AB Calculus @ Hendrickson High School 2013-2014
Jeremiah Lucas
Room: F205
Voicemail: 512-594-1323
Email: jeremiah.lucas@pfisd.net
Website: https://sites.google.com/site/jlucasmath/
Amanda Gass
Room: F204
Voicemail: 512-594-1322
Email: Amanda.gass@pfisd.net
Website:https://sites.google.com/site/gasshhsmath/
Tutorial Hours: (or by appointment)
Mr. Lucas: A-Days 8:00-8:50, B-Days 4:10-4:50
Ms. Gass: Tuesday, Wednesday, Friday 8:00-8:50
Course Overview
Calculus is a powerful and important part of the study of Mathematics. Differential and Integral
Calculus are the two main branches of Calculus. Differential Calculus deals with changing
quantities, while Integral Calculus deals mainly with finding sums of infinitesimally small
quantities. It is the goal of this course for all students to develop an appreciation of Calculus and to
pass the AP Calculus AB exam on May 8, 2013.
Teaching Strategies
It is stressed throughout this course that students should be able to work with functions, limits,
derivatives and integrals represented graphically, numerically, analytically, or verbally and should
understand the connections among these representations. Therefore it has been a major part of this
course to incorporate the use of graphing calculators. TI-83, TI-84, and TI-89 will be used most
often as an aid in assisting in the learning. Geometer’s Sketchpad will also be used as a visual aid
in understanding the applications of integration in relationship to geometric figures.
Grading:
 80% - Major Assessments (60% Tests/Projects, 20% Quizzes)
 20% - Minor Assessments (Homework)
Major Assessments:
A minimum of three major assessments will be given each grading period. In addition to tests,
projects and writing assignments will be given periodically. All major assessments in which a
student earns less than a 70% may be redone once all pre-requisite work has been completed. All
re-tests/re-projects/re-writing will be taken for a maximum grade of 70% at dates and times agreed
upon by the teacher.
Quizzes will then be used to ensure student mastery of topics covered on homework and class
work. Students scoring below “70” on a quiz shall be allowed to re-quiz after completing all
prerequisite work. The prerequisite work will include the student completing all the homework
problems from the section(s) from which the quiz concepts were covered. The higher grade with a
maximum of “70,” shall be recorded. Re-quizzes must be completed within two class meetings.
The lowest quiz grade will be dropped at the end of the nine weeks.
Minor Assessments:
Homework and class work will be assigned daily and be checked frequently and randomly to be
graded on completion. No credit will be given if necessary work is not shown! If you are absent, it
is your responsibility to get the notes and assignments. Late homework will receive a penalty of
25% off for every class late, with a maximum of 50% after two or more days late.
Course Requirements:
1. Requested Supplies: Graphing Calculator (highly encouraged), 4-pack dry erase markers
2. Required Supplies: pencils, paper, and a binder or spirals and folder.
3. Required Text: Finney, Demana, Waits, and Kennedy. Calculus – Graphical, Numerical,
Algebraic. Third edition, Pearson, Prentice Hall, 2007
AP Calculus AB Course Outline
Unit 1: Pre-Calculus Review (3 wks)
A. Lines
1. Slope as rate of change
2. Parallel and perpendicular lines
3. Equations of lines
B. Functions and graphs
1. Functions
2. Domain and Range
3. Viewing and Interpreting Graphs
4. Even and Odd functions-Symmetry
5. Families of function
6. Piecewise functions
7. Composite of functions
C. Exponential functions
1. Exponential growth and decay
2. The number e
D. Functions and Logarithms
1. One to One and Inverse functions
2. Logarithmic functions
3. Properties of logarithms
E. Trigonometric functions
1. Radian Measure
2. Graphs of basic trigonometric functions
a. Domain and Range
b. Transformations
c. Inverse trigonometric functions
3. Periodicity
4. Even and Odd Trig Functions
5. Applications
Unit 2: Limits and Continuity (4 wks)
A. Rates of change
1. Average and Instantaneous
