Der. App Word Problems
Motion Problems: Position, Velocity, and Acceleration
1) Relationship of position, velocity, and acceleration and applied extrema.
2) Speed increasing/decreasing and moving away/towards the origin.
- Practice Problems:
3) Interpreting the graph of motion functions
4) AP Free Response Questions
- AP questions: Motion along a line WS – derivatives only
- 2007 Q4 - part a
- 2005 (Form B) Q3 - parts a and b
- 2004 Q5 - parts a, b, and c
- 2003 Q2 - Given v(t) as an equation - parts a and b
- 2003 (Form B) Q4 - Given v(t) as an equation - parts a, b, and c
- 2002 Q3 - Given v(t) as an equation - part a and b
- 2000 Q2 - Given v(t) as a graph and as an equation - parts a & b
- 1999 Q1 - Given v(t) as an equation - parts a & b
- 1998 Q3 - Given v(t) as an equation and as a table - parts a, b and c
5) Derivative Review
6) Applied Max./Min. Problems or Optimization Problems
- Notes | Annotated
- Notes #2
- Worldwide Center of Mathematics: Optimization (best example at 46:50
- Hollis: applied optimization problems: slides 1, 3, and 4 (slide 2 is more advanced)
- Khan: Optimization with Calculus 1: minimize x^2 + y^2 if xy = -16
- Khan: Optimization with Calculus 2: open box problem
- Khan: Optimization Example 4: minimum cost of an open box
- Websites: Optimization Problems from Visual Calculus: website with to help with visualization
- Java applets illustrating the solution to finding the maximum area of a rectangle which can be inscribed in a semicircles
- Java applet illustrating the solution to finding the longest ladder which can be carried through a hallway with a corner.
- Java applet illustrating the solution to finding the shortest time to move through the desert to a town.
- Java applet illustrating the solution to finding the shortest ladder that can lean over a fence against a building.
- Practice Problems
- Website: Animated gifs or quicktime movies that are visually represented of different related rates problems
- AP Free Response:
12) Word Problem Review: Worksheet
Finals Review: in addition to previous review worksheets, here is one more