This article should make you rethink your example: http://www.theguardian.com/science/2013/sep/29/chimp-intelli...
It doesn't have to be. But it does vary from person to person (even if non linearly). What would you say affects the intelligence of people with mental retardation?
Second, is there any evidence that the evolutionary history of intelligence was linear? How do we know that there wasn't a binary-like change where one generation didn't have our level of intelligence and the next did, and all humans today are descended from that single change, as opposed to it happening gradually?
The only reason we consider humans to be descended from rather than being apes, is that we don't look at the evolutionary tree from the outside. Biologically it makes no sense.
This question seems kind of confused. But we can say with complete certainty that it's not the case that "one generation didn't have our level of intelligence and the next did" because generations don't happen at any particular time. Imagine your ancestor through the paternal line 30 generations back from you (that is, your father's father's father's... father). If you call him generation 1, then you're generation 31. But other people born in the same year as you, also descended from him, will not all be generation 31. And if you married one of them who was, for the sake of argument, only 28 generations removed from him, your children would be, in this labeling scheme, simultaneously generation 32 and generation 29.
The reason I say your question is confused is that the model where there was a "single change", and all humans today descend from it, requires several generations to take hold (as it gradually increases its population share), but you appear to posit only one.
I'm incredibly not an expert on evolution (it shows I'm sure!), but from a logical point of view that seems like it's feasible at least - whether it's incredibly likely or incredibly unlikely I've no idea.
Because it's very, very rare for evolution to actually work that way.