AP Calculus Syllabus

 

Primary Text: 
Stewart, James.  Single Variable Calculus:  Concepts and Contexts.  Belmont, CA:      Brookes/Cole.

Alternative Resource: 
Best, George and J. Richard Lux.  Preparing for the (AB) AP Calculus Examination.  Andover, MA: Venture Publishing.

The following is an outline of topics covered and an estimate of time spent on each unit.  Each of the students is provided a TI-83 Plus graphing calculator.  We use graphing calculators daily to explore, discover and reinforce the concepts. I stress finding a root, sketching functions in different windows, finding the derivative of a function at a point and approximating the value of a definite integral using numerical methods.

  • Chapter 2:  Limits and Derivatives  (sixteen 75 minute blocks)
  • Tangent and Velocity Problems

Problem set pages 100-101:  1a, 3,5, 7ab

  • Limits of Functions

Problem set pages 109-110:  1-15 odds

  • Calculate Limits using the Limit Laws

Problem set pages 118-119: 1-19 odds, 25

  • Continuity

Problem set pages 128-130:  1-19 odds, 23,25,29,33 & 35

  • Limits Involving Infinity

Problem set pages 140-141:  1-29 odds

  • Quiz 2.1-2.5
  • Tangents, Velocities, and Other Rates of Change

Problem set pages 149-150:  1-21 odds

  • Derivatives

Problem set pages 156-157:  1-9, 13-19, 23-29 odds

  • Derivative as a Function

Problem set pages 168-171:  3-15, 19, 21, 27, 29, 37 odds

  • Linear Approximations

Problem set pages 174-175:  1,5, & 6

  • Quiz 2.6-2.9
  • What does f’ say about f?

Problem Set pages 180-181:  1,5,11,13,15,17 & 21

  • Chapter 2 Test

Activity:  Limit Lab

  • Chapter Three:  Differential Rules  (twenty 75 minutes blocks)
  • Derivatives of Polynomials and Exponential Functions

Problem set page 199:  1-25, 29-37, 41-45, 49, 53 odds

  • The Product and Quotient Rules

Problem set page 206:  1-15, 19, 21, 25-29 odds

  • Rates of Change in the Natural and Social Sciences

Problem set page 217:  1-11 odds

  • Derivatives of Trigonometric Functions

Problem set page 225: 1-31 odds

  • Quiz 3.1-3.4
  • The Chain Rule

Problem set page 234:  1-33 odds, 37 & 39
Worksheet: 1-27 odds

  • Implicit Differentiation

Problem set page 245:  1-7, 11-17, 25-31 odds
Worksheet:  2-28 evens

  • Quiz 3.5 & 3.6
  • Derivatives of Logarithmic Functions

Problem Set page 252:  3-19, 25,29 & 31 odds

  • Linear Approximations and Differentials

Problem set page 258:  1-7 all

  • Chapter Three Test

Activities:  Function & Derivative Match, Cheaper by the Dozen function activity, and Aquarium Problem

                  AP Essay Questions:
1984 #2, 1986 #1, 1996 #6, 1998 #6,

  • Applications of Differentiation (twenty 75 minute blocks)
  • Related Rates

Worksheet
Problem Set page 372:  1-11, 12 & 17 odds

  • Maximum and Minimum Values

Problem Set page 279: 1-29, 37-47 odds

  • Quiz 4.1 & 4.2
  • Derivatives and the Shapes of Curve

Problem Set page 292: 3,5,7,9,13,15 & 21

  • Indeterminate Forms and L’Hospital’s Rule

Problem Set page 308: 1-21 odds

  • Optimization Problems

Problem Set page 316:  1, 3, 7, 9, 11 &13
Worksheet 1-19 all

  • Newton’s Method

Problem Set page 331: 3-15 odds

  • Antiderivatives

Problem set page 338:  1-21 odds and 31

  • Chapter 4 Review Sheet
  • Chapter 4 Review page 340: 1-7,23,25,29,47,51 & 53
  • Chapter 4 Test

Activities:  Powerpoint Presentation, skill building sheets, Graph Theory Group Activity

AP Essay Questions:  1996 #1, 1999 #6, 1998 #2, 1996 #4, 2000 #3,2000 #5

  • Integrals  (eighteen 75 minute blocks)
  • Areas and Distances

Problem Set page 359: 1,3,9 &11

  • The Definite Integral

Problem Set page 370:  1-33 odds

  • Evaluating Definite Integrals

Problem Set page 380:  1-29 odds, 43-53 odds

  • Fundamental Theorem of Calculus

Problem Set page 390:  7-23 odds

  • Quiz 5.1-5.4
  • Substitution Rule

Worksheet
Problem Set page 400: 1-51 odds

  • Integration by Parts

Worksheet
Problem Set page 407: 1-23 odds

  • Quiz 5.5 & 5.6
  • Improper Integrals

Problem Set page 425: 1-9 odds

  • Chapter Review

Problem Set page 438: 1-33 odds, 39, 45-49 odds, 53 & 55

  • Chapter 5 Test

Activities: Spud Problem, Group Link Sheet, and Jeopardy Review

AP Essay Questions:  1999 #5, 1997 #5, 2000 #4, 1995 #6, and 1998 #3

  • Applications of Integration  (ten 75 minute blocks)
  • Areas

Problem Set page 453: 1-19 odds

  • Volumes

Slicing worksheet:  1-10, 12-17 all
Shells worksheet:  1-11 odds
Problem Set page 462:  1-13 odds

  • Average Value of a Function

Problem Set page 472:  1-13 odds

  • Chapter Review

Problem Set:  1-6 all, 15 & 22

  • Chapter Six Test

AP essay Questions:  1990 #3, 1997 #3, 1996 #5, 1987 #3, 1999 #2

  • Differential Equations
  • Modeling with Differential Equations

Problem Set page 508: 1-7 all

  • Direction Fields

Problem Set page 513: 1-13 odds

  • Separable Equations

Problem Set page 524: 1-17 odds, 21 & 23

  • Exponential Growth and Decay

Problem Set page 534: 1,3,5,8,10,11 & 16a

  • Particle Motion

Worksheet 9-53 odds

                  AP Essay Questions:  2000 #2, 1997 #1, 2000 #6, 1997 #6, 2000 BC 6,
1998 BC 4, 1998 #4,

  • Calculator ( two 75 minute blocks)
  • The secrets of the graphing calculator for the AP Exam

Find the derivative at a point
Evaluate definite integrals
Riemann Sums
Newton’s Method

  • AP Exam Review
  • Multiple Choice Questions Review
  • Essay Questions Review