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Algebra
Review
1.
Evaluate
the
expression
2
2b
3a
+
when
a
=
-3
and
b
=
-4.
A)
2
1
-
B)
2
17
-
C)
2
1
D)
2
17
2.
Simplify:
6
-4
3+5·
A)
17
B)
29
C)
16
D)
30
3.
Simplify:
5
2
2
2
6
+
·
-
A)
40
B)
18
C)
34
D)
12
4.
Evaluate:
x
y
-
-
6z
3x
if
x
=
2,
y
=
8,
and
z
=
–2.
A)
7
1
B)
7
1
-
C)
5
1
D)
5
1
-
5.
Simplify:
4)
14
2(-
-30
A)
–2
B)
2
C)
2
11
D)
2
11
-
6.
Use
the
distributive
property
to
simplify.
-
3(x-10)+
x
A)
-
+
30
4x
B)
-
-
30
4x
C)
-
+
30
2x
D)
-
-
30
2x
7.
Simplify:
8y
–
2
–
3(y
–
4)
A)
11y
–
6
B)
5y
–
6
C)
5y
–
14
D)
5y
+
10
8.
Write
the
fraction
in
lowest
terms:
2
4
2 3
c 24ab
bc 36a
A)
3
2
2a
3b
B)
2
3
3a
2b
C)
3
2
2b
3a
D)
3
2
3b
2a
9.
Solve
for
x
:
3
1
6
(
)
x
+
=
-
A)
-
2
B)
-
3
C)
1
D)
7
3
10.
Add
the
polynomials:
b
a
b
a
7
5
3
2
-
+
+
A)
b
a
4
7
-
B)
b
a
4
7
+
C)
ab
3
D)
b
a
10
7
-
11. Subtract the polynomials: ( ) ( ) 2 2 3 11 4 9 2 2 + - - + - x x x x
A)
9
2
6
2
+
-
x
x
B)
13
2
6
2
+
-
x
x
C)
9
6
6
2
+
-
x
x
D)
13
6
6
2
+
-
x
x
12.
(
)(
)
=
+
-
+
4
2
2
2
x
x
x
A)
8
3
+
x
B)
8
8
4
2
3
+
-
+
x
x
x
C)
8
8
4
2
3
+
+
-
x
x
x
D)
8
8
3
+
+
x
x
13.
The
difference
of
twice
a
number
and
six
is
four
times
the
number.
Find
an
equation
to
solve
for
the
number.
A)
2x
–
6
=
4
B)
2x
–
6
=
4x
C)
2x
+
6
=
4x
D)
2x
–
6
=
x
+
4
14.
Expand:
(
)
2
3
2
-
x
A)
9
4
2
-
x
B)
9
4
2
+
x
C)
9
12
2
2
+
-
x
x
D)
9
12
4
2
+
-
x
x
15.
Which
of
the
following
numbers
is
the
smallest?
A)
4
3
-
B)
2
3
-
C)
-1
D)
3
2
-
16.
Which
of
the
following
is
the
largest?
A)
2
5
-
B)
2
-5
C)
2-5
-
D)
5
2-5
+
-2
17.
Solve:
-8
-5)£
x
3(x
A)
2
7
£
x
B)
7
2
£
x
C)
-1
£
x
D)
-1
³
x
18.
A
flower-bed
is
in
the
shape
of
a
triangle
with
one
side
twice
the
length
of
the
shortest
side
and
the
third
side
15
feet
longer
than
the
shortest
side.
If
the
perimeter
is
100
feet
and
if
x
represents
the
length
of
the
shortest
side,
find
an
equation
to
solve
for
the
lengths
of
the
three
sides.
A)
x
+
2x
+
x
+
15
=
100
B)
x
+
15
=
2x
C)
x
+
15
+
2x
=
100
D)
x
+
2x
=
x
+
115
19.
If
John
has
$50
more
money
than
Mary
and
you
choose
to
represent
John’s
amount
of
money
as
X
how
should
you
represent
Mary’s
amount
of
money
in
terms
of
X?
