Well I am prone to making such mistakes in exam and I am also trying to overcome . So I think I am eligible to answer.
These are the reason why you make mistakes :
1) May be you lack conentration and presence of mind while studying, so you just read passively skiping minute details of the problemproblem.
2) Lack of concentraion and presence of mind during exam.
3) overconfidence : you feel that you know the techinque and you will solve the problem, so you not go through problem minutely .
4) Exam fear : It takes over your mind reducing your ability to focus onon what you are solving in exam .
Solution :
1) Change the way you study . Go through problem step by step highlight what is special in the problem and solutions. Analyse every step of the solution while studying and write special remarks and conclusions.
2) For lack of concentration and presence of mind ..
.
.
Mediate and exercise
3) The only way to overcome your fear is to face it.
But
Face it with preparation and strategy. Prepare for exam from the beginning of semester.Study everyday observing , analysing and learning as we used to do in school , and revise .
If you are prepared well and know you can solve any damn problem , you won't fear of exam.

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