No, I don't think you need to know the exact equations and numbers to calculate the various changes in an acid base disorder.
It's important however that you know (by heart) the normal values of the PH, CO2, and Bicarb so that then you can judge what is the problem.
See the PH first then look at the CO2 then see the bicarb.
Do practice questions as much as you can. This is a very high yield topic.
There's one exception (I think) which is the Winter's formula that you need to memorize.
Expected pCO2 = 1.5 X HCO3- + 8
this is to measure the adequacy of respiratory compensation in cases of metabolic acidosis (specially in DKA cases).
Patient with DKA and his bicarb is only 8, then his pCO2 should be 20 if it's higher than that then he's not adequately compensating (respiratory fatigue or ensuing coma) then you need to think of assisting his ventilation.