AP Calculus AB/BC Syllabus
Course Structure
This course is being taught in a year long 4 x 4 block scheduling format of 90 minutes
classroom time each school day. The first semester is considered Calculus AB and the
second semester is considered Calculus BC. However, all Calculus AB students and all
Calculus BC students are placed in classes together for the entire year. Students may
choose to take the first semester only, but all AP Calculus students must take the first
semester. All students enrolled in this course are required to take either the AP Calculus
AB Exam or the AP Calculus BC Exam.
Course Overview
Course content is tied directly to the College Board AP Calculus AB and AP Calculus BC
Topic Outlines and indirectly by objective to state and district guidelines. The overall
instructional approach is one which introduces concepts using the “Rule of Four”
approach in the spirit of reformed pedagogy while not neglecting the rigor of analytical
skills and appropriate theory. The TI-83 plus and TI-89 graphing calculators are used
almost daily for demonstration and classroom use. Students are assigned approximately
45 minutes of homework each day, and unit tests are administered after each unit.
Numerous supplementary materials and activities are incorporated into each unit as
supplements to the primary textbook. Deference to suggestions, materials, and
approaches recommended by the College Board through institutes published materials,
and on-line support is routinely incorporated into course content and daily classroom
activities. Students are taught to communicate mathematics verbally. This
occurs in the classroom on a daily basis both orally and written. Correct
nomenclature as well as preciseness and clarity is emphasized in both oral and
written communication. Students are taught and required to answer and
explain solutions to free response questions in written sentences. Written and
oral verbal communication including interpretation of numerical, analytical, and
graphical data, processes, and results are an integral and vital part of this
course. A strong two to four week review for the AP Exam is incorporated as a part of
the course. Students practice multi-step, multi-concept problems, bringing together the
entire scope of the course. Free response and published multiple choice questions from
previous exams are practiced and thoroughly discussed. Especially emphasized at this
time are non-algebraic methods of solving problems. At least one full length practice
exam is taken by each student within a short time of the AP Calculus examination date.
Graphing Calculators
Graphing calculators are an integral and vital part of this course. They are
used within lessons and student activities for exploration and experimentation.
They are used in problem solving as well as for verification, support, and
interpretation of results and conclusions obtained by various means. Graphing
calculators are indispensable as a teaching and learning aid with such topics as
limits and continuity, graphs, Riemann sums of all types, area, volume,
Newton’s method, Euler’s method, slope fields, parametric equations, and
series to name a few. The four competencies listed by the AP Calculus
Development Committee are taught and used extensively in instruction, in
student activities and homework, and on tests throughout the course as they
are appropriate and applicable. Almost all unit tests (including exams) have a
graphing calculator and a non-graphing calculator section.
Pacing Guide for AP Calculus AB/BC
(6 days)
Goal 1:
The learner will demonstrate knowledge of Pre-Calculus.
Objective:
Apply graphical interpretations of functions.
Discuss rate of change in linear functions.
Fit models to data.
(9 days)
Goal 2:
The learner will apply the concept of limits and continuity.
Objective:
Find limits graphically, numerically, and
analytically.
Discuss asymptotic behavior in terms of
infinite limits.
Apply the definition of continuity through the
use of limits.
(10 days)
Goal 3:
The learner will apply rules for differentiation to a variety
of problems.
Objective:
Apply the various differentiation rules to all
types of functions.
(11 days)
Goal 4:
The learner will sketch a curve using appropriate calculus
techniques.
Objective:
Find the absolute and relative extrema of a
function.
Determine the concavity of a function.
Draw the first and second derivatives of a
function from the function’s graph and vice
versa.
(7 days)
Goal 5:
The learner will apply the concept of differentiation to
application problems.
(11 days)
Goal 6:
The learner will interpret definite integrals.
Objective:
Find the area under the curve.
Calculate Riemann sums.
Apply the Fundamental Theorem of Calculus.
Determine values using both integration by
substitution techniques and numerical
integration.
(17 days)
Goal 7:
The learner will apply differentiation and integration
techniques to logarithmic, exponential and inverse
trigonometric functions.
Objective:
Apply the various differentiation rules to
these types of problems.
Apply the various integration rules to
these types of problems.
(7 days)
Goal 8:
The learner will find the area between two curves, the
volume of solids, the measure of arc length and surface
area using appropriate calculus techniques.
(14 days)
Goal 9:
The learner will apply basic integration techniques as well
as integration by parts, trig integrals, and improper
integrals.
(11 days)
Goal 10:
The learner will apply basic differentiation and integration
techniques to parametric and polar equations.
(20 days)
Goal 11:
The learner will find the sum of convergent and divergent
series.
Objective:
Find sums, including partial sums, of
geometric, harmonic, alternating, Taylor and
MacLaurin series.
(20 days)
Goal 12:
The learner will review all materials taught in this course in
preparation for the AP exam.
(15 days)
Goal 13:
The learner will explore applications of calculus in careers
and will explore formal proofs of calculus concepts.
The balance of the days will be used for Formal Mid-term and Term Examinations.
References and Materials
Primary Textbook:
Larson, Hostetler, Edwards. Calculus of a Single Variable. 7th ed. Boston: Houghton
Mifflin Co., 2002.
References:
Finney, Demana, Waits, Kennedy. Calculus—Graphical, Numerical, Algebraic. Upper
Saddle River: Pearson Prentiss Hall. 2007.
Hughes-Hallett, Gleason, McCallum et al. Calculus. 4th ed. Hoboken, NJ: Wiley, 2005.
Stewart, Calculus Concepts & Contexts. 3rd ed. Belmont, CA: Thompson, 2005.
Technology:
TI-83 plus and TI-89 graphing calculators
Weeks, Calculus in Motion. CD-ROM. Burbank, CA: Calculus in Motion. 2005.
On-line Calculus sites such as http://mathdemos.gcsu.edu/mathdemos/