AP Calculus AB Review
Q1Test 1 (2012-13)
Mathematician _________________________
Date _______________ Period _________
50 Point Total
CALCULATOR ACTIVE
-------------------------------------------------------------------------------------------------------------------------------------------(12 points)


1. A bucket containing 5 gallons of water has a leak. After t seconds, there are Q (t )  51 
2
t 
 gallons of
25 
water in the bucket. (Show work and label answers.)
5 pts a) Find the average rate of change for the time interval [5, 5.1]. Why is the rate negative?
4 pts b) Find a better estimation of the instantaneous rate of change at t = 5 seconds.
3 pts c) In words, describe the instantaneous rate of change. What concept in calculus is this called?
(5 points)
2. The coordinates s of a moving body for various values of t are given. Estimate the velocity of the body at
time t = 1.7. (Show work and label answers.)
t (sec)
1.1
1.3
1.5
1.7
1.9
2.1
s (ft)
12
15
21
23
24
25
----------------------------------------------------------------------------------------------------------------------------- --------------(13 points)
3. The graph provided shows the velocity of a car moving along a track.
4 pts a) Estimate the distance the car covered over the first 6
seconds.
(Show your method and explain your answer thoroughly.)
1 pt b) What name is given to this calculus concept?
4 pts c) From the graph, estimate the instantaneous rate of change
of the velocity at time t = 6 seconds. (Show you method
and explain your answer thoroughly.)
1 pt d) What special name is given to the rate of change of velocity?
3 pts e) Was the car speeding up or slowing down at time t = 6 seconds?
How can you tell?
(6 points)
4. Tell whether the function is increasing, decreasing or not changing at x = a, b and c. If it is increasing or
decreasing, tell whether the rate of change is slow, fast or none.
a)
x = a _______________
_______________
b)
x = b _______________
_______________
c)
x = c _______________
_______________
-------------------------------------------------------------------------------------------------------------------------------------------(5 points)
5. The data in the table below shows the velocity of a body at various values of time t. Estimate the distance
covered over the 10 second period using trapezoids. (Show work and label answer clearly.)
t (sec)
0
2
4
6
8
10
vel (ft/sec)
0
10
14
15
17
14
----------------------------------------------------------------------------------------------------------------------------- --------------(4 points)
6. If the trapezoidal rule were applied to the graph of y 
be an underestimate or overestimate? Justify your answer.
 x 2  2 x  5 on the interval [0, 3], would the result
Are you ready for calculus?
7. Find the equation of a line that has a slope of 5 and passes through the point (3, -4).
8. Find the equation of the line that passes through the points (4,1) and (3, -2).
9. Find the equation of the line that passes through theh points (-2,1) and is parallel to the line 4x + 2y = -1.
10. Find the equation of the line that passes through the origin and is perpendicular to the line 3x + 4y = -7.
11. Write the equation for the following graphs:
12. Given the slope sketch the following lines:
a. Sketch a line with
a slope of 2.
b. Sketch a line with c. Sketch a line with
a slope of
1
2
a slope of -2.
d. Sketch a line with
a slope of -
1
2
.