[Note: Many course materials are on the web. Since HTML documents are not accepted, I have reformatted to MS Word.]
WELCOME TO
AP CALCULUS AB
NOTE: Course materials are on the web at: [identifying material removed]
COURSE DESCRIPTION
AP Calculus AB is a 1-credit course covering topics from Differential Calculus,
Integral Calculus, and Differential Equations. The ideas of limits, continuity,
derivatives and integrals are explored at a depth of understanding consistent
with college-level study. Broad concepts and widely applicable methods are emphasized,
rather than memorization of particular problem types. A multi-representational approach
is taken, with concepts expressed graphically, numerically, analytically, and verbally.
The graphing calculator is used as an aide in understanding, estimating and confirming
results.
PREREQUISITES
Completion of Precalculus (or the equivalent) and permission from the Mathematics
Department are prerequisites for this course. Students are required to sit for the AP
Calculus AB exam [date removed].
TEXTS
Calculus, Concepts and Contexts, Single Variable, James Stewart, Brooks/Cole
Publishing Company. This text has very good exposition, examples, and problem sets.
AP Calculus AB, Kaplan Publishing. This is a dedicated AP prep book, which gives a
good supply of multiple-choice questions.
SUPPLIES
TI-83 GRAPHING CALCULATOR: You need a TI-83 graphing calculator for class,
homework, exams, and the AP exam. Calculator skills will be developed throughout the
course. Homework problems in your textbook that are marked with the “graph” symbol
require use of the graphing calculator, and many of these are assigned throughout the
year.
3-RING BINDER and DIVIDER SHEETS: A 3-ring binder (at least 1.5" ring size) is
strongly recommended to organize all class materials. Please make tabs for SYLLABUS,
GRADE SHEET, and INDEX CARDS.
INDEX CARDS: cards (4"  6", both sides un-ruled, about 100 cards) are used
to summarize important material. You may want to purchase a 3-hole punched plastic
zippered pouch in which to keep your cards.
THE “INDEX CARD” LECTURE METHOD
All the important ideas in the course are summarized on index cards, which become
a primary study source for exams and quizzes. Here's how the “index card method”
works:
 You will receive copies of the index card material; the sheets are pre-punched to
put in your 3-ring notebook.
 Quickly read over the sheet(s) before coming to class. This way, you have a
preview of what we'll be talking about, making you more receptive to the
ideas.
 After class, copy the material onto an actual index card. As you write the card,
THINK! Make sure that you understand everything you're writing down. Feel
free to add additional material to make the index cards more useful to you.
 Index cards are passed in and graded at the midterm and end-of-term.
Each card is worth 2 points (1 point for each side).
Since our class is small, you should expect to be called on every day to practice speaking
mathematics. In particular, every time a new mathematical object is introduced, we will
go around the room and each person will practice reading the notation aloud. It is
important to be able to communicate mathematics effectively, both in writing and in
speaking.
QUICK QUIZZES
At the beginning of each class, there is a Quick Quiz over material from the previous day.
This Quick Quiz may be:
 doing one of the assigned homework problems (including algebra review
problems), or a similar problem
 answering a basic question from the previous day's index card(s)
The Quick Quizzes are graded with a 1 (one point) or an N (Not completely correct).
Points accumulated on the Quick Quizzes are added into your point total as BONUS
POINTS. Consequently, they can't hurt your grade, but can certainly help! There are no
make-ups on Quick Quizzes. Quick Quizzes are discarded immediately after grading.
An unexcused late or unexcused absence causes you to lose a Quick Quiz point.
(I record -1 on the Quick Quiz sheet.)
QUIZZES and EXAMS
Almost every week there will be a major quiz over the material covered since
the previous quiz/test.
PREREQUISITE QUIZ: The first major quiz will cover all the Sample Prerequisite
problems [web reference deleted] that you were given at the end of last year.
In the Fall term, there will be a midterm exam and a cumulative final exam.
You will do a comprehensive review of Algebra I, Geometry, and Algebra II skills
throughout the year, using over 200 web-based exercises that offer instruction, unlimited
randomly-generated online practice, and randomly-generated worksheets and solutions
for work away from the computer. Math Markup Language (MathML) is used to
correctly display the mathematics—this is the future of math on the web! Go to [web
reference deleted] for a complete yearly review schedule and links to the web exercises.
These review exercises are a WIN-WIN situation: ones that are difficult for you are
filling in gaps in your understanding; ones that are easy for you are building up your
course grade, since these points will be easier to earn than the Calculus points.
