I believe that the exams in question are both conducted within the same semester. Indeed, in the link Viviane provided for FSM, this is clear. This would make the first round of assessment the ‘mid-semester examinations’ and the second assessment the ‘end of semester examinations’.

E.g. http://www.sau.uts.edu.au/assessment/exams/central.html

However, you didn’t specify in your question which English variant you need. The information above is valid for Australia. For the US:

‘midterm examination’

http://en.wikipedia.org/wiki/Midterm_exam

I’m less clear on the UK, but found some interesting references. The University of Nottingham, for example, states: “end of semester examinations, and any other examinations arranged during the course”.

http://www.nottingham.ac.uk/academicservices/qualitymanual/a...

Hhhm. I found a blog discussing the differences between the US and UK, with the author saying that it’s not common to have exams during the semester in the UK but that they are called ‘coursework tests’ in his/her experience.

http://separatedbyacommonlanguage.blogspot.com.br/2009/07/mi...

Personally, I think ‘mid-semester exam’ would be understood by a UK audience as well.


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Note added at 16 hrs (2012-10-19 20:54:52 GMT)
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Regarding the weight of midterms/mid-semester exams, each university, and even faculty and school, has different policies. For example:

Ryerson University:

“2.2.1 Each course must have at least two, independent assessments per semester in the evaluation scheme. Where appropriate, these should be of different types. An individual assessment may not be worth more than 70% of a student's final grade.”

…

“Different types of courses (e.g. lectures, labs, studios) have different types and number of assessments, ranging from a number of smaller assessments spread over the semester to a single mid-term test and a final exam.”

http://www.ryerson.ca/studentguide/AcademicMatters15.html

The weight of each individual assessment tool is usually specified for individual subjects, rather than for a university or degree as a whole.

An economics subject at the University of Maryland:

“Grading: The final grade will be based on five problem sets (each worth 5% of your final
course grade except for the lowest one), quizzes and class-participation (worth 10% of
your final grade), a midterm exam (worth 30% of your final course grade) and a
cumulative final exam (worth 40% of your final course grade).”

http://econweb.umd.edu/~torul/econ305syllabus.pdf

A health sciences subject at the University of Western Ontario:

“Your grade in this course is based on two midterm tests and a final exam. Each midterm test is worth 25 percent of your final grade, and the final exam is worth 50 percent of your final grade.”

http://www.uwo.ca/fhs/health_studies/files/downloads/pdf/out...

The important point is that the marks for the midterm exam and final exam are combined to find the final grade. For this reason, ‘midterm exam’ is the appropriate term for ‘primeiro exercício escolar’.


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Note added at 18 hrs (2012-10-19 22:59:01 GMT)
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Be careful with ‘prova final’. In some instances, it’s not a compulsory end of semester exam, but rather a last chance to pass a subject when the average of all other assessment items is below 7:

“Para ser aprovado, o aluno precisará ter média igual ou superior a 7,0 (sete). Caso contrário, terá que se submeter à Prova Final, precisando, neste caso, atingir a média final igual ou superior a 5,0 (cinco) para ser aprovado.”

http://www.fja.edu.br/g_pa.asp#19

If the university in your text follows this system, then:

primeiro exercício escolar = midterm exam / mid-semester exam

segundo exercicio escolar = final exam / end of semester exam

prova final = supplementary exam / retake exam

While this ‘prova final’ system is certainly not routine in Australia, there are instances where a student may be granted the opportunity to re-do assessment. A reference for ‘supplementary exam’: http://monash.edu/exams/deferred-supplementary.html

For US universities, ‘retake exam’, e.g. http://medicine.stonybrookmedicine.edu/sompolicies

A Canadian University uses the term ‘supplemental exam’: http://ugradcalendar.uwaterloo.ca/page/ENG-Examinations-and-...

Many UK universities use ‘resit exam’, e.g. http://www.dur.ac.uk/physics/students/exams/