Math 111 Winter 2004 First Midterm Examination Solutions, Exams of Algebra

The solutions to the first midterm examination for math 111 at the university, held in winter 2004 by chris phan. The examination covers various topics in mathematics, including true or false questions, multiple choice questions, open-answer questions, and graph sketching. Students are required to sign a statement of academic honesty before taking the exam.

Typology: Exams

Pre 2010

Uploaded on 07/23/2009

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First Midterm Examination
Math 111, Winter 2004, Chris Phan
3 February 2004
Name:
Please read, complete, and sign the following:
I, , completed the following examina-
tion in accordance the University’s policies on academic honesty. Specifically, I did
not receive unauthorized assistance from another person and I did not use any unautho-
rized testing aids.
Signed:
Good luck! Be sure to do all pages! (50 points total)
1
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pf4
pf5

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First Midterm Examination

Math 111, Winter 2004, Chris Phan

3 February 2004

Name:

Please read, complete, and sign the following:

I, , completed the following examina- tion in accordance the University’s policies on academic honesty. Specifically, I did not receive unauthorized assistance from another person and I did not use any unautho- rized testing aids.

Signed:

Good luck! Be sure to do all pages! (50 points total)

True or False (2 points each) Please circle “T” if the statement is true, and “F” if the statement is false.

  1. T F If A is directly proportional to t, then A is a function of t.
  2. T F Every function is even or odd.
  3. T F It is always true that (f ◦ g)(x) = (g ◦ f )(x).
  4. T F The graph of f (x) = − 3 x + 2 is a line perpendicular to the line given by 3 y − x − 1 = 0.

Multiple Choice (2 points each) Please write the letter of the correct answer in the blank.

  1. For what value(s) of k does the equation x^2 + kx + 9 = 0 have exactly one real solution?

a) k = 3 b) k = 3 or k = − 3 c) k = 6 d) k = 6 or k = − 6

  1. If x is 2 or more units away from − 3 on the real number line, then which of the following is true?

a) |x + 3| ≥ 2 b) |x − 3 | ≤ 2 c) |x + 3| < 2 d) |x − 3 | > 2

  1. There are 109 miles between Portland and Eugene (using I-5). Chris leaves Eugene for Portland, driving north along I-5 at 70 miles per hour. A half-hour later, Linnea leaves Portland for Eugene, driving south along I-5 at 65 miles per hour. If t is the number of hours since Chris left, we could find when they will meet in-between Portland and Eugene by solving for t in which of the following?

a) 109 − 70 t = 65t. b) (70 + (65 − 12 ))t = 109. c) 70 t − 65(t − 12 ) = 109. d) 70 t + 65(t − 12 ) = 109.

  1. (8 points) Graph

f (x) =

2 x + 3, if x < − 1 , (x + 1)^2 − 4 , if x ≥ − 1.

carefully (i.e., plot some points, label axes, include details about which points are on the graph.) Show complete reasoning—don’t just plug into a graphing calculator. Make it clear what transformations you used.

  1. (8 points) Let f (x) = x^2 − 1 and g(x) =

x. Find (g ◦ f )(x) and express its domain in interval notation.

  1. (6 points) Let f (x) = x^2 + 3x − 3. Find the difference quotient

f (x) =

f (x + h) − f (x) h , h 6 = 0.

  1. (5 points) For which value(s) of k do the points (3, 6) and (9, k) have a distance of 10?
  2. ( EXTRA CREDIT , 3 points) Give me an example of a function with x-axis symmetry.