Maths quiz

It was not that difficult. Basically it was a test of speed plus understanding and applying the concepts. However, it is inevitable that you might not remember that formula or theorem at the crucial moment. What makes you feel even more awful is that when you managed to figure it out, time's up. I was quite sure that there was one question which I must have made a careless mistake but method wise it was ok. Let's see what the result will be next week...