I doubt I'd be surprised: my mother is a retired school psychologist, and her trainees used me as a guinea pig for lots of different IQ tests over the years. I've pretty much seen it all.
With respect to the content of IQ tests, I tend to avoid the term "biased", as cultural knowledge is relevant in many real-life contexts, but the best IQ tests focus on exactly the kinds of questions described in the OP: math, logic, shapes, etc.
There’s a long history of discussion about what exactly intelligence is, how whatever it is is measured, and why some social groups have statistically higher scores than others. Here’s an easy place to start looking into it:
The Wikipedia article raganwald kindly linked to has an archived set of talk pages that go on almost endlessly, as the article has long been the subject of edit-warring. That article and related pages have been the subject of an Arbitration Committee case (opened at about the time I became a wikipedian, by coincidence)
with ongoing administrative sanctions. In other words, I'm not sure if the article is currently in good enough shape to recommend. The Wikipedia user bibliography "Intelligence Citations"
I think you'd be surprised just how biased some of them are, and how reliant on cultural knowledge.