Does a non-knowledge based, or knowledge corrected IQ test exist, and what are its results per race? If you google 


  IQ gap race


and open the google images, you will see many diagrams showing the differences.



I went on some IQ test pages, and I noticed that the test includes mathematical questions, that have nothing or less to do, with IQ.

That is:
if your school you went to is bad, you will have less knowledge after leaving it. For example solving a mathematical question formulated in an IQ test. You cannot solve, but others will be able to solve, because they dealt with it in school, and you didn't. But the real IQ is the same.  

So what I am asking is:

does a non-knowledge based, or knowledge corrected IQ test exist, and what are its results per race?
No, such a completely knowledge-free test has not been devised. Fluid intelligence (a component of IQ tests) is probably the closest thing to the claim of being "knowledge-free", but it isn't quite so. As typically measured, e.g. using Raven's progressive matrices one still needs to have some clue what the test is talking about in terms patterns etc. And prior exposure to similar test makes a difference (see Hayes et al. 2015) in test results, i.e. there's a learning effect.

In the US, where most such race-intelligence research is conducted, there's still a racial group difference on fluid intelligence tests (e.g. Raven's) in the usual test settings, although some evidence suggests it depends how the test is interpreted by the takers may matter, e.g. Brown &amp; Day (2006): 


  This study addresses recent criticisms aimed at the interpretation of stereotype threat research and methodological weaknesses of previous studies that have examined race differences on Raven's Advanced Progressive Matrices (APM). African American and White undergraduates completed the APM under three conditions. In two threat conditions, participants received either standard APM instructions (standard threat) or were told that the APM was an IQ test (high threat). In a low threat condition, participants were told that the APM was a set of puzzles and that the researchers wanted their opinions of them. Results supported the stereotype threat interpretation of race differences in cognitive ability test scores. Although African American participants underperformed Whites under both standard and high threat instructions, they performed just as well as Whites did under low threat instructions.


A slightly more recent meta-analysis (Nguyen &amp; Ryan 2008) still found an effect though


  For minorities, moderately explicit stereotype threat-activating cues produced the largest effect, followed by blatant and subtle cues: ds = |.64|, |.41|, and |.22|, respectively; explicit removal strategies enhanced stereotype threat effects compared with subtle strategies: ds = |.80| and |.34|, respectively.


Alas most such meta-analytic research does not isolate just one type of IQ testing.

IQ testing under stereotype threats is still a pretty controversial area of research in itself, see Ziegler (2017) and reply by Nguyen &amp; Ryan.