Andover Central High Schoolroom: 904

Andover Central High SchoolRoom: 904

Mr. Randolph

Butler County Community College

AP®Calculus AB Syllabus 2016-2017

Course Overview:

Calculus is the mathematical tool used to analyze changes in physical quantities and investigate the properties and graphs of functions. The goal of this course is to give students a strong conceptual understanding of calculus concepts such as: limits, continuity, differentiation, integration of elementary and transcendental functions and their inverses, and trigonometry. Applications of differentiation and integration both inside and outside mathematics will be covered. Topics are investigated from three perspectives: graphically (using a TI-Nspire CX CAS graphics calculator), numerically (using the table capabilities of the TI-Nspire CX CAS), and algebraically, which validates the other perspectives. Standards held for the students are high and their knowledge is probed with high level questions in class, on labs, and on tests. Memorization of the basic derivative and integration formulas are expected by the students, but deep conceptual understanding is stressed. When students take other courses in calculus, it is hoped that they will be among those that truly understand what is happening and can set the standard for the class.

Major Text: Calculus, tenth edition, by Larson, Edwards, Brooks/Cole, 2014

Student Evaluation:

Class meets for fifty (50) minutes every day for one-hundred seventy-eight (178) days. Semester grades are calculated using homework (5%), labs (5%), and exams (90%). A standard grading scale will be used in this course. All exams include released AP multiple choice and free-response questions, and usually are three class periods long. Explanation and justification for answers are expected to be defended verbally (orally) and in writing using numerical, graphical, and algebraic support. All free-response questions that appear on the exam are evaluated according to the guidelines of the AP test.

A variety of application problems are used in the class to model physical, biological, or economic situations. Students are asked to solve these problems using appropriate differentiation and/or integration techniques. When integration applications are chosen, emphasis is on using the method of setting up an approximating Riemann sum and representing its limit as a definite integral. At least one lab is given to the students per chapter (a short explanation is given in the assignments). Labs are intended to be done in small groups and are designed to introduce, supplement, complement, or expand on concepts presented in the chapter. Labs involve the use of technology, typically the TI-Nspire CX CAS graphics calculator. A majority of the writing component of the course is done on the labs.

Once all required material is covered, review for the AP test begins around the end of March. This review consists of up to five practice exams, which include the free-response questions from the last five years AP exams. Students use the same rubric that is used on the AP exam for grading the free-response questions. Finally a few days before the AP test, students are given the final exam for the course. This exam is modeled and graded like the actual AP test.

Homework is an opportunity for students to practice concepts that are being taught and are not evidence of mastery, and thus will not constitute a major portion of the grade. Students will be given homework daily and will be asked to complete selected homework problems regularly for feedback from the instructor.

After the completion of a chapter exam, if a student did not show mastery of content objectives, then they may request to earn retroactive points provided the student meets eligibility requirements. The specific eligibility requirements and process will be described to the student when the request for retroactive points has been made. Retroactive points are earned by developing a study plan with the instructor, completing that study plan, and then showing mastery of specified content objectives on a subsequent exam(s). Retroactive points will not be available for arithmetic or algebraic mistakes, only for content objectives.

Resources Available:

Calculators:Every student in the course has the choice to purchase a TI-Nspire CX CAS graphics calculator on their own or to rent one from the library at school. Becoming quite familiar with the capabilities and understanding the limitations of their TI-Nspire CX CAS graphics calculator is expected from the students. Several short calculator activities are done in class. These include: finding regression equations for several different types data, graphing tables of data, graphing algebraic, trigonometric, logarithmic, exponential, and differential equations, graphing slope fields, estimating integrals and finding numerical derivatives. With all problems, students are expected to examine the results from a graphical and tabular approach using the TI-Nspire CX CAS graphics calculator to predict and explain the observed local and global behavior of a function and then justify their answer with an analytic approach.

Videos:A number of videos are available. These would be used to give the student an alternative perspective on a topic being covered:

1. Standard Deviants School-Calculus 2002 Cerebellum Corporation, these are a set of nine videos which cover calculus basics which include: limits, derivatives, and work-saving rules, finding derivatives, derivative applications, figuring out curves, practical applications, and the anti-derivative.
2. The videos that accompany our text Larson, Edwards Calculus10th edition.
3. Calculus in the Year 2000: New Ways of Teaching the Derivative and the Definite Integral, a three hour video by Steve Olson.
4. Videos available at and at

Desmos:Desmos which is available as an app and on the Internet for free is used in class as a supplementary aid in graphing. Particularly for implicit functions, slope fields, solids of revolution, and volumes of solids with a known cross-section.

