Name : MATH 1113 Section I, Precalculus, Test 2, Fall 2007

DIRECTIONS: Work each of the following problems. You may use a calculator, but in order to receive credit, you must show all necessary work to indicate your understanding of the relevant concepts. The use of books, notes, two-way communication devices, laptop computers, etc. are all prohibited.

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1. (8 pts) Let f (x) = x3 − 7x + 6. (a) According to the rational roots theorem, what are the possible rational roots of f (x)?

(b) Find the fully factored form of f (x).

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2. (36 pts) Consider the graph of x2 + x − 2 . x2 + 2x − 3 Find each of the following. If any of the following do not exist, state so. f (x) =

(a) the coordinates of the y-intercept

(b) the coordinates of all x-intercepts

(c) equations of horizontal asymptote(s)

(d) equations of vertical asymptote(s)

(e) equation of slant asymptote(s)

(f) coordinates of any “holes”, i.e. discontinuities where there is no vertical asymptote.

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(g) Sketch the graph of f clearly indicating the information found on the previous page.

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3. (20 pts) Solve the following equations. 1 (a) 9x = √ 3 3

(b) ln(3x − 3) = ln(x + 1) + ln 4

1 x

 

(c) ln(x + 2) − ln(4x + 3) = ln

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4. (5 pts) Rewrite y = 3(9.8)x in terms of base e.

5. (10 pts) The half-life of the radioactive element krypton-91 is 10 seconds. (This means that if A0 grams are initially present, then ten seconds later there will be 21 A0 grams present.) Suppose that 16 grams of krypton-91 are initially present. (a) How many grams are present after 30 seconds?

(b) How long will it take for the size of the sample to be reduced to 3 grams?

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6. (8 pts) Perform the indicated conversions. Answers should be exact (not decimal approximations) expressed in terms of π if necessary. (a) Convert 35◦ to radians.

(b) Convert

5π 12

radians to degrees.

7. (6 pts) The distance from the center of a clock to the tip of the minute hand is 6 inches. How far does the tip of the minute hand travel in 35 minutes?

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8. (7 pts) Suppose that the orbit of the Earth around the Sun is a circle and the distance from the Sun to the Earth is 92,952,000 miles. It takes one year for the Earth to make a complete revolution around the sun. Given that there are about 365.25 × 23.93 ≈ 8740 hours in a year, find the Earth’s approximate linear speed in miles per hour as it travels around the Sun.

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