Some of the IA topics for HL Math in calculus can be optimization of area/volume or a hard optimization problem, the Riemann rearrangement theorem, the Monty Hall problem, Motion of a projectile, etc.

Some of the IA topics for HL Chemistry in Atomic structure can be investigating fluorescence for instance. However, this topic is quite narrow since investigating atomic structure is majorly done on a microscopic level. Therefore, experiments cannot be performed in a school laboratory.