Practice Test 1 - Calculus AB Review
Questions with "*" could be non-calculator.



1.
*Find the limit (if it exists):

A.
8
B.
C.
D.
–2
E.


2.
*Find the vertical asymptotes (if any) of the function .
A.
x = 5
B.
x = 4
C.
x = –5
D.
x = –4
E.
A and B
F.
C and D


3.
Find the derivative of the following function using the limiting process. Will not be a multiple choice question.

A.
B.
C.
D.
E.
None of the above


4.
*Find an equation of the tangent line to the graph of f at the given point.

at
A.
B.
C.
D.
E.


5.
*Find dy/dx by implicit differentiation.

A.
B.
C.
D.
E.


6.
*Locate the absolute extrema of the function on the closed interval [0,7].
A.
Absolute max: f(7) = 154 ; Absolute min: f(3) = –54
B.
Absolute max: f(3) = –54 ; Absolute min: f(7) = 154
C.
Absolute max: f(7) = 154 ; No absolute min
D.
No absolute max; Absolute min: f(7) = 154
E.
No absolute max or min


7.
Determine whether the Mean Value Theorem can be applied to the function on the closed interval [1,3]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (1,3) such that .
A.
MVT applies; 1
B.
MVT applies; 3
C.
MVT applies; 2
D.
MVT applies; 4
E.
MVT applies; 0


8.
*Find the points of inflection and discuss the concavity of the function .
A.
Inflection point at x = 14. Concave down on
B.
No inflection points. Concave down on
C.
Inflection point at x = 14. Concave up on
D.
No inflection points. Concave up on
E.
Inflection point at x = 0. Concave up on ; concave down on


9.
A sector with central angle is cut from a circle of radius 7 inches, and the edges of the sector are brought together to form a cone. Find the magnitude of such that the volume of the cone is a maximum.
A.
radians
B.
radians
C.
radians
D.
radians
E.
radians


10.
Solve the differential equation.

A.
B.
C.
D.
E.


11.
Evaluate the following definite integral.



Use a graphing utility to check your answer.
A.
B.
C.
D.
E.


12.
* (Probably not multiple choice.) Locate any relative extrema and inflection points of the function . Use a graphing utility to confirm your results.
A.
Relative maximum value at ; inflection point at x = 0.
B.
Relative minimum value at ; inflection point at x = 0.
C.
Relative minimum value at ; no inflection points.
D.
Relative minimum value at ; no inflection points.
E.
Relative maximum value at ; no inflection points.


13.
Find the indefinite integral.

A.
B.
C.
D.
E.


14.
*Find the area of the region bounded by the graphs of the algebraic functions.

A.
B.
C.
D.
E.


15.
*Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.

A.
B.
C.
D.
E.


16.
Find the arc length of the graph of the function over the interval [1,2].
A.
B.
C.
D.
E.
None of the above


17.
Neglecting air resistance and the weight of the propellant, determine the work done in propelling a 6-ton satellite to a height of

(i) 300 miles above Earth

(ii) 400 miles above Earth

Assume that Earth has a radius of 4000 miles.
A.
(i) 1,004.65 miton; (ii) 1,309.09 miton
B.
(i) 2,511.63 miton; (ii) 3,272.73 miton
C.
(i) 1,339.53 miton; (ii) 1,745.45 miton
D.
(i) 1,674.42 miton; (ii) 2,181.82 miton
E.
None of the above


18.
Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.

A.
832 lb
B.
1,040 lb
C.
208 lb
D.
93.6 lb
E.
10.4 lb



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