CHAPTER R, FORM F
COLLEGE ALGEBRA
NAME
DATE
1. Let
15 5
10, 1.55, 12, , , 64, 0,
5 14
B
ìü
ïï
ïï
= – –
íý
ïï
ïï
îþ
.
List the elements of B that belong to the given set.
A. Irrational numbers 1. A. ____________
a.
15 5
10, 1.55, 12, , , 64, 0,
5 14
ìü
ïï
ïï
—
íý
ïï
ïï
îþ
b.
{ }
10, 1.55, , 64, 0
—
c.
{ }
10, , 0
–
d.
{ }
10,
–
B. Natural numbers B. ____________
a.
b.
15
12, , 64
5
ìü
ïï
ïï
íý
ïï
ïï
îþ
c.
15
12, , 0, 1.55, 64
5
ìü
ïï
ïï
–
íý
ïï
ïï
îþ
d.
15
12, 5
ìü
ïï
ïï
íý
ïï
ïï
îþ
C. Integers C. ____________
a.
15
12, , 64
5
ìü
ïï
ïï
íý
ïï
ïï
îþ
b.
c.
15
12, 5
ìü
ïï
ïï
íý
ïï
ïï
îþ
d.
15 5
12, , 0, 1.55, 64,
5 14
ìü
ïï
ïï
–
íý
ïï
ïï
îþ
2. Evaluate the expression if
2x=-
,
1y=
, and
3z=-
: 2. _____________
2
52
2
xy
xz
–
+
a.
1
3
–
b.
3
5
c.
1
4
–
d.
1
3
3. Identify the property illustrated. Let a and b represent any real numbers.
A.
1 3 3×=
3. A. ___________
a. Associative b. Inverse
c. Identity d. Distributive
B.
( ) ( )
00x y x y+ + = + +
B. ___________
a. Associative b. Commutative
c. Identity d. Distributive
CHAPTER R, FORM F
C.
31
3
×=
C. ___________
a. Commutative b. Inverse
c. Identity d. Distributive
D.
( ) ( )
99a b b a+ = +
D. ___________
a. Associative b. Distributive
c. Commutative d. Inverse
Perform the indicated operations.
4.
( )
2
3 2 2ab
éù
+-
ëû
4. _____________
a.
22
9 4 4ab+-
b.
22
9 12 4 12 8 4a ab b a b+ + – – +
c.
22
9 12 4 6 4 4a ab b a b+ + – – +
d.
22
9 4 4ab++
5.
( )( )
2 5 2 8x y x y– – – +
5. _____________
a.
22
4 6 6x xy y—
b.
22
4 10 40x xy y+-
c.
d.
22
4 16 40x xy y—
6.
( ) ( ) ( )
2 3 2
2 5 8 7 2 4 3x x x x x x– + + – – – + –
6. _____________
a.
32
3 2 14 6x x x– – +
b.
32
5 2 14 6x x x– – – +
c.
32
5 2 14 6x x x– – +
d.
32
3 2 10xx-+
7.
( ) ( )
2 3 2 3r s r s
é ùé ù
– + – –
ë ûë û
7. _____________
a.
22
49rs+-
b.
22
49rs—
c.
22
4 4 9r r s– – –
d.
22
4 4 9r r s– + –
8.
( )
4
3x+
8. _____________
a.
4 3 2
6 18 54 81x x x x+ + + +
b.
4 3 2
6 36 54 81x x x x+ + + +
c.
481x+
d.
4 3 2
12 54 108 81x x x x+ + + +
CHAPTER R, FORM F
9.
3
3 5 8
2
xx
x
+-
–
9. _____________
a.
236
3 11 22 2
xx x
+ + + –
b.
214
3 11 2
xx
x
++
–
c.
242
3 6 17 2
xx x
– + – –
d.
226
3 6 17 2
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 2002?
a. 14.63 billion b. 1.463 billion
c. 1.463 trillion d. 14.63 trillion
Factor completely.
