A useful IA idea has to fit the exact course and level. Math AA SL needs focused modelling and clean optimisation. Math AA HL needs richer derivation, stronger comparison and deeper functions. Physics SL needs a controlled experiment with clear uncertainty. Physics HL needs stronger theory, graph transformation and a sharper model test.
This page is now a focused IA hub based on the supplied guide. Pick the course you are writing for, then use the deeper article to choose an idea, sketch a diagram, identify the IB topics, and plan the variables before you ask your teacher for approval.
Before using any idea: change the research question, collect your own data, and follow your current subject guide, teacher instructions and school safety rules.