Calculus 42S – Course Outline
Teacher:
Mrs. Ashley Dupont
Room: 102
Email: adupont@stmaurice.mb.ca
Course Description
Calculus AB is an introduction to calculus and is essentially what every subsequent calculus course that
you may take in the future is built upon. Calculus AB focuses on the fundamentals – specifically limits,
and the differentiation and integration of elementary functions, with applications to maxima and minima,
rates of change, area, and volume.
Teaching Methods/Strategies
 A variety of teaching methods will be used throughout the course including
o Lectures with discussion
o Student-centered learning
o Brainstorming/Critical thinking
o Reading assignments
o Cooperative learning
o Guided discovery
o Problem solving/Investigations
 The course provides students the opportunity investigate problems, which students are
encouraged to explore analytically, graphically, numerically and verbally. The course
emphasizes the connections between each of these representations.
 The course uses the graphing calculator as a tool to help solve problems, experiment, interpret
results, support conclusions and to make connections to the varied representations.
 Students are encouraged to offer solutions in class and to fully explain their answers
 Students are encouraged to form study groups/compare solutions to homework/etc
Textbooks
Primary Text:
 Calculus: Graphical Numerical Algebraic, Finney, Demana, Waits, Kennedy, Prentice Hall
2003.
Secondary Texts:
 Single Variable Calculus Early Transcendentals, 4th Edition, James Stewart, Brooks/Cole
Publishing Company, 1999.
 Calculus: A Complete Course, 4th Edition, Robert A. Adams, Addison Wesley Longman
Ltd., 1999.
 830 Worked examples in OAC Calculus, George Tam, 1999.
 Other handouts and websites will be used throughout the course
Web Resources
Content Based
 College Board Website - http://www.collegeboard.com/student/testing/ap/sub_calab.html?calcab
 Paul Dawkins – Lamar University – http://tutorial.math.lamar.edu/classes/calcI/calcI.aspx
 Prentice Hall Mathematics – http://www.phschool.com/atschool/calculus
 Pre-Calculus Mathematics 40S – http://www.math40s.com
Internet Based
 Department of Mathematics, University of Manitoba http://umanitoba.ca/science/mathematics/
 Department of Mathematics and Statistics, University of Winnipeg-http://mathstat.uwinnipeg.ca/
 University of Manitoba’s Actuarial Program – http://umanitoba.ca/actuarial/undergrad.html
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Materials –(Bring to each class)
 A binder with paper to write on
 A writing utensil (preferably a pencil with eraser)
 Your textbook
 A TI-83 graphing calculator
 Come to class prepared to learn
Note: Several handouts are used to supplement the course material. You will also receive many practice exams from a
variety of sources. As such, it is suggested that you keep a separate organized binder.
Tentative Course Outline
1) Limits
September - October
a) Rates of Change
b) Limits at a point
1. Properties of limits
2. Two-sided limits
3. One-sided limits
c) Limits involving infinity
1. Asymptotic Behavior
2. End Behavior
3. Properties of limits involving infinity
d) Continuity
1. Continuous functions
2. Discontinuous Functions
i.
Removable discontinuity
ii.
Jump Discontinuity
iii.
Infinite Discontinuity
e) Instantaneous Rates of Change
2) Derivatives
a) Definition of the Derivative
b) Differentiability
1. Local linearity
2. Numeric Derivatives and the TI-83
3. Differentiability and continuity
c) Derivatives of algebraic functions
d) Derivative rules when combining functions
e) Applications to velocity and acceleration
f) Derivatives of trigonometric functions
g) The Chain Rule
h) Implicit Derivatives
i) Derivatives of Inverse Trigonometric Functions
j) Derivatives of Logarithmic and Exponential functions
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October - November
3) Applications of Derivatives
November - December
a) Extreme values
a. Local (relative) and Global (absolute) extrema
b) Using the derivative
a. Mean Value Theorem
b. Rolle’s Theorem
c. Increasing and Decreasing functions
c) Analysis of graphs using the first and second derivative
a. Critical values
b. First derivative Test
c. Concavity and points of inflection
d. Second derivative test
d) Curve Sketching
e) Optimization Problems
f) Related Rates
4) Integrals
a) Antiderivatives
b) Approximating Area under the Curve
1. Adding Rectangles
c) Riemann Sums & Trapezoidal Rule
d) The Fundamental Theorem of Calculus (Part I)
e) Indefinite Integrals
f) Definite Integrals
g) The Fundamental Theorem of Calculus (Part II)
h) Substitution Rule (U-Sub)
5) Applications of Integrals
a) Average Function Value
b) Particle Motion
c) Differential Equations
a. Growth and Decay
b. Slope Fields
c. General differential equations
d) Area Between curves
e) Volumes
1. Volumes of solids with known cross sections
2. Volumes of Revolution
i. Method of rings (Disk)
ii. Method of cylinders (Shell)
Evaluation
40% Tests
50% Midterms (November and March)
10% Quizzes
January - March
March - April
Tests – Will generally occur twice a month evaluating the content that we are focusing on in class. Most
of the tests will be done in class time but some of the tests will be take home tests (making it more like an
assignment) where students are encouraged to communicate with each other and compare solutions.
Midterms – Exams set up in the AP College Board style – with a mix of multiple choice, and written
response sections. Each midterm is 1.5 hours in length and there are calculator sections and noncalculator sections.
Quizzes – Will generally occur twice a chapter and are a way to demonstrate what has been learned fully
and what needs further review before the test.
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**Students who choose to write the College Board Final Exam will have their mark based upon their
tests, the November Midterm and the March Midterm and their quizzes in order to determine their
final mark. Students who do NOT choose to write the College Board final exam, will write a final
exam work 40% of their total mark.
Students are reminded to refer to their student handbooks regarding evaluation procedures.
Comments
 You can’t learn Calculus by cramming before the final. It just isn’t that kind of subject; it
involves ideas and computational methods that can’t be learned without practice.
 Students who miss a class are responsible for catching up on missed notes and assigned work.
Students should get the notes from another student, read through them, address their textbook
and then come to me with any questions.
 Students who miss a test or a midterm will receive a zero score, unless you make alternate
arrangements with me PRIOR to the scheduled time of the test. (Parental note required) The
student will generally write the test the first day the student returns to school.
How to Succeed
 Record notes & examples, participate in discussions and ask questions if necessary.
 If you don’t understand something, please ask. Sharing your questions or comments during class
helps me teach the class and helps you and your classmates learn.
 To be successful in this course, you must keep up with the homework. You should do some
homework/review everyday. I encourage you to work with other students in the class on the
assigned questions or check your solutions with your peers.
 Keep up and don’t be lazy! The more work/effort you put in at the beginning the better chance
you will have of understanding later. It is extremely hard to “catch-up” in this course.
 I will always assign more questions than I expect you to do overnight. Do as many questions as
it takes until you understand the concept – be sure to look at more challenging questions.
 Retests will not be allowed.
 You will find that you will need help in this course. Please don’t wait to get help. If you don’t
understand a question or are seriously struggling with a concept, you need to come to see me
that day after school or the next morning before school. The longer you wait the worse the
problem will become.
Attendance Policy
Attendance will strictly conform to school policy. It is recommended that students attend class on time
with all the appropriate materials and be prepared to learn. See student agenda for more details.
***Changes to this course outline and the stated requirements may be made at the discretion of the
teacher. Necessary changes will be based on sound reasons such as student interests for example, but will
keep within the course outcomes.
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