A)
X
+
$50
B)
X
-
$50
C)
$50
–
X
D)
$50·
X
20.
Multiply:
(
)
2
-3
-5x
3x
2x
A)
6x
5x
6x
2
3
-
-
B)
3
-3
-
5x
6x
C)
6x
2
3
-3x
-10x
D)
6x
6x
2
3
-
-10x
21.
Divide:
7m
7m 28m 14m 8 2 + -
A)
7m
28m
2m
8
+
-
B)
7
+1
-
4m
2m
C)
7
4m
2m-
D)
m
+
-
8
2
4m
2m
22.
Factor
completely:
2
3
4
4x
20x
12x
+
-
One
factor
is:
A)
4
4x
B)
+1
3x
C)
-1
x
D) 2 +1 - 5x 3x
23.
Factor
completely:
36
2
+
-12x
x
One
factor
is:
A)
6x
B)
-6
x
C)
-12
x
D)
+3
x
24.
Factor
completely:
21
2
-
+14x
7x
One
factor
is:
A)
7x
B)
+1
x
C)
-3
x
D)
+3
x
25.
Solve:
0
2
=
-10
-3x
x
One
solution
is:
A)
x
=
10
B)
x
=
1
C)
x
=
–2
D)
x
=
2
26.
Solve:
0
2
=
-5x
2x
The
solutions
are:
A)
x
=
0
B)
x
=
0,
x
=
5
C)
x
=
0,
x
=
–5
D)
x
=
0,
2
5
=
x
27.
Simplify
and
reduce:
2
+18
-12
9x
3x
A)
6
-2 x
B)
3
2
-
3x
C)
3
2 + x
D)
3
2 - x
28.
Given
the
equation
–2x
+
3y
=
12,
find
the
missing
value
in
the
ordered
pair
(–
3,___)
A)
–6
B)
–2
C)
6
D)
2
29. What are the coordinates of the x-intercept in the graph below?
-2 -1 0 1 2 3
2
1
Y
X
A)
(-1,2)
B)
(0,-2)
C)
2,0)
(-
D)
(0,1)
30.
Graph
the
line
3x
+
y
=
6.
A)
B)
C)
D)
31.
Solve
and
simplify
if
possible:
9
2
-3
-
-3
x
x
x
=
A)
x
x
3
-
-3
B)
-1
C)
3
+
x
D)
3
-
x
32.
Solve
the
following
system
of
equations
for
the
y-value:
7
=13
=
+
+2y
2x
2y x
A)
2
1
=
y
B)
6
=
y
C)
5
=
y
D)
4
13
=
y
33.
=
-
2
2 5
3a 6a
A)
2
3
6a
B)
3a
3
C)
2
1
6a
D)
2
4
6a
5a -
34.
3b
9b
2
-3b
=
A)
2
-1
9b
B)
-1
3b
C)
-1
b
D)
9b
35.
The
DoBee.Com
Corporation
has
5
more
than
three
times
as
many
female
as
male
supervisors.
If
“x”
represents
the
number
of
male
supervisors
write
an
expression
that
would
represent
the
total
number
of
female
supervisors
in
terms
of
“x”.
A)
x
+
5
B)
3x
+
5
C)
4x
+
5
D)
9x
36. Which of the following is not an equivalent statement?
A)
÷
ø
ö
+
øè
öæ
è
æ
-
=
-
5
֍2
5
ç2
25
4
2 b b b
B)
(
)
3
2
2
5
-3
=
x
x
-3x
x
C)
(
)
7
3
4
x
x
=
D)
4
1
x x =
-4
37.
Charles
needs
enough
fencing
to
enclose
a
rectangular
garden
with
a
perimeter
of
140
feet.
If
the
width
of
his
garden
is
to
be
30
feet,
write
the
equation
that
can
be
used
to
solve
for
the
length
of
the
garden.