LATE POLICY
Any missed work due to unexcused lates or absences will receive a grade of zero.
Furthermore, school policy dictates that a girl's class average will be reduced by one-half
a percentage point for each unexcused absence.
Recall that there are no make-up Quick Quizzes. The [identifying info removed] School late
policy applies to any other missed work: “A student who has been absent must be
prepared to submit all missed class work within 48 hours of her return. A student should
be prepared to take a quiz or test upon her return if the material was covered prior
to her absence. A 10% per day grade reduction will be applied to any outstanding work
after the 48 hour grace period.”
It is your responsibility to get a Missed Work Form [web reference deleted] whenever you
miss a graded assignment. This form indicates the arrangements for making up missed
work, including the date by which make-up work may be submitted penalty-free. Your
failure to get this form in a timely fashion does not exempt you from late penalties!
EFFORT HONOR ROLL
A student is voted to the Effort Honor Roll when she has worked consistently
throughout the term to be the best student she can be in all of her classes. Any one of the
following reasons is sufficient to prevent a girl from receiving a recommendation for
Effort Honor Roll: an unexcused absence; non-participation in class; lack of
preparation for class; tardiness to class.
YOUR NUMBER IS ...
On the first day of class, a form will be passed around where you will select your number
for the year. This number will be written on all passed-in material. Also, your personal
folder is identified with this number. If you miss class, check your folder for papers that
may have been distributed while you were absent.
MY NUMBER IS: [students record number here]
USING PREVIOUS COURSE MATERIALS
Sometimes girls gain possession of class materials from previous years. You are
welcome to use such materials, subject to the following conditions:
 You must show me any materials that you are using from previous years. I
reserve the right to disallow use of these materials.
 You must make a copy of any materials that you are using and put them on
reserve in the library, so that all students in the class can benefit from their use.
GRADING
You will accumulate points throughout each term. Here's an example: if there are 2000
possible points, and you accumulate 1543 points, then your numerical term grade will be
determined by computing 1540/2000 and using normal rounding, yielding 77%. Each
student is provided with a grade sheet which is used to keep track of your grade
throughout the term.
AP classes have the option of not taking the Spring term final exam, since the AP test
is itself a major final exam!
TERM GRADE
(no grade of A+)
A: [93,)
A-: [90,93)
B+: [87,90)
B: [83,87)
B-: [80,83)
C+: [77,80)
C: [73,77)
C-: [70,73)
D+: [67,70)
D: [63,67)
D-: [60,63)
F: < 60
EXAM DATES
Fall midterm: [date]
Fall term final exam: [date and time]
COURSE GRADE
Your course grade will be the average of the Fall and Spring term grades.
WEIGHTED GRADES FOR AP COURSES:
The semester average of a student enrolled in an Advanced Placement course is weighted
by two points. This weight affects the student's grade point average, when the GPA is
computed and recorded on the transcript and shared with prospective colleges.
Additionally, this weight can favorably influence a student's semester average, helping
her to earn recognition on the Head's List or Honor Roll.
DAILY SYLLABUS: AP CALCULUS AB
[web reference deleted; the entire daily schedule is available on the web; all specific dates have been
removed and daily schedules have been consolidated into weekly schedules]
There are 119 MTThF class meetings in the academic year: 64 in the Fall term; 45 in the
Spring term before the AP test; 10 in the Spring term after the AP test.
AP Calculus AB meets four days per week, MTThF, with 50 minutes per class on MThF,
and an 80-minute class on Tuesday. This schedule offers an approximate syllabus that
will complete the course objectives by the AP Calculus AB exam.
ALL HOMEWORK ASSIGNMENTS ON INDEX CARDS ARE
AUTOMATICALLY ASSIGNED AS THE CARDS ARE COVERED.
The assignments are NOT repeated here.
WEEK #1 [Stewart 1.1, 1.2]
- Welcome!
