Is there a rule for when to use "of" and when not to? For example, why say "English test" and not "test of English"? Also, why "movement of modern art" and not "modern art movement"? Thank you.
First, take a look here, of - Definitions from Dictionary.com. Second, when an adjective is extraposed as in test of English and movement of modern art, it carries less emphasis. In other words, put something in a topic position (e.g., test and movement are in topic position) and it becomes the topic.
Does that help?