You will need to remember the oxidation number of oxygen & sulfur [-2], all the halides [-1], know which elements are Group 1 & their ox# [+1] and which are Group 2 [+2] - know them all the way down to Cesium and Barium. This is to do the redox questions, some of which are just "what is the charge of sulfur in NaHSO4 ??" [it's +6] without any reaction done to it. Might have to know a few group 3s: boron, aluminum, scandium.
It's helpful for organic questions to know that C & Si are gp4; N, P, and As are gp5 and so on. As they say, no periodic table or charges are given, no formulas either.