AP Calculus AB/BC is taught as a year-long 4x4 class. Each period is 90 minutes. Students
interested in AP Calculus AB take the first semester portion of the course followed by periodic
sessions after school for review purposes. Students taking the second semester are expected to
know the AP Calculus AB material. AP Calculus BC topics are taught during the second
semester. The students taking this portion of the class are required to enroll for the entire year.
Students enrolled for the entire year must take either the AP Calculus AB Exam or the AP
Calculus BC Exam in May.
COURSE CONTENT
The course is based on the objectives listed in the topic outline for
Calculus AB and Calculus BC from the College Board. Students are assigned approximately 60
minutes of homework a night. Unit tests are administered about every two weeks as units are
completed. Supplementary materials and activities are used in each unit to complement the text.
A four week review for the AP Exam is built into the pacing guide.
Students regularly practice previously administered Free Response questions. In the
process of solving Free Response questions students practice writing explanations for the
numerical value found. These explanations are based on the appropriate Theorems/processes
used to draw conclusions from the calculated values. In addition, students are taught to
communicate the mathematics they are learning orally through group work, classroom,
presentations and oral responses to questions asked during instruction. Both written and oral
communication is expected when interpretation of numerical, graphical, and analytical processes
are involved.
The graphing calculator is an essential tool for students learning Calculus. The TI-83
plus and TI-89 are used daily by both the instructor, to model their use, and students for
calculations, exploration and experimentation. Students are asked to use calculators, regularly to
discover a connection between graphical displays and the concept of the day. Calculators are
used to verify and support results and conclusions found through numerical, graphical and
analytical means. Calculators are used for instruction and student calculations involving 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. Since it is vital for
students to demonstrate an understanding of all materials graphically, numerically, analytically
and verbally students are taught that calculators provide a vital link in connecting these
competencies. Consequently, almost all unit tests, including semester exams, have a graphing
calculator portion to complement the non-graphing calculator portion of the test.
Students will take a full length practice exam prior to the May test date. A released Exam
will be used for this purpose.
COURSE SYLLABUS
(6 days)
Goal 1:
The learner will demonstrate knowledge of Pre-Calculus.
Objective:
Apply graphical, numerical, algebraic and
verbal 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.
Use Intermediate Value Theorem and Extreme
Value Theorem to determine continuity.
(10 days)
Goal 3:
The learner will apply rules for differentiation to a variety
of problems.
Objective:
Apply the various differentiation rules to
polynomial, power, rational, trigonometric
and radical functions.
Compare instantaneous and average rate of
change.
Explore the connection between derivations
and continuity.
Derivate implicitly.
(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.
Calculate velocity and acceleration.
(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, vector 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, p-, power,
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