AP Calculus AB
Syllabus
Course Overview
Our Calculus AB course is a full year course in a “block schedule” format. The first
semester is a 95minute block class with the second semester being a 45minute
“singleton”. Students are required to take this whole year sequence and take the AP
exam in May.
Instructional Materials
Our primary textbook is “Calculus of a Single Variable; Larson, Hostetler, Edwards; DC
Heath and Company; c 1994; Fifth Edition”. Supplementary materials include: “ Multiple
Choice and Free Response Questions for the AP Calculus (AB) Examination; D & S
Marketing Systems, Inc.; Eighth Edition”. Also graphing calculators are used on a daily
basis as a tool to assist the student when appropriate. We also use CBR/CBL to gather data
and generate graphs for further analysis. TI-92 calculators (class set) are used for their
computer algebra capabilities. The internet is used to access “real world” data.
Teaching Strategies
Throughout the course emphasis is placed on using calculus to more fully interpret
graphical data. This will include representing problems numerically, using tables of values
in their graphing calculators to interpret tendencies of a problem, and graphically by
generating and interpreting graphs by hand as well as technologically. Analytically, we use
Calculus, Algebra, and Plane Geometry to study rates of change (both instantaneous and
average) as well as determining and interpreting the area between curves. Students are
then required to describe their results using appropriate terminology and notation.
Students are required to have a graphing calculator for use in the course. Also we have a
class set of TI-92 calculators for students to use when a computer algebra system is
appropriate. By the end of the course, our goal is for the student to realize that Calculus,
technology, Algebra, paper and pencil, and Geometry are all “tools of the trade” in
mathematics. It is their job to be able to use and understand the appropriate tools necessary
to be mathematical problem solvers.
The Rule of Four
Throughout the course students are required to approach mathematics in four distinct ways.
First, each student needs to understand what the numbers represent in the problem and be
able to experiment with numerical examples to observe tendencies and make
approximations. Emphasis is placed on using correct units as well. Secondly, the student
must use appropriate algebraic and calculus manipulations to further analyze the problem.
Thirdly, the students will interpret the graph of a mathematical model for further analysis.
Emphasis is placed on the interrelationship between a graph of a function, its derivative, its
second derivative, and the area under the curve. And finally, students are required to
communicate mathematics both verbally and in written sentences (HIGHLIGHTED
THROUGHOUT THE SYLLABUS AND STUDENT ACTIVITIES). Examples include
describing how to use the graph of a derivative of a function to determine relative extrema
of a function. In a problem involving flow rates (in cubic feet/min) of a local river, groups
of students are asked to describe the meaning of the area under the curve and how would
you use it to approximate the average rate of flow for a seven-day period.
Calculus AB Course Outline
Section
P.1
P.2
P.3
P.4
P.5
P.6
1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.1-2.4
2.5
2.6
2.1-2.6
P.1-2.6
3.1
3.2
3.3
Topics
Real numbers, notation, inequalities, absolute value
Cartesian plane, distance and midpoint, conic equations
Graphs, intercepts, symmetry, models, points of intersection
Lines: graphs, slopes, equations parallel and perpendicular
Assessment P.1 - P.4
Functions; domain, range, graph, transformations, classify
Assessment P.1 - P.5
Angle measure: radian & degree, trigonometric functions
trigonometric equations and graphs.
Assessment of the Trigonometric topics
Timeline
Day 1
Day 2
Day 3
Day 4
Day 5
Days 6 - 7
Day 8
Day 9 - 11
Introduction to limits, limits that fail to exist, definition
Limit properties, limits of algebraic and trigonometric function
Techniques for finding limits, cancellation, rationalization
and the Squeeze Theorem.
Assessment on early limits
Continuity: at a point, on an interval; one sided limits and
continuity on a closed interval. The Intermediate Value Thm.
Infinite limits and vertical asymptotes
Assessment on limits
Day 13-14
Day 15
Day 16-17
Derivative of a function, differentiability and continuity.
Basic differentiation rules, power, constant, trig…
Assessment on derivatives
Product & quotient rules, trigonometric deriviatives, higher
Chain rule, trig functions with chain rule, simplifying derivitive
Comprehensive derivitive review
Assessment on derivatives Test.
Implicit differentiation
Related rates, problem solving with related rates
Comprehensive review - implicit diff and related rates
Assessment on Chapter 2
Midterm review
Midterm exam
Extrema and relative extrema of functions, critical numbers
Finding extrema on a closed interval.
