Advanced Placement Calculus AB Practice
Section II Part A
1. Let f be the functions given by:
Find the area of the region enclosed by the graphs of f(x) and -f(x).
2. Let f and g be the functions given by:
Let R be the region in the first and second quadrants enclosed by the graphs of f and g. Find the area of R.
3. Let f and g be the functions given by:
Let R be the region in the first and second quadrants enclosed by the graphs of f and g. Find the volume of the solid generated when R is revolved about the x axis.
4. Let f be a function derivabile on the (0, .6) interval. If f '(x) = 3 + ln(x + 1) and f(.1) = 2, what is f(.6)?.
5. Let R be the region in the first quadrant bounded by the y axis and the graphs of f(x) = 3 + ln(x + 1) and g(x) = 23x. Find the area of R.
6. Let R be the region in the first quadrant bounded by the y axis and the graphs of f(x) = 3 + ln(x + 1) and g(x) = 23x. Region R is the base of a solid. For this solid, each cross-section perpendicular to the x-axis is a square. Find the volume of this solid.
7. A checking account has $120,000 at time t=0. During the interval 0 ≤ t ≤ 18 months, money is deposited into the checking account at a rate d(t) = 2,000(t+1)sin(t/4) dollars/month. At the same time, money is withdrawn from the checking account at the rate w(t) = 10,000/(t+1) dollars/month.
Is the dollar amount increasing at t=9 months?
How many dollars are in the account at time t=18 months?
Verify your answers. 5 Steps to a 5 AP Calculus AB and BC, 2010-2011 Edition (5 Steps to a 5 on the Advanced Placement Examinations Series)
The official AP Calculus webpage