CHARLES HENDERSON HIGH SCHOOL
Calculus
2015-2016
Teacher Information
Michelle Armstrong
Math Teacher
armstrongm@troyschools.net
334-566-3510
Instructor Education
M.S.E. Mathematics Education, Troy State University
B. S. Mathematics, Troy State University
Course Description
Calculus emphasizes limits and derivatives of functions of one variable. The primary aims of the course
are to help students develop new problem solving and critical reasoning skills and to prepare them for
further study in mathematics, the physical sciences, or engineering.
Course Objectives
1. Interpret a function from an algebraic, numerical, graphical and verbal
perspective and extract information relevant to the phenomenon modeled
by the function.
2. Verify the value of the limit of a function at a point using the definition of the limit
3. Calculate the limit of a function at a point numerically and algebraically using
appropriate techniques including l’Hospital’s rule.
4. Find points of discontinuity for functions and classify them.
5. Understand the consequences of the intermediate value theorem for continuous functions
6. Interpret the derivative of a function at a point the as the instantaneous rate of change
in the quantity modeled and state its units.
7. Interpret the derivative of a function at a point as the slope of the tangent line
and estimate its value from the graph of a function
8. Sketch the graph of the derivative from the given graph of a function.
9. Compute the value of the derivative at a point algebraically using the (limit) definition
10. Derive the expression for the derivative of elementary functions from the (limit)
definition
11. Be able to show whether a function is differentiable at a point.
12. Compute the expression for the line tangent to a function at a point
13. Interpret the tangent line geometrically as the local linearization of a function
14. Compute the expression for the derivative of a function using the rules of differentiation
Including the power rule, product rule, and quotient rule and chain rule.
15. Compute the expression for the derivative of a composite function using the chain rule of
differentiation.
16. Differentiate a relation implicitly and compute the line tangent to its graph at a point
17. differentiate exponential, logarithmic, and trigonometric and inverse trigonometric
Functions.
18. Obtain expressions for higher order derivatives of a function using the rules of
differentiation
19. Interpret the value of the first and second derivative as measures of increase and
concavity of a functions.
20. Compute the critical points of a function on an interval.
21. Identify the extrema of a function on an interval and classify them as
minima , maxima or saddles using the first derivative test.
22. Use the differential to determine the error of approximations.
23. Understand the consequences of Rolle’s theorem and the Mean Value theorem
for differentiable functions
24. Find the anti-derivative of elementary polynomials, exponential,
logarithmic and trigonometric functions.
25. Interpret the definite integral geometrically as the area under a curve
26. Construct a definite integral as the limit of a Riemann sum
27. Approximate a definite integral using left sum, right sum, midpoint and
trapezoidal rules
28. Interpret the indefinite integral as a definite integral with variable limit(s).
29. Interpret differentiation and anti-differentiation as inverse operations (Fundamental
Theorem of Calculus, part 1)
30. Interpret the anti-derivative as a definite integral with variable limit and implement this
expression on graphing platforms
31. Evaluate a definite integral using an anti-derivative (Fundamental Theorem of Calculus,
part 2)
32. Use substitution to find the anti-derivative of a composite function.
33. Apply basic optimization techniques to selected problems arising in various fields such
as physical modeling , economics and population dynamics.
Student Learning Outcomes
 compute limits by graphical, numerical, and analytical methods;
 mechanically calculate derivatives of algebraic and trigonometric functions and
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combinations of functions;
use derivatives to sketch graphs and solve applied problems;
represent functions graphically, numerically, analytically, and verbally;
interpret derivatives as rates of change;
analyze and solve complex problems;
 understand the relationship between the derivative and the definite integral as
expressed in both parts of the Fundamental Theorem of Calculus
 provide clear written explanations of the ideas behind key concepts from the course.
Course Prerequisites
Algebra I, Geometry, Algebra II with Trigonometry, Pre-Calculus
Specific Course Requirements
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Follow all rules as defined in the Troy City Schools and Charles Henderson High School
Codes of Conduct.
Bring all materials to class daily.
1.) Ipad – Textbook
2.) Notebook
3.) Calculator – Scientific calculator
4.) Pencil
Required Textbook
Calculus (Larson) 9th edition
Method of Evaluation
Grades will come from tests, homework checks, quizzes, group work, daily grades. Grades will
be posted in INOW, and should be checked regularly by the student. All major test are counted
twice and are graded out of 100 points. Quizzes are at least 30 points and no more than 50
points. Homework checks are worth 20 points. Group work, daily grades are graded depending
on the assignment. There will be a quiz EVERY THURSDAY.
Make-Up Work Policy
Make up work must be completed within 3 days. Tests, quizzes and daily grades are required to
be made up. Make up work may be done before school and after school Monday - Thursday.
NO make-up work is done on Fridays. A make-up form must be filled out completely and given
to the teacher. Failure to make up work will result in a 0 for the assignment.
Communication Requirements:
INOW – each student will need to get their INOW account number in order to check grades.
Remind (remind101)
Text @cal5th to 81010
Edmodo
Edmodo is required for this class. You will be given your edmodo code for this class at a later
date. Edmodo can be used on any ipad, smartphone or computer.
Test Date
Registration Deadline
(Late Fee Required)
September 12, 2015
August 7, 2015
August 8–21, 2015
October 24, 2015
September 18, 2015
September 19–October 2, 2015
December 12, 2015
November 6, 2015
November 7–20, 2015
February 6, 2016*
January 8, 2016
January 9–15, 2016
April 9, 2016
March 4, 2016
March 5–18, 2016
June 11, 2016**
May 6, 2016
May 7–20, 2016