How can I prepare for an introductory real analysis exam? I am taking an introductory real analysis this year and I have an exam in a week time. Apart from knowing the materials, how can I prepare myself for unseen proof questions? no matter how many problems I do to exercise my proof writing there will certainly be problems in the exam that I have not seen before. How can I prepare myself for these type of problems? On the other hand, when I have a proof problem to solve for homework, it usually takes me at least two or three days to figure it out so I can not certainly spend that much time when I am doing my exam.
 A: It always depends on where you are taking the test. The country, the university, even the professor holding the class can make a big difference.
Thus two tips: 
1) Find out how the exams were done in previous years. Find students that took the course with the same professor before you and talk to them. There might even be old exam sheets flying around, try to ask your seniors.
2) Revisit your homework problems. The exam questions are often similar (but shorter) and if you really understood the homework problems and the ideas to the solution, that will help.
Also don't worry that it takes you a few days in the homeworks: Homeworks are designed (normally) for a whole week, exam questions for a few hours - so as long as you figured the homework problems out yourself in the end, that is great. :)
A: The proof problems you get on exams are easier than the ones you usually get as homework. Additionally, you can prepare by just doing proofs you don't know yet. By doing so, you get familiar with thinking about new proofs. That's all you can do.
A: I'd also recommending brainstorming questions: - 


*

*Vary the past problems 

*Ask questions relating to existence, can you find counterexamples? 

*Ensure you can easily discuss and explain all concepts without reference. 