2. Definition and Properties of Limits
3. One and Two-sided limits
B. Limits involving infinity
1. Asymptotic behavior
2. End behavior
3. Properties of limits
4. Visualizing limits
C. Continuity
1. Continuity at a point
2. Discontinuous functions
a. Removable discontinuity
b. Jump discontinuity
c. Infinite discontinuity
3. Continuous functions
4. Intermediate Value Theorem for continuous
functions
D. Rates of change
1. Average rate of change
2. Secant and Tangent to a curve
3. Slope of a curve
4. Normal to a curve
Unit 3: The Derivative (6 wks)
A. Derivative of a Function
1. Definition of the derivative
2. Relationships between f and f’
3. One sided derivatives
B. Differentiability
1. How f’(a) might fail to exist
2. Local linearity
3. Numeric derivatives using the calculator
4. Differentiability and continuity
5. Intermediate Value Theorem for derivatives
C. Rules for Differentiation
1. Product and Quotient Rules
2. Power rules
3. Second and Higher Order Derivatives
D. Velocity and Other rates of Change
1. Instantaneous rates of Change
2. Motion along a line
3. Sensitivity to change
E. Derivatives of trigonometric functions
1. Derivatives of Sine and Cosine
2. Simple Harmonic Motion
3. Derivatives of Other Basic Trig Functions
F. The chain rule
1. Derivative of a composition function
2. Repeated use of the Chain Rule
G. Implicit derivatives
1. Implicitly defined functions
2. Implicit differentiation process
H. Derivatives of inverse trigonometric functions
1. Derivatives of Inverse functions
2. Derivatives of inverse trig functions
I. Derivative of logarithmic and exponential
functions
1. Derivative of ex
2. Derivative of ax
3. Derivative of ln(x)
4. Derivative of log a x
Unit 4: Application of the Derivative (5 wks)
A. Extreme value of Functions
1. Global (absolute) extrema
2. Local (relative) extrema
B. Mean Value Theorem
1. Mean Value Theorem
2. Increasing and decreasing functions
C. Connecting f’ and f’’ with the graph of f
1. First derivative test for extrema
2. Concavity and points of inflection
3. Second derivative test for extrema
4. Applications to velocity and acceleration
5. Curve sketching
D. Modeling and Optimization
1. Examples from business & industry
2. Examples from Mathematics
3. Strategy for solving max-min problems
E. Linearization and Newton’s Method
1. Linear Approximation
2. Newton’s Method
3. Differentials
4. Estimating change with differentials
F. Related Rates
1. Related rate equations
2. Related rate problem strategy
Unit 5: The Definite Integral (4 wks)
A. Approximating Areas
1. Riemann sums
2. Trapezoidal rule
3. Definite integrals
B. The Fundamental Theorem of Calculus (Part 1)
1. FTC by Graphical, Numerical, and
Analytical methods
C. Definite integrals and anti-derivatives
1. The Average Value Theorem
D. The Fundamental Theorem of Calculus (Part 2)
1. How to find total area analytically
2. How to find total area numerically
3. Applications
Unit 6: Differential Equations and Modeling (5 wks)
A. Anti-derivatives
1. Solving Initial Value problems
2. Antiderivatives and indefinite integrals
3. Properties of integrals
4. Applications
B. Integration using u-substitution
1. Power rule
2. Trigonometric Integrands
3. Separable differential Equations
C. Differential Equations
1. Slope Fields
2. Euler’s Method
D. Exponential Growth and Decay
1. Law of Exponential Change
2. Newton’s Law of Cooling
Unit 7: Applications of Definite Integrals (4 wks)
A. Integral as Net Change
1. Linear Motion Revisited
2. Strategy for Modeling Integrals
3. Consumption over Time
B. Particle motion
C. Areas in the plane
1. Areas between curves
2. Area enclosed by intersecting curves
3. Boundaries with changing functions
4. Integrating with respect to y
D. Volume
1. Volume as an Integral
2. Volumes of known cross sections
3. Volumes of solids of revolutions
The timing on this schedule is approximate and leaves several weeks for flexibility with teaching and
learning time management. This leaves 6 weeks to prepare for the AP exam. After the AP exam there
will be projects to apply the skills learned in AB Calculus and the fill the last major grade.