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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.
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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.
Multiple Choice (2 points each) Please write the letter of the correct answer in the blank.
a) k = 3 b) k = 3 or k = − 3 c) k = 6 d) k = 6 or k = − 6
a) |x + 3| ≥ 2 b) |x − 3 | ≤ 2 c) |x + 3| < 2 d) |x − 3 | > 2
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.
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.
x. Find (g ◦ f )(x) and express its domain in interval notation.
f (x) =
f (x + h) − f (x) h , h 6 = 0.