This really looks like a final exam. I think I haven't given you enough answers to pass. Based on the level of knowledge you have demonstrated, you need to fail this exam and back up to retake more fundamentals.
Good luck with your future endeavors. When you are ready to study and learn smoe mathematics, feel free to bring a few specific problem and show your best work. If you just want to memorize a few techniques and slide through an exam, you DO know there's an end to that, right? It's called utter and dismal failure.