A)
x
+
30
=
140
B)
2x
+
30
=
140
C)
2x
+
60
=
140
D)
140
–
x
=
60
38.
Which
one
of
the
following
ordered
pairs
is
NOT
a
solution
for
the
equation:
3x
+
y
=
12?
A)
÷
ø
ö
ç
è
æ
2
1
,10
2
1
B)
(6,2)
C)
(12,
-24)
D)
(2,6)
39.
For
what
value(s)
of
x
will
each
expression
be
undefined?
x
x
x
2
2
4
6
+4x
+
+
-
A)
6
B)
-2
C)
-2
and
3
D)
2
and
-3
40.
Which
of
the
following
is
a
factor
of
both
expressions?
2
2
-5 +
-5
+
3x
2x
4x x
A)
+5)
(x
B)
-5)
(x
C)
-1)
(x
D)
-3)
(x
Solutions
Elementary
Algebra
Sample
Items
1.
B
Evaluate
the
expression
2
2b
3a
+
when
a
=
-3
and
b
=
-4
2
2
2
-17
-8 + -9
2(-4) 3(-3)+
2.
B
Simplify:
6
-4
3+5·
29
4
4
4
= 33-
- 3+30
6- 3+5·
3. C Simplify: 5 2 2 2 6 + · -
34 2
6
2 6
2 2 6 5
= +32
+32 -4
+32 -2·
+ -2·
4.
A
x
y
-
-
6z
3x
if
x
=
2,
y
=
8,
and
z
=
–2.
2
2
6
(8) 3
=1
-
-
-2
-8
(-2)
(2)-
5.
B
Simplify:
4)
14
2(-
-30
2
4)
14
=
-8
-16
2(-
-30
6.
C
Use
the
distributive
property
to
simplify.
-
3(x-10)+
x
+30
-
+ +30
-10)+
2x
x -3x
x -3(x
7.
D
Simplify:
8y
–
2
–
3(y
–
4)
2
2
+10
+12 -
-4) -
5y
-3y 8y
-3(y 8y
8.
C
Write
the
fraction
in
lowest
terms:
2
4
2 3
c 24ab
bc 36a
3
2
3
0 2
2 4
2 3
2b
3a
2b
c 3a
2b
c 3a
c 24ab
bc 36a
4-1
2-2 3-1
9.
B
Solve
for
x
:3(x
+1)
=
-6
3
3
-3
=
-9
=
-9 =
-(3) -6 (3)= +3-
-6 = +3
-6 +1)=
x
3x
3x
3x
3x
3(x
10.
A
Add
the
polynomials:
5a
2a
-7b
+
+3b
4b
7a
7)b 5)a
3b 2a
-
(3- + (2+
-7b +5a +
11.
A
Subtract
the
polynomials:
(
)
(
)
2
2
+2
-
-
+11
-
2x
3x
4x
9x
(
)
(
)
9
2
2
2
2 2
+
- +
+2 - +11 -
-2x 6x
+2x 11-3x -4x 9x
-2x 3x 4x 9x
12.
A
)
4
2
+
+
-2x
2)(x
(x
)
4
(x
3
2 3
2 2 3
2
+8
+8 +
+8 - + +
+ -
x
+0x 0x x
4x 2x 4x -2x x
2x +2)(x
13.
B
The
difference
of
twice
a
number
and
six
is
four
times
the
number.
Find
an
equation
to
solve
for
the
number.
4x 2x Therefore
equal
means
is
subtract,
means
Difference
=
-6
14.
D
Expand:
2
-3)
(2x
2
2
2
+9
+9 -
-3)
-3)
-12x 4x
-6x 6x 4x
-3)(2x (2x
(2x
15.
B
Which
of
the
following
numbers
is
the
smallest?
Make
all
of
the
numbers
have
common
denominators
and
compare.
