13
CHAPTER R, FORM E
COLLEGE ALGEBRA
NAME
DATE
1. Let
5 12
, 3.2, , 4, 64, 3, , 0
8 8 2
A
ìü
ïï
ïï
= – –
íý
ïï
ïï
îþ
.
List the elements of A that belong to the given set.
A. Rational numbers 1. A. ____________
a.
5 12
, 3.2, 4, 64,
82
ìü
ïï
ïï
—
íý
ïï
ïï
îþ
b.
12
4, 64, , 0
2
ìü
ïï
ïï
–
íý
ïï
ïï
îþ
c.
5 12
, 4, 64, , 0
82
ìü
ïï
ïï
–
íý
ïï
ïï
îþ
d.
5 12
, 3.2, 4, 64, , 0
82
ìü
ïï
ïï
—
íý
ïï
ïï
îþ
B. Real numbers B. ____________
a.
b.
12
4, 64, , 0
2
ìü
ïï
ïï
–
íý
ïï
ïï
îþ
c.
5 12
, 3.2, , 4, 64, 3, , 0
8 8 2
ìü
ïï
ïï
—
íý
ïï
ïï
îþ
d.
3.2, , 3
8
ìü
ïï
ïï
–
íý
ïï
ïï
îþ
C. Natural numbers C. ____________
a.
5 12
, 3.2, 4, 64, , 0
82
ìü
ïï
ïï
—
íý
ïï
ïï
îþ
b.
12
4, 64, , 0
2
ìü
ïï
ïï
–
íý
ïï
ïï
îþ
c.
12
64, , 0
2
ìü
ïï
ïï
íý
ïï
ïï
îþ
d.
12
64, 2
ìü
ïï
ïï
íý
ïï
ïï
îþ
2. Evaluate the expression if
5x=-
and
2y=-
: 2. _____________
42
34
xy
yx
—
—
a.
5
23
b.
5
26
c.
5
14
d.
1
2
14
CHAPTER R, FORM E
3. Identify the property illustrated. Let a and b represent any real numbers.
A.
1 2 1 2
0
3 7 3 7
æö
÷
ç+=
÷
ç÷
ç
èø
××
3. A. ___________
a. Associative b. Inverse
c. Identity d. Commutative
B.
( ) ( )
88a b b a+ = +
B. ___________
a. Associative b. Distributive
c. Identity d. Commutative
C.
( )
4 2 3 4 2 4 3+ = +××
C. ___________
a. Associative b. Distributive
c. Commutative d. Inverse
D.
( )
0aa+ – =
D. ___________
a. Inverse b. Identity
c. Associative d. Distributive
Perform the indicated operations.
4.
( )
2
27ab
éù
-+
ëû
4. _____________
a.
22
4 49ab++
b.
22
4 4 28 14 49a ab b a b– + + – +
c.
22
4 49ab-+
d.
22
4 4 14 7 49a ab b a b– + + – +
5.
( ) ( )
22
8 3 4 7 9 8x x x x+ – + + +
5. _____________
a.
2
15 12 4xx+-
b.
2
15 12 4xx-+
c.
2
15 12 4xx++
d.
2
3 17 11xx++
6.
( )
( )
2
3 1 4 2s s s– – +
6. _____________
a.
32
3 13 10 2s s s– – –
b.
32
3 13 2 2s s s– + –
c.
32
3 13 10 2s s s– + –
d.
32
3 13 2 2s s s– – –
7.
( ) ( )
2 3 2 3s t s t
é ùé ù
+ – + +
ë ûë û
7. _____________
a.
22
49st+-
b.
22
4 4 9s st t+ + –
c.
22
4 4 9s st t+ + +
d.
22
49st++
8.
( )
3
43x–
8. _____________
a.
32
64 96 72 27x x x– + –
b.
3
64 27x–
c.
32
64 144 108 27x x x– + –
d.
32
64 192 144 27x x x– + –
15
CHAPTER R, FORM E
9.
32
2 7 7 12
21
x x x
x
– + – +
–
9. _____________
a.
214
32
21
xx x
– + – + –
b.
223
4 11 21
xx x
– + – + –
c.
21
4 11 21
xx x
– + – + –
d.
