A.P. Calculus AB Syllabus
Text: Finney, Demana, Waits, & Kennedy, Calculus Graphical, Numerical, Algebraic, Prentice Hall, 2003
I. Review of Pre-calculus materials
Chapter 1 in text: Lines, functions and graphs, exponential functions, parametric equations, functions and logarithms, trigonometric functions
Supplement: Concept Worksheet 1.2-1.6 Prentice Hall
Topics of interest: Analysis of graphs (Concept Worksheet) Comparing relative magnitudes of functions and their rates of change (Page 24 #19-22) Assessment: 1 exam
II. Limits and Continuity
Chapter 2 in text: Rates of change and limits, limits involving infinity, continuity, rates of change and tangent lines
Supplement: Reading assignment: “What is calculus?” Sec 1.1 in Calculus by Bradley & Smith, Prentice Hall Concept Worksheet 2.2-2.3 Prentice Hall
Topics of interest: Limits of functions (including one-sided limits) (2.1, 2.2) Asymptotic and unbounded behavior (2.2) Continuity as a property of functions (2.3) Intermediate Value Theorem (2.3) Concept of the derivative (2.4) Derivative at a point (2.4) Assessment: 1 exam
III. Derivatives
Chapter 3 in text: Derivatives of a function, Differentiability, rules for differentiation, velocity and other rates of change, derivatives of trigonometric functions, chain rule, implicit differentiation, derivatives of inverse trigonometric functions, derivatives of exponential and logarithmic functions Supplement: Concept worksheets 3.1-3.3, 3.4, 3.7, 3.8 A.P. practice problem #3 & #6 from 1998 AB Additional practice Pages 155, 333, 355,379 from Calculus, 4th Ed., Larson, Hostetler, Edwards, Heath L’Hopital’s Rule handout Pg 245 Calculus Bradley&Smith
Topics of interest: Concept of the derivative (3.1, 3.2) Intermediate Value Theorem (3.2) Derivative at a point (3.1, 3.4) Applications of derivatives (3.4, 3.7, 3.8) Computation of derivatives (Ch 3) Assessment: 2 exams
IV. Applications of Derivatives
Chapter 4 in text: Extreme values of functions, Mean Value Theorem, connecting f’ and f’’ with the graph of f, modeling and optimization, linearization and Newton’s Method, related rates
Supplement: Graphing Unit Pg 211/218 Calculus, Bradley&Smith Concept 4.3 Related Rates Practice Sheets Pg 226/141/236 Calculus, Bradley Pg 203 Calculus, 4th ed., Stewart A.P. Practice over Derivatives 1997 misc. M. C. questions 1995 free-response
Topics of interest: Analysis of graphs (4.1) Continuity as a property of functions (4.1, 4.2) (Extreme Value Theorem) Derivative as a function (4.2, 4.3, 4.6) Derivative at a point (4.5) Second derivatives (4.3) Applications of derivatives (4.2, 4.3, 4.6)
Assessment: 2 exams
V. The Definite Integral
Chapter 5 in text: Estimating with finite sums, definite integrals, definite integrals and anti-derivatives, Fundamental Theorem of Calculus, Trapezoidal Rule Supplemental: Area as limit of sum packet Sec 4.1Calculus, Bradley&Smith (Reading and practice) Anti-derivatives/definite integrals handout Pg 251 Calc, Bradley A.P. 1999 AB-3
Topics of Interest: Interpretations and properties of definite integrals (5.2, 5.3, 5.4) Fundamental Theorem of Calculus (5.4) Numerical Approximation to definite integrals (5.1,5.5)
Assessment: 2 exams
VI. Differential Equations and Mathematical Modeling
Chapter 6 in text: Anti-derivatives and slope fields, integration by substitution, integration by parts, exponential growth and decay, population growth
Supplemental: Slope field packet Sec 10.2 Calculus Single Variable 2nd ed., (Reading and practice) Hughes-Hallett, Gleason, et al. Differential equations packet Pg 421-425 Calculus, Bradley (Reading and practice)
Topics of Interest: Computation of derivatives (slope fields) (6.1) Techniques of anti-differentiation (6.1, 6.2) Application of anti-differentiation (6.1, 6.4, 6.5)
Assessment: 2 exams
VII. Applications of Definite Integrals
Chapter 7 in text: Integrals as net change, areas in the plane, volumes, lengths of curves
Supplemental: Hooke’s Law/ Work handout Pg 413 Calculus Bradley&Smith Volume practice handout Pg 393 Calculus Bradley&Smith Pg 348 Calculus Single Variable, 3rd ed. Hughes-Hallett, Gleason, McCallum, et al. Length/Surface Area handout Pg 401-402 Calc Bradley&Smith Area of Surface of Revolution Pg 582-586 Calculus 4th ed., (Reading) Stewart
Topics of Interest: Application of integrals (7.1-7.4) Application of anti-differentiation (7.1)
Assessment: 2 exams VIII. Review for the A. P. Calculus AB test
