Business Mathematics
Written exam – online version (15/12/2020)
Instructions
This online version consists of 30 questions. each of which is worth 3 points. You cannot obtain partial
points: an answer is correct or wrong. The exam grade is calculated as follows:
10 + number of points
grade = min ( , 10)
9.7
In this way, there is one “bonus” question: if you make one mistake, you still have a grade 10.0.
You must carefully read the instructions, in particular those [in square brackets] about how to enter your
answer.
The exam will be available for 2 hours. Students with extra time will have 30 minutes extra at the end. A
clock will be running in TestVision. Do not use your phone as a time keeper.
We assume that you have studied the overall instructions about online exams and digital proctoring, and
that you understand the rules and procedures, including those for allowing access to camera, microphone,
screen, for not using the bathroom, for having your ID ready, etc.
It is unfortunately not possible to pose questions to the teacher during the exam. If you think there is a
mistake in the exam, you must make a clever choice. Of course you can after the exam send a message to
the teacher, which will then be judged to adjust the grading if needed.
You can use the chatbox of Proctorio only for technical issues.
Allowed items
You are allowed to use scrap paper and pen/pencil (at start, the scrap paper must be empty).
You are allowed to use a non-graphical hand-held calculator (but not a computer or phone calculator).
You are allowed to have your ID and student card on your desk.
You are allowed to have something to drink.
Forbidden items
You are not allowed to use your phone.
You are not allowed to use other programs or websites than TestVision and Proctorio.
You are not allowed to use a graphical calculator.
You are not allowed to use your book or notes.
You are not allowed to wear headphones, earphones, etc.
You are not allowed to communicate with other persons inside or outside your room.
, Q1
To what is the following expression equivalent?
√𝑒 𝑥 𝑒 𝑦
𝑒𝑥
[Choose one capital letter, e.g., A]
A √𝑒 𝑦 − √𝑒 𝑥
B √𝑒 𝑦 − 𝑒 𝑥
C √𝑒 𝑦−𝑥
D 𝑒 √𝑦−𝑥
E 𝑒 √𝑦 − 𝑒 √𝑥
F 𝑒 √𝑦−√𝑥
G None of the above
Q2
Given is
2 1
𝐗=( )
1 3
Which statements are true?
[Choose all correct answers in alphabetical order, using capital letters, e.g., AE]
3 1
A 𝐗′ = ( )
1 2
3 2
B 𝐗+𝐈=( )
2 4
9 1
C 𝐗2 = ( )
1 4
5 4
D 𝐗+3=( )
4 6
E None of the above
Q3
Given is
𝑓(𝜃, 𝜆) = 𝜃 𝜆
𝜕𝑓
Find .
𝜕𝜆
[Choose one capital letter, e.g., A]
A 𝜆𝜃 𝜆−1
B 𝜃𝜆
C 𝜃 𝜆 ⋅ ln 𝜆
D 𝜃 𝜆 ⋅ ln 𝜃
E 0
F None of the above
Q4
Give all solutions of the following equation:
𝑥
√−2𝑥√− = 1
2
[Use 2 decimal places and a decimal point, and enter all solutions with a “;” in between and without spaces
or +-signs, for instance “-3.00;12.50”. Insert “N/A” if no answer is possible.]
Written exam – online version (15/12/2020)
Instructions
This online version consists of 30 questions. each of which is worth 3 points. You cannot obtain partial
points: an answer is correct or wrong. The exam grade is calculated as follows:
10 + number of points
grade = min ( , 10)
9.7
In this way, there is one “bonus” question: if you make one mistake, you still have a grade 10.0.
You must carefully read the instructions, in particular those [in square brackets] about how to enter your
answer.
The exam will be available for 2 hours. Students with extra time will have 30 minutes extra at the end. A
clock will be running in TestVision. Do not use your phone as a time keeper.
We assume that you have studied the overall instructions about online exams and digital proctoring, and
that you understand the rules and procedures, including those for allowing access to camera, microphone,
screen, for not using the bathroom, for having your ID ready, etc.
It is unfortunately not possible to pose questions to the teacher during the exam. If you think there is a
mistake in the exam, you must make a clever choice. Of course you can after the exam send a message to
the teacher, which will then be judged to adjust the grading if needed.
You can use the chatbox of Proctorio only for technical issues.
Allowed items
You are allowed to use scrap paper and pen/pencil (at start, the scrap paper must be empty).
You are allowed to use a non-graphical hand-held calculator (but not a computer or phone calculator).
You are allowed to have your ID and student card on your desk.
You are allowed to have something to drink.
Forbidden items
You are not allowed to use your phone.
You are not allowed to use other programs or websites than TestVision and Proctorio.
You are not allowed to use a graphical calculator.
You are not allowed to use your book or notes.
You are not allowed to wear headphones, earphones, etc.
You are not allowed to communicate with other persons inside or outside your room.
, Q1
To what is the following expression equivalent?
√𝑒 𝑥 𝑒 𝑦
𝑒𝑥
[Choose one capital letter, e.g., A]
A √𝑒 𝑦 − √𝑒 𝑥
B √𝑒 𝑦 − 𝑒 𝑥
C √𝑒 𝑦−𝑥
D 𝑒 √𝑦−𝑥
E 𝑒 √𝑦 − 𝑒 √𝑥
F 𝑒 √𝑦−√𝑥
G None of the above
Q2
Given is
2 1
𝐗=( )
1 3
Which statements are true?
[Choose all correct answers in alphabetical order, using capital letters, e.g., AE]
3 1
A 𝐗′ = ( )
1 2
3 2
B 𝐗+𝐈=( )
2 4
9 1
C 𝐗2 = ( )
1 4
5 4
D 𝐗+3=( )
4 6
E None of the above
Q3
Given is
𝑓(𝜃, 𝜆) = 𝜃 𝜆
𝜕𝑓
Find .
𝜕𝜆
[Choose one capital letter, e.g., A]
A 𝜆𝜃 𝜆−1
B 𝜃𝜆
C 𝜃 𝜆 ⋅ ln 𝜆
D 𝜃 𝜆 ⋅ ln 𝜃
E 0
F None of the above
Q4
Give all solutions of the following equation:
𝑥
√−2𝑥√− = 1
2
[Use 2 decimal places and a decimal point, and enter all solutions with a “;” in between and without spaces
or +-signs, for instance “-3.00;12.50”. Insert “N/A” if no answer is possible.]
