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AP AB Calculus Syllabus
Pre-Requisites
Three years of High School Mathematics (including Precalculus) with emphasis on functions and
their behavior and modeling real world applications.
Course Overview
Calculus provides students a framework for putting together many of the pieces of their
mathematical education into a coherent whole and provides students with a powerful tool for
understanding the world around them.
This AP Calculus AB is an enriched mathematics course and curriculum that is designed to help
students in their understanding of the calculus curriculum and to provide and prepare them for
the mathematics needed to be successful in post secondary studies. Students should not be
merely skilled in the various techniques of calculus; they should appreciate it as an integrated
system for observing, studying, and describing motion and change. Students are introduced to the
wonderful and exciting world of higher mathematics through a comprehensive study of all of the
objectives outlined in the AP Calculus Course Description. In addition, students are encouraged
to take the AP Calculus AB exam.
The following Curricular and Resource requirements below will be sited:
Curricular Requirements
C 1 The teacher has read the most recent AP Calculus Course Description, available as a free
download on the AP Calculus AB Course Home Page.
C 2 The course teaches all topics associated with Functions, Graphs, and Limits; Derivatives;
and Integrals as delineated in the Calculus AB Topic Outline in the AP Calculus Course
Description.
C 3 The course provides students with the opportunity to work with functions represented in
a variety of ways -- graphically, numerically, analytically, and verbally -- and
emphasizes the connections among these representations.
C 4 The course teaches students how to communicate mathematics and explain solutions to
problems both verbally and in written sentences.
C 5 The course teaches students how to use graphing calculators to help solve problems,
experiment, interpret results, and support conclusions.
Resource Requirements
R 1 The school ensures that each student has a college-level calculus textbook (supplemented
when necessary to meet the curricular requirements) for individual use inside and outside
of the classroom.
R 2 The school ensures that each student has a graphing calculator for individual use inside
and outside of the classroom, with all the required capabilities listed in the AP Calculus
Course Description. (A list of approved graphing calculators is available on AP Central
on the AP Calculus AB Course Home Page.)
1
Course Planner, Guide, and Topic Outline [C1 and C2].
Note: Our school is on a following combined schedule: every subject is taught three classes a
week – one class lasting 43 minutes (one period) on Monday and two classes lasting 88 minutes
each (two periods) and meeting every other day. This way the equivalent of the five days
(periods) a week is achieved.
The primary text used:
Stewart, James. Calculus 7e. Brooks/Cole, Cengage Learning, © 2012. [R1].
Below is the sequence of our AP Calculus AB course. Section numbers refer to the primary text.
All timelines are approximate and include review and testing times. These will be adjusted
according to student comprehension.
Unit Section-description Planned
(in periods)
1 Functions and Limits 14
Graphing Calculators and Computers (Appendix G). Calculus AB item I.1 1
1.1 Four ways to represent a function. Calculus AB item I.1 1
1.2 Mathematical Models: A Catalog of Essential Functions. Prerequisite for later AP 1
Calculus Material
1.3 New Functions from Old Functions. Prerequisite for later AP Calculus Material 1
1.4 The Tangent and Velocity Problems. Calculus AB item I.2(a) 1
1.5 The Limit of a Function. Calculus AB items I.2(c), I.3(a), and I.3(b) 1
1.6 Calculating Limits Using the Limits Laws. Calculus AB item I.2(b) 1
1.8 Continuity. Calculus AB items I.4(a)-(c) 2
Unit Review. Include Principles of Problem solving (p.97)and AP AB Review 3
questions AP1-1
Unit 1 Test day 2
2 Derivatives 25
2.1 Derivates and Rates of Change. Calculus AB items II.1, II. 3
Writing Project “Early Methods for Finding Tangents” – assigned for homework
2.2 The Derivative as a Function. Calculus AB items II.1, II.3(a), II.4(a), II.5(f) 2
2.3 Differentiation Formulas. Calculus AB items II.1(b), II.6(a), II.6(b). 4
Applied Project “Building a better Roller Coaster”
2.4 Derivatives of Trigonometric Functions. Calculus AB item II.6(a) 2
2.5 The Chain Rule. Calculus AB item II.6(c) 3
Applied Project “Where Should a Pilot Start Descent?”
