Would the MCAT ever ask a weak pH question that didn't qualify for use with the TBR shortcut? The acid bases chapter didn't have any questions that didn't use the shortcut in the answer key. Is this type of question too time-consuming for the MCAT? What do we do if the shortcut doesn't work? 10^-7 would go in the initial for [H+] from autoionization so ... (x+10e-7)(x) =Ka?
For the MCAT, if you are asked to calculate the pH of a weak base 99.9% of the time, they will provide a weak acid that dissociates only very little. The golden rule is, if it dissociates less than 5% of the original species then it's safe to ignore the amount that dissociates relative to the initial concentration of weak acid. You can assume this is usually the case. This simplification makes the problem significantly easier to solve because we avoid time using the quadratic. It simply boils down to this equation: [H+] = sqrt([HA] x Ka]), and then solving for the pH of it.
We also make this assumption for many other equilibrium problems as well. In particular, scenarios were we are told there are some reactants and some products in a given reaction that is at non-equilibrium conditions, and then asked what those concentrations will be at equilibrium. These too would require you to make an ICE chart and then solve for "x" by plugging in these expressions into the equilibrium expression for that reaction. But again, because this is a timed test, generally, we'll assume that the amount of products produced is very little and this again, simplifies the question.
From a conceptual understanding, if you're looking for some basis as to when to ignore something, look at the equilibrium expression. For instance, weak acids have a Ka value that is generally some value to the power of 10^-6 (for example). If you recall, values under 10^-3 favor reactants. Therefore, if you start with excess reactants (compared to equilibrium), we know some products must be produced to re-establish equilibrium (LeChatleir's Princ), and because it favors reactants (defavors products), very little of the reactants will actually dissociate. The same can be said about most equilibrium expressions under 10^-3 (that is, an increasingly negative exponent).
And one other thing to note about Acid/Base chemistry in general, another thing to watch out for is this common trick. They may give you, let's say 1x10^-8 M HCl and ask you to find the pH. We know strong acids fully dissociate, which means 1x10^-8 H+ will be produced. What is the pH of solution? You would be wrong to say 8.