Discussion of procedures, scoring guide, guessing, etc. 1998 AB-3 Practice Pack #1 Free-response 2001 Practice Pack #2 Released multiple-choice Practice Pack #1B Free-response 2002 Exam 1 Multiple-Choice and Free-Response Questions in Preparation for the AP Calculus (AB) Exam, 8th ed., Lederman, 2003, 2004 D&S Marketing Systems Inc. Review Trigonometric Identities Student’s Mathematics Handbook, Calculus, Bradley & Smith, 1995 Prentice Hall Review substitution Pg 285 Calculus, Bradley & Smith Practice Pack #3 Selected multiple-choice over trig. and substitution Review area and volume Practice Pack #4 Selected questions over area and volume 6 Big Theorems Major Theorems Happen… AP Summer Institute, WKU, Albert/Hillis, Oak Ridge High School Practice Pack #5 Selected free-response over theorems Exam 2 (individually) Practice Book, 8th ed., Lederman Continue practice of multiple-choice from 1993 and 1997 in game form (Trivial Pursuit or Who Wants to be A. Pcalcunaire?) Mock Exam One of released year’s multiple-choice and very recent free-response “Most Challenging” multiple-choice AP Summer Institute Previous year’s free-response if not used on the mock exam
Assessment: 4 exams
Teaching Strategies:
When topics are introduced, lecture is used. An assignment is given for practice. Students are allowed to ask each other for help on daily assignments. There is little to much discussion depending on the topic. Problems are placed on the board as we check assignments. Students offer explanations in addition to instructional explanations when needed. At times groups may present one of the topics. For instance in the volume sections, one group discusses the disk method; one group discusses the washer method; and one group discusses the cross-section method. They use pipe cleaners to form a model to use in the presentation along with overhead sheets or board work. Calculators are used throughout the course. For example, students are taught how to use the calculator for graphical and numerical verification for analytically found limits. The text has calculator explorations throughout. Most of these are discussed or given as part of the assignment. The students are required to have their own graphing calculator. Most have TI 84+. During review for the A.P. Calculus AB test there are activities that include games, Students are expected to work the problems at the board or on paper. They explain to each other how to reach the correct answer. They explain why they follow certain paths. They seem to enjoy the review better because they are playing a game. Calculators are allowed on some review questions and not on others. When allowed, they must also explain how they used them to arrive at their answers.
Student Activities:
Students work lots of problems throughout. The calculators are used when needed. They are taught programming in order to create a program the Trapezoidal Rule and Simpson’s Rule as part of the students’ knowledge of the calculators as well as use borrowed programs for area (midpoint, left-, and right-endpoint) and slope fields. Students are also required to work a slope field on paper for display.
One of the written projects deals with velocity and acceleration. In the project there are “students” that have serious issues and disrupt the class; the others decide to drop one off a building and the other off a bridge. The class is to determine in the fall will kill them or if one survives and can save the other one. By the time they finish this project, they have worked numerous velocity and acceleration problems, have converted units of measure, and have written several sentences explaining the work.
During the review leading up to the A.P. test, students work through many practice tests. For some of the practice exams the students are asked to mark when they are guessing, some with calculator, some without calculators, some short versions of the A.P. test, and one out of class mock test (timed to match the real test). Students will be familiar with the test format by test day. Bibliography:
Text: Finney, Demana, Waits, & Kenney, Calculus: Graphical, Numerical, Algebraic, Prentice Hall, 2003, revision
Supplemental Sources: Materials from The College Board including 1993, 1997, 1998, 2003 Released Exams and materials from the AP Summer Institute
Bradley & Smith, Calculus, Prentice Hall, 1995, 1st ed.
Larson, Hostetler, Edwards, Calculus, Heath, 1990, 4th ed.
Stewart, Calculus, Brooks/Cole, 1999, 4th ed.
Hughes-Hallett, Gleason, et al., Calculus Single Variable, Wiley, 1998, 2nd ed.
Hughes-Hallett, Gleason, McCallum, et al., Calculus Single Variable, Wiley, 2002, 3rd ed.
TI 83 Plus calculators or similar is required of every student taking this course.