TI-Nspire CX CAS Software:TI-Nspire CX CAS Software is a program made by TI that allows a TI-Nspire CX CAS calculator to appear on the computer screen as an interactive emulator. It is used in class as a supplement and an aid in doing graphs and calculations.

Equipment:The room is equipped with an LCD projector, a 27” television, a VHS player, a high-speed Internet connection, TI-Nspire CX CAS Software, and has access to 24 Chromebooks with high-speed Internet access.

Other Resources: The instructor has access to a small volume mathematics library, including supplementary workbooks, AP review books, CBL workbooks, and calculus texts.

Assignments: AP® Calculus AB

Note: Each section assignment is for one class period and may be adjusted by the instructor at their discretion

Session / Learning Activities
Section 1.1 A Preview of Calculus / What I Want From Calculus?
Sect 1.1 p.45 Exploration, p.46 Exploration, p.47 #1-10
Section 1.2 Finding Limits Graphically and Numerically / Sect 1.2 p.55 #1-27(odds)
Sect 1.2 p.57 #51-63(odds), 67-73
Limits of a Function Lab (1 day) – This lab examines the idea of a limit of a function through numerous examples and builds a solid foundation for further work with limits.
Section 1.3 Evaluating Limits Analytically / Sect 1.3 p.67 #5-25(odds), 37-45(odds)
Sect 1.3 p.67 #47-61(odds), 75, 85
Sect 1.3 p.67 #27-33(odds), 67-71(odds), 81, 101, 102, 115-120
Section 1.4 Continuity and One-Sided Limits / Sect 1.4 p.79 #1-6, 7-33(odds)
Sect 1.4 p.80 #53-65 (odds), 87, 89, 95, 103-106, 111
Section 1.5 Infinite Limits / Sect 1.5 p.88 #1-31(odds)
Sect 1.5 p.88 #33-51(odds), 58, 61, 63-68
Chapter 1 Review / Chapter 1 Review
p.91 #1-37(odds)
p.92 #49-83(odds)
Chapter 1 Test / 3 days
Section 2.1 The Derivative and the Tangent Line Problem / Discovering the Derivative Lab (1 day) - This activity develops the derivative of function by analyzing the slope of secant lines.
Sect 2.1 p.103 #1-31(odds)
Sect 2.1 p.104 #65-89(odds), 93-96
Section 2.2 Basic Differentiation Rules and Rates of Change / Sect 2.2 p.114 #1-29 (odds)
Sect 2.2 p.114 #35-67(odds)
Sect 2.2 p.116 #87-92, 93-97(odds), 101, 103, 109-115(odds)
Section 2.3 Product and Quotient Rules and Higher-Order Derivatives / Sect 2.3 p.125 #13-23(odds), 31-53(odds)
Sect 2.3 p.126 #63-71(odds), 81, 82, 86, 91, 95, 101, 116, 119, 126, 129-134
Derivative and It’s Graph Lab (2 days) - This activity looks at the graphical relationship between a function and its first and second derivatives.
Section 2.4 The Chain Rule / Sect 2.4 p.136 #1-17(odds), 43-63 odds
Sect 2.4 p.136 #69-79(odds), 81, 85, 95, 99, 102, 103, 105, 125-128
Section 2.5 Implicit Differentiation / Sect 2.5 p.145 #1-27(odds)
Sect 2.5 p.146 #45, 51-59, 69, 74
Section 2.6 Related Rates / Sect 2.6 p.153 #1-23(odds)
Sect 2.6 p.154 #25-49(odds)
Chapter 2 Review / Chapter 2 Review
p.157 #3-13(odds), 25-49(odds)
p.159 #59-87(odds)
Chapter 2 Test / 3 days
Section 3.1 Extrema on an Interval / Sect 3.1 p.167 #1-11(odds), 17-35(odds)
Sect 3.1 p.167 #39, 41, 43, 55-58, 60, 62-66
Section 3.2 Rolle's Theorem and the Mean Value Theorem / Sect 3.2 p.174 #1-35(odds)
Sect 3.2 p.175 #37, 41, 45, 49-57(odds), 65, 73-76
Section 3.3Increasing and Decreasing Functions and the First Derivative Test / Sect 3.3 p.183 #1-37(odds)
Sect 3.3 p.184 #57-67(odds), 73, 79, 83, 87, 91-96
Increasing/Decreasing Lab (1 day) - This activity looks at
the relationship between the graph of a function, its
derivative and whether it is increasing or decreasing or
constant. It also examines the relative extrema of a function