- Remember the prerequisite material you got at the end of last term? (test next Monday;
we'll be reviewing this week) [web reference deleted]
- go over Greek Letter sheet (hand-write on board; take notes)
- CARD #1 (functions; reading info from a graph)
- CARD #2 (creating a graph from a story; piecewise-defined functions)
- CARD #3 (even and odd functions)
- CARD #4 (basic function models; composition of functions)
- GRAPHING CALCULATOR SKILL (plotting the graph of a function in a
specified viewing window; practice)
- GRAPHING CALCULATOR SKILL (finding the zeros of a function; solving
equations numerically; practice)
- Geometric Transformations sheet (shifting up/down, left/right, horizontal and vertical
stretching and shrinking, reflecting about the x-axis and y-axis, absolute value
transformation)
WEEK #2 [Stewart 1.2, 1.5]
- MAJOR QUIZ
- CARD #5 (transformations involving x and y )
- sample quiz over AP Calculus AB Test Information [web reference deleted]
- Geometric Transformation Practice [web reference deleted]
- multiple-choice questions on functions
- CARD #6 (exponential functions; rewriting exponential functions)
- CARD #7 (exponential growth/decay problems; comparing exponential and power
functions)
WEEK #3 [Stewart 1.5, 1.6]
- MAJOR QUIZ
- CARD #8 (comparing linear and exponential functions; recognizing functions from
tables of data)
- CARD #9 (one-to-one functions; inverse functions)
- worksheet (identifying functions from tables of data)
- CARD #10 (finding inverse functions; graph of the inverse function)
- CARD #11 (inverse function pairs: exponential and logarithmic functions; two
views of logarithms)
- CARD #12 (comparing power and logarithmic functions)
- REVIEW CARD (properties of logarithms)
WEEK #4 [Stewart 1.7, 2.1, 2.2, 2.3]
- MAJOR QUIZ
- CARD #13 (regression; interpolation versus extrapolation)
- worksheet (creating graphs from stories)
- CARD #14ab and worksheet (tangent and velocity problems; intro to differential
calculus)
- CARD #14cd (greatest integer/floor function)
- CARD #15 (intro to limit of a function; three cases where the limit of f(x), as x
approaches a , equals l )
- CARD #16 (one-sided limits; describing a two-sided limit using one-sided limits)
- CARD #17 (limit laws; renaming before investigating a limit)
- CARD #18 (the squeeze/pinching theorem; using the squeeze theorem)
WEEK#5 [Stewart 2.4, 2.5]
- MAJOR QUIZ
- CARD #19ab (continuity at a point; three ways a function can fail to be continuous
at a point)
- CARD #19cd (key idea: when a function is continuous at a point, evaluating a limit
is as easy as direct substitution)
- CARD #20 (one-sided continuity; continuity on an interval)
- CARD #21 (What functions are continuous? Intermediate Value Theorem)
- CARD #22 (classifying discontinuities; classic use of the Intermediate Value
Theorem)
- CARD #23 (precise statements of limits involving infinity; we'll be spending several
days on these)
- CARD #24 (punctured neighborhoods; how many types of limit statements are
there?)
- worksheet (Intermediate Value Theorem)
WEEK #6 [Stewart 2.5, 2.6]
- MAJOR QUIZ
- (continue working on precise limit statements; one-sided statements involving
infinity)
- CARD #25 (epsilon-delta limit definition)
- CARD #26 (sheet on precise limit statements)
- CARD #27 (worksheet for next few cards: equivalent statements of differentiability
at a point)
- CARD #28 (average rate of change versus instantaneous rate of change)
- worksheet (equivalent statements involving derivative information; memory device
“Carol Likes To Ice-skate Past Dark”)
WEEK #7 [Stewart 2.6]
- QUIZ OVER ALL PRECISE LIMIT STATEMENTS
- CARD #29 (tangent lines; equivalent statements for " f has a tangent line at
(x, f (x)) with slope m ")
- CARD #30 (GRAPHING CALCULATOR SKILL: using the TI-83 to find slopes of
tangent lines; worksheet)
- REVIEW FOR MIDTERM
- MIDTERM EXAM
- CARDS GRADED
- HAVE A WONDERFUL LONG WEEKEND!
WEEK #8 [Stewart 2.7, 2.8]
- CARD #31 (the derivative of f at a ; interpreting the number f '(a) )
- worksheets (verbally translating derivative info in ways that are meaningful to noncalculus students)
- CARD #32 (recognizing derivatives from the limit definition; finding equations of
tangent lines)
- worksheet (identifying limits as derivatives)
- worksheet (identifying limits from graphs)
- worksheet (finding slopes using definition; shortcut)
- CARD #33 (sketching the graph of f ' ; Leibnitz notation for the derivative)
- worksheet (sketching graphs of derivatives)
WEEK #9 [Stewart 2.9, 2.10]
- MAJOR QUIZ
- CARD #34 (the d/dx operator; relationship between differentiability and
continuity)
- CARD #35 (implications and equivalent sentences; relationship between an
implication and its contrapositive)
- CARD #36 (how a function can fail to be differentiable; higher order derivatives)
- CARD 37 (the linearization of f at a ; intuition for the linearization)
- CARD 38 (slopes increasing/decreasing at a ; concave up/down)
- CARD #39 (increasing/decreasing functions, precise definitions; monotonic
functions; getting increasing/decreasing behavior from the derivative)
- worksheet (exploring increasing/decreasing function/slope behavior)
- CARD #40 (local max/min precise definitions; concavity)
- CARD #41 (getting concavity information from the second derivative; interpreting
common phrases in terms of derivative info)
- worksheets (sketching different combinations of function, 1st and 2nd derivative
behavior)
WEEK #10 [Stewart 3.1, 3.2]
- MAJOR QUIZ
- CARD #42 (simple power rule for differentiation; practice using the power rule)
- CARD #43 (derivative of a constant times a function; derivative of kxn )
- worksheet (practice with the simple power rule)
- CARD #44 (derivatives of sums and differences; the derivative of ex )
- CARD #45 (the product rule for differentiation; proof of the product rule)
- CARD #46 (When is the limit of f (x+h), as h approaches 0, equal to f (x)?)
