250
FINAL EXAMINATION, FORM B
COLLEGE ALGEBRA
NAME
DATE
Choose the best answer.
Perform each indicated operation.
1.
32
( 1)( 1)x x x x+ − + −
1. ____________
a.
41x+
b.
4 3 2
2 2 2 1x x x x+ + + −
c.
41x−
d.
42
1xx−−
2.
2
2
5 24 3
5
11 30
p p p
p
pp
− − +
+
++
2. ____________
a.
6
8
p
p
+
−
b.
8
6
p
p
−
+
c.
3
6
p
p
+
−
d.
8
6
p
p
+
−
Factor completely.
3.
3. ____________
a.
22
(9 6 )(9 6 )a a ab a+−
b.
2 2 2
9 (3 2)(3 2)a b b+−
c.
22
9 ( 2)( 2)( 2)a b b b++−
d. prime
4.
33
125xy−
4. ____________
a.
22
(5 )(25 )x y x y−+
b.
22
(5 )(25 5 )x y x xy y− + +
c.
3
(5 )xy−
d.
22
(5 )(25 5 )x y x xy y− − +
Simplify each expression. Assume that all variables represent positive real numbers.
5.
3/ 4
1/ 4
625
625
−
−
5. ____________
a.
1
25
b.
1
5
c. 125 d. 5
6.
83
564xy
6. ____________
a.
3 2 3
5
22x x y
b.
33
5
22x x y
c.
33
5
4x x y
d.
23
5
4x xy
7. Find the quotient. Write the answer in standard form. 7. ____________
3
42
i
i
−
+
a.
71
10 10 i+
b.
11
22
i+
c.
11
22
i−−
d.
11
22
i−
251
FINAL EXAMINATION, FORM B
Solve each equation.
8.
3 12
14 ( 4)x x x
+=
−−
8. ____________
a. {3} b. {–3, 4} c. {4} d. {–3}
9.
3
3 2 1 0xx− + =
9. ____________
a.
12
3





b.
12
33
i





c.
1
1, 3

−


d.
12
33
i


−+



10.
42
11 28 0xx
−−
− + =
10. ____________
a.
{2, – 2, 7, 7}−
b. {4, 7}
c.
1 1 7 7
, , ,
2 2 7 7


−−



d.
1 1 1 1
, , ,
4 4 7 7

−−


11.
44xx+ − =
11. ____________
a. {4} b. {5} c. {4, 5} d. {8}
12.
3 7 19x+=
12. ____________
a. {4} b. {–4} c.
26
4, 3

−


d.
26
4, 3

−


13. A rectangular garden is located at the edge of a lake. The remaining three 13. ____________
sides are enclosed by 48 ft of fencing. If the area of the garden is 270 sq ft,
what are the dimensions of the garden?
a. 15 ft
18 ft b. 15 ft
18 ft, or 9 ft
30 ft
c. 9 ft
30 ft d. 8 ft
32 ft
Solve each inequality. Write the answer in interval notation.
14.
34
2
x
x
−
14. ____________
a. [2, 8] b.
(– , 2) [8, )  
c. (2, 8] d.
[8, )
252
FINAL EXAMINATION, FORM B
15.
7 5 12x−
15. ____________
a.
19
1, 5



b.
( )
19
, –1 ,
5

− 


c.
19 , 1
5

−


d.
19
, (1, )
5

− −


16. Find the center and radius of the circle with equation 16. ____________
22
2 4 0x y x y+ − + =
.
a. center (–1, 2); radius
5
b. center (1, –2); radius 5
c. center (–1, 2); radius 5 d. center (1, –2); radius
5
17. Give the domain and range of the function
2
( ) 36 .f x x=−
17. ____________
a. domain: [0, 6]; range: [0, 6] b. domain: [– 6, 6]; range [– 6, 0]
c. domain: [– 6, 6]; range: [0, 6] d. domain: [0, 6]; range [– 6, 6]
18. Write an equation in standard form for the line through (–3, 8) and 18. ____________
perpendicular to the line 3x – 2y = 3
a. 3x – 2y = –25 b. 2x + 3y = 18
c. 2x + 3y = 3 d. 3x – 2y = 15
19. Graph the function
( ) 4 3f x x= − − +
. 19. ____________
a.
b.
c.
d.
253
FINAL EXAMINATION, FORM B
20. Use the tests for symmetry to determine all symmetries of the graph of the 20. ____________
relation
2
25xy=−
.
a. x-axis only b. y-axis only
c. origin only d. x-axis, y-axis, and origin
21. Let
2
( ) 2 3 and ( ) 1f x x g x x= + = −
. Find each of the following.
A.
( 3)
f
g

