Standard tests of scholarship (including IQ tests) typically tap linguistic and logical-mathematical intelligences. In fact, students who are strong in these intelligences are likely to do well on tests, and in school. As long as they stay in school, they will think they are smart!
We now know that at the extremes of abilities, linguistic and logical-mathematical intelligence are quite distinct.
In other words, having high linguistic intelligence does not predict high logical mathematical intelligence or vice versa.
As this article points out, it is very important not to confound these two forms of intelligence. Accordingly, tests of mathematical intelligence are not reliable if they require linguistic sophistication.
If we feel the need to test for individual intelligences, we should make sure that we do so in as ‘pure’ a form as possible.