IMBA 线上笔试 BA


BA- MSc in IMBA - Admission Examination

IMBA Admission Exam BA

- You will have 60 minutes to complete this exam.
- Questions in this exam will be presented one at a time.

- During this exam you won’t be permitted to review previous questions.
- You may ask questions about this exam paper.

- Please give your answers in English.

- Partial credit will be given when steps or thinking flow are shown.
- The answers in the Math part within 2 decimal places whenever necessary.

- Answer mathematics term or equation in scientific method,

e^2, sin(x), ln(x), a/b, …

- You must only attempt this exam once. Any additional attempts should only be used in the event where a serious technical issue has occurred and supporting evidence supporting this will be required.




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Candidate Declaration

By attempting this exam, I acknowledge that


I agree to be bound by the university’s rules, codes of conduct, and other policies relating to examinations

I have read and understood the examination conduct requirements for this exam

I am aware of the university’s rules regarding misconduct during examinations

I am not in possession of, nor do I have access to, any unauthorized material during this examination

I am promised will not to obtain assistance by improper means or ask for help from or give help to any other person.


I am promised will not to take screenshots, record the screen, copy and paste questions or answers or otherwise attempt to take any of the content of this exam out of the exam for any purpose.

In attempting this examination and submitting an answer, candidates are undertaking that the work they submit is a result of their own unaided efforts and that they have not discussed the questions or possible answers with other persons during the examination period. Candidates who are found to have participated in any form of cooperation or collusion or any activity which could amount to academic misconduct in the answering of this examination will have their marks withdrawn and disqualified.

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There are four cars: Audi, BMW, Mercedes, and Volvo. Each car is a different color: black, blue, red, and silver. The following clues are given:

  1. The black car is not a BMW.
  2. The red car is not a Volvo.
  3. The silver car is not an Audi.
  4. The blue car is a Mercedes.

Based on these clues, can you determine the color of each car and which brand it belongs to?

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In a math class, 60% of the students passed the test, and the remaining 40% failed. If there are 80 students in the class, how many students passed the test?

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Find the derivative of the function f(x) = sin(2x) + cos(3x).

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Evaluate the definite integral of the function f(x) = 2x^3 + 5x^2 - 3x + 1 from x = 0 to x = 2.

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The average weight of five boxes is 20 kilograms. If the weights of four of the boxes are 15 kg, 18 kg, 22 kg, and 25 kg respectively, what is the weight of the fifth box?

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The unemployment rate is around 9%.  What is the average number of people who will be unemployed if you randomly select groups of 30 people? (10 pts)

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A mathematics book containing 20 pages. One sheet is missing among them. Sum of the page numbers of the remaining pages of the mathematics book is 195. The numbers written on both the sides of the missing sheet of the mathematics book must be?   (10pts)

Show steps

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A, B and C entered into a partnership. A invested $ 2560 and B invested $ 2000. At the end of the year, they gained $ 1105, out of which A got $ 320.C’s capital was –  (10pts)

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If the digits of a two-digit number are interchanged, the number so formed is 18 more than the original number. The sum of digits is 8. What is the thrice value of original number? (10pts)  *trice means three times, show steps

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A man spends 1/5 of his salary on food, 1/10 of his salary on house rent, and 3/5  of his salary on clothes. He still has $18000 left with him. Find his salary. (10pts)

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729 ml of mixture contains milk and water in the ratio 7:2. How much more water is to be added to get a new mixture containing milk and water in the ratio 7:3? (10pts)

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In a group of 100 persons, 72 people can speak English and 43 can speak French. How many can speak English only? How many can speak French only and how many can speak both English and French? (10 pts)

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Find dy/dx when y=ln(x+e^2x). (5 pts)

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The sum of the first n terms of an arithmetic sequence is given by the formula Sn = (n/2)(2a + (n-1)d), where a is the first term and d is the common difference. Find the sum of the first 10 terms of the arithmetic sequence 3, 7, 11, 15, ...

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A company's revenue in a given year is given by the equation R = 5x^2 + 10x + 15, where x represents the number of units sold. Find the number of units sold when the revenue is maximized.

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