Math Exam 1 - Instructions and Problems - Prof. Jennifer R. Mcneilly, Exams of Mathematics

The instructions and problems for exam 1 of math 115. The exam covers topics such as functions, sequences, and series. Students are prohibited from wearing hats or sunglasses, using cell phones, or bringing book bags into the exam room. The exam consists of questions related to finding the domain of a function, identifying arithmetic and geometric sequences, and evaluating series. The document also includes instructions for handing in the exam and information about the exam format.

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2010/2011

Uploaded on 10/12/2011

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Math 115 โ€“ Exam 1 โ€“ 12PM V1 Name:
February 19, 2010
50 points possible
1. No hats or dark sunglasses. All hats are to be removed.
2. All book bags are to be closed and placed in a way that makes them inaccessible. Do
not reach into your bag for anything during the exam. If you need extra pencils, pull
them out now.
3. No cell phones. Turn them off now. If you are seen with a cell phone in hand during
the exam, it will be construed as cheating and you will be asked to leave. This includes
using it as a time-piece.
4. No music systems โ€“ IPODs, MP3 players, etc. โ€“ or calculators; same rules as with cell
phones.
5. If you have a question, raise your hand and a proctor will come to you. Once you stand
up, you are done with the exam. If you have to use the facilities, do so now. You will
not be permitted to leave the room and return during the exam.
6. 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 9 pages.
7. Be sure to print your proper name clearly.
8. If you finish early, quietly and respectfully get up and hand in your exam. You need
to show your student ID when you hand in the exam. (Drivers license, passport, etc.
will work also.) No exam will be accepted without ID.
9. When time is up, you will be instructed to put down your writing utensil, close the
exam and remain seated. Anyone seen continuing to write after this announcement
will have their exam marked and lose all points on the page they are writing on. We
will come and collect the exams from you. Have your ID ready.
10. Good luck. You have fifty minutes to complete the exam.
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Math 115 โ€“ Exam 1 โ€“ 12PM V1 Name:

February 19, 2010

50 points possible

  1. No hats or dark sunglasses. All hats are to be removed.
  2. All book bags are to be closed and placed in a way that makes them inaccessible. Do not reach into your bag for anything during the exam. If you need extra pencils, pull them out now.
  3. No cell phones. Turn them off now. If you are seen with a cell phone in hand during the exam, it will be construed as cheating and you will be asked to leave. This includes using it as a time-piece.
  4. No music systems โ€“ IPODs, MP3 players, etc. โ€“ or calculators; same rules as with cell phones.
  5. If you have a question, raise your hand and a proctor will come to you. Once you stand up, you are done with the exam. If you have to use the facilities, do so now. You will not be permitted to leave the room and return during the exam.
  6. 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 9 pages.
  7. Be sure to print your proper name clearly.
  8. If you finish early, quietly and respectfully get up and hand in your exam. You need to show your student ID when you hand in the exam. (Drivers license, passport, etc. will work also.) No exam will be accepted without ID.
  9. When time is up, you will be instructed to put down your writing utensil, close the exam and remain seated. Anyone seen continuing to write after this announcement will have their exam marked and lose all points on the page they are writing on. We will come and collect the exams from you. Have your ID ready.
  10. Good luck. You have fifty minutes to complete the exam.
  1. (5pts) Consider the function f (x) :=

โˆš (^39) โˆ’ x 2 x^2 โˆšx + 2. (a) State the domain of f (x) using set notation.

(b) State the domain of f (x) using interval notation.

  1. (7pts) Consider a arithmetic sequence whose third term is a 3 = โˆ’11 and whose tenth term is a 10 = โˆ’^1733. Find the function a(n) that describes this sequence.

(a) (3pts) Suppose an is an arithmetic sequence such that lim nโ†’โˆž an = a 1. What do you know about the common difference d? Briefly explain your answer.

(b) (3pts) Suppose an is a geometric sequence such that (^) nlimโ†’โˆž an = 0. What do you know about the common ratio r? Briefly explain your answer.

  1. Evaluate the following series. (You do not need to simplify your answer.)

(a) (4pts) 4 + 4

(b) (4pts) 4 + 1 + (โˆ’2) + (โˆ’5) +... + (โˆ’35)

(c) (2pts) Write the series in (b) using sigma notation.

  1. (5pts) Write the summation

โˆ‘^7

i=

(i^2 โˆ’ 2 i) as an explicit sum and evaluate (by fully sim-

plifying) the sum.

  1. For each of the following evaluate the associated infinite series. If the series is finite, you do not need to simplify your answer. If the infinite series is not defined, you must clearly show why.

(a) (3pts) 9999 + 9998 + 9997 + 9996 +...