1.
Find

f (x) = x – 4      g (x) = x2


A.
x2 – 4
B.
x2 – 16
C.
x2 + 16
D.
x2 – 4x + 16
E.
x2 – 8x + 16


2.
Find the midpoint of the line segment joining the points.

(3, –5), (–5, –7)
A.
(1, 6)
B.
(–6, –1)
C.
(1, 4)
D.
(4, 1)
E.
(–1, –6)


3.
Find the slope and y-intercept of the equation of the line.

y – 6x = 3
A.
slope: 6;   y-intercept: 3
B.
slope: 3;   y-intercept: 6
C.
slope: 6;   y-intercept: –1
D.
slope: –3;   y-intercept: –6
E.
slope: –6;   y-intercept: –3


4.
Find the distance between the points.

(–9, 3), (–9, 6)
A.
3
B.
9
C.
–18
D.
18
E.
0


5.
Find the slope-intercept form of the line passing through the points.

(–1, –5), (1, 0)
A.
B.
C.
D.
E.


6.
Find the difference quotient and simplify your answer.

f (x) = –5x2 + 5x,      , h ≠ 0
A.
9 + h
B.
C.
D.
5 – 5h
E.
–15 – 5h


7.
Find the zeroes of the functions algebraically.

A.
x = 4, x = –3,
B.
x = 4, x = –3
C.
D.
x = –4, x = 3
E.
x = –4, x = 3,


8.
Evaluate the indicated function for f (x) = x2 – 9 and g (x) = x + 7.

( fg )(–1)
A.
–48
B.
–60
C.
–64
D.
64
E.
–62


9.
Find the inverse function of
A.
B.
C.
D.
E.


10.
Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither.

L1 : (0, –8), (3, –1)
L2 : (–9, 7), (–12, 0)
A.
parallel
B.
perpendicular
C.
neither


11.
Determine whether the function has an inverse function. If it does, find the inverse function.

A.
No inverse function exists.
B.
C.
D.
E.


12.
Assume that y is directly proportional to x. If and, determine a linear model that relates y and x.
A.
B.
C.
D.
E.


13.
Find the constant of proportionality for the following situation:
   "y is jointly proportional to x and ."
   , and
A.
B.
C.
D.
E.


14.
Determine the vertex of the graph of the quadratic function .
A.
B.
C.
D.
E.


15.
Write the quadratic function, , in standard form.
A.
B.
C.
D.
E.


16.
Describe the right-hand and the left-hand behavior of the graph of .
A.
Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
B.
Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right.
C.
Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.
D.
Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E.
Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right.


17.
Use long division to divide.
   
A.
B.
C.
D.
E.


18.
Use synthetic division to divide.
   
   
A.
B.
C.
D.
E.


19.
Write the complex number in standard form.
A.
B.
C.
D.
E.


20.
Write the complex conjugate of the complex number .
A.
B.
C.
D.
E.


21.
Determine the quadrant in which the angle lies. (The angle measure is given in radians.)
   
A.
I
B.
II
C.
III
D.
IV
E.
The angle lies on a coordinate axis.


22.
Find (if possible) the complement and supplement of the given angle.
   
A.

B.

C.

D.

E.



23.
Rewrite the given angle in radian measure as a multiple of . (Do not use a calculator.)
   
A.
B.
C.
D.
E.


24.
Rewrite the given angle in degree measure. (Do not use a calculator.)
   
A.
–600°
B.
–270°
C.
–330°
D.
–285°
E.


25.
Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
    radius: r = 3 miles     arc length: s = 14 miles
A.
B.
C.
D.
E.


26.
Find the length of the arc on a circle of radius r intercepted by a central angle .
    radius: r = 5 centimeters     central arc:
A.
B.
C.
D.
E.


27.
Find the area of the sector of the circle with radius r and central angle .
    radius: r = 11 feet     central arc:
A.
B.
C.
D.
E.


28.
Evaluate the trigonometric function using its period as an aid.
   
A.
B.
C.
D.
E.


29.
Find the exact value of the given trigonometric function of the angle shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)



      b = 24, c = 51
   
     
A.
B.
C.
D.
E.


30.
Use the given function values and the trigonometric identities (including the cofunction identities), to find the indicated trigonometric function.
   ; find
A.
B.
C.
D.
E.


31.
The point is on the terminal side of an angle in standard position. Determine the exact value of .
   
A.
B.
C.
D.
E.


32.
Use the function value and constraint below to evaluate the given trigonometric function.
   Function Value          Constraint      Evaluate:
                      
A.

B.

C.

D.

E.



33.
Use the function value and constraint below to evaluate the given trigonometric function.
   Function Value          Constraint      Evaluate:
                         
A.
B.
C.
D.
E.
undefined


34.
The terminal side of lies on the given line in the specified quadrant. Find the value of the given trigonometric function of by finding a point on the line.
   Line      Quadrant      Evaluate:
               IV               
A.
B.
C.
D.
E.


35.
Find the reference angle for the given angle .
   
A.
B.
C.
D.
E.


36.
Find the reference angle for the given angle .
   
A.
B.
C.
D.
E.


37.
Evaluate the tangent of the angle without using a calculator.
   
A.
B.
C.
D.
E.
0


38.
Find the indicated trigonometric value in the specified quadrant.

   
A.
B.
C.
D.
E.
undefined


39.
Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set to the correct angle mode.)
   
A.
572.9572
B.
0.1003
C.
10.0167
D.
9.9666
E.
–1.6179


40.
Determine the period and amplitude of the following function.
   

A.
 
 
B.
 
 
C.
 
