.
Click here for a key to the sample test:
1. Find the domain and range of y = .
A) Domain : x >=3, Range: y <= 2
B) Domain : x >= 3, Range: y >= 2
C) Domain : x <= 3, Range: y <= 2
D) Domain : x <= 3, Range: y >= 2
2. Using the sketch at the top, which of the following statements is FALSE?
A) G(x) is the derivative of F(x)
B) F(x) is concave downward at 0.2.
C) F(x) is decreasing on [0,0.8]
D) F(x) is the derivative of G(x)
3. If y = f(x) = (x - 1)3 (x - 3)2 , then y = f(x) has point(s) of inflection at
A) x = 3 but not at x = 1
B) x = 1 and x = 3
C) x =1 but not at x = 3
D) neither x = 1 nor x = 3
4. Find 
.
A) 0
B) -infinity
C) 3
D) infinity
5. Write an equation for the tangent line to 
at x = 2.
A) y - 8 = 12(x - 2)
B) y - 8 = 8(x - 2)
C) y - 2 = 12(x - 8)
D) 
6. Find 
.
A) infinity
B) -infinity
C) 1
D) 
7. Find y'' if 
.
A) 
B) 
C) 
D) 
8. The figure at the top represents the position function s = f(t) of a body moving on a coordinate line (t represents time). Which of the following is true?
A) The body's velocity is zero at t = 0.5 and 1.5.
B) The body's velocity is zero at t = 0, 1, and 2.
C) The body's velocity is zero at t = 0, 0.5, 1, 1.5, 2
D) The body's velocity is never zero
9. Find the area of the region enclosed by y = x2 and y = 2x.
A) 0
B) 
C) 
D) 
10. Find the slope of the tangent line to the curve x2 + y2 = 25 at the point P(-3,4).
A) 
B) 
C) 
D) 0
11. If 
,
then y' = f '(x) =
A) 
B) 
C) 
D) 
12. If 
,
then f '(x) =
A) 
B) 
C) 
D) 
13. The smallest positive root of sin(2x) + cos(x + 3) = 0 is A) 0.5708
B) 1.4292
C) 2.6652
D) 0.2854
14. Evaluate 
.
A) 
B) 
C) 
D) 
15. Find the area bounded by the x-axis, x = 1, x = 3, and y =3x2 + 2.
A) 25
B) 22
C) 33
D) 30
16. Apply the First FundamentalTheorem
to find F'(x) if 
.
A) 
B) 
C) 
D) 
17. Find the volume generated by revolving the region bounded by y = x - x2 and the x-axis about the x-axis.
A) 
B) 
C) 
D) 
18. If 
,
then f'(x) =
A) 
B) 
C) 
D) 
19. If f(x) = x sin (x2), then f'(x) =
A) 
B) 
C) 
D) 
20. Determine where f(x) = 3x4 - 16x3 + 18x2 has any local minimum values on [-1,4].
A) x = 1, x = 2
B) x = 1, x = 3
C) x = 0, x = 3
D) x = 0, x = 1
21. Find c if 
where f(x) =
, a = 1 and b = 2.
A) 
B) 1.5
C) 1
D) 
22. Evaluate 
.
A) 1.5
B) 
C) 0
D) 
23. If
,
which of the following must be true:
A) Given any number, there is an x near 3 where f(x) = 3.
B) Given any number, there is an x near 3 where x is greater than the given number.
C) Given any number, there is an x near 3 where f(x) is greater than the given number.
D) Given any number, there is an x near 3 where f(x) is less than the given number.
24. Suppose s = f(t), where s is the distance and t is the time. Then v = f' (t) means
A) The velocity is the derivative of the distance function.
B) The height is the derivative of the distance function.
C) The volume is the derivative of the distance function.
D) The concavity is the derivative of the distance function.
Based on the graph at the top, answer the questions below. 25. The graph has an x-intercept at A) 1.5 B) 0.5 C) 2.1 D) 1
26. f (x) is zero at A) 0.5 B) 2 C) 0.2 D) 1
27. f (x) at 0.3 is A) does not exist B) zero C) positive D) negative |
28. Which of the following statements is always true?
A) The left hand limit is always equal to the right hand limit
B) The limit of a function is equal to the derivative of that function.
C) The limit of a constant times a function is equal to the constant times the limit of the function, provided the function has a finite limit.
D) The limit as x goes to infinity is always zero.
29. Write an equation for the normal line to y = x3 at x = 2.
A) y - 8 = 12(x - 2)
B) 
C) y - 2 = 12(x - 8)
D) 
| Two cars leave an intersection traveling at right angles to one another.
One car travels east at 80 mph, the other travels north at 60 mph. The
cars continue at the same speed without turning.
30. After one hour, how far apart are the cars? A) 120 mph B) 100 miles C) 100 mph D) 20 miles
31. Let x be the distance the first car has traveled and let y be the distance the second car has traveled and let s be the distance between the two cars. An equation relating x and y and s is: A) x + y = s B) x2 + y2 = s C) x2 + y2 = s2 D) x2 + y2 = 120
32. An equation relating the rates of the two cars is: A) dx/dt + dy/dt = 120 B) dx/dt + dy/dt = ds/dt C) (dx/dt)2 + (dy/dt)2 = (ds/dt)2 D) 2 x dx/dt + 2 y dy/dt = 2 s ds/dt
33. A correct solution to the problem of finding ds/dt after one hour is: A) ds/dt = 100 mph B) ds/dt = 120 mph C) ds/dt = 100 miles D) ds/dt = 120 miles |