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Review of Algebra I
Math
Study Guide
Further Study
Review Test
Further Reading
Writing Help
How to Cite This SparkNote
Review Test
Further study
Review Test
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1. Which of the following is a solution set to
x
^{2}
 12 = 5
x
+ 2
?
{2, 7}
{ 7, 2}
{ 2, 7}
{ 2, 7, 0}
2. Solve for
y
in
2
y
+ 5 =  3
y
 10
.
y
=  3
y
= 3
y
=  1
y
= 1
3. Which property is illustrated in the following:
y
= 5
x
and
5
x
= 3
. Thus,
y
= 3
.
Commutative Property of Equality
Transitive Property of Equality
Associative Property of Equality
Addition Property of Equality
4. Meredith and Molly go shopping. Meredith buys a shirt for $10 and two pairs of pants for $10 each. She has $15 left over. Molly buys a dress for $50 and two packs of cards. If Molly started with $20 more than Meredith, and if Molly spent all her money, how much does one pack of cards cost?
$15
$7.50
$6.50
$2.50
5. Tobin rows
2
miles per hour faster than her opponent. If it takes Tobin
30
minutes to finish a race, and it takes her opponent
45
minutes to finish the same race, how fast does Tobin row?
4
mph
5
mph
6
mph
30
mph
6. Greg receives the following scores on his math tests:
{90, 83, 78, 95}
. What is the minimum score he needs on the last math test in order to get an
85
average in the class?
79
83.5
85
94
7. Solve for
x
in
3
x
+ 2≤ 
x
 2
.
x
≤  1
x
≥  1
x
≤ 0
x
≥  2
8. What inequality does the following graph represent?
x
≤2
x
≠2
x
< 2
2 <
x
9. Solve for
y
in

y
+ 6 <  4
y
.
y
<  2
y
>  2
y
< 2
y
> 2
10. Name all the members of set
A
:
A
= {1, 2, 9}
A
= { 1, 0, 1, 2, 9}
A
= { 12, 1, 2, 3, 5, 8, 9}
A
= { 12, 1, 0, 1, 2, 3, 5, 8, 9}
11. If
P
= {2, 3, 0, 8, 7, 1}
and
Q
= {0, 1, 6, 8, 3, 2}
, what is
Q
∩
P
?
Q
∩
P
= {2, 3, 0, 8, 7, 1, 0, 1, 6, 8, 3, 2}
Q
∩
P
= { 3, 2, 1, 0, 1, 2, 3, 6, 7, 8}
Q
∩
P
= { 3, 2, 0, 2, 3, 8}
Q
∩
P
= {0, 8}
12. What inequality does the following graph represent?
x
< 2∩
x
≥ 0
x
≤ 2∩
x
> 0
x
< 2∪
x
≥ 0
x
≤ 2∪
x
> 0
13. Compute
3× 4  5× 15    2
.
47
43
43
47
14. Solve for
x
in
4
x
 3 =  16
.
x
= 1
x
=  7, 1
x
=  1, 7
There are no solutions.
15. Solve for
y
in
6    3
y
+ 1 = 8
.
y
=  1
y
= 1
y
=  2
There are no solutions.
16. If Marsha grabs one shirt from a drawer containing
2
white shirts,
6
black shirts, and
8
striped shirts, what is the probability that she will grab a black shirt?
17. What is the probability of an event if the probability of its complement is
?


18. The mean of
{5, 6
x
 1, 12,
and
 2}
is
8
. What is
x
?
x
=
x
= 2
x
= 3
x
=
19. The median of
{2, 3, 6,
x
, 11, 2}
is
4.5
. Which of the following numbers could be a value of
x
?
x
= 1
x
= 3
x
= 4.5
x
= 6
20. The mode of
{2, 8, 9, 8, 4, 4, 8,
x
}
is 8. Which of the following could
not
be a value of
x
?
2
4
8
9
21. Which of the following ordered pairs
(
x
,
y
)
is a solution to
xy
= 3
x
 9
?
(6, 1.5)
(1.5, 6)
(3, 3)
(0,  9)
22. Which of the following could be a graph of
y
 3 = 2
x
?
A
B
C
D
23. What is the
x
intercept of
y
 6 = 3(
x
+ 2)
?
( 2, 6)
(0, 12)
( 4, 0)
(0, 0)
24. What is the slope of the line that passes through
( 2, 4)
and
(7, 1)
?

