# IMBA 线上笔试

IM MSc in IMBA - Admission Examination

**IMBA Admission Exam IM**

**Instructions**

- 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.

请写入真实信息,用于记录IP地址,

**请注意！试图打开其他网页、截图、复制题目或提交时候IP地址与此记录的不相同等影响线上考试行为，**

**取消参加考核的权利。**

1 / 17

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or any activity which could amount to academic misconduct in the answering of this examination will have their marks withdrawn and disqualified.

Good, 放松一下，开始答题

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In a game you pay $5, to have a 45/47 probability of losing your $5 and a 2/47 probability of winning $200 (you do not get your original $5 back).

What is your expected value for this game if you decide to play? (10 pts)

3 / 17

If the sum of three consecutive even integers is 270, what is the largest of the three integers?

4 / 17

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

5 / 17

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?

6 / 17

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.

7 / 17

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, ...

8 / 17

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

9 / 17

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

10 / 17

In mathematics exam a student scored 30% marks in the first paper, out of a total of 180. How much should he score in second paper out of a total of 150. If he is to get an overall average of at least 50 %. (5pts)

11 / 17

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

12 / 17

A bag contains 30 cards, numbered 1 to 30. A card is drawn at random from a bag. Write the number of favourable outcomes for the following events:

(i) getting a card with a number divisible by 6

(ii) getting a card with a number divisible by 3 or 4.

(10pts)

13 / 17

If n(A - B) = 18, n(A ∪ B) = 70 and n(A ∩ B) = 25, then find n(B). (10pts)

14 / 17

Determine the area of the region bounded by y=x^2+2 , y=sin(x), x=−1 and x=2. (10 pt)

15 / 17

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

16 / 17

How many ways can the letters of the word "CUHKSZ" can be arranged?

17 / 17

场景：假设你在一个购物商城工作，需要计算顾客购物车中商品的总价。

写一个循环程序，要求用户逐个输入每个商品的价格，输入0表示结束输入，然后计算并输出购物车中商品的总价。

示例输入/输出：

请输入商品价格（输入0结束）：10

请输入商品价格（输入0结束）：25

请输入商品价格（输入0结束）：15

请输入商品价格（输入0结束）：0

购物车中商品的总价为：50

#这个循环程序会反复提示用户输入商品价格，直到用户输入0为止。

#每次输入的价格会被累加到total_price变量中，最后输出购物车中商品的总价。