You can pause the game at any time and google the answers if you wish so this isn't too hard.
There are 6 category types in the game:
Sports & Leisure
Arts & Literature
Science & Nature
Each correct answer in 'Grab Bag' count as correct answers so you can quickly get some categories done in grab bag.
The easiest way to keep track of how many questions you've answered correctly in each category is to view your achievement progress for the achievements for answering 50 questions correctly in each category using the achievement app/TA.