MOUNT PLEASANT AREA
COURSE SYLLABUS
Title: Calculus
Department: Mathematics
Grades Taught: 12th Grade
Course Description:
This course is designed for the advanced academic student who has successfully completed Precalculus in his/her junior year. The basic material consists of the differential and integral calculus
of functions of a single variable and plane analytic geometry. The theoretical and geometrical
interpretations of calculus concepts are stressed. An emphasis is placed upon the algebraic
(symbolic), graphical, and numerical interpretations of these concepts. Graphing utilities such as
the graphing calculator and computer activities are used for visual analysis of mathematics.
Problem solving utilizing real world applications and mathematical modeling is emphasized. The
importance of technology to solve these real word problems is stressed.
Prerequisites: C grade in Pre-calculus
Strong skills in algebraic manipulation and trigonometry are essential.
Length of Course: 2 periods on alternating days (year)
Credit: Weighted Course worth 1.5 Credits
Course Standards:
Mount Pleasant Curriculum
Learning Objectives and Course Outline:
1. Prerequisites for Calculus











write the equation of a line when given a point and the slope, two points, and slope
and y-intercept and sketch a graph
-write equations of parallel and perpendicular lines
superimpose the graph of the linear regression equation on a scatter plot of given
data and make predictions using technology
interpret the C  / F  function
discuss the algebraic and geometric interpretations of a function, domain and range
sketch complete graphs of common functions
state whether a function is even, odd, or neither and describe the geometrical
interpretation of this in reference to symmetry
graph piecewise functions
graph the absolute function and graph it
calculate the composition of functions
memorize 15 Trig Identities
Page 1 of 9
MOUNT PLEASANT AREA
COURSE SYLLABUS











calculate the domain and range of a function and discuss the geometrical
interpretations
solve real world application word problems relating to exponential growth and decay
solve investment application problems involving interest compounded continuously
and at specified intervals
graph curves that are described using parametric equations
find parameterizations of circles, ellipses, line segments and other curves
determine whether a function is 1-1 by inspecting its graph and referring to the
horizontal line test
determine whether a function has an inverse function
discuss the definition of the inverse of a function in reference to the identity
function and composition of this function with its inverse
find the inverse of a 1-1 function algebraically
graph the inverse of a function parametrically
solve exponential and logarithmic equations-verify an inverse of a function using the
1

1
composition rule f(f (x)) = f (f(x)) = x (the identity function or mirror)
review basic trigonometry concepts involving radian measure, graphs of
trigonometric functions and their inverses, transformations of trig graphs, and
inverse trig values
2. Limits and Continuity


discuss the concept of a limit
determine the limit of a function graphically
use substitution to determine the limit of a function and state the graphical
interpretation
calculate the average speed of a free falling object
predict the instantaneous velocity of a free falling object using the concept of a
limit
discuss and apply the Sandwich Theorem
apply the concept of two-sided limits in determining if the limit exists
graph piece-wise functions and apply both algebraic and graphical limit theory
determine the limit of a function graphically
use substitution to determine the limit of a function and state the graphical
interpretation
apply algebraic techniques to evaluate limits with final substitution
prove a limit using the definition for lim f(x) = L using epsilons and deltas


discuss a limit using its  -  definition
apply the two Special Trig Limits










x a
sin x
x
 lim
1
x 0
x  0 sin x
x
lim



cos x  1
1  cos x
 lim
0
x 0
x 0
x
x
lim
calculate limits involving Trig functions
evaluate limits at infinity using algebraic, numerical, and graphical approaches
locate horizontal and vertical asymptotes
Page 2 of 9
MOUNT PLEASANT AREA
COURSE SYLLABUS



discuss the end-behavior of a function
state the definition of continuity of a function at x = a
prove or disprove continuity of a function at a given point using the definition of a
continuity
3. Derivatives























