IQ tests seem woefully outdated and highly biased at best. As many note, the ability to do well on these tests is greatly increased by practice, as with most testing procedures. The notion that an IQ test is a standalone measure of innate intelligence is not well supported.

Perhaps specific areas could be tested, such as memory - but even with such a basic concept, we know that the ability to memorize a long string of numbers is a highly trainable skill. If we go to 'higher level' mental processes, such as pattern recognition, symbolic interpretation, analytical capabilities (i.e. higher maths), and creative capabilities (inventiveness), again we see that these abilities are highly trainable.

The only real way to sort this out would be to apply the same educational program to a large cohort of individuals, over the course of at least a year, involving intensive one-on-one tutoring, and administer the prospective IQ test both before and after this process takes place. This has come up before and such a study has never been done to my knowledge, nor has anyone ever pointed one out.