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(MATH006)832523 - midterm-math006-F08.pdf
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HKUST
MATH 006 Calculus and Linear Algebra
Midterm Examination Name:
27th October 2008 Student I.D.:
19:00C20:30 Tutorial Section:

Directions:
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Write your name, ID number, and tutorial section in the space provided above.

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DO NOT open the exam booklet until instructed to do so.

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When instructed to open the exam booklet, check that you have, in addition to this cover page, 10 pages of questions.

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Turn o. all mobile phones and pagers during the examination.

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This is a closed book examination.

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Graphical calculators are NOT allowed.

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Unless otherwise speci.ed, numerical answers should be either exact or correct to 2 decimal places.

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You are advised to try the problems you feel more comfortable with .rst.

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You may write on both sides of the examination papers.

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You must show the working steps of your answers in order to receive full points.

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You must not possess any written or printed papers that contains information related to this examination.

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Cheating is a serious o.ense. Students caught cheating are subject to a zero score as well as additional penalties.


Question No. Points Out of
Q. 1 7
Q. 2 5
Q. 3 8
Q. 4 6
Q. 5 7
Q. 6 7
Q. 7 5
Q. 8 5
Total Points 50

Answer ALL questions on the space provided.
1. [7 pts] The brokerage .rm charge commissions based on the amount of the trade. The following table shows the commission schedule for one of these .rms.
Transaction Size Commission
$0-$2,499 $2,500-$9,999 $10,000+ $30+1.5% of principal $50+0.8% of principal $100+0.3% of principal

An investor purchases 100 shares of a stock at $23.52 per share. After 240 days, the investor sells the stock for $28.10 per share. Using the above commission schedule, .nd the annual rate of interest earned by this investment. (Note: 1 year = 360 days)
2. [5 pts] Suppose the parents of a newborn child decide that on each of the childs birthdays up to the 17th year, they will deposit $PMT in an account that pays 5% compounded annually. The money is to be used for the college expenses.
(a)
What should the annual deposit $PMT be in order for the amount in the account to be $90,000 after 17th deposit?

(b)
How much interest will the parents earn?


3.
[8 pts] A person purchased a $150,000 home 10 years ago by paying 20% down and signing a 30-year mortagage at 10.2% compounded monthly. Interest rates have dropped and the owner wants to re.nance the unpaid balance by signing a new 20-year mortgage at 6.5% compounded monthly. How much interest will re.nancing save?

4.
[6 pts] Using Gauss-Jordan Elimination, solve the following system of linear equations.


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. 3x1 . 2x2 + x3 = .7 2x1 + x2 . 4x3 =0 . x1 + x2 . 3x3 =1
5. [7 pts] A chemical manufacturer wants to lease a .eet of 20 railroad tank cars with a combined carrying capacity of 54000 gallons. Tank cars with three di.eren