- worksheet (practice with derivative and continuity statements)
- HAVE A WONDERFUL THANKSGIVING BREAK!
WEEK #11 [Stewart 3.2, 3.3, 3.4]
- Welcome back from Thanksgiving Break!
- CARD #47 (the Quotient Rule for differentiation; proof of the quotient rule)
- CARD #48 (particle motion in a straight line; speeding up/slowing down versus
positive/negative acceleration)
- small group work: particle motion in a straight line
- CARD #49 (the limit, as h goes to 0 , of sin(h)/h ; derivatives of sine and cosine)
- CARD #50 (derivatives of tan x, cot x, sec x, and csc x)
WEEK #12 [Stewart 3.5, 3.6, 3.7]
- MAJOR QUIZ
- CARD #51 (differentiating composite functions, motivation)
- CARD #52 (the Chain Rule, prime and Leibnitz notation)
- CARD #53 (Why is it called the Chain Rule? Using the Chain Rule to differentiate
(f(x))n )
- CARD #54 (Generalizing all the basic differentiation formulas; differentiating
exponential functions, y = ax )
- questions on derivatives from KAPLAN
- CARD #55 (explicit versus implicit; implicit differentiation)
- CARD #56 (derivatives of the inverse trigonometric functions; a typical derivation)
- CARD #57 (derivatives of logarithms; typical proof)
- worksheet (differentiation practice)
WEEK #13 [Stewart 3.7, 4.1]
- MAJOR QUIZ
- CARD #58 (generalizing the formula for the derivative of ln x ; logarithmic
differentiation for complicated products/quotients)
- CARD #59 (logarithmic differentiation for variable expressions to variable powers)
- CARD #59.5abc (finding the derivative of an inverse function; practice using the
formula)
- CARD #60 (related rate problems; classic falling ladder problem)
- additional differentiation practice sheet
- CARD #61abcd (optimization problems, introduction; open and closed intervals;
absolute/global maximum/minimum)
- worksheet (absolute max/min)
WEEK #14 [Stewart 4.2]
- CARD #61def (relative/local maximum/minimum)
- worksheet (local/global max/min)
- CARD #62 (Where can a function have a local max/min?)
- CARD #63 (Careful! Just because the derivative is zero does NOT mean there's a
max/min; critical numbers as candidates for places where local max/min occur)
- MAJOR QUIZ
WEEK #15 [Stewart 4.2]
- Welcome back!
- CARD #64ab (finding local max/min; the Extreme Value Theorem)
- CARD #64cd (finding absolute max/min for a continuous function on a closed
interval; example)
WEEK #16 [Stewart 4.3, 4.4, 4.5]
- MAJOR QUIZ
- CARD #65 (the Mean Value Theorem)
- CARD #66abcd (the First and Second Derivative Tests)
- Handout: "On the Role of Sign Charts in AP Calculus Exams for Justifying Local or
Absolute Extrema"
- CARD #67 (producing graphs by hand versus calculator; a sign analysis of a
rational function)
- worksheet (efficiently finding the sign of a rational function)
- CARD #68 (indeterminate forms; deciding if you do or don't have an
indeterminate form)
- worksheet (indeterminate forms)
WEEK #17 [Stewart 4.5, 4.6]
- MAJOR QUIZ
- CARD #69 (l'Hospital's Rule; motivation for the "0/0" case)
- CARD #70 (using l'Hospital's Rule)
- CARD #71 (optimization problems)
- more optimization problems
WEEK #18 [Stewart 4.9]
- CARD #72 (“undoing” differentiation; antidifferentiation; definition of
antiderivative)
- CARD #73 (some basic antiderivative formulas)
- worksheet (finding basic antiderivatives)
- CARD #74 (find a particular antiderivative; examples)
- REVIEW FOR FINAL EXAM (quickly go over all cards)
END OF FALL TERM
FALL FINAL EXAM IS [date and time removed]
BEGINNING OF SPRING TERM
WEEK #1 [Stewart 5.1, 5.2]
- CARD #75 (estimating areas beneath a curve; general notation for the area
problem)
- CARD #76 (summation notation; left and right estimates using summation
notation)
- CARD #77 (GRAPHING CALCULATOR SKILL: using the RSUM program on
the TI-83; practice)
- CARD #78 (definition of a definite integral; notation for the definite integral)
- CARD #79 (dummy variable in definite integrals; Riemann sums; area beneath xaxis treated as negative)
- CARD #80 (properties of sums; a useful summation formula)
- CARD #81 (finding a definite integral by using the definition–there must be an
easier way!)
