Elementary Calculus

Carleton University, Mathematics 69.1007

Updated December 19, 2005

Final Examination Solutions

TA: Abeer Al-Azzawi

TA: Luan Nguyen

TA: Chiara Mingarelli

Problem Set Review for Final examination (70 questions)

Scantron Sheets- 2005- for final examination

How to study for this course (my idea)
How to study for this course (someone else's idea)

NEW!!

Diagnostic Test Results

NOTE: Homework will be assigned but NOT collected.

Additional 2 FREE new Chapters to the text:

******** A Chapter on Review of Trigonometry
Erratum/Corrigendum:
page 2, box:    Replace the square root of 2 there by the number 1,
page 4, third line of the solution of Example 1 (2):  Replace 2Pi/3 by Pi/3.
page 4, last line of the solution of Example 1 (2):  Replace the "sin" there by "cos" and the square root of 3 by 1,
page 5, Table 1.1:  The fourth zero in the first column should be replaced by 1.
page 8, Figure 18:  The angle theta in the picture should extend from OR to OP and not only to the x-axis.
page 13, Exercise 33: Insert a "+" sign between the two trig functions on the right.

page 14, Exercise 42:  Replace the right-hand side by - sin (theta).

Office Hours:

Dr. Mingarelli, Herzberg Building # 4250
Tuesdays and Thursdays, 4:00-5:30 p.m.

Classes:           MATH 1007  Sec. D:
Tuesdays 5:30 p.m.- 7:30 p.m., Room 302, Azrieli Pavillion
Thursdays 5:30 p.m.- 6:30 p.m., Room 302, Azrieli Pavillion

Detailed Class Outline The Calculus Plotter (Free with a copy of the textbook)

2001 CLASS NOTES (from a Whiteboard)

Limits of functions
Trigonometric Functions and their Derivatives
Inverse Functions and their Derivatives
Derivatives of Inverse Trigonometric Functions
Exponential and logarithmic functions and their derivatives
Exponential and logarithmic functions and their derivatives-continued
Curve sketching
Integration by substitution
Integration by substitution-continued
Integration of trigonometric functions
Integration by Parts
Integration by Parts-continued
Introduction to area
Area between two curves
Arc length of a curve
Partial Fractions

MATHEMATICS 69.107D, CLASS OUTLINE FOR FALL 2005

 WEEK DATES TESTS SECTIONS TOPICS 0 Sept. 8 ~ A history of Calculus Review your math. definitions  above. Review of Trigonometric functions 1 12-16 ~ 2.1-2.5; 3.1-3, 3.5 Limits, Continuity and Derivatives.  Derivatives of Trigonometric Functions. 2 19-23 ~ 3.8, 3.9, 3.12 Derivatives of Inverse Trigonometric Functions. L'Hospital Rule 3 26-30 Test 1 Sep 29 3.4, 3.7-8 Implicit differentiation, Exponential and Logarithmic Functions and Their Derivatives 4 Oct. 3-7 ~ 5.3 Maximum and Minimum Values. 5 10-14 ~ 5.1-5.3 First and Second Derivative Test. Curve Sketching. 6 17-21 Test 2 Oct. 20 6.1-6.4 Antiderivatives and Indefinite Integrals, Area Under a Curve, Definite Integrals, 7 24-28 ~ 7.2-7.3 Fundamental Theorem of Calculus, Integration by substitution. Integration by Parts. 8 31-Nov. 4 Test 3 Nov. 3 7.4-7.5 Integration by Partial Fractions. Products and Powers of Trigonometric Functions. 9 7-11 ~ 7.6 Trigonometric Substitutions 10 14-18 Test 4 Nov 17 8.2-8.3 Areas Between two Curves, The Volume of a solid of revolution. 11 21-25 ~ 9.3 Laws of Growth and Decay (if time permits) 12 28-Dec.2 ~ ~ Review and Sample Final Exams.

TEXTBOOK(S):
Calculus, by Angelo B. Mingarelli (The Millennium Series), along with a Solutions Manual (bundled together). Available at the Bookstore or at Haven Books on Sunnyside Avenue near the Campus. The current Edition is dated August 26, 2002.
OR, if you really want to spend more you can buy,
Single Variable Calculus Early Transcendentals, fiftth edition, by James Stewart.
In this case, go to the web site of the coordinator for this course, Dr. Alaca, for corresponding section locations.

