AP Calculus Study Guide for Semester 1 Final – 2016-17

The calculus final will cover the material on chapters 2, 3, 4 and 5.1-2.

  1. For a quick review, you may work through the old final exam that I passed out in class and cover the concepts associated with the problems that you missed. See my website for the answers. After this study all the tests that you had for each chapter. You may download blank ones from my website.

For a more thorough study follow the following guide as time allows.

  1. How to study chapter 2, Limits & Continuity:
  1. Do quizzes on page, 77 and 94 at the bottom of the page.
  2. Work through all the Problems on the Ch2 test as if you have done them for the first time. Email Mr. Garcia to request a blank copy.
  3. Know the 4 types of discontinuity and the definition of continuity, 79
  4. If you have more time, do all the highlighted problems at the end of the chapter.
  5. Request solution from Mr. Garcia if you do not find them on his website.
  1. How to study chapter 3, Derivatives
  1. Do quizzes on pages: 126, 156, and 180.
  2. Review all the derivative rules, (sum & difference, product, power, and quotient, chain, implicit differentiation) and know the derivatives of all the main functions that you have studied. For example: , sinx, cosx, , , lnx,…
  3. Work through all the test 3 problems on separate sheets of paper. Mark those problems that you had trouble with and look up the material.
  4. There are more problems highlighted at the end of chapter 3 on pages 198 – 200 for more practice.
  1. How to study chapter 4, Applications of Derivatives
  1. Do quizzes on pages: 218 and 255.
  2. Read all the theorems in the chapter at least one. Refer to the handout that was passed out in class with all the theorems and definitions listed.
  3. Work through all the test 4 problems on separate sheets of paper. Mark those problems that you had trouble with and look up the material.
  4. There are more problems highlighted at the end of chapter 4 on pages 256 – 259 for more practice.
  1. Review: Chapter 5.1 and 5.2.
  1. Go back through the homework problems, pg.270:9-12.
  2. Go through problems, pg. 282:3-27(3x).

CHAPTER 2 REVIEW: AP Calculus

1. Limits

  • About the TREND of a graph, NOT the function value
  • Limit from the left must = limit from the right for a general limit to exist
  • Evaluating a limit

Direct substitution: or is indeterminate and means you must find another way

means the limit is =0

means the limit increases or decreases without bound (

Factor and reduce

Rationalize

Sandwich

Calculator

  • If, then y=L is a Horizontal Asymptote
  • If , there is a Vertical Asymptote at x=c

2. Rates of Change

  • Average rate of change: just slope formula. m =
  • Instantaneous rate of change: slope at one point = slope of tangent =

3. Continuity

  • “Can draw without picking up pencil”
  • Removable (hole in the graph) and Non-Removable (jump and infinite) discontinuities
  • Intermediate Value Theorem ( f(x) must be continuous)