3
3
25. What is the slope of the line given by the equation
6
y
 3
x
= 12
?
2

2
26. Which equation describes the following graph?
y
=
x
 1
y
+ 2 =  (
x
 1)
y
 2 =  (
x
 1)
y
 2 =  (
x
+ 1)
27. What is
y
 4 =
(
x
 2)
in general linear form?
y
=
x
+ 3
2
x

y
=  3
x
 2
y
=  3
x
 2
y
=  6
28. What is
4
x
 3
y
= 8
in slopeintercept from?
y
=
x
 2
y
=
x

y
= 
x
+
y
=
x
 8
29. If
y
varies directly as
x
, and
y
= 6
when
x
= 9
, which of the following equations describes this variation?
y
=
x
y
=
y
=
x
xy
= 45
30. If
y
varies directly as
x
, and
y
= 7
when
x
= 14
, what is
x
when
y
= 18
?
x
=
x
= 9
x
= 12
x
= 36
31. If
y
varies inversely as
x
, and
y
= 4
when
x
= 2
, which of the following equations describes the variation?
xy
=
y
= 2
x
xy
= 2
xy
= 8
32. Solve the following system of equations for
(
x
,
y
)
:
x
+
y
=
5
2
x
 3
y
=
5
( 1, 1)
( 1, 6)
(3, 2)
(2, 3)
33. Solve the following system of equations for
(
x
,
y
)
:
4
x
+
y
=
0
2
x
+ 5
y
=
22
( 4, 1)
( 1, 4)
(1,  4)
(4,  1)
34. Which statement is true about the system:
4
y
 5
x
=
16
y
=
+ 4
The system is consistent and dependent.
The system is inconsistent and dependent.
The system is consistent and independent.
The system is inconsistent and independent.
35. Which of the following is an inconsistent system?
3
x
+ 4
y
= 18
x
= 2
6
y
+ 3
x
=  6
y
= 
x
 6
3
x
+ 4
y
= 6
4
y
= 6  3
x
5
x
+ 6
y
= 7
5
x
 6
y
= 7
36. Simplify and rationalize the denominator:
37. Simplify and rationalize the denominator:
×
38. Simplify
.
5
xz
15
xy
225
x
^{2}
y
^{2}
15
x
^{2}
y
39. Simplify
(
x
^{2}
)(4
x
) + ( 6
x
^{2}
)
^{3}

.
216
x
^{6}
+4
x
^{4}
+4
x
^{3}
216
x
^{6}
+4
x
^{3}
+4
x
^{2}
216
x
^{5}
+4
x
^{3}
+4
x
^{3}
216
x
^{5}
+4
x
^{4}
+4
x
^{3}
40. Write the answer in scientific notation:
4.5×10
^{1}
7  5.6×10
^{1}
6
1.1×10
^{1}
1.1×10
^{1}
6
1.1×10
^{1}
7
3.94×10
^{1}
7
41. Write the answer in scientific notation:
(3.0×10
^{5}
)×(1.5×10
^{9}
)
4.5×10
^{}
45
4.5×10
^{4}
1.5×10
^{4}
1.5×10
^{1}
4
42. Write the answer in scientific notation:
(7.5×10
^{6}
)÷(2.5×10
^{3}
)
3.0×10
^{18}
3.0×10
^{9}
3.0×10
^{3}
3.0×10
^{2}
43. What is the degree of the polynomial
5
x
^{6}
y
^{2}
+2
x
^{7}
+3
x
^{2}
+
xyz
^{5}
?
5
4
7
8
44. Simplify
5
x
^{2}
y
( 3
x
 2
xy
+
x
^{2}
y
)
.
15
x
^{2}
y
 10
x
^{2}
y
^{2}
+5
x
^{3}
y
^{2}
15
x
^{3}
y
 10
x
^{3}
y
+ 5
x
^{4}
y
15
x
^{3}
y
 10
x
^{3}
y
^{2}
+5
x
^{4}
y
^{2}
25
x
^{2}
y
+ 5
x
^{4}
y
45. Multiply and simplify:
(4
x
 3)( 2
x
+ 1)
6
x
^{2}
+ 4
8
x
^{2}
+ 10
x
 3
8
x
^{2}
 2
x
 3
8
x
^{2}
+ 10
x
 3
46. Factor
x
^{2}
 10
x
 24
.
(
x
 6)(
x
 4)
(
x
 6)(
x
+ 4)
(
x
 12)(
x
+ 2)
(
x
 12)(
x
 2)
47. Solve for
x
in
x
^{2}
+ 6
x
+ 9 = 0
.
x
= 3
x
=  3
x
=  3, 3
No solutions.
48. Solve for
x
in
12
x
^{2}

x
 2 = 0
.
x
= 1,  5
x
=
, 
x
= 9,  9
x
=
, 
49. How many times does the graph of
y
=  5
x
^{2}
+ 6
x
 2
cross the
x
axis?
0
1
2
Infinitely many times.
50. Complete the square in the equation
y
= 8
x
^{2}
+ 8
x
+ 1
.
y
= 8(
x
+ 1)
^{2}
+ 1
y
= 8(
x
+
)
^{2}
 1
y
= 8(
x
+
)
^{2}
 1
y
= 8(
x
+
)
^{2}
+
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