AP Syllabus for AB Calculus

Text:Calculus: Graphical, Numerical, Algebraic by Finney, Demana, Waits, and Kennedy. Published by Pearson for Prentice Hall

Copyright 2003. ISBN 0-13-063131-0

Topics:

  1. Functions, Graphs and Limits
  2. Analysis of graphs
  3. Calculating limits using algebra
  4. Estimating limits from graphs or tables of data
  5. Understanding asymptotes in terms of graphical behavior
  6. Describing asymptotic behavior in terms of limits involving infinity
  7. Comparing relative magnitudes of functions and their rates of change
  8. Understanding continuity in terms of limits
  9. Geometric understanding of graphs of continuous functions
  10. Derivatives
  11. Derivative defined as the limit of the difference quotient
  12. Relationship between differentiability and continuity
  13. Slope of a curve at a point
  14. Tangent line to a curve at a point and linear approximation
  15. Instantaneous rate of change as the limit of average rate of change
  16. Approximate rate of change from graphs and tables of values
  17. Corresponding characteristics of the graphs of a function and its derivative
  18. Relationship between the increasing and decreasing behavior of a function and the sign of its derivative
  19. The Mean Value Theorem and its geometric consequences
  20. Equations involving derivatives
  21. Corresponding characteristics of a function, its derivative and its second derivative
  22. The relationship between concavity and the sign of the second derivative
  23. Points of inflection as places where concavity changes
  24. Analysis of curves, including the notions of monotonic and concavity
  25. Optimization, both absolute and relative extrema
  26. Modeling rates of change, including related rate problems
  27. Use implicit differentiation to find the derivative of an inverse function
  28. Interpretation of derivative as a rate of change in varied applied contexts, including velocity, speed and acceleration
  29. Knowledge of derivatives of basic functions including power, exponential, trigonometric and inverse trigonometric functions
  30. Basic rules for the derivatives of sums, products, and quotients of functions
  31. Chain rule and implicit differentiation
  32. Integrals
  33. Concept of a Riemann sum over equal subdivisions
  34. Computation of a Riemann sum using left, right and midpoint evaluation points
  35. Definite integral as a limit of Riemann sums
  36. Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval
  37. Basic properties of the definite integral
  38. Applications of the definite integral
  39. Use of the fundamental theorem to evaluate definite integrals
  40. Use of the fundamental theorem to represent particular antiderivatives, and the analytical and graphical analysis of functions so defined
  41. Antiderivatives following directly from the derivatives of the basic functions
  42. Antiderivatives by substitution of variables
  43. Finding specific antiderivatives using initial conditions, including applications to motion along a line
  44. Solving separable differential equations and using them in modeling
  45. Approach to problem solving

This course is taught in such a way that

  1. Students will solve problems analytically.
  2. Students will use graphing calculators to find solutions through the use of graphs and data analysis.
  3. Students will be able to verbally express their solutions and be able to write meaningful explanations of their solutions.
  1. Time line (based on the textbook)

