Take another look at the sentence:
Rapping the pencil on the edge of the desk, the fourth cause of the French
Revolution would not come to mind.
Rapping the pencil on the edge of the desk, a participle phrase, has no target in the sentence to describe. When a modifier has no word to describe, it is dangling.
To fix the problem, you should revise the sentence like this: Rapping the pencil on the edge of the desk, Rodney could not remember the fourth cause of the French Revolution. Adding Rodney to the sentence lets the reader know who is having trouble with the exam.