Exam 1 - Part I – 28 questions – No Calculator Allowedtheriddles-brhs.weebly.com/.../5033946/abmcstudentexam1.pdfExam 1 - Part I – 28 questions – No Calculator Allowed 1. Find
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6. Newton the cat begins to walk along a ledge at time t = 0. His velocity at time t, 0 ≤ t ≤ 8, is given by the function whose graph is given in the figure to the right. What is Newton’s average speed from t = 0 to t = 8?
v t( ) , of a particle moving along the x-axis. At time t = 0, the particle is at the origin. Which of the following could be the graph of the position,
x t( ) , of the particle for 0 ≤ t ≤ 4 ?
t 0 1 2 3 4
v t( ) 3 0 -1 1 3
A. B. C.
D. E.
8. The graph of a twice-differentiable function f is shown in the figure
14. The function f is continuous and non-linear for
!3 " x " 7 and
f !3( ) = 5 and f 7( ) = !5. If there is no value c, where
!3 < c < 7 , for which
! f c( ) = "1, which of the following statements must be true?
A.
For some k, where ! 3 < k < 7, " f k( ) < !1. B.
For some k, where ! 3 < k < 7, " f k( ) > !1. C.
For some k, where ! 3 < k < 7, " f k( ) = 0. D.
For ! 3 < k < 7, " f k( ) exists. E.
For some k, where ! 3 < k < 7, " f k( ) does not exist.
15. If
x2
+ 2y2
= 34 , find the behavior of the curve at (-4, 3). A. Increasing, concave up B. Increasing, concave down C. Decreasing, concave up D. Decreasing, concave down E. Decreasing, inflection point
16. A large block of ice in the shape of a cube is melting. All sides of the cube melt at the same rate. At the time that the block is s feet on each side, its surface area is decreasing at the rate of
24 ft2
hr . At what rate is the volume of the block decreasing at that time?
A.
12s ft3
hr B.
6s ft3
hr C.
4s ft3
hr D.
2s ft3
hr E.
s ft3
hr
17. A squirrel climbs a telephone pole and starts to walk along the
telephone wire. Its velocity v of the squirrel at time t, 0 ≤ t ≤ 6 is given by the function whose graph is to the right. At what value of t does the squirrel change direction?
A. 1 and 5 only B. 2 only C. 2 and 4 only D. 1, 3, and 5 only E. 1, 3, 4 and 5 only
18. The graph of
! f x( ), the derivative of f , is shown to the right. Which of the following statements is not true?
A. f is increasing on 2 ≤ x ≤ 3. B. f has a local minimum at x = 1. C. f has a local maximum at x = 0. D. f is differentiable at x = 3. E. f is concave down on -2 ≤ x ≤ 1.
Exam 1 - Part II – 17 questions – Calculators Allowed
29. The slope field for the equation in the figure to the right could be
A.
dy
dx= x + y
2 B.
dy
dx= x ! y
2 C.
dy
dx= xy
D.
dy
dx= x + y E.
dy
dx= x
2! y
30. Let R be the region between the graphs of
y = 2sin x and y = cos x as shown in the figure to the right. The region R is the base of a solid with cross sections perpendicular to the x-axis as rectangles that are twice as high as wide. Find the volume of the solid.
A. 4.472 B. 7.854 C. 8.944 D. 15.708 E. 31.416
31. The first derivative of a function f is given by
! f x( ) = x " 2( )esin 2x . How many points of inflection does the graph of f have on the interval 0 < x < 2π?
32. A conical tank is leaking water at the rate of
75in3min. At the same
time, water is being pumped into the tank at a constant rate. The tank’s height is 60 in while its top diameter is 20 inches. If the water level is rising at the rate of
5in min when the height of the water is 10 inches high, find the rate in which water is being pumped into the tank to the
nearest
in3min . (The volume of a cone is given by
V =1
3!r
2h )
A.
44 in3
min B.
175 in3
min C.
250 in3
min D.
119 in3
min E.
31 in3
min
33. At which points is the tangent line to the curve
8x2
+ 2y2
= 6xy +14 vertical? I. (-2, -3) II (3, 8) III. (4, 6) A. I only B. II only C. III only D. I and II only E. I and III only
34. For the function f ,
! f x( ) = 4 x " 3 and f 2( ) = 4. What is the approximation for
f 2.1( ) found by using the tangent line to the graph of f at x = 2.
A. -15.879 B. -11.629 C. 7.274 D. 15.879 E. 11.629
36. What is the area of the region in the first quadrant enclosed by the graph of
y = 2cos x,y = x, and the x-axis?
A. 0.816 B. 1.184 C. 1.529 D. 1.794 E. 1.999
37. A particle moves along the x-axis so that at any time t > 0, its acceleration is given by
a t( ) = cos 1! 2t( ) . If the velocity of the particle is -2 at time t = 0, then the speed of the particle at
t = 2 is
A. 0.613 B. 0.669 C. 1.331 D. 1.387 E. 1.796
38. A right triangle has legs a and b and hypotenuse c. The lengths of leg a and leg b are changing but at a certain instant, the area of the triangle is not changing. Which statement must be true?
39. A particle moves along a straight line with velocity given by
v t( ) = t ! 2.5cos2t . What is the acceleration
of the particle at t = 2 ?
A. 0.168 B. 0.238 C. 0.451 D. 0.584 E. 1.450
40. If the graph of
! f x( ) is shown to the right, which of the following could be the graph of
y = f x( )?
I. II. III. A. I only B. II only C. III only D. I and III only E. II and III only
41. The rate at which the gasoline is changing in the tank of a hybrid car is modeled by
f t( ) = t + .5sin t ! 2.5 gallons per hour, t hours after a 6-hour trip starts. At what time during the 6-hour trip was the gasoline in the tank going down most rapidly?