Chapter 13 weeks

Chapter 2 2 weeks

Chapter 37 weeks

Chapter 46 weeks

Chapter 55 weeks

Chapter 65 weeks

Chapter 74 weeks

Suggested Assignments

Section / Problems
1.1 / 3-36 (multiples of 3),37,39,43,49
1.2 / 3-33 (multiples of 3),35,36,39,42,45,49,53,57,63,65,66
1.3 / 3-21 (multiples of 3),21,24-29,34,38
1.4 / 3,6,7-27 odd,30,42
1.5 / 3-42 (multiples of 3),43,48,50
1.6 / 2-34 even,38,45
2.1 / 3-30 (multiples of 3),32,35,39,42,44,45-52,55,58
2.2 / 3-48 (multiples of 3),54,57,59
2.3 / 2-30 even,36,39,42,43,48
2.4 / 1-33 odd,41
3.1 / 1-6,7-25 odd
3.2 / 1-17 odd,18-23,29,31
3.3 / 1-33 odd,34
3.4 / 1,2,4,5,10,13,14,16,24,25,27,29,30,31,33,37,38
3.5 / 1-10,12-22 even,25,27,29,31,33
3.6 / 3-69 (multiples of 3),
3.7 / 3-45 (multiples of 3),46,50
3.8 / 1-17 odd,21,24,27,30
3.9 / 1-41 odd,47,48,50,52
4.1 / 1-9 odd,11-30,37-45 odd,48,49,52
4.2 / 3-33 (multiples of 3),39,42,43,45,48,52
4.3 / 1-29 odd,37,40,42-46,48
4.4 / 1,5,8,9,12,17,19,20,26,31,35,36,38,40,41,43,45,46,49,50
4.5 / 3,5-9,11,14,15,18,19,22,25,27,30,33,36,39,44,50,51
4.6 / 3,6,9,12,13,15,18,21,22,24-39 (multiples of 3)
5.1 / 1-4,6,9,12,14,15,18,20,21,24,26
5.2 / 1,3-27 (multiples of 3),39-41,42,46,47
5.3 / 1,3,4,6,7-17,20,21,24,25,28,29,32,36,38,40,43,44
5.4 / 1-13 odd,15-48 (multiples of 3),49,51,52,54,59,60
5.5 / 1,4,6-8,10,11,13,16-18,23
6.1 / 3-24 (multiples of 3),25,27-51(multiples of 3),52,61
6.2 / 1-17 odd,18-42(multiples of 3),43,44,49
6.3 / 3-24(multiples of 3),26,27,30,33
6.4 / 1-9 odd,12,14,15-33 (multiples of 3),
6.5 / 1-29 odd
6.6 / 2,3,6,7,9,12,15,17,19,22,24,25,28
7.1 / 1-17,20-22,24-27,29,31
7.2 / 1-29 odd,33,36,40,42,43,46
7.3 / 1-25odd,28,29,33,39,42,44,49,53,57,60,63
7.4 / 3-21 (multiples of 3),27,30
7.5 / 1,3,5,6,8,10,12,17,21,24,33,35,37,39
  1. Specific Assignments

Section / Problems
1.1 / 3-36 (multiples of 3),37,39,43,49
1.2 / 3-33 (multiples of 3),35,36,39,42,45,49,53,57,63,65,66
1.3 / 3-21 (multiples of 3),21,24-29,34,38
1.4 / 3,6,7-27 odd,30,42
1.5 / 3-42 (multiples of 3),43,48,50
1.6 / 2-34 even,38,45
2.1 / 3-30 (multiples of 3),32,35,39,42,44,45-52,55,58
2.2 / 3-48 (multiples of 3),54,57,59
2.3 / 2-30 even,36,39,42,43,48
2.4 / 1-33 odd,41
3.1 / 1-6,7-25 odd
3.2 / 1-17 odd,18-23,29,31
3.3 / 1-33 odd,34
3.4 / 1,2,4,5,10,13,14,16,24,25,27,29,30,31,33,37,38
3.5 / 1-10,12-22 even,25,27,29,31,33
3.6 / 3-69 (multiples of 3),
3.7 / 3-45 (multiples of 3),46,50
3.8 / 1-17 odd,21,24,27,30
3.9 / 1-41 odd,47,48,50,52
4.1 / 1-9 odd,11-30,37-45 odd,48,49,52
4.2 / 3-33 (multiples of 3),39,42,43,45,48,52
4.3 / 1-29 odd,37,40,42-46,48
4.4 / 1,5,8,9,12,17,19,20,26,31,35,36,38,40,41,43,45,46,49,50
4.5 / 3,5-9,11,14,15,18,19,22,25,27,30,33,36,39,44,50,51
4.6 / 3,6,9,12,13,15,18,21,22,24-39 (multiples of 3)
5.1 / 1-4,6,9,12,14,15,18,20,21,24,26
5.2 / 1,3-27 (multiples of 3),39-41,42,46,47
5.3 / 1,3,4,6,7-17,20,21,24,25,28,29,32,36,38,40,43,44
5.4 / 1-13 odd,15-48 (multiples of 3),49,51,52,54,59,60
5.5 / 1,4,6-8,10,11,13,16-18,23
6.1 / 3-24 (multiples of 3),25,27-51(multiples of 3),52,61
6.2 / 1-17 odd,18-42(multiples of 3),43,44,49
6.3 / 3-24(multiples of 3),26,27,30,33
6.4 / 1-9 odd,12,14,15-33 (multiples of 3),
6.5 / 1-29 odd
6.6 / 2,3,6,7,9,12,15,17,19,22,24,25,28
7.1 / 1-17,20-22,24-27,29,31
7.2 / 1-29 odd,33,36,40,42,43,46
7.3 / 1-25odd,28,29,33,39,42,44,49,53,57,60,63
7.4 / 3-21 (multiples of 3),27,30
7.5 / 1,3,5,6,8,10,12,17,21,24,33,35,37,39