12
9
4
3
-
=
-
numerator
smallest
the
-18is
since
number
smallest
the
is
This
12
18
2
3
®
-
=
-
12
12
-
=
-1
12
8
3
2
-
=
-
16.
C
Which
of
the
following
is
the
largest?
Solve
each
absolute
value
and
compare
results.
Remember
absolute
value
is
always
positive.
3 3 5 = = -2
3
2
=
-3
=
-5
7
7
=
-
=
-5
-2
?
This
is
the
largest
6
3
3
5
=
3+
=
-3
+
=
2-5
+
-2
17. A Solve: -8 -5)£ x 3(x
2
7
2
7
2
7
£
£
£
-8+15 £ +15 -15
-8 £ -15
-8 - £ -15 -
-8 £ -15
-8 -5)£
x
2x
2x
2x
2x
x x x 3x
x 3x
x 3(x
18.
A
A
flower-bed
is
in
the
shape
of
a
triangle
with
one
side
twice
the
length
of
the
shortest
side
and
the
third
side
15
feet
longer
than
the
shortest
side.
If
the
perimeter
is
100
feet
and
if
x
represents
the
length
of
the
shortest
side,
find
an
equation
to
solve
for
the
lengths
of
the
three
sides.
2x
x+15
x x+2x+x+15=100
19.
B
If
John
has
$50
more
money
than
Mary
and
you
choose
to
represent
John’s
amount
of
money
as
X
how
should
you
represent
Mary’s
amount
of
money
in
terms
of
X?
If
John
has
$50
more
than
Mary
than
Mary
must
have
$50
less
than
John.
Therefore
if
John
is
represented
by
X,
Mary
would
be
represented
by
X-$50.
20.
D
Multiply:
(
)
2
-3
-5x
3x
2x
(
)
6x
6x
3x
2x
2
3
2
- -10x
-3 -5x
21.
B
Divide:
7m
7m 28m 14m 8 2 + -
7
8 2
8 2
+1 -
= + -
= + -
4m 2m
7m
7m
7m
28m
7m
14m
7m
7m 28m 14m
22.
D
Factor
completely:
2
3
4
4x
20x
12x
+
-
.
One
factor
is:
(
)
2
2
2
3
4
+1
+
-5x
3x
4x
4x -20x 12x
Therefore the correct listed factor is 2 +1 -5x 3x
23.
B
Factor
completely:
2
+
-12x
x
36.
One
factor
is:
2
-6)
+36
-6)(x
(x
-12x x
Therefore the correct listed factor is - x 6.
24.
D
Factor
completely:
2
-
+14x
7x
21.
One
factor
is:
(
)
7
2
2
-1) +
-3
-21
3)(x 7(x
+2x x
+14x 7x
Therefore
the
correct
listed
factor
is
+
x
3.
25.
C
Solve:
0
2
=
-10
-3x
x
One
solution
is:
5 or x
0 or 0 2
0
0 2
= -2 =
= -5 = +
= -5) +
= -10
x
x x
2)(x (x
-3x x
Therefore
the
correct
listed
solution
is
–2.
26.
D
Solve:
0
2
=
-5x
2x
.
The
solutions
are:
2
5
x
5 2x
0 or 0
0
0
=
=
= -5 =
-5)=
=
2x x
x(2x
-5x 2x
Therefore
your
answers
are
2
5
and
0
.
27.
D
Factor
and
reduce:
2
+18
-12
9x
3x
(
)
3
2)
2)
2)
2)
4
3
2
2
-
=
+
-
+
=
+
-
=
+18
-12
(x
9(x
2)(x
3(x
9(x
x
9x
3x
28.
D
Given
the
equation
–2x
+
3y
=
12,
find
the
missing
value
in
the
ordered
pair
(–
3,___).
Substitute
the
“-3”
into
the
equation
for
x
and
solve
for
y.
2
6
=
=
=12 6+
=12 2(-3) -
=12 +
y
3y
3y
+3y
3y -2x
29.
C
The
x-axis
is
the
horizontal
axis.