and some implications of a function’s derivative and the
number of zeros of a function. Finally, students are asked to
look at a table of values for a function and its derivative and
sketch a possible solution for the conditions.
Section 3.4 Concavity and the Second Derivative Test / Sect 3.4 p.192 #3-41(odds)
Sect 3.4 p.192 #51-57, 63, 65, 73, 75-78, 80
Section 3.5 Limits at Infinity / Sect 3.5 p.202 #13-45(odds)
Sect 3.5 p.203 #58, 59, 71, 77, 83-87(odds), 99, 103-104
Section 3.7 Optimization Problems / Sect 3.7 p.220 #1, 5, 9-13(odds), 21-25(odds)
Sect 3.7 p.222 #33, 35, 41-47(odds), 50-52
Section 3.9 Differentials / Sect 3.9 p.236 #1-25(odds)
Sect 3.9 p.236 #27-41(odds), 47-50
Differentials Lab (1 day) - This activity deals with the
various geometrical ideas connected with differentials using
multiple choice and short answer questions.
Chapter 3 Review / Chapter 3 Review
p.238 #1-43(every other odd), 55-65(odds)
p.239 #67, 71, 75, 77-83(odds), 93, 95
Chapter 3 Test / 3 days
Section 4.1 Antiderivatives and Indefinite Integration / Sect 4.1 p.251 #1-29(odds)
Sect 4.1 p.251 #35-45(odds), 50
Sect 4.1 p.252 #53-67(odds),88, 69-74
Section 4.2 Area / Sect 4.2 p.263 #1-19(odds), 31-35(odds)
Sect 4.2 p.264 #37, 39, 45-57(odds)
Sect 4.2 p.264 #59, 63, 67, 69, 71-72
Section 4.3 Riemann Sums and Definite Integrals / Sect 4.3 p.273 #1-29(odds)
Sect 4.3 p.274 #41-61(odds), 63-68
Average Value of a Function Lab(2 days) - This activity
explores what is meant by the average value of a function
through various examples, Riemann sums, and the use of the
TI 84 Plus graphics calculator. It also asks the student to
estimate the height of the rectangle that will give the
approximate area under the curve being investigated.
Section 4.4 The Fundamental Theorem of Calculus / Sect 4.4 p.288 #1-37(every other odd)
Sect 4.4 p.288 #39-63(odds), 67-73(odds)
Sect 4.4 p.290 #75-93(odds), 99, 101, 111, 112
Functions Defined by Integrals Lab (2 days) - This activity
examines the Fundamental Theorem of Calculus, part 2, and
how functions defined by integrals behave, how they are
computed both analytically and using a graph of the their
derivative, and how the integral compares with the
antiderivative of the integrand.
Section 4.5 Integration by Substitution / Sect 4.5 p.301 #1-29(odds)
Sect 4.5 p.301 #31-61(odds)
Sect 4.5 p.302 #63-77(odds),85, 91-96
Section 4.6 Numerical Integration / Sect 4.6 p.310 #1-21(odds)
Sect 4.6 p.310 #23, 27, 31, 35-43(odds)
Numerical Integration Lab (2 days) - This activity looks at
the geometry behind two methods of numerical integration,
the Trapezoid rule and Simpson’s Rule. It also gives the
student a feel for the relative speeds of convergence of
Riemann sums, Trapezoid Rule, and Simpson’s Rule.
Chapter 4 Review / Chapter 4 Review
p.312 #1-19(odds), 29, 31, 37-49(odds)
p.313 #51, 57, 59-83(odds), 87, 89
Chapter 4 Test / 3 days
Section 5.1 The Natural Logarithmic Function: Differentiation / Sect 5.1 p.325 #1-39(odds)
Sect 5.1 p.325 #41-63(odds)
Sect 5.1 p.326 #67, 71, 73, 79, 81, 85, 89-93(odds), 99-102
Section 5.2 The Natural Logarithmic Function: Integration / Sect 5.2 p.334 #1-39(odds)
Sect 5.2 p.334 #41, 47-55(odds), 63-73(odds), 77, 89, 93, 97, 103-106
Section 5.3 Inverse Functions / Sect 5.3 p.343 #1-33(odds)
Sect 5.3 p.344 #51-59(odds), 71-74, 89-92
Section 5.4 Exponential Functions: Differentiation and Integration / Sect 5.4 p.352 #1-53(every other odd)
Sect 5.4 p.352 #57-65(odds), 71, 73, 79-85(odds)
Sect 5.4 p.354 #91-121(odds), 125-139(odds)
Section 5.5 Bases Other Than e and Applications / Sect 5.5 p.362 #1-57(every other odd)
