How can you memorize periodic table charges?
Understand the elemental families on the Periodic Table.
For example, all Noble Gases have 0 charges - their stable and will not react under normal circumstances, or Alkali Metals, which all have a 1+ charge.
By understanding the family of each element (or certain elements) and where it belongs, you can follow the trend and determine each element's charge (in that family).
For elements with multiple charges, know the major ones - minor ones are not often tested. Major ones may include: chromium, iron, copper, tin, gold, and/or mercury. Iron and copper (and maybe gold) are probably the most important.
Certain elements besides the Noble Gases have 0 charges. These include boron, carbon, and silicon. These are non-metals and therefore, will share their electrons.
Teachers normally use common elements on assessments. Very rarely would you see Neodymium or Meitnerium on it.
In addition, most assessors often hand out a Periodic Table because it is unreasonable for a student to not have one. HOWEVER, assessors may quiz students on specific/basic chemistry knowledge.
Hope this helps :)