IMBA 线上笔试


IM MSc in IMBA - Admission Examination

IMBA Admission Exam IM

- 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or any activity which could amount to academic misconduct in the answering of this examination will have their marks withdrawn and disqualified.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?

4 / 18

A company wants to increase its sales by 20%. If the current sales are $50,000, what should the new sales target be?

5 / 18

Find the derivative of the function f(x) = 3x^4 - 2x^3 + 5x^2 - 7x + 2.

6 / 18

A jar contains 10 red balls and 12 blue balls. If two balls are randomly selected from the jar without replacement, what is the probability that both balls are red?

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A car travels at a constant speed of 60 miles per hour. If the car travels for 3 hours and 30 minutes, how far does it travel?

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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

Show steps

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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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A card is drawn at random from a well-shuffled pack of 52 playing cards. What is the probability of drawing

(i) a queen

(ii) a red card

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How much water must be added to a bucket which contains 40 litres of milk at the cost price of $ 3.50 per litre so that the cost of milk reduced to $ 2 per litre? (10pts)

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Tell me your opinion about advantages and disadvantages of Cloud Computing. (10 Pt)

13 / 18

Mr. Tony sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:


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A mother is twice as old as her son. If 20 years ago, the age of the mother was 10 times the age of the son, what is the present age of the mother? (5 pt)

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In a certain code language ‘RISE’ is written as ‘8419’,   and  ‘MEAL’ is written as ‘5927’.   How is ‘RAIL written in that code ? (10 Pts)

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There are five friends: Alice, Bob, Claire, David, and Emily. They all have different heights:

  1. Alice is taller than Claire but shorter than Emily.
  2. David is taller than Bob but shorter than Emily.
  3. Claire is taller than Bob.

Based on this information, rank the friends from shortest to tallest.

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18 / 18

Write a Python program that checks if a given number is a prime (*该题仅作为背景考察,不计入考核总分)


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