Sect 5.5 p.362 #59, 63, 65, 69, 71-83(odds), 97, 101, 104, 111-116
Section 8.7 Indeterminate Forms and l'Hopital's Rule / Sect 8.7 p.564 #1, 5-35(odds)
Sect 8.7 p.564 #43-59(odds), 69, 71, 79, 81, 83, 111
Indeterminate Limits and l'Hopital's Rule Lab (1 day) - This activity gives the student experience recognizing limits
of quotients that are indeterminate, understanding
L’Hopital’s rule and its applications, and appreciating why
L’Hopital’s rule works.
Section 5.6 Inverse Trigonometric Functions: Differentiation / Sect 5.6 p.372 #1-11(odds), 21-33(odds), 39-47(odds)
Sect 5.6 p.372 #56, 57-61(odds), 65, 71, 78, 85-90, 93
Section 5.7 Inverse Trigonometric Functions: Integration / Sect 5.7 p.380 #1-29(odds), 55, 56
Sect 5.7 p.380 #33-45(odds), 49, 53,61, 65, 69, 71, 75, 80
Chapter 5 Review / Chapter 5 Review
p.393 #1-25(odds), 37-41(odds)
p.393 #47-55(odds), 59-65(odds), 69, 71
Chapter 5 Test / 3 days
Section 6.1 Slope Fields / Sect 6.1 p.403 #1-5(odds), 11,13, 24, 29, 33, 35, 41-51(odds)
Sect 6.1 p.404 #53-71(odds), 89-92
Section 6.2 Differential Equations: Growth and Decay / Sect 6.2 p.412 #1-23(odds)
Sect 6.2 p.412 #27, 33-37(odds), 41, 43, 47, 51, 55, 63, 65
Section 6.3 Separation of Variables / Sect 6.3 p.421 #1-23(odds), 26, 31, 33-36
Slope Fields Lab (3 days) - This activity pulls together a
number of examples of slope fields. The student is asked to
sketch particular solutions of differential equations using the
graph of their slope field, graph differential equations using
the TI 84 Plus graphics calculator, solve the differential equationsrepresenting slope fields (using separation of variables),identify which differential equation matches which slopefield, which particular solution matches a particular slopefield, and asks the student to sketch the slope fields of somedifferential equations.
Chapter 6 Review / Chapter 6 Review
p.431 #1-23(odds), 29, 35-37(odds), 41
Chapter 6 Test / 3 days
Section 7.1 Area of a Region Between Two Curves / Sect 7.1 p.442 #1-29(odds)
Sect 7.1 p.443 #31-49(odds)
Sect 7.1 p.443 #51-69(odds), 78, 83-86
Section 7.2 Volume: The Disk Method / Sect 7.2 p.453 #1-15(odds), 21, 25, 27, 31, 35, 37
Sect 7.2 p.455 #55, 61-69(odds), 72, 76
Section 7.3 Volume: The Shell Method / Sect 7.3 p.462 #1-29(odds)
Sect 7.3 p.463 #33, 41, 49, 51, 54, 55, 57
Section 7.4 Arc Length and Surfaces of Revolution / Sect 7.4 p.473 #1-13(odds), 17-29(odds)
Sect 7.4 p.474 #35-55(odds), 54, 64, 67
Applications of Integration Lab (2 days) - This activity
gives the student some real-life examples of finding the area
between two curves, the volume and surface area of a solid
of revolution, and the arc length of a function.
Chapter 7 Review / Chapter 7 Review
p.503 #1-25(odds)
Chapter 7 Test / 3 days
AP Review - Approximately one month / Various AP exams to be done as assignments. A total of five
exams are given, along with a test over calculator usage.
Course Final / 3 days
AP Calculus Exam / 3 hours
Final Lab Project - Construction of a
Solid of Revolution / Solid of Revolution Lab (Approximately 1 week) - In this
activity, the student and a partner use cardboard to construct
a solid of revolution. A report is handed in which includes
the volume and surface area of the solid of revolution, the
arc length of the curve used to generate the solid, and the
area of the region being rotated.

The schedule and procedures in this course are subject to change in the event of extenuating circumstances.

We, the undersigned, have read and understood the terms of this syllabus.

Student: ______Parent/Guardian: ______