−


21. A. ____________
a.
21
4
−
b.
4
15
c.
4
21
−
d. 35
B.
( )( )f g t
B. ____________
a.
2
22t+
b.
2
21t+
c.
2
42t+
d.
2
2 4 5tt−+
22. Give the vertex of the parabola with equation 22. ____________
2
( ) 2 8 5f x x x= − + −
.
Also give the range of this function.
a. vertex: (3, 2); range:
( , 2]−
b. vertex: (2, 3); range:
( , 3]−
c. vertex: (3, –2); range:
( , 2]− −
d. vertex: (2, 3); range:
(3, )
23. The polynomial
4 3 2
( ) 8 4 48f x x x x x= − − − −
has –2i as a zero. Find the 23. ____________
other zeros.
a. 4, –3 b. 2i, 4, –3 c. 2i, – 4, 3 d. – 4, 3
254
FINAL EXAMINATION, FORM B
Graph each function.
24.
42
( ) 5 4f x x x= − +
24. ____________
a.
b.
c.
d.
25.
256
() 2
xx
fx x
−+
=−
25. ____________
a.
b.
c.
d.
255
FINAL EXAMINATION, FORM B
26. Find all asymptotes of the graph of the function 26. ____________
.
a. vertical: x = 2; horizontal: y = 0
b. vertical:
3
2
x=−
; horizontal: y = 2
c. vertical: x = –2, x = 2; oblique:
13
22
yx=−
d. vertical: x = –2, x = 2; horizontal: y = 0
27. Determine whether the following function is one–to–one. If it is one-to–one, 27. ____________
write an equation for the inverse in the form
1( ).y f x
−
=
a. one–to-one;
15
() 23
x
fx y
−+
=−
b. one–to-one;
121
() 35
x
fx x
−−
=+
c. one–to-one;
135
() 21
x
fx x
−+
=−
d. not one-to-one
28. Use a calculator to find
6
log 32
to four decimal places. 28. ____________
a. 1.9343 b. .5170 c. .2509 d. 2.6876
Solve each equation.
29.
31
27 81
xx−=
29. ____________
a. {1} b.
1
2



c.
3
5



d.
3
5

−


30.
33
log ( 2) log ( 1) 3xx+ − − =
30. ____________
a.
29
28



b.
29
26



c.
25
26



d.
25
28



31. If the population of a city increases at a continuous rate of 4.7% per year, 31. ____________
how long, to the nearest tenth of a year, will it take for the population to
double?
a. 6.4 yr b. 14.7 yr c. 42.6 yr d. 14.5 yr
256
FINAL EXAMINATION, FORM B
32. Solve the system of equations. Give only the x-value of the solution. 32. ____________
3 2 10
47
2 3 2 3
x y z
x y z
x y z
− + =
− + =
+ − =
a. –2 b. 0 c. 3 d. –1
33. Solve the system of equations. 33. ____________
22
3
2
xy
xy
−=
=
a. {(1, 2), (2, 1), (2i, –i), (–2i, i)} b. {(2, 1)}
c. {(2, 1), (–2, –1), (i, –2i), (–i, 2i)} d.
34. Solve the system by the Gauss-Jordan method. Give only the x-value of 34. ____________
the solution.
3 13
2 3 7
3 2 7
x y z
x y z
x y z
− + =
+ − = −
− − + =
a. –3 b. 2 c. –2 d. 3
35. Find the value of the determinant. 35. ____________
4 2 1
2 0 3
5 0 1
−
a. –13 b. 26 c. –26 d. 0
36. Solve the system by Cramer’s rule. Give the x-value of the solution. 36. ____________
2 3 13
21
3 4 3 7
x y z
x y z
x y z
− + = −
+ − = −
− − + =
a. – 4 b. 0 c. 2 d. 1
257
FINAL EXAMINATION, FORM B
37. Find the following matrix product, if it can be found. 37. ____________
3
2 1 7 3 2
1 2 0 1 1
4


− − −




−



a. [3 11] b.
3
11



c.
85
74
−



d.
8
7



38. Find the inverse of the following matrix, if it exists. 38. ____________
21
34
−


−

a.
3
2
55
14
55
−−


−−

b.
41
55
32
55



c.
41
55
32
55
−−


−−

d. The inverse does not exist.
39. Give the directrix for the parabola
2
( 6) 16( 2)xy− = +
. 39. ____________
a. x = –2 b. y = –2 c. x = 6 d. y = – 6
Graph each relation.
40.
22
4yx=+
40. ____________
a.
b.
c.
d.
258
FINAL EXAMINATION, FORM B
41.
22
4 16xy+=
41. ____________
a.
b.
c.
d.
42. Find an equation for the ellipse having center at the origin with minor axis 42. ____________
of length 10 and foci at (0, –7) and (0, 7).
a.
22
1
25 74
xy
−=
b.
22
1
25 74
xy
+=
c.
22
1
74 25
xy
+=
d.
22
1
25 49
xy
+=
43. Identify the type of conic section represented by the equation 43. ____________
22
8 16 9 36 2x x y y+ − + = −
.
a. ellipse b. parabola c. hyperbola d. circle
44. Find
5
S
for the arithmetic sequence with
37a=
and d = 9. 44. ____________
a. 25 b. 63 c. 33 d. 35
45. Find
6
a
for the geometric sequence with
1100a=
and
1.
10
r=−
45. ____________
a.
1
1000
b.
1
10,000
c.
1
1000
−
d.
1
10,000
−
259
FINAL EXAMINATION, FORM B
46. Find the following sum if it exists. 46. ____________
1
3
65
i
i
=



a. 9 b.
9
5
c. 6 d. The sum does not exist.
47. Write out the binomial expansion of
4
(3 2 )ab−
. 47. ____________
a.
44
81 16ab+
b.
4 3 2 2 3 4
81 216 216 96 16a a b a b a b+ + + +
c.
4 3 2 2 3 4
81 216 216 96 16a a b a b ab b− + − +
d.
4 3 2 2 3 4
81 27 36 24 16a a b a b ab b− + − +
48. Find the fifth term of the expansion of
6
( 2 )xy−
. 48. ____________
a.
24
16xy−
b.
2
10xy−
c.
24
16xy
d.
24
240xy
49. In how many different ways can a chairman, vice-chairman, secretary, and 49. ____________
treasurer be chosen from a 25-person board of trustees?
a. 12,650 b. 303,600 c. 13,800 d. 15,600
50. A card is drawn at random from a well-shuffled deck of 52 cards. Find the 50. ____________
probability that a black 3 or a spade is drawn.
a.
15
52
b.
4
13
c.
7
26
d.
1
4
260
FINAL EXAMINATION, FORM B
261