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(math005)[2005](f)mid1~PPSpider^_10388.pdf
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HKUST
MATH005 ALGEBRA AND CALCULUS I
First Mid-Term Examination (Version A) Name:
8th October 2002 Student I.D.:
19:00C20:30 Tutorial Section:

Directions:
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Do NOT open the exam until instructed to do so.

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Please write your name, ID number, and Section in the space provided above.

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Answer ALL questions.

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This is a closed book examination.

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No graphical calculators are allowed.

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You may write on both sides of the examination papers.

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Once you are allowed to open the exam, please check that you have 7 pages of questions in addition to the cover page.

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

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All mobile phones and pagers should be switched o. during the examination.

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Cheating is a serious o.ense. Students who commit this o.ense may receive zero mark in the examination. However, more serious penalty may be imposed.


Question No. Q. 1 Q. 2 Q. 3 Q. 4 Q. 5 Q. 6 Q. 7 Q. 8 Q. 9 Q. 10
Points (4 each)

Question No. Points Out of
Q. 11 15
Q. 12 13
Q. 13 16
Q. 14 16
Q. 1-10 40
Total Points 100

Part I: Answer each of the following 10 multiple choice questions.
Each is worth 4 points. No partial credit.
1. If f(x)= g(x + 3) and g(x)= x2 +2x + 1, compute f(1).
(a) 24 (b) 25 (c) 16 (d) 17 (e) None of the previous
2. Jenny has decided to pay o. two loans on which she has not made any previous repayment. The .rst loan is a loan in which she obtained $9, 000 two years ago at an annual interest rate of 8% compounded semiannually. The second is a loan where $12, 500 is due two years from now at an annual interest rate of 16% compounded quarterly. To the nearest dollar, how much is due now?
(a) $23, 391 (b) $25, 235 (c) $22, 032 (d) $19, 662 (e) $22, 378
x2 . 1
3. The domain of the function de.ned by the formula f(x) = is:
2x3
(a)
All real numbers except 0

(b)
All real numbers except 1

(c)
All real numbers except 1

(d)
All real numbers > 0

(e)
All real numbers except 1/2


x2 +1 1
4. The derivative of f(x)= is:
.
2 x
3
2
2x +1 3 33(a) (b) (c)
+
x +x .
5
55 2
2 2x
2x 2x
2
2
2x +1 3 3(d) (e)
11 2
2
2
x2 . 2x +1
5. Find the limit lim
x1 x2 +2x . 3
.1
(a) .1 (b) 1 (c) (d) 0 (e) Does not exist
3
6. Determine the tangent line to the graph of the function y = f(x)= .6x2 +3x . 2 at the point (2,f(2)).
(a) y = .21x + 22 (b) y = 23x . 22 (c) y = 12x +4
(d) y = 23x + 22 (e) y =4x . 1

7. Compute g.(4) for g(x) = (31 . 15 x)(x 2 . 16).
(a) .8 (b) 263 (c) 24 (d) 0 (e) 8
8. Conversion between temperature measured in Fahrenheit F and measured in Celsius C is a linear function. Water freezes at 32F and 0C, and boils at 212F and 100C. The temperature in New York City is 68F. What is this temperature in C?
.160 230
(a) 20 (b) (c) (d) .10 (e) 30
99
9. Find the maximum/minimum of the function