# Math 103(106L) Exam 2 Solutions

Read each question very carefully. You are **NOT **
permitted to use a calculator on any portion of

this exam. You are **not** allowed to use any textbook, notes, cellphone, or
laptop on either portion

of the exam. No part of this exam may be removed from the examination room.

In order to receive full credit for the free response portion of the exam, you
must:

1. Show legible and logical (relevant) justification which supports your final
answer.

2. Use complete and correct mathematical notation .

3. Include proper units, if necessary.

4. Give exact numerical values whenever possible.

You have **90 minutes **to complete the entire exam

**On my honor, I have neither given nor received
inappropriate or unauthorized information
during this exam.
Student’ s Signature : ________________________________________________**

Do not write below this line .

Free Response Problem |
Possible Points |
Points Earned |
FreeResponse Problem |
Possible Points |
Points Earned |

1 | 5 | 6b | 5 | ||

2 | 10 | 7a | 2 | ||

3 | 5 | 7b | 2 | ||

4a | 5 | 7c | 2 | ||

4b | 1 | 8 | 1 | ||

4c | 2 | FreeResponse |
50 | ||

5 | 5 | MultipleChoice |
50 | ||

6a | 5 | Exam Total |
100 |

** Multiple Choice . There are 22 multiple choice
questions. Each question is worth 2 – 3
points and has one correct answer. The multiple choice problems will count 50%
of the
total grade. Use a number 2 pencil and bubble in the letter of your response on
the
scantron sheet for problems 1 – 22. For your own record, also circle your choice
on your
exam since the scantron will not be returned to you. Only the responses recorded
on your
scantron sheet will be graded. You are NOT permitted to use a calculator on any
portion of
this exam.**

1.Match the graph to its equation y = ln(x - 1) + 2 .

**(2 pts.)**

2.Evaluate the following:

**(2 pts.) **

3. It can be shown that the inequality
holds for all .Find .

**(2 pts.)**

4. Solve for x :

**(2 pts.)**

5. Factor the following expression completely:

**(3 pts.)**

6.If , find

**(3 pts.)**

7.Find .

**(2 pts.) **

8.Use the graph below to find the largest possible
> 0 such that for all x,

**(2 pts.)**

9.Evaluate the following:

**(2 pts.)**

10.Find the average rate of change of f (x) = 4x^{2} over the
interval

**(3 pts.)**

11.Factor the following expression completely :

**(2 pts.)**

12.Find .

**(3 pts.)**

13.Find

**(3 pts.) **

14.Evaluate

**(2 pts.) **

15.Solve for x:

**(2 pts.)**

16.State the domain and range of

**(2 pts.)**

17.Find

**(2 pts.) **

18.Find

**(3 pts.)**

19.Simplify

**(2 pts.)**

20.Simplify .

**(2 pts.)**

21.Simplify

**(2 pts.)**

22. Simplify tan (sec^{-1} x) and indicate where the
simplification is valid.

**(2 pts.)**

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