I'm pretty sure IQ tests aren't supposed to work that way. At least theoretically, they're measuring intelligence, not education.

1) They are a measure of a very specific kind of intelligence: the kind of intelligence required to score high on IQ tests. I score pretty high on IQ tests but I can say without a shadow of a doubt that my intelligence in other areas is, at least as it appears to me, below average.

2) intelligence does have some elasticity. When you think of intelligence has a culmination of pathways/heuristics/low-level-techniques, it’s easy to see how many pathways are self-reinforcing and not easily taught or measured. You can be predisposed to a particular kind of intelligence, and not everything is attainable by everyone, but what we call intelligence is close to what we call talent: seems like an innate quality, but actually reflects long-term hard practice with countless hours dedicated.

Intelligence is a complex interplay of nature and nurture. There is no way to test only the "nature" component, it's akin to unmixing a pot of purple paint to extract the red and blue.

A lot of IQ test questions get easier the more mathematics you have studied.

that is the goal but at the extremes i imagine it fails. imagine you are a chess prodigy that was homeschooled and never had a sit down exam before. don’t know if hikaru fits the description.

IQ tests just measure your ability to complete IQ tests.