Honors AP Calculus / Mr. Hansen
Sample Questions for Test #1

Name: ______________________
9/26/2000 [rev. 1/6/2004]

Multiple Choice.
There is no need to show work in this section. Find the answer by any ethical means. To discourage random guessing, a 25% penalty will be deducted from each wrong answer. Hint: If you can rule out one or more choices, it is to your advantage to guess. However, if you guess, you should really guess (i.e., flip a coin or use a random number generator) in order to select from the remaining choices, since if you try to make an educated guess, you will probably fall into a trap.

1.

Let f be defined as follows, where a 0.

 

 

Which of the following are true about f ?



(A) None
(B) I only
(C) II only
(D) I and II only
(E) I, II, and III

 

2.

Let the function h(x) = 3 - |x - 2| be defined only on {x: -5 < x < 3}. Which of the following are true?

I. The domain of the derivative of h is the open interval (-5, 3).
II. h is continuous on the open interval (-5, 3).
III. The derivative of h is positive on the open interval (-5, 2).

(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III

 

3.

Let f be the function whose graph is shown below. At which of the five points in the figure are f and f both negative?

(A) Point A
(B) Point B
(C) Point C
(D) Point D
(E) Point E

 

 

For #4 and #5, an automobile strays northward and southward along a road that passes through its owner's home. The automobile's distance d in miles from home is given by the following function of time t in hours, where positive distance is to be interpreted as "north" and negative distance as "south":

 

4.

The automobile's average velocity during the first 6 hours is

(A) -1 mph
(B) -1/3 mph
(C) 0 mph
(D) 1/3 mph
(E) 1 mph

 

5.

The automobile's velocity at t = 2 hours is

(A) -1 mph
(B) -1/2 mph
(C) -1/3 mph
(D) -1/Ö3 mph
(E) -Ö3 mph

 

6.

The extreme value theorem (EVT) states that

(A) a continuous function on a closed interval attains both a maximum and a minimum value
(B) a continuous function on any interval attains both a maximum and a minimum value
(C) a function that is continuous or has only step discontinuities attains both a maximum and a minimum value on any interval that is a subset of its domain
(D) a continuous function on any interval attains a maximum or a minimum value, or possibly both
(E) none of these