11.
2
18 78 60xx—
11. _____________
a.
b.
( )( )
6 3 2 5xx+-
c.
( )( )
6 3 2 5xx-+
d.
( )( )
6 3 2 5xx++
12.
33
125 216xy+
12. _____________
a.
( )
( )
22
5 6 25 30 36x y x xy y– + +
b.
( )
( )
22
5 6 25 30 36x y x xy y+ – +
c.
( )
( )
22
5 6 25 60 36x y x xy y+ – +
d.
( )
( )
22
5 6 25 60 36x y x xy y– + +
13.
2
100 16a–
13. _____________
a.
( )( )
10 4 10 4aa-+
b.
( )
2
2 5 2a–
c.
( )( )
4 5 2 5 2aa-+
d.
( )
2
4 5 2a–
14.
3 2 3 2
4 8 32r s r s+ – –
14. _____________
a.
( )( ) ( )( )
2
2 2 2 2r r s s– + – +
b.
( )
( )( )
22
2 2 4 4r r r s– + + +
c.
( )
( )
( )( )
2
2 2 4 2 2r r r s s– + + – +
d.
( )
( )
( )( )
2
2 2 4 2 2r r r s s– – + – +
Perform the indicated operations.
15.
22
22
5 14 12 35
4 12 20
x x x x
x x x
+ – + +
¸
– + +
15. _____________
a.
10
5
x
x
+
+
b.
5
10
x
x
+
+
c.
1
2
x
x
+
+
d.
2
1
x
x
+
+
CHAPTER R, FORM F
16.
22
3 7 5
5 6 2 3
aa
a a a a
+-
–
+ + + –
16. _____________
a.
( )( )( )
2
2 3 17
2 3 1
aa
a a a
—
+ + –
b.
( )( )
21
12
a
aa
+
-+
c.
( )
( )
26
33
a
a
+
+
d.
( )( )( )
2
4 17
2 3 1
aa
a a a
+-
+ + –
17.
12
33
21
33
x
x
–
+
–
+
17. _____________
a.
32
3
x
x
+
–
b.
1–
c.
32
1
x
x
—
+
d.
6
3x+
18.
8 2 7
55
s t t s
s t t s
++
–
—
18. _____________
a.
5
st
st
–
–
b.
5
ts
st
–
–
c.
15 3
5
st
st
+
–
d. 3
19. Evaluate
23
64
27
–
æö
÷
ç÷
ç÷
ç
èø
19. _____________
a.
9
16
b.
16
9
–
c.
16
9
d.
9
16
–
20. Simplify
18
5 3 3 2
1 6 5 3 5 6
xy
x y z
–
–
æö
÷
ç÷
ç÷
ç÷
ç
èø
so that there are no negative exponents. 20. _____________
Assume that all variables represent positive real numbers.
a.
27 57
15
xy
z
b.
27 15
57
xz
y
c.
33 3
15
xy
z
d.
15
33 3
z
xy
Simplify. Assume that all variables represent positive real numbers. 21. _____________
21.
87
625xy
a.
34
25x y xy
b.
47
25xy
c.
87
25x y xy
d.
43
25x y y
22.
4 2 2
33
81 4 3x y x xy+
22. _____________
a.
2
3
73x xy
b.
22
3
12 3x xy
c.
3
73xy x
d.
22
3
12 9x y x y
CHAPTER R, FORM F
23.
( )( )
2 15 5 3 3 5+ – +
23. _____________
a.
15 5 3—
b.
11 15 5 3—
c.
11 15 3 5—
d.
15 3 5—
24. Rationalize the denominator of
9
17 3 2+
. 24. _____________
a.
( )
9 17 3 2+
b.
( )
9 17 3 2—
c.
( )
9 17 3 2-+
d.
( )
9 17 3 2–
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
6a=
,
13b=
, and
8c=-
.
a. 4 b.
1
2
c.
13 23
12
-+
d.
13 23
12
—
CHAPTER R, FORM F