Embedded Files
Quick Notes
These are the in-context problems, and the most challenging part is usually reading and "translating" the problem into calculus.
This is almost always #1 on both the AB and BC exams.
You are usually given a rate function or two rates acting simultaneously. Be sure to check what your given information is, and remember that a rate is the derivative. CHECK YOUR UNITS!
These tend to be on the calculator-active section of the exam, so use that to your advantage.
FTC is going to be your main tool on these problems (see below). Be ready to write a general expression using integrals for a quantity at a general time.
Make sure you understand whether to use Average Value or Average Rate. Again, CHECK YOUR UNITS!
You might be asked to find the maximum or minimum value. Use Candidate Test for this.
You may need to approximate derivative or integral values from a table using AROC or Riemann Sums respectively.
Often, these questions ask you to interpret the meaning of something in context. Remember to include "NUT" (Number, Units, Time).
Fundamental Theorem of Calculus
The main idea here is that if you integrate a rate/derivative, you get the net change in the quantity (left). If we expand that idea, we can find the quantity at any time by adding the initial value to the net change given by integrating the rate/derivative (right).
~ Related CED Units ~ 4, 5, 6, 8
Page updated
Report abuse