Intelligence is the ability to solve entirely new problems.
Being able to apply a formula has little to do with such capacity.
Being able to derive a new formula is far more important.
Many IQ tests, can be studied for, and they have thus lost their capacity
to test intelligence. Increasingly, they only test memory.
A good test would be to place the person in a group of people that use
an entirely unknown language, and then see how long it takes them
to be able to communicate effectively.
Or : create an entirely original computer game, that has never been seen before.
Or : write a novel about your entire life.