Can the brain work better in stressful conditions? I was watching a documentary about the brain the other day, BBC's Human Body - Brain Power. It said that the perception power of the brain increases when you are in a tense situation. For example; if you know that you are about to die because your house is on fire, the brain will perceive everything more quickly than normal. In other words, the brain works better when you are under stress or tensed a lot (because brain wants you to survive; this is only in life or death situations of course)

I was wondering if the same thing happens to a student during an exam. Is it good for a student to be tensed a bit while taking an exam? I mean if you are solving a question at home, you usually make a lot of mistakes, but the frequency of those mistakes decreases during an exam.

Is my observation correct? Or does a student need to be completely calm during an exam?
A little stress is good, as it leads to greater psychological arousal, but lots of stress will decrease performance. This is known as the Yerkes–Dodson law, from the famous experiment by Yerkes and Dodson (1908) which related strength of motivational electric shocks to performance; performance increased up to a point and then plummeted.

One more comment about something you said:


  For example; if you know that you are about to die because your house is on fire, the brain will perceive everything more quickly than normal.


People do report subjective time dilation for scary events but quantitative attempts have found no evidence for such, see Stetson et. al. (2007).

References

Stetson, Chess, Matthew P. Fiesta, and David M. Eagleman. "Does time really slow down during a frightening event?." PLoS One 2.12 (2007): e1295.

Yerkes RM, Dodson JD (1908). "The relation of strength of stimulus to rapidity of habit-formation". Journal of Comparative Neurology and Psychology 18: 459–482.