 
D.
 
 
E.
 
 


41.
Which of the following functions is represented by the graph below?
A.

B.

C.

D.

E.



42.
Use the graph shown below to determine if the function is even, odd, or neither.

                         
A.
B.
C.


43.
Evaluate without using a calculator.
A.
B.
C.
D.
E.


44.
Use an inverse function to write as a function of x.

A.
 
 
B.
 
 
C.
 
 
D.
 
 
E.
 
 


45.
Use an inverse function to write as a function of x.

A.
 
 
B.
 
 
C.
 
 
D.
 
 
E.
 
 


46.
Find the exact value of .
A.
B.
C.
D.
E.


47.
Write an algebraic expression that is equivalent to .
A.
B.
C.
D.
E.


48.
Write an algebraic expression that is equivalent to.
A.
B.
C.
D.
E.


49.
Find the exact value of .
A.
B.
C.
D.
E.


50.
If , evaluate the function below.
   
A.
 
 
B.
 
 
C.
 
 
D.
 
 
E.
 
 


51.
Which of the following is equivalent to the expression below?
     
A.
 
 
B.
 
 
C.
 
 
D.
 
 
E.
 
 


52.
Rewrite as a single logarithm and then simplify the result.
A.
B.
C.
D.
E.


53.
If and , determine the value of c. Round to two decimal places.
A.
12.77
B.
32.97
C.
35.09
D.
4.37
E.
4.10


54.
Find (if possible) the complement and supplement of the given angle.
   
A.
complement: 49°; no supplement
B.
complement: 41°; supplement: 49°
C.
complement : 49°; supplement: 229°
D.
no complement; supplement: 229°
E.
no complement; supplement: 49°


55.
Determine the quadrant in which the angle lies.
   
A.
Quadrant I
B.
Quadrant IV
C.
Quadrant II
D.
Quadrant III


56.
Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
   
A.
sq. units
B.
sq. units
C.
sq. units
D.
sq. units
E.
sq. units


57.
Solve the following equation.

   
A.
 
 
B.
 
 
C.
 
 
D.
 
 
E.
 
 


58.
Find all solutions of the following equation in the interval .

   
A.
 
 
B.
 
 
C.
 
 
D.
 
 
E.
 
 


59.
Find the exact value of the given expression.
   
A.
B.
C.
D.


60.
Find the exact value of the given expression using a sum or difference formula.
   
A.
B.
C.
D.


61.
Write the given expression as the cosine of an angle.
   
A.
B.
C.
D.
E.


62.
Write the given expression as the tangent of an angle.
   
A.
B.
C.
D.
E.


63.
Find the exact value of given that and . (Both u and v are in Quadrant II.)
A.
B.
C.
D.
E.


64.
Use a double-angle formula to find the exact value of when .
A.
B.
C.
D.
E.


65.
Given , , and , use the Law of Sines to solve the triangle (if possible) for the value of b. If two solutions exist, find both. Round answer to two decimal places.
A.
B.
C.
D.
E.
not possible


66.
Given , , and , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.
A.
B.
C.
D.
E.


67.
Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
   
A.
sq. units
B.
sq. units
C.
sq. units
D.
sq. units
E.
sq. units


68.
Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

A.
B.
C.
D.
E.


69.
Find the magnitude of vector v.


A.
 
 
B.
 
 
C.
 
 
D.
 
 
E.
 
 


70.
Find the component form of vector v.


A.
 
 
B.
 
 
C.
 
 
D.
 
 
E.
 
 


71.
Find the component form of vector v with initial point and terminal point .
A.
B.
C.
D.
E.


72.
Given and , determine .
A.
B.
C.
D.
E.


73.
Find a unit vector in the direction of .
A.
B.
C.
D.
E.


74.
Find the magnitude and direction angle of .
A.
B.
C.
D.
E.


75.
Find the component form of v if and the angle it makes with the x-axis is .
A.
B.
C.
D.
E.


76.
Given and , find .
A.
B.
C.
D.
E.


77.
Given vectors , , and , determine whether the result of the following expression is a vector or a scalar.
   
A.
vector
B.
scalar


78.
Use the dot product to find the magnitude of u if .
A.
B.
C.
D.
E.


79.
Find the angle between the vectors u and v if and . Round answer to two decimal places.
A.
B.
C.
D.
E.


80.
Determine whether u are v and orthogonal, parallel, or neither.
   
A.
orthogonal
B.
parallel
C.
neither


81.
Find the absolute value of the complex number .
A.
B.
C.
D.
E.


82.
Find the trigonometric form of the complex number shown below.
   
A.

B.

C.

D.

E.



83.
Find the standard form of the complex number shown below.
   
A.
B.
C.
D.
E.


84.
Perform the operation shown below and leave the result in trigonometric form.
   
A.
B.
C.
D.
E.


85.
Perform the operation shown below and leave the result in trigonometric form.
   
A.
B.
C.
D.
E.


86.
Perform the operation shown below and leave the result in trigonometric form.
   
A.
B.
C.
D.
E.


87.
Perform the indicated operation using trigonometric form. Leave answer in trigonometric form.
   
A.
B.
C.
D.
E.


88.
Use DeMoivre's Theorem to find the indicated power of the following complex number.
   
A.
19,683
B.
6,561
C.
2,187
D.
46,656
E.
243


89.
Use DeMoivre's Theorem to find the indicated power of the folllowing complex number.
   
A.
B.
C.
D.
E.


90.
Use DeMoivre's Theorem to find the indicated power of the following complex number.
   
A.
B.
C.
D.
E.



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