MTR CORPORATION
This job was posted on 19 Feb 2013

BUILD A CAREER BY CARING FOR OTHERS AS WE MOVE FORWARD TO SERVE HONG KONG BETTER, WE NEED YOU TO BE A PART OF IT As a diversified and dynamic company, the MTR Corporation is involved in a wide range of business activities, including railway construction and operations, property development and management, additional commercial activities, investment projects and consultancy services worldwide. These provide excellent career development opportunities for you to join us in serving the community with caring service. We are looking for applicants for the position of:

Retail Marketing Officer (Ref: P13026)
Retail Marketing Officer (Ref: P13026) You will carry out marketing activities to promote the brand awareness of one of our Hong Kong shopping centres and drive patronage both locally and from the Mainland of China. You will supervise promotion activities of the shopping centre including implementation and execution of promotion programmes and marketing events, as well as manage and coordinate with marketing agencies on public relations, event management, festive decorations, promotion and advertising matters. You will work during non-office hours and public holidays when necessary. Applications You are invited to apply online at http://www.mtr.com.hk/careers or send in your application stating the position you are applying for and relevant reference number, together with your current and expected salary, either by email to recruit@mtr.com.hk or by mail to Human Resource Management Department, MTR Corporation, G.P.O. Box 9916, Hong Kong on or before 22 February 2013 All 2013. information provided by applicants will be treated in strict confidence and used for recruitment purpose only. All personal data of unsuccessful applicants will be destroyed within six months. recruit@mtr.com.hk...

...Algebra
Archit Pal Singh Sachdeva
1. Consider the sequence of polynomials deﬁned by P1 (x) = x2 − 2 and Pj (x) = P1 (Pj−1 (x)) for j = 2, 3, . . .. Show that for any positive integer n the roots of equation Pn (x) = x are all real and distinct. 2. Prove that every polynomial over integers has a nonzero polynomial multiple whose exponents are all divisible by 2012. 3. Let fn (x) denote the Fibonacci polynomial, which is deﬁned by f1 = 1, f2 = x, fn = xfn−1 + fn−2 . Prove that the inequality
2 fn ≤ (x2 + 1)2 (x2 + 2)n−3
holds for every real x and n ≥ 3. 4. Find all polynomials f with with real coeﬃcients satisfying, for any real number x, the relation f (x)f (2x2 ) = f (2x3 + x). 5. Consider the equation with real coeﬃcients x6 + ax5 + bx4 + cx3 + bx2 + ax + 1 = 0, and denote by x1 , x2 , . . . , x6 the roots of the equation. Prove that
6
k=1
(x2 + 1) = (2a − c)2 . k
6. Let a, b, c, d be real numbers such that (a2 + 1)(b2 + 1)(c2 + 1)(d2 + 1) = 16. Prove that −3 ≤ ab + bc + cd + da + ac + bd − abcd ≤ 5. 7. Solve the equation x3 − 3x = 1 √ x + 2.
8. For positive numbers a, b, c prove the inequality a2 − ab + b2 + b2 − bc + c2 ≥ a2 + ac + c2 .
9. Let a, b, c be real numbers. Show that a ≥ 0, b ≥ 0, and c ≥ 0 if and only if a + b + c ≥ 0, ab + bc + ca ≥ 0, and abc ≥ 0. 10. Find the minimum possible value of a2 + b2 if a and b are real numbers such that x4 + ax3 + bx2 + ax + 1 = 0 has at least one real root. 11. If x and y are positive real numbers...

...Rethinking Rocky Mountain Outfitters
Chapter 13
Questions
Update the RMO relational database design in Figure 13-9 based on the changes that you made to the ERD. Be sure that all your database tables are in 3NF.
Write ODL schema specifications for all new classes and relationships that you added to the class diagram.
Verify that the new classes and relationships are accurately represented in the updated relational database design that you developed for question 1.
Answers
Professor, I am confused about the third normal form. I think I understand the example on page 501, figure 13-13, but I don't know how to determine whether one function is dependent on another. I have attempted to create a table in 3NF showing the steps from 1NF. Please let me know if I am in the least bit on the right track or if I am missing the mark completely.
CustomerTable (1NF)
CustomerTable (2NF) CustomerAddressTable (2NF)
CustomerTable (3NF) CustomerAddressTable (3NF)
(Q) Should I have a separate table for the phone numbers as well?
2. class Customer {
attribute string accountNo
attribute string name
attribute string billingAddress
attribute string shippingAddress
attribute string dayTelephoneNumber
attribute string nightTelephoneNumber
}
I'm not sure that number 2 actually reflects what I have for number 1. If I were to create a schema for the 3NF it may look similar to this:
class Customer {
attribute string...

...diameter passing
through the centre of S2 and ∠Y XO = 30◦ . If the radius of S2 is 100 then what is the radius
of S1 ?
18. What is the maximum possible value of k for which 2013 can be written as a sum of k consecutive positive integers?
19. In a triangle ABC with ∠BCA = 90◦ , the perpendicular bisector of AB intersects segments
AB and AC at X and Y , respectively. If the ratio of the area of quadrilateral BXY C to the
area of triangle ABC is 13 : 18 and BC = 12 then what is the length of AC?
20. What is the sum (in base 10) of all the natural numbers less than 64 which have exactly three
ones in their base 2 representation?
The answer key will be uploaded on October 21, 2013 at
http://olympiads.hbcse.tifr.res.in/subjects/mathematics/pre-rmo-2013-answers
2
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