
Information on exams of Mathematics II
 General conditions:

 Only students registered in SIS for Mathematics II in this semester are allowed to pass the exam.
 Students are allowed to pass the exam only if they have gained the credit in this semester.
 The exam has two parts  the written one and the oral one.
 Before passing the oral part students have to succesfully pass the
written part.
 If a student fails at the exam and retake exam is possible,
one proceeds as follows:

 If the student obtained in the written part less than 75% of points, he or she has to
pass the written part again.
 If the student obtained in the written part at least 75% of points, he or she need not
pass the written part again, but it is enough to pass the oral part.

 On the exam the students are supposed to prove their identity by some document.

 Conditions for the written part:

 It consists of five problems.
 Students will have 120 minutes to solve the problem.
 It is possible to use any written or printed materials (tables, textbooks,
lecture notes etc.).
 It is not possible to use electronic devices (such as mobile phones,
calculators, notebooks, tablets etc.).
 The solutions are evaluating by giving certain number of points. The maximal number
of points for the test is 60.
 A student will succesfully pass the written part, if he or she gets at least 50%
of points, i.e., at least 30 points.
 Structure of the written part will be as follows:

 Problem on matrix calculus (rank of a matrix, inverse of a matrix, determinant,
solving system of linear equations). There may be an addititional question similar
to those solved at seminars (to compute the inverse or the determinant of a modified
matrix, to answer for which righthand sides is the given system solvable etc.).
The maximum for the first problem is 10 points.
 Problem on partial derivatives  to determine and draw the domain of a given
function, to compute partial derivatives at all points where they exist. This
will be similar to the problems from the first homework. The maximum for the second problem
is 10 points.
 Application of the implicit function theorem  to verify the assumptions,
to compute first and second derivatives, to write down equation of tangent line.
The maximum for the third problem is 10 points.
 Finding extrema using Lagrange multiplier theorem. The problems will be similar
to the problems from the second homework. The maximum for the fourth problem
is 15 points.
 Computing an antiderivative. The maximum for the fifth problem is 15 points.

 Sample problems for the written test
are available here.

 Conditions for the oral part:

 Oral part takes place after succesfull passing the written part, usually the same day.
 The student will draw a set of questions. He or she will then prepare the answers on a sheet of
paper. Then the examiner will evaluate the answers.
 The structure of each set of questions is the following:

 Definition of a key notion (no points for that).
 Definitions of three notions and statement of two theorems (each item for 4
points).
 Two questions testing understanding of the notions (each of them for 10 points).
 Statement and proof of a given theorem (20 points  5 for statement and
15 for the proof).

 List of key notions, definitions and theorems to state is given
here.
This list contains also some key notions from Mathematics I.
There will be no explicit questions to these notions
in the sets of questions, but it is necessary to prove
the knowledge and understanding of all of them which appear to be
related to the other questions.
 List of questions for the third part of the set is given here.
 List of theorems to prove is given here.
 Knowledge of a definition necessarily includes understanding of the respective notion
and ability to use it correctly.
 Knowledge of a theorem statement necessarily includes understanding of its assumptions
and its conclusion and ability to apply it in concrete cases.
 The description of an example necessarily includes a proof that it has all the required
properties.
 By knowledge of a proof of a theorem I mean the ability to explain
an arbitrary mathematically correct proof to the examiner, referring only
to theorems stated at lectures earlier (or to other theorems, which the student is able to prove).
 An appropriate knowledge of notions and theorems from Mathematics I is assumed,
especially if they are necessary to understand the topics of Mathematics II.

 Evaluation of the exam:

 To pass the exam succesfully it is necessary and sufficient to fulfil all
the following conditions:

 To pass succesfully the written part.
 At the oral part to prove the knowledge and understanding
of the key notion from the first question and of all the other key notions
from Mathematics II which appear in the drawn set.
 Upon request of the examiner to prove the knowledge and understanding
of all the key notions from Mathematics I or Mathematics II which are related
to the drawn set.
 To get at least 30 points from the oral part.

 A student will get the grade 1, if he or she passes succesfully the exam
by the item 4a, gets at least 45 points from the oral part, at least 5 points from
the proof and gets at least 90 points from the whole exam (summing up the written and oral
part).
 A student will get the grade 2, if he or she passes succesfully the exam
by the item 4a, does not get the grade 1, gets at least 40 points from the oral
part and gets at least 75 points from the whole exam.
 A student will get the grade 3, if he or she passes succesfully the exam
by the item 4a, does not get the grade 1 or 2.

 Dates of the exams:

 Dates of the written part are announced in SIS.
They will take place on:

 Thursday May 30
 Thursday June 13
 Thursday June 20
 Tuesday June 25
 Thursday September 5

All the tests take place from 9:30 till 11:30 in the lecture room O206.
 Students are required to register for the written part in SIS
by the date and time which are set there.
 The oral part will take place in the same day afternoon, after the written part
has been corrected. In case of necessity (large amount of students) it will take
place also later. This possibility will be announced before each test.
 The written tests will take place only in the above mentioned dates.
There will be no more written tests.
 Individual dates for oral part are possible in exceptional cases for students
who got 75% points from the written test but failed the oral part. Such exams
can be fixed only within the standard exam period. This possibility is not guaranteed and
depends on the availability of the examiner.

