1. crack the books (idiom) = read or study
E.g: You’d better start cracking the books if you want to pass the test.
2. rack your brain(s) (idiom) = try very hard to remember or think of sth
E.g: We racked our brains but we couldn’t come up with a solution.
3. draw a blank (idiom) = get no response or result
E.g: So far, the police investigation has drawn a blank.
4. keep/put your nose to the grindstone (idiom) = work very hard for a long time
E.g: She kept her nose to the grindstone all year and got the exam results she wanted.
5. eager beaver (idiom) = someone who is extremely enthusiastic and enjoys working extremely hard
E.g: When she first started working she was a real eager beaver.
6. put your thinking cap on (idiom) = try to solve a problem by thinking about it
E.g: I need some interesting suggestion so if you can put your thing cap on I’d be grateful.
7. crash course = a course that teaches you a lot of basic facts in a very short time
E.g: I did/took a crash course in French before my trip to Paris.
8. bookworm (n) = a person who reads a lot
E.g: She was always a bookworm when she was a kid.