Rolle's Theorem, Mean Value Theorem
First derivative test, increasing and decreasing functions
Day 23-24
Day 25
Day 26
Day 27-28
Day 29-30
Day 31
Day 32
Day 33-34
Day 35-37
Day 38
Day 39
Day 40-41
Day 42
Day 43-44
Day 12
Day 18
Day 19-20
Day 21
Day 22
Day 45-46
Day 47-48
3.4
3.1-3.4
3.5
3.6
3.7
3.8
3.9
3..10
3.7-3.10
4.1
4.2
4.3
4.4
4.4
4.1-4.4
4.4
4.5
4.6
4.1-4.6
5.1
5.2
5.3
5.4
5.5
Assessment - Extrema, Increasing, Rolle's, M.V.T
Concavity, Points of inflection, Second deriviative test
Review on Chapter 3
Assessment Chapter 3.1 - 3.4
Limts at infinity, Horizontal asymptotes
Summary of all curve sketching techinques - increasing and
decreasing, concavity, asymptotes, limits at infinity
Assessment Chapter 3.5 - 3.6
Applied problems on Maximums and minimums
Assessment on Maximum and minimums
Newtons method
Day 49
Day 49-50
Day 51
Day 52
Day 53
Day 54
Day 55
Day 56 - 58
Day 59
Day 60
Differentials, Linear approximations, calculating differentials
Business and Economic applications
Comprehensive review 3.7 - 3.10
Assessment Chapter 3.7 - 3.10
Antiderivatives, notation for, basic integration rules
Particular solutions and conditions
Sigma notation, areas under curves, upper and lower sums
Riemann sums, definite intergrals, properties of definite int
Assessment Chapter 4.1 - 4.3
Fundamental Theorem of Calculus I and II.
Mean value theorem for intergrals, average value of a function
Comprehensive review 4.1 - 4.4
Assessment Chapter 4.1 - 4.4
Review of Fundamental theorem (Back from break)
Change of variable technique for integration
General power rule, change of variable for definite integrals
Assessment Chapter 4.5
Trapezoidal rule, error analysis on approximations
Comprehensive review of chapter 4
Assessment Chapter 4
Day 61-62
Day 63-64
Day 65
Day 66
Day 67-68
SEMESTER EXAM Review Chapters P through 4
Semester Exam
Day 86-88
Day 90
Review properties of natural logarithmic function and the
exponential function
Define natural log function as area under the curve f(x)=1/x
Differentiate logarithmic functions
Use logarithmic differentiation to find derivatives of complicated
functions
Log rule for integration, Integrals of Trig functions
Determine the existence of an inverse function, find the derivative
of an inverse function
Differentiate and integrate general exponential and logarithmic
functions
Assessment Chapter 5.1-5.4
Differentiate and integrate exponential functions with bases
other than "e".
Day 91-92
Day 69-70
Day 71-72
Day 72
Day 73-74
Day 75
Day 76
Day 77
Day 78
Day 79-80
Day 81
Day 82-83
Day 84
Day 85
Day 93
Day 94
Day95
Day 96-97
Day 97-98
Day 99-100
Day 101
Day 102-103-104
5.6
5.7
5.8
6.1
6.2
6.3
7.1
7.3
Apply derivative and integration to exponential growth and decay
models
Find derivatives of inverse trig functions
Evaluate integrals involving inverse trig functions
Assessment Chapter 5.1-5.8
Day 105-106
Day 107-108
Day 109
Use definate integral to find area between curves
Find the volume of a solid of revolution by both disk and washer
method. Find volume of solid with known cross sections.
Find the volume of a solid of revolution by the shell method
Assessment Chapter 6.1-6.3
Day 110-111
Day 112-116
Use more than one integration rule to evaluate integrals
Evaluate trigonometric integrals.
Use trig identities to change an integral to a form that can be
evaluated directly.
Assessment Chapter 7.1,7.3
Day 121-122
day 123-124
Day 116-119
Day 120
Day 125
supplement Generate a slope field when given a differential equation
material Find a particular solution to a differential equation's slope field
when given a sample point
Assessment Slope fields
Day 126
Day 127-128
Supplement Review for AP Calculus test
Material Weekly assessments on multiple choice, free response
practice questions
Day 130-154
AP Calculus Exam
Day 129
Day 155
6.4
6.5
6.6
6.7
Use integration to compute arc length an surfaces of revolution
Compute work done by a variable and constant force
Use integration to find fluid force
Find center of mass of a planar laminate
Assessment Chapter 6.4-6.7
Day 156-157
Day 157-158
Day 159
Day 160
7.2
7.4
7.7
Integration by parts
Integration by trigonometric substitution
Indeterminant forms and L'Hopital's rule
Assessment Chapter 7.2,7.4,7.7
Day 161-162
Day 163-166
Day 167-168
Day 169
Supplement Newton's law of cooling lab
Material
Use trapezoidal approximation to find total water flow given
USGS real time water data of local river flow rates.
Day 170-171
Day 172-174
Find position, velocity, acceleration,and total distance traveled
of a ball rolling up an inclineplane using CBR and time-distance
graph
Day 175-177
Assessment Applications of Calculus
Day 178-180