MHB Help Needed: Preparing for End-of-Semester Math Exam

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Hey guys.
I am not sure if thread abides by the rules, I understand we're a mathhelpboard so feel free to remove the thread if it violates anything.

I am looking for practice exams with solutions in preparation for an upcoming end of semester exam in 30 days and was hoping someone could help me out?

Our math faculty only uploads 2 exams, 1 of which doesn't get uploaded with any solutions.
I learn best by doing a variety of questions and that isn't so much available to me, as the exams are harder than textbook questions.

So if anyone could help me out with exams with worked solutions, that would be fantastic.

I have attached a copy of a previous exam for you to get the gist of what sort of work we do. (I literally cannot do any questions so far :( surely this is considered a difficult exam?)

Thanks in advance for any help
 

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For the first question, namely compute $i^{1+i}$, how were powers of complex numbers by complex exponent defined? What do you know about complex logarithm?
 
I find it difficult to believe that you can do nothing from this exam. Did you attend any lectures or take any notes? There is no reason why you can't study with your notes next to you. It's better to at least ATTEMPT the problems BEFORE saying you can't do any of it...
 
A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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