Not being able to pay attention does not mean that you don't know what is happening around you...
I took an IQ test at the age of 6 to test my condition, ADHD. Well it turns out my mental age was 24, so that would mean I came out with an IQ of 144 at such an early age. I'm not necessarily one to believe in the fact that IQ can increase, but if it really does, I'm sure it has increased over the 10 more years I have lived. Despite the ADHD, it has little affect on me at all, and I have somewhat excelled from previous bumps along the way.