Practice Exam 2 for Preparation for Calculus | MATH 115, Exams of Mathematics

Material Type: Exam; Professor: McNeilly; Class: Preparation for Calculus; Subject: Mathematics; University: University of Illinois - Urbana-Champaign; Term: Fall 2010;

Typology: Exams

2010/2011

Uploaded on 10/12/2011

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Math 115 Exam 2 V1 Name:
October 11, 2010 Lecture: A1-8AM X1-Noon F1-2PM
60 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 IPODs, MP3 players, etc. 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 above and circle your lecture time.
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 60 minutes to complete the exam.
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Math 115 – Exam 2 – V1 Name:

October 11, 2010 Lecture: A1-8AM X1-Noon F1-2PM

60 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 – IPODs, MP3 players, etc. – 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 above and circle your lecture time.
  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 60 minutes to complete the exam.
  1. Consider the series − 5 − 2 + 1 + 4 + ... + 112. (a) (5pts) Write this series using summation notation.

(b) (2pts) Evaluate the series.

  1. Consider the sum

∑^9

k=

k − 5 2 k − 13 (a) (4pts) Expand the sum.

(b) (3pts) Compute the sum.

  1. Consider the series

∑^ ∞

n=

4 rn−^1. For each indicated value of r, tell whether the series is convergent

or divergent. If convergent, state the value of the series. (a) (2pts) r = 1

(b) (2pts) r =^45

(c) (2pts) r = − 109

  1. Consider the series S = 2 + 3 +^92 +^274 + ... (a) (3pts) Find and fully simplify the first 3 partial sums.

(b) (3pts) Find the 20th partial sum. (You do not need to completely simplify.)

(c) (2pst) Find the N th^ partial sum. (You do not need to completely simplify.)

(d) (4pts) Evaluate the series.

  1. Consider the real number represented by the series α = 5 + 10 1 + 10362 + 10364 + 10366 + ...

(a) (2pts) Express α as a decimal.

(b) (2pts) Explain what about the decimal representation of α tells you it is a rational number.

(c) (5pts) Find the rational number representation of α.