IMPORTANT INSTRUCTIONS FOR FINAL EXAM
▯ Make sure to bring a dark pencil or blue or black pen to the exam. The scanner can not read light
pencil marks; if you fail to comply your exam could receive a score of 0.
▯ The exam is in the RED gym. Make sure to consult the seating chart posted outside the gym to ﬁnd
your seat. You may only sit in an assigned sheet.
▯ Do not bring electronic devices to the exam. You are not permitted to use a calculator. Bringing one
of these devices to your seat could be considered academic misconduct.
▯ Please note that there is NO written portion to the ﬁnal exam, it is multiple choice.
▯ You MUST produce a student ID at the ﬁnal exam, don’t forget to bring it with you!
▯ We are Lecture 01 and the instructor name is Bauer; please be sure to remember this to ﬁll in the front
page of the exam. There will be more than one lecture in the RED gym; you must be careful to make
sure to hand your exam into the right instructor (Kristine Bauer). MATH 253 L01, L02, L03 - FINAL EXAM Winter 2012
Faculty of Science
Department of Mathematics & Statistics
MATH 253 L01, L02, L03
FINAL EXAM – WINTER 2012
April 21, 2012
COURSE INFORMATION AND STUDENT IDENTIFICATION
VERSION LECTURE INSTRUCTOR I.D. LAST FIRST
NUMBER NUMBER NAME NUMBER NAME NAME
1. No Calculators, electronic equipment, or other paper material than this examination and scantron sheet allowed.
2. Use the back of the previous page for rough drafts or calculations.
3. Students late in arriving will not normally be admitted after one-half hour of the examination time has passed.
4. No candidate will be permitted to leave the examination room until one-half hour has elapsed after the opening of the examination, nor during the last
15 minutes of the examination. All candidates remaining during the last 15 minutes of the examination period must remain at their desks until their
papers have been collected by an invigilator.
5. All enquiries and requests must be addressed to supervisors only.
6. Candidates are strictly cautioned against:
(a) speaking to other candidates or communicating with them under any circumstances whatsoever;
(b) bringing into the examination room any textbook, notebook or memoranda not authorized by the examiner;
(c) making use of calculators and/or portable computing machines not authorized by the instructor;
(d) leaving answer papers exposed to view;
(e) attempting to read other students’ examination papers.
The penalty for violation of these rules is suspension or expulsion or such other penalty as may be determined.
7. Candidates are requested to write on both sides of the page, unless the examiner has asked that the left half page be reserved for rough drafts or
8. Discarded matter is to be struck out and not removed by mutilation of the examination answer book.
9. Candidates are cautioned against writing in their answer books any matter extraneous to the actual answering of the question set.
10. The candidate is to write his/her name on each answer book as directed and is to number each book.
11. A candidate must report to a supervisor before leaving the examination room.
12. Answer books must be handed to the supervisor-in-charge promptly when the signal is given. Failure to comply with this regulation will be cause for
rejection of an answer paper.
13. If a student becomes ill or receives word of domestic afﬂiction during the course of an examination, he/she should report at once to the Supervisor, hand
in the unﬁnished paper and request that it be cancelled. Thereafter, if illness is the cause, the student must go directly to University Health Services so
that any subsequent application for a deferred examination may be supported by a medical certiﬁcate. An application for Deferred Final Examinations
must be submitted to the Registrar by the date speciﬁed in the University Calendar.
Should a student write an examination, hand in the paper for marking, and later report extenuating circumstances to support a request for
cancellation of the paper and for another examination, such request will be denied.
Page 2 MATH 253 L01, L02, L03 - FINAL EXAM Winter 2012
Each question is worth 5 points. Exam version: 00
1. Evaluate the integral.
1 2 1 2 1
(a) 2x ln(x) ▯ x4+ 2x2+ x + C
1 1 1
(b) 2(x ▯ 1)ln(x) ▯ x 4 x + C2
(c) 1x ln(x) ▯ x + C
(d) 1x ln(x) ▯ x + x + C
(e) 1x ln(x) + x + C
2. Evaluate the integral.
0 4 + x
(a) 5 ▯ 2
(c) 3 ▯ 1
(e) 3 ▯ 5
Page 3 MATH 253 L01, L02, L03 - FINAL EXAM Winter 2012
Exam version: 00
3. Evaluate the integral.
(4 ▯ x ) 3=2
(d) 4 5
4. Evaluate the integral. Z
3 2 dx
x ▯ x ▯ 2x
(a) ln(jxj) + ln(jx ▯ 2j) ▯ 2 + C
(b) ln(jxj) + ln(jx ▯ 2j) ▯ 3ln(jx + 1j) + C
(c) ln ▯ x+1 ▯ + C
(d) ln(jxj) + 3ln(jx ▯ 2j) ▯ 1ln(jx + 1j) + C
(e) ▯ln(jxj) + 1 ln(jx ▯ 2j) + 2 ln(jx + 1j) + C
Page 4 MATH 253 L01, L02, L03 - FINAL EXAM Winter 2012
Exam version: 00
5. Consider the function f (x) = 2x + 2x + 3: Denote by g(x) = f (x) the inverse function of f(x).
Find g (▯1).
(e) ▯ 1
6. Consider the solid of revolution obtained by rotating the plane region enclosed by y = ▯x; y = 2x
and y = 2 about the axis y = 3. Which integral computes the volume of this solid?
Z ▯ ▯
(a) 2▯ (3 + y) dy
Z 2 ▯ ▯
(b) 2▯ (3 ▯ y) dy
(c) 2▯ 2y(y + 1) dy
(d) 2▯ (2 ▯ y) dy
(e) 2▯ (1 + y)(3y) dy
Page 5 MATH 253 L01, L02, L03 - FINAL EXAM Winter 2012
Exam version: 00
7. Find the arc length of the curve y = 2e + x 1e▯x in the domain 0 ▯ x ▯ ln2.