WEEK #2 [Stewart 5.2, 5.3, 5.4]
- MAJOR QUIZ
- GRAPHING CALCULATOR SKILL (computing a definite integral; practice)
- CARD #82 (properties of the definite integral; the linearity of the integral;
integrating backwards)
- CARD #83 (connection between AREA and ANTIDERIVATIVES; why it's
plausible; making it precise)
- CARD #84 (the Evaluation Theorem)
- CARD #85 (general antiderivatives; indefinite integrals; antiderivative formulas)
- CARD #86 (the Total Change theorem; displacement versus total distance
traveled)
- CARD #87 (the Fundamental Theorem of Calculus)
- worksheet (functions involving integrals)
WEEK #3 [Stewart 5.5, 6.1]
- MAJOR QUIZ
- CARD #88 (the substitution method for integration)
- continue the substitution method; go over Kaplan problems
- CARD #89 (substitution with definite integrals)
- CARD #90 (area between curves; vertical slices; horizontal slices)
- worksheet (technical aspects of areas between curves)
WEEK #4 [Stewart 6.2, 6.4]
- MAJOR QUIZ
- CARD #91 (a technique for functions of y , as opposed to functions of x )
- CARD #92 (volumes of revolution; the disk method; volume of a cone)
- CARD #93 (volumes of revolution; the shell method; volume of a cone)
- worksheet (finding the volume of a cone in many different ways)
- CARD #94 (average value of a function; derivation)
- CARD #94.5 (Careful! average rate of change versus average value)
WEEK #5 [Stewart 6.4, 7.1, 7.2, 7.4 ]
- MAJOR QUIZ
- CARD #95 (geometric interpretation of the average value)
- CARD #96 (differential equations; initial value problems)
- CARD #97 (separable differential equations)
- CARD #98 (slope fields)
WEEK #6
- "in a nutshell" pages summarizing all the important ideas in the entire course
- problem day/review for midterm
- MIDTERM EXAM (over "in a nutshell" pages)
HAVE A WONDERFUL SPRING BREAK!!
MAJOR EXAM OVER ALL CARDS ON THE DAY OF YOUR
RETURN
WEEK #7
- MAJOR EXAM over all index cards
- “catch-up” and/or extra time for questions and discussion
- unforeseen circumstances throughout the year can sometimes cause us to lose class days
unexpectedly
WEEK #8
- With all the course concepts now in place, it is time to practice, practice, practice!
- You will continue to practice writing skills, calculator skills, estimating answers and
interpreting results, expressing yourselves in complete mathematical sentences,
recognizing concepts (when they’re all mixed up!), and developing strategies for
multiple-choice questions.
- Every day this week, you will be paired in groups of two (different groups each day).
- Each group will be given a word problem; you will have 20 minutes to explore it with
your partner. Some will require a calculator; others will not.
- You will estimate an answer; write down a complete solution (which will be passed in);
compare your answer with your initial estimate and determine its reasonableness.
- One member from each group will give a presentation to the class summarizing their
results. Every student will make at least one class presentation.
WEEKS #9 – #12
- free response practice questions (calculator and non-calculator)
- multiple choice practice questions (calculator and non-calculator)
- sample tests (both timed and un-timed)
- additional practice with calculator skills
WEEKS #13 and #14
Post-AP material. We do different things each year, depending on student interest. In the
past, we have covered additional topics not covered on the AP syllabus, e.g., infinite
sequences and series, integration by parts, and arc length. Students have also had fun with
Peter Jipsen’s calculus text puzzles [http://www1.chapman.edu/~jipsen/calc/].