Advanced Placement Calculus AB
Textbook
Calculus of a Single Variable, Roland Larson, Robert Hostetler, Bruce Edwards,
Houghton-Mifflin, 6th Edition, 1998.
Calculus Calculator Labs, Benita Albert, Phyllis Hillis, Skylight Publishing
General Educational Requirements
1. Each chapter will be accompanied by a homework assignment which must be
completed and submitted at the beginning of class on the day of the test.
Many of these problems will require the student to develop plans and
processes for finding solutions.
2. Open-ended problems will be posed to student groups who will then research,
develop, present, and defend their own solution.
3. Students are required to have a graphing calculator. Calculators are an
essential tool for this course. They will be used extensively, not only for
solving problems, but for exploration of basic concepts. Calculator labs will
be used to illustrate and explore various concepts throughout the course.
4. Each student will practice the “Rule of Four” when approaching problem
solving. Graphical analysis, numerical analysis, analytic analysis, and verbal
or written analysis will be employed.
Topics Covered
Chapter P
Chapter 1
Chapter 2
Review
Section 1
Section 2
Section 3
Section 4
Graphs and Models
Linear Models and Rates of Change
Functions and Graphs
Fitting Models to Data
Limits
Section 1
Section 2
Section 3
Section 4
Section 5
A Preview of Calculus
Finding Limits Graphically and Numerically
Evaluating Limits Analytically
Continuity and One-Sided Limits
Infinite Limits
Mechanics of Derivatives
Section 1
Derivatives as Tangent Lines
Section 2
Basic Differentiation Rules and Rates of Change
Section 3-4 More Differentiation Rules
Section 5
Implicit Differentiation
Section 6
Related Rates
Chapter 3
Applications of Derivatives
Section 1
Extrema on an Interval
Section 2
Rolle’s Theorem and Mean Value Theorem
Section 3
First Derivative Test, Increasing/Decreasing Functions
Section 4
Concavity and the Second Derivative Test
Section 5
Limits at Infinity
Section 6
Summary of Curve Sketching
Section 7
Optimization Problems
Section 8
Newton’s Method
Section 9
Differentials
Section10
Business and Economic Applications
Chapter 4
Mechanics of Integration
Section 1-2 Finding Area
Section 3
Riemann Sums and Definite Integrals
Section 4
Fundamental Theorem of Calculus
Section 5
Integration by Substitution
Section 6
Numerical Integration, Trapezoidal Rule & Simpson’s Rule
Chapter 5
Section 1-2
Section 3
Section 4
Section 5
Section 6
Section 7
Section 8-9
Section 10
Chapter 6
Applications of Integration
Section 1
Area Between Curves
Section 2-3 Volumes of Solids of Revolution
Section 4
Surface Area and Arc Length
Section 5
Work
Section 6
Moments of Inertia, Centers of Mass
Section 7
Fluid Pressure and Force
Review
April 21 – May 5, 2009
Review of released exams from years 2007, 1998, 1997, and 1993
Natural Logarithms
Inverse Functions
Exponential Functions
Bases Other than “e”
Differential Equations: Growth and Decay
Differential Equations: Separation of Variables
Inverse Trigonometric Functions
Hyperbolic Functions
Pedagogical Style
Students will be expected to investigate multiple representations of topics. They will be
able to sketch tangent lines. They will show a table to approximate derivatives. They
will use a derivative to find the slope of a tangent line. Students will then explain, not
only their results, but any relationships derived. Student will be expected to show all
work and use complete sentences when explaining their solutions. When a calculator is
used, students must give the setup as well as the calculator result. All mathematical steps
must be shown and justified in complete written sentences.
Assessment
Assessment consists of chapter tests, projects, semester and final exams. Connections to
real-world application of the concepts are stressed. Exams contain both calculator active
and calculator on active items. Explaining the “why” is just as important as the “how”.
Justification of answers is required in written form. Summative assessments are used at
the end of each chapter. Students will practice the “Rule of Four” when approaching
problem solving. Graphical, analytical, numerical, and written formative assessments
will allow students to self-assess.
Technology
Students are required to have a graphing calculator. Calculators are an essential tool for
this course. They will be used extensively, not only for solving problems, but for
exploration of basic concepts. Calculator labs will be used to illustrate and explore
various concepts throughout the course. All students will be able to graph a function
within a window, find roots, find a numerical derivative of a function, and find a
numerical value for a definite integral. Students will perform selected calculator
experiments that will enhance their ability, not only to justify their answers but to explore
other possible outcomes. All of these skills will enable the students to solve problems.
Graphing calculators will be used frequently to solve problems, experiment, interpret
results, and support their conclusions.