The
line
intersects
the
x-axis
at
(-
2,0).
30.
C
Using
the
intercept
method
to
graph
a
line,
substitute
“0”
in
for
the
x
value
and
solve
for
y.
Then
substitute
“0”
in
for
the
y
value
and
solve
for
x.
Then
plot
these
point
and
draw
the
line.
(2,0) and (0,6) are intercepts
2 x 6
6 3x 6 0
6 3x 6 3(0)
= =
= = +
= +0 = +
y
y
y
31.
C
Solve
and
simplify
if
possible:
9
2
-3
-
-3
x
x
x
9
2
2
+3
=
-3
-3)
+
=
-3
-9
=
-3 - -3 x x
3)(x
(x
x
x
x
x
x
32.
A
Solve
the
following
system
of
equations
for
the
y-value:
7
=13
=
+
+2y
2x
2y x
2y 2x
7)
2y
2(x
-
2
-
by
multiply
7
=13
+
=13
=
+
=
+
+2y
2x
2y x
Now add the equations vertically
2
1
y
2 2 -
2y -
-1 2y -
=
-
-1
=
=
=13 +
-14
=
-
2y
2x
4y -2x
33.
D
=
-
2
2 5
3a 6a First find common denominators for your fractions.
2
2
2
2
4
numerators the Nowsubtract
4
2
2
2
and
5
6a
5a
6a x 3a 6a
5a
a
a
x
6a
-
= =
34.
B
3b
9b
2
-3b
Factor
the
numerator
3b
3b(3b
-1)
.
Now
reduce.
Answer
3b-1
35.
B
The
DoBee.Com
Corporation
has
5
more
than
three
times
as
many
female
as
male
supervisors.
If
“x”
represents
the
number
of
male
supervisors
write
an
expression
that
would
represent
the
total
number
of
female
supervisors
in
terms
of
“x”.
The
statement
“five
more
than”
indicates
adding
“5”
to
the
product
of
3x.
Answer
?
+5
3x
36. C Which of the following is not an equivalent statement?
÷
ø
ö
+
øè
öæ
è
æ
-
=
-
5
֍2
5
ç2
25
4
2
b
b
b
This
is
the
correct
factored
form
of
the
given.
(
)
3
2
2
5
-3
=
x
x
-3x
x
This
is
the
correct
factored
form
of
the
given.
(
)
7
3
4
x
x
=
This
is
incorrect.
(
)
12
3
4
x
x
=
4
1
x x =
-4 This is correct
37.
C
Charles
needs
enough
fencing
to
enclose
a
rectangular
garden
with
a
perimeter
of
140
feet.
If
the
width
of
his
garden
is
to
be
30
feet,
write
the
equation
that
can
be
used
to
solve
for
the
length
of
the
garden.
2 lengths + 2 widths = perimeter Let the unknown length be “x”
=140 +60
(30)=140
+2
2x
2x
38.
B
Which
one
of
the
following
ordered
pairs
is
NOT
a
solution
for
the
equation:
3x
+
y
=
12?
The
solution
is
(6,2)because
when
substituted
into
the
equation
your
solution
is incorrect. 12 3 ¹ (6)+2
39.
D
For
what
value(s)
of
x
will
each
expression
be
undefined?
x
x
x
2
2
4
6
+4x
+
+
-
An
expression
is
undefined
when
the
denominator
equals
zero.
To
solve
set
the
denominator
equal
to
zero
and
solve
for
x.
2 or
0 2 - x 0or 3
0
0 2
= -3 =
= = +
-2)=
= -6 +
x x
x
+3)(x (x
x x
40.
C
Which
of
the
following
is
a
factor
of
both
equations?
2
2
-5 +
-5
+
3x
2x
4x x
Factor
both
equations
and
compare
results
2
-1)
-5
+
+5)(x
(x
4x
x
2
-1)
-5
+
+5)(x
(2x
3x
2x
The
matching
factor
is
(x-1)