apply the definition of the slope of the tangent line to selected problems
write equations of both tangent and normal lines to a curve at a given point
investigate real world problems involving instantaneous rates of change involving free
fall
state and use the definition of a derivative to calculate the slope of a curve or slope of
the tangent line to a curve at an indicated point and write equations of both tangent and
normal lines at this point
sketch the graph of a derivative when given the original function and vice versa
interpret when a function is differentiable by using the concept of One-Sided
Derivatives and discuss the geometrical interpretation of this concept
discuss when a function is not differentiable at a given point by comparing right and left
hand derivatives
state geometrically the 4 ways the graph of a function shows non differentiability
discuss the relationship between differentiability and continuity
calculate numerical derivatives using the symmetric difference quotient by paper/pencil
use the nDeriv key to calculate derivatives at specific values and graph derivative
functions
find derivatives using the basic 7 rules only
apply the basic 7 rules of differentiation to problems involving tangent and normal lines
and real world application problems involving formulas
find the average velocity, instantaneous velocity, and acceleration of a moving object on
a line
perform real world application word problems involving instantaneous rates of change
perform a real world application word problem where a ball is thrown upward from the
top of a building where s = directed distance of ball from starting point
perform a real world application word problem where a stone is thrown upward from the
top of a building where s = directed distance of stone from the ground
find derivatives of the six basic trigonometric functions
discuss and evaluate problems that involve periodic motion such as simple harmonic
motion and make reference to the graphs of the position, velocity, acceleration, and
jerk functions
state the theoretical relationship of The Chain Rule to the algebraic concept of a
composite function
find derivatives using The Chain Rule to include all 6 Trigonometric Functions
recognize the format for a “formula” or “chain rule” start for trigonometric
differentiation
find derivatives using the Chain Rule to include Trig Functions and Power Functions for
Rational Exponents
Page 3 of 9
MOUNT PLEASANT AREA
COURSE SYLLABUS

apply this differentiation process to find equations of both tangent and normal lines to
curves at indicated points

find

relate tangent and normal lines to real world problem situations to include special graphs
throughout the history of mathematics in which the equations are written in implicit
form
differentiate inverse trig functions using the 6 rules and simplify
use the graphing calculator to find the 6 inverse trig functions of selected domain
values to include arcsecant, arccosecant, and arccotangent.
find the derivatives of 4 Special Transcendental Functions



dy
using implicit differentiation
dx
d u
du
d u
du
and
e = eu
a = a u (ln a)
dx
dx
dx
dx
1 du
d
1 du
d
ln u =
and
log a u =
u ln a dx
dx
u dx
dx
4. Applications of Derivatives














approximate nth roots using both Linear Approximation and Differential methods
apply the First Derivative Test to find on which intervals a function is increasing and/or
decreasing
locate the extrema of a function
apply the Second Derivative Test to find on which intervals a function is concave up or
concave down
graph polynomial and rational functions completely naming local and absolute max/min
and critical points where f  = 0 or f  does not exist
state the geometrical interpretation of The Mean Value Theorem
locate the value of c within a given domain to satisfy the Mean Value Theorem
discuss the physical interpretation of the Mean Value Theorem
apply Newton’s Method to calculate roots of Real Numbers
apply Newton’s Method to calculate the zero of a function
solve related rate word problems
solve minimum and maximum word problems
construct a box to model an optimization word problem
use differentiation concepts to solve a box optimization problem
5. The Definite Integral




estimate areas with finite sums
discuss the relationship between the definite integral and area by referring to the
graph of the integrand using the given boundaries
estimate areas with finite Riemann Sums using RRAM, LRAM, MRAM
discuss the relationship between the definite integral and area by referring to the
Page 4 of 9
MOUNT PLEASANT AREA
COURSE SYLLABUS







graph of the integrand using the given boundaries and area formulas for geometrical
figures such as the circle, triangle, rectangle, and trapezoid
find general antiderivatives to include the Chain Rule for Integration and Substitution
Methods
find velocity and position of a falling body in two situations in free fall and with an initial
velocity when propelled downward using the Concept of Antidifferentiation
recover a position from velocity, velocity from acceleration
recover a functions from its growth rate or derivative
use the Mean Value Theorem for Integrals to calculate the average value of a function
and calculate the value of c in the domain of the function that satisfies this theorem
use the Fundamental Theorem of the Calculus (part 1) to calculate the derivative of a
given integral
use the Fundamental Theorem of the Calculus (part 2) to evaluate a given definite
integral
6. Applications of Definite Integrals

find the area of a region bounded by given equations using the most appropriate
technique of vertical or horizontal rectangles