210
32
21
xx x
– + – + –
10. The amount spent on health care on in the United States can be 10. _____________
determined by the polynomial
2
1.45 5.36 261.9,y x x= + +
where x = 0 corresponds to 1975 and y is in billions of dollars. Based on this
model, approximately how much was spent on health care in 2000?
a. 1.302 trillion b. 1.302 billion
c. 13.02 billion d. 13.02 trillion
Factor completely.
11.
26 72xx+-
11. _____________
a.
( )( )
12 6xx-+
b.
( )( )
12 6xx+-
c.
( )( )
12 1xx-+
d.
( )( )
12 6xx++
12.
3
8 125x–
12. _____________
a.
( )
( )
2
2 5 4 10 25x x x+ – +
b.
( )
( )
2
2 5 4 20 25x x x– + +
c.
( )
( )
2
2 5 4 10 25x x x– + +
d.
( )
( )
2
2 5 4 20 25x x x+ – +
13.
42
75 147yy–
13. _____________
a.
( )( )
22
3 5 7 5 7yy+-
b.
( )( )
2
3 5 7 5 7y y y+-
c.
( )
2
2
3 5 7yy–
d.
( )
2
3 5 7yy–
14.
22
4 6 9x y y– – –
14. _____________
a.
( )( )
4 3 4 3x y x y– + + –
b.
( )( )
2 3 2 3x y x y– + + –
c.
( )( )
2 3 2 3x y x y– – + +
d.
( )( )
4 3 4 3x y x y– – + +
Perform the indicated operations.
15.
22
22
3 2 4
22
x x x
x x x x
+ + –
×
+ – – –
15. _____________
a.
1
2
x
x
+
–
b.
2
1
x
x
–
–
c.
2
1
x
x
–
+
d.
2
1
x
x
+
–
16
CHAPTER R, FORM E
16.
22
2 2 8
4 16
yy
y y y
-+
–
—
16. _____________
a.
( )( )
2
3 14 8
44
yy
y y y
+-
-+
b.
( )( )
214 8
44
yy
y y y
+-
-+
c.
2
( 4)
y
yy
+
+
d.
( )( )
10
2 4 2
y
yy
–
-+
17.
2
41
4
21
2
x
x
–
–
17. _____________
a.
3
2x
b.
3
2x–
c.
4
2
x
x
+
d.
4
2
x
x–
18.
3 12 5 20
10 20
xx++
¸
18. _____________
a.
3 12
50
x
x
+
b.
8 32
30
x+
c.
3
40
d.
6
5
19. Evaluate
32
49
25
–
æö
÷
ç÷
ç÷
ç
èø
. 19. _____________
a.
125
343
–
b.
343
125
c.
125
343
d.
343
125
–
20. Simplify
10
2 5 1 4 3 4
3 4 1 5
x y z
xy
–
–
æö
÷
ç÷
ç÷
ç÷
ç
èø
so that there are no negative exponents. 20. _____________
Assume that all variables represent positive real numbers.
a.
23 2 1 2
15 2
xy
z
b.
23 20 1 20 37 4
x y z
c.
92
7 2 15 2
y
xz
d.
393 20 409 20 37 4
x y z
Simplify. Assume that all variables represent positive real numbers.
21.
56
3125xy
21. _____________
a.
22
3
5x y xy
b.
3
5xy xy
c.
3
22
5xy x
d.
3
5xy x
17
CHAPTER R, FORM E
22.
3 2 12 4 18x x x-+
22. _____________
a.
96x
b.
3 8 2xx+
c.
3 3 12 2xx-+
d.
93x
23.
( )
2
10 2 5+
23. _____________
a. 30 b.
30 20 2+
c.
30 10 2+
d. 20
24. Rationalize the denominator of
15
2 7 10–
. 24. _____________
a.
( )
5 2 7 10
6
–
b.
( )
15 2 7 10
4
+
c.
( )
5 2 7 10
6
+
d.
( )
15 2 7 10
4
–
25. One of the two solutions of a quadratic equation, x, can be found by the formula 25. _____________
24,
2
b b ac
xa
– + –
=
where a is the coefficient of the squared term, b is the coefficient of the linear term,
and c is the constant term. Find one of the solutions if
5a=
,
7b=-
, and
6c=-
.
a. 2 b.
4
5
–
c.
7 71
10
–
d.
7 71
10
+
18
CHAPTER R, FORM E