2.6 Implicit Differentiation. Calculus AB item II.6(c) 2
Lab project “Families of Implicit Curves”
2.7 Rates of Change in the Natural and Social Sciences. Calculus AB items II.2(c), 1
II.3(d), II.5(f)
2.8 Related rates. Calculus AB items II.3(d), II.5(d) 1
2
2.9 Linear Approximations and Differentials. Calculus AB item II.2(b) 2
Unit Review. Include Problems Plus (p.194) and AP AB Review questions AP2-1 3
Unit 2 Test day 2
3 Applications of Differentiation 21
3.1 Maximum and Minimum Values. Calculus AB items I.4(c), II.5(c) 3
Applied Project “The Calculus of Rainbows”
3.2 The Mean value Theorem. Calculus AB item II.3(c) 1
3.3 How Derivatives Affect the Shape of a Graph. Calculus AB items II.3(b), II.4(b),(c), 4
II.5(a),(c)
3.4 Limits and Infinity: Horizontal Asymptotes. Calculus AB items I.3(a),(b) 1
3.5 Summary of Curve Sketching. (optional material, skip if time issue – will be 1
addressed during the Review and Preparation for the AP exam)
3.6 Graphing with Calculus and Calculators. Calculus AB item I.1 1
3.7 Optimization Problems. Calculus AB item II.5(c) 2
Applied Project “The Shape of a Can”
3.9 Antiderivatives. Calculus AB items II.4(a), III.4(a),(c), III.5(a) 3
Unit Review. Include Problems Plus (p.341) and AP AB Review questions AP3-1 3
Unit 3 Test day 2
MIDTERM Exam 3
4 Integrals 14
4.1 Areas and Distances. Calculus AB items III.1(a), III.2 2
4.2 The Definite Integral. Calculus AB items III.1(a),(b),(c), III.6 3
Discovery Project “Area Functions”
4.3 The Fundamental Theorem of Calculus. Calculus AB items III.1(b), III.2, III.3.(a),(b) 2
4.4 Indefinite integrals and the Net Change Theorem. Calculus AB items III.1(b), III.4(a), 1
III.5(a)
4.5 The Substitution Rule. Calculus AB item III.4(b) 1
Unit Review. Include Problems Plus (p.341) and AP AB Review questions AP4-1 3
Unit 4 Test day 2
5 Applications of Integration 14
5.1 Areas between curves. Calculus AB item III.2 3
Applied Project “The Gini Index”
5.2 Volume. Calculus AB item III.3 3
5.5 Average Value of a Function. Calculus AB item III.2 3
Applied Project “Calculus and Baseball’
Unit Review. Include Problems Plus (p.380) and AP AB Review questions AP5-1 3
Unit 5 Test day 2
6 Inverse Functions (Exponential, Logarithmic, and Inverse Trigonometric 12
functions)
6.1 Inverse Functions. Calculus AB item II.5(e) 1
3
6.2 Exponential Functions and their Derivatives. Calculus AB items I.3(c), II.6(a) 1
6.3 Logarithmic Functions. Calculus AB item I.3(c) 2
6.4 Derivative of Logarithmic Functions. Calculus AB item II.6(a) 1
6.5 Exponential Growth and Decay. Calculus AB items II.3(d), III.5(b) 1
6.6 Inverse Trigonometric Functions. Calculus AB item II.6(a) 1
Unit Review. Include Problems Plus (p.485) and AP AB Review questions AP6-1 3
Unit 6 Test day 2
7 Techniques of Integration 7
7.2 Trigonometric Integrals. Calculus AB item III.4(b) 2
7.7 Appropriate Integration. Calculus AB item III.6 1
Unit Review. Include Problems Plus (p.557) and AP AB Review questions AP7-1 2
Unit 7 Test day 2
8 Differential equations (Chapter 9) 10
9.1 Modeling with Differential Equations. Calculus AB items II.3(d), III.5(b),(c) 2
9.2 Direction Fields and Euler’s Method. Calculus AB items II.5(g), Skip Euler’s Method 2
Calculus BC II.5(b)
9.3 Separable Equations. Calculus AB item III.5(b) 2
Unit Review. Include Problems Plus (p.657) and AP AB Review questions AP9-1 2
Unit 9 Test day 2
9 Review and Preparation for the AP Exam 20
10 AP Exam
11 Post AP Exam topics and various projects 38
12 Preparation for the Final Exam 5
13 Final Exam 3
Explaining the Content
In Unit One, multiple representations of functions are stressed: verbal, numerical, visual and
algebraic. A discussion of mathematical models leads to a review of standard functions from
these points of view. Students develop a library of basic functions, with their various
characteristics (domain, continuity, symmetry, end behavior, etc.). Throughout the course, these
functions are referred back to again and again so that students begin to “see” those basic
functions arise from information given in exercises. The material of limits is motivated by a prior
discussion of the tangent and velocity problems. Limits are treated from descriptive, graphical,
numerical, and algebraic point of view. A limit exploration is done using graphing calculators.
Using tables, students use differing values of h that they select to determine the effect on the
limit of a function. After completing Unit One students will be able to calculate average and
instantaneous speeds; define and evaluate limits analytically (algebraically); use the concept of
limits to define continuity; identify continuous functions graphically and analytically; apply the
Intermediate Value and Squeeze Theorems; find equations of the tangent line and normal line to
a curve at a given point. [C2], [C3], [C4], and [C5]
4
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