PREREQUISITES:
The prerequisites for this course are:
Ontario Grade 12 Mathematics: Advanced Functions and Introductory Calculus; or an OAC in Calculus, or MATH 0007 (formerly 69.007*), or equivalent.

WITHDRAWAL:
The last day for withdrawal from the course is November 07, 2005.

EVALUATION

Tests: 40%. Tutorial Work: 10%. The final examination is 50%.

If you do all the weekly quizzes, homework and tests, as well as the sample tests and final exams on this website, you'll likely pass (maybe even Ace it!).

TERM MARK:
There will be four 50-minute tests in the tutorial hours on September 29, October 20, November 3, November 17, 2005. You are expected to take all the tests. No make up, early, or delayed tests. Any missing test will be counted as zero. It is your responsibility to pick up your tests in the following tutorial hours. The average of best three tests out of four tests will be counted as 40%.

SUPPLEMENTAL EXAMINATION
No Supplemental examinations

CALCULATORS
You may use a non-programmable calculator for the examinations and tests in this course: One of either Sharp EL-531 (usually available in the Bookstore) or Casio FX-991 or any other approved non-programmable calculator.  The course instructor reserves the right to disallow any calculator.

TUTORIALS:

Tutorial Work: There will be problem solving sessions during the Tutorial Hour. At the end of the Tutorial Hour you will requested to hand in your work in order to be evaluated. Your Tutorial work during the term will be counted as 10%. Tutorials are on Thursdays from 6:30-7:30 p.m. You will be taking your Tests during these hours and only during these hours.

All tutorials usually begin the second week of September (TBA) in various locations depending on your section and the first letter of your family name (surname, cognome(n)) or on the information given to you at registration.  Please consult your Instructor otherwise.

Do I HAVE to go? YES! This is strongly recommended, esp. if you want your 10%...

Who is my T.A.? Go the required class and ask him/her (there are always last minute changes in the TA's).

Where do I go? Normally your section is given to you at registration time. Otherwise, this depends on your section letter and/or on the first letter of your family name; see the next table for details about which room you'll go to.

D1      Go to 403 SA (Southam Building)  T.A.   Mingarelli, Chiara    (cmfminga@connect.carleton.ca)     Consultation: Thursdays, 2221 HP, 5-6 p.m.
D2      Go to 516 SA (Southam Building)  T.A.   Al-Azzawi, Abeer    (aaazzawi@connect.carleton.ca)     Consultation: 8:30-9:30 in  HP 1160.
D3      Go to 505 SA (Southam Building)
T.A.   Luan Nguyen          (lnguyen2@connect.carleton.ca      Consultation: Wednesdays, 11-12, HP 1160

TUTORIAL CENTRE:

Please note that the mathematics TUTORIAL or HELP CENTRE, in Herzberg Physics Building, Room 1160, tunnel level, will be opening Monday, Sep. 19
Tutors advertise frequently on the Notice Boards around the Centre.
Hours for the center are as follows:
MONDAYS TO THURSDAYS: 10 AM TO 4 PM
FRIDAYS: CLOSED

 WEEK TUTORIALS HOMEWORK &  ASSIGNMENTS Week 0 Exercise Set 1, pages 13-14 of Quick Trigonometry Review pdf file Week 1 Tutorials begin All Exercise sets  in stated sections Week 2 Tutorials All Exercise sets  in stated sections Week 3 Tutorials All Exercise sets  in stated sections Week 4 TEST 1 Old Test 1- Solutions All Exercise sets  in stated sections Week 5 and 6 TEST 2 Old Test 2  - Solutions Practice Assignment 1 Week 7 and 8 Curve sketching software Solutions to   Practice Assignment 1 Week 9 TEST 3 Old Test 3 - Solutions Homework Sets 16   and Set 24 Week 10 TEST 4 Old Test 4 Practice Assignment 2  Solutions Week 11 1997 Sample Final Exam Practice Assignment 2  Solutions Week 12 1998 December Sample Final Exam  1998 December FINAL Exam Practice Assignment 2  Solutions