Unique IB Maths IA Ideas (that aren't overdone!)

We know just how difficult it is to come up with mathematical investigation ideas so we have done the hard work and compiled a list of 20 ideas that haven't already been done way too times. We've even included the mathematical concepts to explore!

Maths AI and Maths AA Ideas for the Internal Assessment:

1. Optimizing Food Delivery Routes

Question: How can mathematical optimization minimize delivery times and costs for food delivery services like Uber Eats or DoorDash?

Mathematics Involved: Graph theory, Dijkstra’s algorithm, optimization.

2. Predicting Viral Trends on Social Media

Question: Can mathematical models predict the likelihood of a post going viral on platforms like TikTok or Instagram?

Mathematics Involved: Exponential functions, statistics, probability, logistic regression.

3. Sports Performance Analysis

Question: How can mathematics improve a soccer/football player’s penalty shoot out percentage?

Mathematics Involved: Projectile motion, calculus, probability, optimization.

4. Carnival Basketball Shooting Game

Question: How do modifications (e.g. smaller rims, higher hoops) impact difficulty in carnival basketball shooting games?

Mathematics Involved: Geometry, Trigonometry, Projectile Motion

5. Analyzing the Mathematics of Voting Systems

Question: Which voting system is the fairest in terms of representation?

Mathematics Involved: Game theory, probability, statistical analysis.

6. Flight Path Optimization

Question: How can airlines minimize fuel consumption through mathematical modeling?

Mathematics Involved: Calculus, optimization, linear programming

7. Airline booking Optimisation

Question: How can mathematical models optimize airline booking systems to maximize profits while accounting for cancellations, no-shows, and overbooking

Mathematics Involved: Probability, optimisation

8. Urban Noise Pollution

Question: How can urban noise pollution be correlated with distance from the CBD?

Mathematics Involved: Statistics and correlations

9. Gender Representation in Media

Question: How does the representation of male and female characters vary across genres over the past decade?

Mathematics Involved: Chi-square tests, correlation, proportions

10. Sports Team Performance

Question: Do higher budgets lead to better team performance in sports leagues?

Mathematics Involved: Regression analysis, correlation, residuals.

11. Video Game Reaction Times

Question: How do reaction times affect performance in competitive gaming?

Mathematics Involved: Probability distributions, mean and standard deviation, t-tests.

12. Geographical Areas

Question: What is the area of land or a specific region between two geographic or economic curves such?

Mathematics Involved: Integration to find the area between curves

13. Optimisation of shapes and volumes

Question: What is the best shape for a water tank to minimize surface area while maximizing capacity?

Mathematics Involved: Calculus for optimization. Volumes of revolution for different shapes (e.g., cylindrical, spherical).

14. Income Inequality

Question: How can the Lorenz curve and Gini coefficient be used to study income inequality?

Mathematics Involved:

Integration to calculate the area under the Lorenz curve.

Derivatives to analyze changes in inequality over time.

15. Spotify Playlists

Question: What factors predict the popularity of songs in playlists?

Mathematics Involved: Statistical analysis, correlation, probability

16. Fairness in Board Games

Question: Is Monopoly truly fair, or do certain properties and strategies give players an advantage?

Mathematics Involved: Probability, game theory, statistical simulations.

17. School Grades

Question: How do school grades follow a normal distribution, and what factors influence outliers?

Mathematics Involved: Normal distribution, hypothesis testing, regression analysis.

18. Loan Repayments

Question: How can sequences model savings accounts or loan repayments to find the most value for money deal?

Mathematics Involved: Series and Sequences, financial mathematics, annuities

19. Volume and Surface Area of Revolution

Question: How can integration be used to calculate the volume and surface area of a historical artefact e.g. vase?

Mathematics Involved: Integration, volumes of revolution.

20. Medical Testing Accuracy

Question: How can the reliability of medical tests be determined by considering sensitivity, specificity and prevalence?

Mathematics involved: Conditional probability

Remember, the Maths IA can actually be interesting! Choose an investigation that you know you will engage with, whether that be because of the topics involved or even if you just want to practice a difficult concept.

General Tips:

• Relate to Syllabus Topics: Focus on topics directly linked to the syllabus (functions, calculus, statistics, etc.).

• Depth Over Breadth: Aim to explore a specific aspect of a topic deeply rather than covering too much.

• Data Availability: Confirm that you can find or generate sufficient data for analysis.

• Engage with Real-Life Applications: Many syllabus topics (e.g., trigonometry, probability, statistics) naturally lend themselves to practical exploration.

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