244
FINAL EXAMINATION, FORM A
COLLEGE ALGEBRA
NAME________________________
DATE ________________________
Perform each indicated operation.
1.
2
(2 3)(3 5)y y y− + −
1. ___________________
2.
2
2
7 18 2
3
9 18
w w w
w
ww
+ − −
−
−+
2. ___________________
Factor completely.
3.
2
2(3 5) 5(3 5) 12zz− + − −
3. ___________________
4.
33
27pq+
4. ___________________
Simplify each expression. Assume that all variables represent positive real numbers.
5.
4/3
2/3
27
27
−
−
5. ___________________
6.
372
625mn
6. ___________________
7. Find the quotient. Write the answer in standard form. 7. ___________________
34
52
i
i
+
−
Solve each equation.
8.
2
3 15
155
xxx
−=
++
8. ___________________
9.
2
3 4 5 0xx− + =
9. ___________________
10.
42
7 10 0yy
−−
− + =
10. ___________________
11.
17 3xx+ = −
11. ___________________
12.
3 7 32x−=
12. ___________________
13. Angeline Tsai wants to buy a rectangular rug for a room that is 13. ___________________
13 ft wide and 17 ft long. She wants to leave a uniform strip of
floor around the rug. She can afford to buy 140 sq ft of carpeting.
What dimensions should the rug have?
Solve each inequality. Write the answer in interval notation.
14.
33
4x
−
14. ___________________
15.
4 1 7x+
15. ___________________
245
FINAL EXAMINATION, FORM A
16. Find the center and radius of the circle with equation 16. center: _____________
22
6 4 4 0.x y x y+ − + + =
radius: _____________
17. Give the domain of each function.
a.
32
() 23
x
fx x
+
=−
17. a. ________________
b.
2
( ) 6 5f x x x= − +
b. ________________
18. Write an equation in standard form for the line through (1, – 4) and 18. ___________________
perpendicular to the line 4x – 2y = 7.
19. Graph the function
( ) 2 3f x x= − +
. 19. domain: ____________
Give the domain and range. range: ______________
20. Use the tests for symmetry to determine whether the graph of 20. ___________________
the equation
3
2y x x=+
is symmetric with respect to the x-axis,
the y-axis, the origin, or none of these. (The graph may have more
than one of the listed symmetries.)
21. Let
2
( ) 2 4f x x x= − +
and g(x) = 2x – 1.
Find each of the following.
a. ( f + g)(–3) 21. a. ________________
b.
(5)
f
g
b. ________________
c.
( )( )f g x
c. ________________
246
FINAL EXAMINATION, FORM A
22. Graph the parabola
266y x x= + +
. Give the vertex, axis, domain, 22. vertex: _____________
and range. axis: _______________
domain: ____________
range: _____________
23. The polynomial 23. ___________________
4 3 2
( ) 4 6 4 15f x x x x x= − + − −
has 1 – 2i as a zero. Find the other zeros.
Graph each function.
24.
4 3 2
( ) 2f x x x x= + −
24.
247
FINAL EXAMINATION, FORM A
25.
21
() 2
x
fx x
−
=+
25.
26. Give the equations of the vertical, horizontal, and/or 26. vertical: ____________
oblique asymptotes of the graph of the function horizontal: __________
4( 3)( 4)
( ) .
(2 1)( 3)
xx
fx xx
−+
=−+
oblique: ____________
27. Determine whether the following function is one-to-one. If it is 27. ___________________
one–to-one, write an equation for the inverse in the form
1( ).y f x
−
=
___________________
21
() 2
x
fx x
+
=−
28. Use a calculator to find
5
log 30
to four decimal places. 28. ___________________
Solve each equation.
29.
21
32 16
xx−
=
29. ___________________
30.
66
log ( 1) log ( 1) 2xx+ − − =
30. ___________________
31. If the population of a city increases at a continuous rate of 5.8% per 31. ___________________
year, how long, to the nearest year, will it take for the population
to triple?
Solve each system of equations.
32.
2 3 4
2 1
4 3 3 2
x y z
x y z
x y z
+ + = −
− + = −
− + = −
32. ___________________
33.
3 2 13
6
xy
xy
+ = −
=
33. ___________________
34. Solve the system by the Gauss-Jordan method. 34. ___________________
2 2 3
38
3 2 13
x y z
x y z
x y z
+ − = −
− + − = −
− + =
FINAL EXAMINATION, FORM A
248
35. Find the value of the determinant. 35. ___________________
4 1 0
2 3 1
2 0 4
−
−
−
36. Solve the system by Cramer’s rule. 36. ___________________
2 3 4
2 3 5
23
x y z
x y z
x y z
− + = −
− + − = −
− + =
37. Find the matrix product, if it can be found. 37. ___________________
14
2 1 5 35
3 0 5 22
−
−
−
−
38. Find the inverse of the matrix, if it exists. 38. ___________________
15
52
−
−
39. Give the vertex, focus, directrix, and axis for the parabola with 39. vertex: _____________
equation focus: ______________
2
( 4) 24( 2).yx− = +
directrix: ___________
axis: _______________
Graph each relation.
40.
22
9xy=+
40.
FINAL EXAMINATION, FORM A
249
41.
22
9 25 225xy+=
41.
42. Find an equation for the hyperbola with center at (4, – 6), a vertex 42. ___________________
at (4, 0), and a focus at (4, 3).
43. a. Identify the type of conic section represented by the equation 43. a. ________________
22
5 30 4 16 45 0x x y y+ + − + =
.
b. Give the center of the graph. b. ________________
44. Find
55
and aS
for the arithmetic sequence with
25 and =3.ad=
44. ___________________
45. Find
55
and aS
for the geometric sequence with 45. ___________________
1
1
4 and .
2
ar= = −
46. Find the following sum if it exists. 46. ___________________
1
2
35
i
i
=
47. Write the binomial expansion of
5
(2 3 )xy−
. 47. ___________________
48. Find the eighth term of the binomial expansion of
11
( 2 )ab−
. 48. ___________________
49. How many different 5-card hands can be dealt from a deck of 49. ___________________
20 different cards?
50. A marble is drawn at random from a bag containing 4 red marbles, 50. ___________________
5 blue marbles, and 7 yellow marbles. Find the odds in favor of
drawing a yellow marble.
250
FINAL EXAMINATION, FORM A
251
252