IA ideas library
Maths IA modelling ideas: fit a function to something real
Modelling is the most common kind of Maths IA, and for good reason: you collect or find data, propose a function that might describe it, fit the function, and then test how well it works. Done well, it hits every criterion — a clear aim, precise notation, real decisions you made, honest reflection on where the model breaks, and mathematics that is used rather than just shown.
The ideas below are chosen so that the modelling is genuinely interesting: there is more than one sensible model, the data is either easy to collect yourself or available from a trustworthy source, and there is a natural way to test the model on data you did not use to build it.
Modelling with functions ideas (13)
- Is a hanging chain a parabola? Catenary versus quadratic modelsAA SLAA HLAI SLAI HLSolid
- Which function best describes the arch of a famous bridge?AA SLAI SLAccessible
- How long does a bottle take to drain? Testing Torricelli's lawAA SLAA HLAI SLAI HLSolid
- Does my phone battery really drain in a straight line?AI SLAI HLAA SLAccessible
- How far does a bouncing ball really travel?AA SLAI SLAA HLAI HLAccessible
- Why do stopping distances grow so fast? Modelling the Highway Code tableAA SLAI SLAccessible
- Exponential or logistic? Modelling my country's populationAA SLAA HLAI SLAI HLSolid
- Is Moore's law still true?AA SLAI SLAA HLAI HLAccessible
- Does a pendulum's period really depend on the square root of its length?AA SLAI SLAA HLAI HLAccessible
- Does light really follow an inverse-square law?AA SLAI SLAccessible
- How many times can you fold a sheet of paper?AA SLAA HLSolid
- Can you predict a tree's height from its trunk?AI SLAI HLAA SLSolid
- Which mug keeps tea hot longest? Newton's law of cooling, comparedAA SLAA HLAI SLAI HLAccessible
Also relevant (39)
- Why aren't drinks cans the optimal shape?AA SLAI SLAA HLAI HLAccessible
- What is the volume of an egg?AA HLAI HLAA SLSolid
- Where should the 125 ml line go on a glass?AA HLAI HLSolid
- Designing a smooth roller-coaster drop with piecewise functionsAA SLAA HLAI SLAI HLAmbitious
- How fast is a sprinter at each moment? Differentiating 100 m splitsAA SLAA HLAI SLAI HLSolid
- Linear or quadratic drag? Testing air resistance with falling coffee filtersAA HLAI HLSolid
- How much of cycling effort goes on air resistance? A coast-down testAA HLAI HLAmbitious
- How does bread dough rise? A logistic model in the kitchenAA SLAA HLAI SLAI HLAccessible
- Does money buy a longer life? GDP and life expectancyAI SLAI HLAA SLAA HLSolid
- How often do big earthquakes happen? The Gutenberg–Richter lawAI SLAI HLAA SLAA HLSolid
- Radioactive decay with dice: does chance produce an exponential curve?AA SLAI SLAA HLAI HLAccessible
- What is the chance of hitting every green light on my route?AI SLAI HLAA SLAA HLAccessible
- Modelling the sun's height from a stick's shadowAA SLAI SLAA HLAI HLAccessible
- Is a satellite dish really a parabola, and where is its focus?AA SLAA HLSolid
- Should I lease or buy my first car?AI SLAI HLSolid
- Will I ever repay my student loan?AI SLAI HLAA SLSolid
- How fast do cars lose value? Modelling depreciation from listingsAI SLAI HLAA SLAccessible
- 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
- Will women's Olympic times ever match men's?AI SLAI HLAA SLAA HLSolid
- Modelling the Keeling curve: trend plus seasonsAA SLAA HLAI SLAI HLSolid
- When might the Arctic be nearly ice-free in September?AA SLAA HLAI SLAI HLSolid
- How strongly is global temperature linked to ln(CO₂)?AI SLAI HLAA SLAA HLAmbitious
- Is solar power growing logistically?AA SLAA HLAI SLAI HLSolid
- Is deforestation in [a country] slowing down?AI SLAI HLAA SLAccessible
- Can a sum of sine waves predict the tides?AA SLAA HLAI SLAI HLSolid
- How does the shape of the daylight curve change with latitude?AA SLAI SLAA HLAI HLAccessible
- 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
- Modelling bacterial growth in the biology labAA SLAA HLAI SLAI HLSolid
- How fast did COVID-19 spread at the start? Comparing doubling timesAA SLAA HLAI SLAI HLSolid
- How do doctors estimate your skin area? Comparing body-surface-area formulasAA SLAA HLAI SLAI HLSolid
- How many primes are there below n? Testing the prime number theoremAA SLAA HLAI SLSolid
- How long is a coastline? Measuring fractal dimensionAA SLAA HLAI SLAI HLSolid
- Why do a flute and a violin sound different on the same note?AA SLAA HLAI SLAI HLSolid
- Why do sunflower seeds form spirals? The golden angleAA SLAA HLAI SLAI HLSolid
- Why are camera f-stops 1.4, 2, 2.8, 4, 5.6?AA SLAI SLAA HLAI HLAccessible
Frequently asked questions
What makes a modelling IA score well?
Comparing at least two plausible models, justifying each choice from the context, measuring how well each fits (residuals, R² or sum of squared errors), and testing the chosen model on data you held back. A single regression line with an R² value rarely gets beyond the middle mark bands for Use of mathematics.
Can I use technology to fit the model?
Yes. Desmos, GeoGebra or your GDC can do the fitting, but you must explain what the technology is doing — for example, that least-squares regression minimises the sum of the squared vertical distances — and interpret the parameters it returns.
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