Math 115 - Exam 3 - Prof. Jennifer R. Mcneilly, Exams of Mathematics

This is an exam for math 115 course, which covers various topics in mathematics including logarithms, trigonometry, and inverse trigonometric functions. The exam consists of 8 questions and is worth 50 points.

Typology: Exams

2010/2011

Uploaded on 10/12/2011

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Math 115 Exam 3 12PM Name:
Due: May 5th, 2010 (at the start of class)
50 points possible
1. Every exam is worth a total of 60 points. Check to see that you have all of the pages.
Including the cover sheet, each exam has 10 pages.
2. Please clearly print your name at the top of the exam in the space provided.
3. You will work on this exam alone. Group work and the use of tutors is strictly
prohibited.
4. You are allowed to use any course materials: lecture notes, materials on the course
website, ALEKS, etc.
5. You are allowed to use any text or website that you find helpful. If you use a source
outside of the course materials, please cite them.
6. You are NOT allowed to use a calculator (or any other graphing or computation device
or software).
7. While grading, I and the other graders will closely monitor for “shared work” and other
evidence of cheating. I reserve the right to ask you to replicate any part of a solution
or answer at a later date to verify that the solutions on the exam are your own and
were not obtained through the use of any graphing or computation device or the aid of
another. Any violations of the above policies will result in the initiation of an academic
integrity case and I will pursue the harshest punishment that my department allows.
8. Please sign the exam below signifying that you have carefully read and are responsible
for the instructions above.
Signature:
pf3
pf4
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Math 115 – Exam 3 – 12PM Name:

Due: May 5th, 2010 (at the start of class)

50 points possible

  1. Every exam is worth a total of 60 points. Check to see that you have all of the pages. Including the cover sheet, each exam has 10 pages.
  2. Please clearly print your name at the top of the exam in the space provided.
  3. You will work on this exam alone. Group work and the use of tutors is strictly prohibited.
  4. You are allowed to use any course materials: lecture notes, materials on the course website, ALEKS, etc.
  5. You are allowed to use any text or website that you find helpful. If you use a source outside of the course materials, please cite them.
  6. You are NOT allowed to use a calculator (or any other graphing or computation device or software).
  7. While grading, I and the other graders will closely monitor for “shared work” and other evidence of cheating. I reserve the right to ask you to replicate any part of a solution or answer at a later date to verify that the solutions on the exam are your own and were not obtained through the use of any graphing or computation device or the aid of another. Any violations of the above policies will result in the initiation of an academic integrity case and I will pursue the harshest punishment that my department allows.
  8. Please sign the exam below signifying that you have carefully read and are responsible for the instructions above.

Signature:

  1. (6pts) The graphs of the functions f (x) := log 2 x, g(x) := log 4 x and h(x) := log 10 x are on the same graph below. Determine which is which and briefly explain your conclusion.

2 4 x

y

  1. (8pts) Beginning with the graph of y = cos x, use shifting and scaling transformations to sketch the graph of the function q(x) := 3.6 cos (πx/24) + 2.
  1. At latitude 40◦^ north (Beijing, Madrid, Philadelphia) there are 12 hours of daylight on the equinoxes (approximately March 21 and September 21), with a maximum of 14.8 hours of daylight on the summer solstice (approximately June 21) and a minimum of 9.2 hours of daylight on the winter solstice (approximately December 21). (a) (3pts) Assume that the daylight is modeled by a sinusoidal function of t in days and that there are 365 days in a year. Defining t = 0 to be January 1st, sketch one full period of the graph of this function.

(b) (4pts) Find a function D(t) that models the number of daylight hours t days after January 1.

  1. Let f (x) := csc

arccos

(√ 16 − x 2 4

(a) (4pts) Using a right triangle, simplify the function f (x).

(b) (3pts) State the domain of f.

  1. Consider the equation 2θ cos θ + θ = 0. (a) (4pts) Find all solutions to this equation in the interval [0, 2 π].

(b) (2pts) Find all real solutions to this equation.

  1. (Continued) Consider the graph of the function f (x) := tan x. (c) (2pts) Determine a restricted domain D′^ on which f (x) is one-to-one and where the range of D′^ is the entire range of the tangent function.

(d) (4pts) Define an inverse function for the tangent function.

(e) (2pts) Evaluate arctan √3.