IA ideas library
Sports Maths IA ideas: from penalty kicks to world records
Sport is one of the easiest places to show genuine personal engagement: you know the game, you can collect your own data, and there are huge public databases of results. The challenge is finding a question with real mathematics in it, not just a table of averages.
These ideas cover modelling (projectiles, world-record progressions), statistics (home advantage, streaks), probability (scoring systems) and optimisation (angles, racing lines).
Sport ideas (10)
- What is the best angle to shoot a free throw?AA SLAA HLAI SLAI HLSolid
- Why don't long jumpers take off at 45°?AA SLAA HLAI SLAI HLSolid
- Is there a limit to how fast humans can run 100 m?AA SLAA HLAI SLAI HLSolid
- When should a Formula 1 driver pit? Modelling tyre degradationAA SLAI SLAA HLAI HLAmbitious
- Where should a winger shoot from? Maximising the angle to goalAA SLAA HLAI SLAI HLSolid
- Are cricket batting scores geometrically distributed?AI SLAI HLAA HLAA SLSolid
- Can a simple rating system predict football results?AI SLAI HLAA HLAmbitious
- Will women's Olympic times ever match men's?AI SLAI HLAA SLAA HLSolid
- Where should I aim on a dartboard?AI SLAI HLAA HLAmbitious
- Where should a pool ball hit the cushion? The geometry of bank shotsAA SLAI SLAccessible
Also relevant (16)
- How far does a bouncing ball really travel?AA SLAI SLAA HLAI HLAccessible
- Designing a smooth roller-coaster drop with piecewise functionsAA SLAA HLAI SLAI HLAmbitious
- The lifeguard problem: what is the fastest route to a swimmer?AA SLAA HLAI SLAI HLSolid
- How fast is a sprinter at each moment? Differentiating 100 m splitsAA SLAA HLAI SLAI HLSolid
- How long does a skydiver take to reach terminal velocity?AA HLAI HLAmbitious
- How much of cycling effort goes on air resistance? A coast-down testAA HLAI HLAmbitious
- Is home advantage in football disappearing?AI SLAI HLAA SLAA HLAccessible
- Do left-handed tennis players have an advantage?AI SLAI HLAA HLSolid
- Are elite footballers more likely to be born early in the selection year?AI SLAI HLAA SLAA HLAccessible
- Are NBA players getting taller?AI SLAI HLAA SLAA HLAccessible
- How much does a small edge on each point matter in tennis?AA SLAA HLAI SLAI HLSolid
- Is a penalty shoot-out fair to the team that shoots second?AA SLAA HLAI SLAI HLSolid
- Is the “hot hand” real? Streaks in my free throwsAI SLAI HLAA SLAA HLSolid
- How fast does my heart rate recover after exercise?AA SLAI SLAA HLAI HLAccessible
- Is BMI's “height squared” right? Evidence from OlympiansAI SLAI HLAA SLAA HLSolid
- Can height predict lung capacity?AI SLAI HLAA SLAccessible
Frequently asked questions
Is a sports IA taken seriously by examiners?
Yes — the context does not matter, the mathematics and the thinking do. Many excellent IAs are about sport because the student cares about the answer.
Where can I find sports data?
Football-Data.co.uk and FBref for football, Basketball Reference for the NBA, Statsguru for cricket, Jolpica-F1 for Formula 1, Olympedia and World Athletics for athletics, and Jeff Sackmann's repositories for tennis.
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