12 tips when facing a Linear Algebra exam

When it comes the time to face an exam, we all want to get good results, and although some people enjoy that moment, the reality is that for most it causes a great deal of tension.

From my personal experiences, first as a student and then as a professor, I would like to share a list of tips that can help you improve your results when you face a demanding and laborious exam, such as those for Linear Algebra, although in general, these tips are valid for any exam.

The tips are mainly oriented to help you optimize your time, keep a focused and positive mind, and distribute your energy more efficiently.

In Linear Algebra, it is essential that besides understanding the subject, you need to solve some exercises from each topic before the exam; it is not enough to see how the teacher solves them on the blackboard or to study exercises solved in a book, and think you already know how to do it, you should try to solve them and train the different calculation methods. It is also important that you learn the basic concepts and not just the resolution methods; this will put you in a favorable position when facing problems that you have not seen before, or those with a theoretical approach. With these recommendations to consider, now let's go to the tips.

The tips:

1. Maintain a state of relaxation before and during the exam. Maintaining a state of tension is counterproductive, learn to enjoy exams, seeing it as a mean to test your knowledge, instead of an instrument to get a mark. Always trust yourself, you must feel that you have the mind of a genius to unlock all your potential.

2. Read the whole exam first, analyze the level of difficulty of each exercise and the associated score (if it is shown on the test). This will allow you to identify the easiest questions and estimate the time you will require for each exercise, so that you can complete the entire exam in time.

3. The exam questions order does not have to match the order you will follow to solve it. Start with the exercises that you consider easier, which you can do faster and with less effort. If you start with the most difficult ones, you could use up all your time and your energy.

4. Use the method that reduces the risk of making mistakes, except when a specific one is required. If the method you select involves an excessive amount of time, then you should evaluate if you will have time to solve the other problems, otherwise, it will be better to use another method.

5. Work in an organized way and make sure to enumerate each additional sheet. Write the question number before every answer, and, if applicable, specify that the answer continues on the next sheet. This way you will avoid that the professor ignores any sheet by mistake and you get a lower score than you deserve. Remember that the professor must grade all the student exams, and not just yours, which is an exhausting task.

6. Pay close attention when copying data from one sheet to another, as it is very common to transcribe an incorrect number or place it in the wrong position within a matrix. Transcription errors are one of the most frequent when grading Linear Algebra exams.

7. Leave the checks for the end, when they are not mandatory. Many exercises have a way of checking whether the final solution is correct or not. If the check is time-consuming or can reduce your energy, leave it to the end. Many professors, myself included, grade based not only on the result, but also on the development of the answer.

8. Cross out what you do not want to be considered, erasing consumes much more time, and sometimes you will notice that the solution you rejected was the correct one, and in that case, you can reproduce more quickly what you had discarded.

9. Reward yourself mentally after completing each question, make positive statements about your good performance. That will put you in a better position to face the next question.

10. If you feel you are stuck in the solution of a problem, move on to another exercise and return to this one later, many times you just need to stop thinking for a few minutes about a problem, so that your mind finds the solution.

11. Check you answered all questions. Run through each question, locating where the corresponding answer is. This seems trivial, but it is very common to find unanswered questions carelessly, keep in mind that our mind gets tired, and we lose the ability to remember clearly.

12. If you finish before the time limit, check the answers, starting with those questions with higher probability of error. If there is no way to check the answer, analyze if there is an alternative way to solve the problem, and use it as a checking method.

When you finish the exam, relax your mind completely, it does not make sense to think about what you did not do correctly or what you could do differently. If when you get the mark you are not satisfied with your performance, that will be an indicator that you will have to work harder next time.

I hope you remember these tips when you have to face an exam again. If you have found them useful or you have other tips, which you would like to share, we would love to read them in the Comments section.