topics often involve exponential, logistic, or polynomial models and can score highly when evaluated properly. The two highest IA's my students have ever achieved were written on modelling.
Student Example: Modelling the Wolf Population in Yellowstone (18/20)
This IA used predator-prey differential equations to model the reintroduction of wolves into Yellowstone National Park. The student applied real data, examined limitations, and reflected on the assumptions in the model — all of which helped meet top-band criteria.
Student Example: Modelling the Growth of Cancer Cells (19/20)
Using published biological data, this IA compared exponential and logistic models to describe tumour cell growth. They also investigated and explained a method that scientists currently use (beyond the scope of the course). The student discussed the real-world implications and evaluated the strengths and limitations of each function, scoring near-perfect marks.
More Modelling Ideas:
Spread of a disease
Population growth in different countries
Rate of caffeine decay in the body
Modelling traffic flow at a busy intersection
Volumes of Revolution IA Topic Ideas
For students confident with calculus, volumes of revolution offer a clear structure and visually engaging output. The key to success here is combining technical precision with real-world relevance.
Student Example: Calculating the Volume of a Sculpture (16/20)
This IA involved photographing a sculpture, fitting functions to its profile, and rotating those curves around an axis to estimate its volume. The student discussed the accuracy of their model, how well the mathematics captured the form, and reflected on possible improvements.
More Volume IA Ideas:
Comparing the volume of different packaging (e.g. bottles vs cans)
Modelling and rotating the profile of a wine glass or vase
Designing a container with maximum volume and minimum surface area
Analysing the volume of objects from art, design, or architecture
Graph Theory IA Topic Ideas
Graph theory is an underused area in IB Maths — which makes it a great opportunity to stand out. It's ideal for students interested in networks, optimisation, and discrete mathematics.
Student Example: Finding the Optimum Walking Route Around a Zoo (16/20)
This IA modelled the zoo layout as a network of vertices and edges, applying algorithms such as Dijkstra’s and the Travelling Salesperson Problem to find the most efficient walking route. The student considered real-world constraints like one-way paths and exhibit order — and reflected on the strengths of the mathematical approach.
More Graph Theory Ideas:
Optimising a school timetable using graph colouring
Modelling transportation networks (bus, train, or subway)
Analyzing social networks or friend groups
Minimising travel time between delivery locations or local landmarks
The best IAs are honest, focused, and clearly explained.
Final Tips for Choosing Your IA Topic
Start with something that genuinely interests you
Make sure the maths fits the topic naturally
Choose depth over breadth — quality over quantity
Reflect on your process, not just your final answer
You don’t need a revolutionary topic — you need clear thinking, solid maths, and a personal connection to what you’re doing.
🔧 Need Help With Your IA?
If you're struggling to find a topic, structure your ideas, or polish your final draft — I can help. I offer personalised 1:1 support for IB students at every stage of the IA journey.
Website: www.mrqmaths.com📩 |Contact: www.mrqmaths.com/contact YouTube: @mrqmaths Instagram: @mr.qmaths Facebook: Mr Q Maths LinkedIn: James Quarrington
Note: All IAs are shared with the permission of the original author for educational and inspirational purposes only. They must not be copied or submitted as original work.