AP Calculus Syllabus (AB)
Mr. Hus
AP Calculus AB
Overview: Calculus Prep is a course designed to match the AP AB Curriculum as set
forth by the College Board. It is a rigorous course which will cover one semester of
college calculus. It is designed for students who have succeeded in Precalculus and who are college bound. The course adheres to the reforms in AP Calculus, that is, emphasis on understanding and problem solving, the rule of four (graphical, data, verbal and analytical), and the use of the graphingcalculator to free up time to examine ideas in more detail.
A detailed examination for the framework of the course can be found via the following links:
Textbook: Calculus, Larson, Hostetler, Edwards. 2002, Houghton Mifflin Company; 7th
Edition
Supplemental Texts: Handouts, videos and other information as announced throughout the course.
Requirements: The course is graphing calculator based. The student are required to have their own graphing calculator. Recommended is the TI-84+ Silver Edition, for its capabilities and ease of use. Note: The TI-89 will not be supported in this course. Students can use the TI Nspire in addition to the TI-84+.
As specified in the AP Bulletin, the calculator is to be used to graph functions in a specified window, find zerosof a function (the intersection of 2 curves), find the numerical derivative and thenumerical integral. Half of the questions, both multiple choice and free response, will be analyzed with the graphing calculator.
Curriculum:
I. Functions, Graphs, Limits.
A. Analysis of graphs.
B. Limits of functions (including one-sided limits).
C. Asymptotic and unbounded behavior
D. Continuity as a property of functions.
II. Derivatives.
A. Concept of derivative.
B. Derivative at a point.
C. Derivative as a function.
D. Second and higher order derivatives.
E. Application of derivatives.
i. Analysis of curves
ii. Optimization, locally and globally.
iii. Modeling rates of change.
iv. Geometric interpretation of differential equations
v. Computation of derivatives.
III. Integral.
A. Interpretations and properties of definite integrals.
B. Fundamental Theorem of Calculus.
C. Techniques of antidifferentiation.
D. Applications of integrals.
i. Area of a region (including bounding by polar curves)
ii. Volume of a solid (of revolution and known cross sections)
iii. Average value of a function.
iv. Distance traveled by a particle along a line.
v. Length of a curve.
E. Applications of anti-differentiation.
i. Motion along a line.
ii. Separable differential equations.
iii. Slope fields.
F. Numerical approximations to definite integrals.
i. Riemann sums.
ii. Trapezoidal sums.
Grading: The period grading will be based on daily homework (10%), tests (65%), and quizzes(25%). Semester grades are calculated on a 40% for each 9 week period and the final exam is worth 20%. It isessential that homework be done consistently and diligently. This is where skills arelearned and fine-tuned. Students should expect special project reports throughout the course. Scores of practice AP exams will be incorporated into the student’s grade.
Absent Work: All homework, quizzes and tests are to be made up according to the school policy. Late work is NOT accepted unless arrangements are made with the instructor.
After the AP exam: When the AP exam is finished, early in May, we will spend the
remaining month learning calculus material which is not part of the exam curriculum.
Included will be the following topics: Infinite integrals, trigonometric integrals, partial
fractions, integration by parts. This will be done in attempt to better
prepare students for further calculus work.
AP Credit: Most universities give credit for passing scores of 4 or higher on the test for science and engineering curriculums.
Nearly every school credits a score of 5. The AB course will usually give students one
semester worth of calculus credit four to five credit hours at Indiana State schools.
Brief Description of Course
AB Calculus is a course that draws upon the concepts and skills from the student’s
previous math courses, especially precalculus. It applies these skills to the main thrusts
of Calculus: the use of the limit concept to the development and use of the derivative
(instantaneous rate of change) and the integral (determination of area under a curve). Thecourse teaches an appreciation of the beauty of the math of Calculus and imparting skillsthat will be invaluable in the technical fields that are so important.
Unit Information
Unit Name or Timeframe:
Summer Work
Summer work is assigned which reviews and hones previously learned concepts that willbe drawn upon heavily in AB Calculus. Among these are trigonometry reviews, algebra,and function work.
Unit Name or Timeframe:
Precalculus practice (4 days)
Content and/or Skills Taught:
Review of Precalculus with group activites.