apply L’Hopital’s Rule to evaluate limits of an indeterminate form

calculate volumes of solids of revolutions using both disk and shell methods
0

or
0

7. Techniques of Integration




Integrate by substitution methods
Integrate powers of sines and cosines
Integrate by parts
Integrate rational functions with linear or quadratic denominators
Expectations:
General Classroom Policies and Information for Students and Parents
1.
It will be necessary for all students to obtain a three-ring binder for the class. A spiral
notebook is unsatisfactory because papers cannot be removed and then replaced again. The
notebook is important for two reasons. First, it will be checked and graded two times
during the year. More importantly, it enables students to organize class notes and
assignments for future work in mathematics.
2.
Students will learn visualization of mathematics and programming through the graphing
capabilities of the Texas Instrument graphing calculator/Viewscreen projector system. All
students will learn graphing analysis by using the graphing calculator. Students will learn
the technology necessary to link the graphing calculator with the computer using the TI
graph link and TI Connect software.
Page 5 of 9
MOUNT PLEASANT AREA
COURSE SYLLABUS
3.
Students will have the opportunity to participate in exercises utilizing technology to solve
real world problems with the graphing calculator and computer.
4.
Students will learn basic arithmetic, algebraic, and graphical commands involving computer
software packages
5.
Grades are determined by adding the points received on tests, quizzes (announced and
unannounced), performance activities, and daily assignments, then taking a percentage of
the total number of points which could have been received. Grades are updated on
classroll.com on a weekly basis. The school’s grading policy is followed.
6.
If a student is absent the day of a test, it will be taken the next day he/she returns. If a
student is absent two days, an extra day will be given to prepare for the make-up test. If
a student is absent the day before a test, he/she will still take the test with everyone else.
Tests and quizzes are announced well in advance to justify these rules.
7.
If a student is absent, it is his/her responsibility to find out the assignments and get them
made up. This is true for daily work as well as tests.
8.
In the case of a prolonged absence, sufficient time will be given for all make up work.
9.
When the bell rings, all students must be in their assigned seats ready to begin work. If
there is a particular circumstance which causes tardiness, a student must notify me
immediately.
10. Daily assignments will be checked and graded periodically. Written assignments play an
important part of the learning process.
11. I am available for extra help to anyone who has been absent or to anyone who needs extra
explanations besides those given class.
12. Classroom participation (both orally and at the board) is highly encouraged.
13. In addition to problem solving, an objective of all courses is that students understand
theoretically and geometrically the meaning of mathematical concepts. Students will be
writing short answer essays and compositions testing for an algebraic, numeric, and
graphical understanding of the math material.
14. Any hint of cheating will result in the student’s paper being destroyed and a zero recorded
for that test, quiz, or assignment.
15. Comprehensive midterms and final exams are administered during the school year. They are
graded according to the school’s grading procedure.
16. If there are any problems or concerns, please do not hesitate to give me a call at school or
home. Parental support and participation are greatly appreciated and needed. Students
must accept responsibility to ask for outside help.
Page 6 of 9
MOUNT PLEASANT AREA
COURSE SYLLABUS
17. Students are asked to notify me by phone or email if an absence due to illness or an
extenuating circumstance results in turning in announced assignments or projects late. If
notification is not received, the grade will be lowered by one letter grade for each day of
absence.
Texts:
Pearson Calculus: Graphical, Numerical, and Algebraic by Finney, Demana, Waits, and
Kennedy, 2009
Resources and Materials Used:
 Basic Text
 Student Binder Notebook
 Classroom Graphing Calculator TI 84 Plus Silver Edition
 Teacher-made worksheets
 Computer generated worksheets and assessments
 TI Viewscreen graphing calculator
 TI Presenter
 Graph Paper
 Computer and Mathematics software
 TI Connect software
Websites:
www.mathxlforschool.com/login_school.htm
www.mpasd.net
www.glencoe.com
www.classroll.com
Activities/Assessments

Notebook

Cumulative Midterm and Final Examinations

Laboratory activities (Graphing Calculator/Computer)

Teacher-made tests

Textbook exams
Page 7 of 9
MOUNT PLEASANT AREA
COURSE SYLLABUS

Math XL For School Activities

Independent Homework Assignments

Homework quizzes

Classroom participation

Composition writings
Homework Procedure:
Daily homework assignments play an important part of the student’s learning process.
Students are expected to spend time outside of class to practice problems and study the
theoretical concepts to be successful in this class. Homework assignment problems are
placed on the board by the teacher or student volunteers upon request. Assignments are
often collected for teacher review and/or points. Take-home assignments quizzes are
announced and problems are randomly selected for correctness and points.
Grading Procedure:
Grades are determined by adding the points received on tests, quizzes (announced and
unannounced), performance activities, and daily assignments, then taking a percentage of
the total number of points which could have been received. Grades are updated on
classroll.com on a weekly basis. The school’s grading policy is followed.
93
84
75
65
–
–
–
–
100 A
92 B
83 C
74 D
Below 64 F
Extra Help:
Students can receive additional help from me during the following times.
Period 6 (With Advance Notice) This is my plan period.
My teaching schedule is as follows. Students can ask for a pass to visit another
class.
Period
Period
Period
Period
Period
Period
Period
1
2
3
4
6
7
8
Algebra 2
Calculus
Calculus
Calculus
Plan
Algebra 2
Algebra 2
Eat Lunch C
Page 8 of 9
MOUNT PLEASANT AREA
COURSE SYLLABUS
Contact Information:
Cheryl Lipko
Phone Number: 724-547-4100 ext. 1301
Email:
clipko@mpasd.net
Page 9 of 9