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Math 150 — Winter 2009
Assigned on: January 9, 2009 Due on: January 13, 2009
Name: Time:
This evaluation does not affect your grade in the course. It is used merely to allow me to assess quantitatively your overall preparedness so that I can target my teaching most effectively. Please work alone and turn this evaluation in at the beginning of our next recitation.
In each problem, an algebraic solution should conclude with an exact^1 answer (and conversely, an exact solution should be done algebraically). Otherwise, you may use your calculator when nec- essary provided that you also provide a complete, appropriately labeled graph. In all instances, show all necessary work and read the questions carefully.
Problem 1 Solve the equation x^2 + 2x − 3 = 0 algebraically.
Problem 2 Solve the equation 2 ln( 1 − x) = ln(x) algebraically.
(^1) You should understand the concepts of exactness and approximation. For example, 1/2 = 0.5 (exactly), but 1/3 6 = 0.3,
although 1/3 = 0.3 and 1/3 ≈ 0.3 (approximately; note ≈ vs =). Similarly, π = π and π 6 = 22/7 just as √ 2 6 = 1. even though
√ 2 ≈ 1.41. In general, writing “a lot of digits that you see on your calculator” may count for greater approximation accuracy but still is not exactness.
Problem 3 A student’s GPA after h credit hours is modeled by
G(h) =
1 + e−0.01h^
Using any appropriate method: (a) What GPA would the student have at the beginning?
(b) Upon graduating with 250 credit hours, about what would the student’s GPA be?
(c) After about how many credit hours would the student’s GPA exceed 3.999?
Problem 4 Find the angle γ (the triangle is generic and may not appear to reflect your calcu- lations).
γ
Problem 8 State the domain and range of the following basic functions:
(a) f(x) = x.
(b) g(x) = ex.
(c) h(x) = ln x.
(d) k(x) =
x.
(e) m(x) = 1/x.
Problem 9 Alice can finish her homework in 25 minutes, and Bob can finish his in a half hour. If they work together, how long will it take to do an assignment (to the nearest whole minute)?
Problem 10 Find the arclength and sector area given a central angle of 45 ◦^ subtending a circle of radius π.
Problem 11 Suspend belief for a moment and suppose that the starship Enterprise leaves Alpha Centauri, 41, 340, 000, 000, 000km from Earth, and flies through space at a handy 1, 000, 000, 000kph for 10, 000 hours. It then stops completely, and uses its transporter to beam Jean-Luc Picard and Data to Earth’s surface. If it takes the transporter only 1 second (1/3600 hours) to finish the journey, at what speed must it have transported them?