Unit Name or Timeframe:
Chapter 1: Limits and Their properties (10 days)
Preview of Derivative and Integral
Limits Graphically and Numerically
Limits Analytically
Continuity and One-Sided Limits
Infinite Limits
Content and/or Skills Taught:
An understanding of the concept of limits and how to determine them.
Unit Name or Timeframe:
Chapter 2: Differentiation (20 days)
Derivative and Tangent Line
Basic Differentiation Rules-Rates of Change
Product and Quotient Rules and Higher Order Derivatives
The Chain Rule
Implicit Differentiation
Related Rates
Content and/or Skills Taught:
The ability to apply limits to the definition of the derivative and acquire the rules vital to
computing derivatives.
Unit Name or Timeframe:
Chapter 3: Applications of the Derivative (24 days)
Finding Extrema on a Closed Interval
Rolle’s Theorem and the Mean Value Theorem
The First Derivative – Increasing and Decreasing
Concavity and the Second Derivative Test
Limits at Infinity
Curve Sketching
Optimization
Differentials: Error and Linear Approximation
Content and/or Skills Taught:
How the concept of the derivative can be used in working with functions and applying
the derivative to certain problems.
Unit Name or Timeframe:
Chapter 4: Integration (18 days)
Anti-derivatives and Indefinite Integration
Slope Fields and Solutions to Differential Equations
Area
Riemann Sums and Definite Integrals
Fundamental Theorems of Calculus
Integration by Substitution
Numerical Integration: Midpoint and Trapezoidal Rules
Content and/or Skills Taught:
The relationship between antidifferentiation and integration-the finding of area.
Unit Name or Timeframe:
Chapter 5: Transcendental Functions (20 days)
Natural Logarithmic Function and Differentiation and Integration
Inverse Functions and Their Derivative
Exponential Functions: Differentiation and Integration
Bases other than e
Differential Equations: Growth and Decay
Solving Differential Equations-Separation of Variables
Inverse Trig Functions: Differentiation and Integration
Content and/or Skills Taught:
How the concepts of integration and differentiation can be applied to the transcendental
function.
Unit Name or Timeframe:
Chapter 6: Applications of Integration (10 days)
Area between Curves
Volumes: Of Revolution and Cross Sections of Known Area
Content and/or Skills Taught:
Use of the concept of infinite sums to total area and volume.
Unit Name and Timeframe:
Additional Topics (15 days)
Accumulation of change
Relation Between Slope Fields and Differential Equations
Second Fundamental Theorem Use with Graphs of a Derivative of a Function
Rectilinear Motion-Position vs Velocity vs Acceleration
Additional Graphing Calculation Review and Practice
Unit Name and Timeframe:
AP Review (20 days)
During this time we review particular key troublesome concepts. Specially prepared
worksheet are handed out and assigned. Perhaps 10 graphing calculator worksheets,
where students use their calculators to answer multiple questions on key concepts are
assigned. We then practice multiple old AP Tests, and practice tests from supplemental materials. Throughout the year I give quizzes on a myriad of multiple choice calculus questions andold free responses to prepare the students to the testing experiences and to improve theircommunication skills.
Students are expected to be available for AP Test Practice the Saturday before the scheduled AP exam. This practice will be held from 8 a.m. – 12 p.m..
Textbooks
Title: Calculus of Single Variable
Publisher: Houghton Mifflin
Published Date: 2002
Author: Roland Larson
Second Author: Robert Hostetler
Description:
Other Course Materials
Material Type: Other
Description:
Additional Information
Requirement: Communication Skills
How Course Meets Requirement:
With the administering of past free response on current topics, the students are given
practice with the written communications skills and how these responses would be
scored. Consistent opportunities are afforded the students to communicate their thought
orally.
Requirement: Use of a Graphing Calculator
How Course Meets Requirement:
Every opportunity is used to interject the use of the graphing calculator, both to explore
and ease the finding of a solution. Students are expected to have their own. Almost daily,problems are assigned which not only finely home their calculation skills, but also review many of the key content ideas from Calculus.
Requirement: Graphically, Numerically, Analytically, and Verbal
How Course Meets Requirement:
Every effort is made to present functions form all four viewpoints. They are focused to
analyze functions from the data in a chart, a graphically presented function, or to a givenfunction and attack it analytically.