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Honors Algebra 2
Chapters 1-2 Review
Name ____________________
Simplify using the ORDER OF OPERATIONS:
1.
( )
5•7 !2 5+1 ÷3
2.
(
)
12 ! "$20 ! 2 62 ÷ 3 • 22 %'
#
&
3.
(
!2 5 ! 9 ! 6 3 ! 7
State all SETS OF NUMBERS to which each of the following belong:
4.
8.
16
5.
3
9.
!3
6.
36
7.
! 81
11.
5
49
5.12121212…
10.
0
State the PROPERTY illustrated in each of the following:
Statement
Property
12.
a (3 + 2) = 3a + 2a
12.
13.
a (3 + 2) = a (2 + 3)
13.
14.
(2a )b = 2(ab)
14.
15.
7 x + 3x = (7 + 3) x
15.
16.
! 1$
! 1$
2# & 6 = 2 6 # &
" 2%
" 2%
()
16.
17.
! 1$
2# & 6 = 1 6
" 2%
17.
18.
1 !3a + (2a + 4) # = 3a + (2a + 4)
"
$
18.
19.
3a + (2a + 4) = (3a + 2a ) + 4
19.
20.
3a + (2a + 4) = 3a + (4 + 2a )
20.
21.
3a + (2a + 4) = (2a + 4) + 3a
21.
22.
3(9 + 4) = 3(9) + 3(4)
22.
()
)
2
Solve for y:
23.
12xy +
25.
4y
5x
5xy
+
=
=
11
24.
14xy
8
26.
!3y
28.
5
!
2 m
30.
6
!
x
!
Solve the following Equations.
27.
6
29.
(3d
3
31.
4
=
1
1
2
x
3x
!
6
+
9
)
4
=
=
( 4d
2
1
24
+
)
2
32.
2b
=
7
6x
=
9
(
3
!
3y
!
+
4
4
!
)
2
!
!
=
3
9
=
=
4
6b
+
1
Solve and Graph the solution to each of the following.
Write your answer on both inequality and interval notation.
33.
(
2 4m
1
!
)
(
3 m
+
4
+
)
"
6m
inequality __________________
interval ____________________
34.
!2
<
5t
+
3
<
!7
inequality __________________
interval ____________________
35.
! 3d
6
+
+
4
"
6
inequality __________________
interval ____________________
36.
! 2x
4
+
<
!6
inequality __________________
interval ____________________
37.
2x
+
4
!
6x
inequality __________________
interval ____________________
Honors Algebra 2
Chapter 2 Review
Name ____________________
38a) How can you determine if a function is linear?
38b) Are absolute value functions linear?
Determine if the following equations are linear. If not, explain why not.
() ( )
39.
6x + 5y = 4 ! x
42.
How can you determine if a relation is a function?
40.
()
41.
f x = x x +1
f x = mx + b
Determine whether each relation is also a function.
Then describe the relations (include domain, range, discrete, continuous, linear, etc.).
{(!2, ! 3), (!1, ! 1), (0, 1), (0, 3), (1, 5)}
43.
Domain: ________________
Range: ________________
Function:
Discrete Continuous
Yes
No
45.
44.
y=4
Domain: ________________
Range: ________________
Function:
Discrete Continuous
Yes
No
46.
Domain: ________________
Domain: ________________
Range: ________________
Function:
Yes
No
Range: ________________
Discrete Continuous
Function:
Yes
No
Discrete Continuous
47.
What are the characteristics of the standard form of an equation?
48.
For ANY function , how do you find x and y intercepts?
Put each of the following equations in Standard Form then find the x- and y-intercepts.
49.
6y =
4
3
x + 2
50.
2
5
y + 3x = ! 8
51.
4x = 7 !
2
5
x
52.
Write the equation of a line in standard form that passes through the following points:
!8, 3 and 2, ! 2 .
53.
Write the equation of a line in standard form of a line parallel to the line in #52 that passes
(
)
(
)
( )
through point 6, 2 .
54.
Write the equation of a line in slope intercept form that passes through the following points:
(2, 3) and (!8 , 3) .
Is this line a function?
55.
Write an equation of a line perpendicular to the line in #54. Is this line a function?.
56.
Find the value of k if the line through the points k ! 9, 3k and 4 ! k, 5k + 2 is perpendicular
"
%
#
2&
(
( )
)
(
)
to the line containing $ !3, ! 5 ' and 6,5 .
( ) = 3x
Given:
57.
(
f x !6
f x
)
2
! 1
58.
and
" !3 %
g$ '
# 4&
60. If asked to find g(0), what are you really
finding in relation to the graph?
( ) = 2x $# 23 ! x '& ,
"
g x
59.
%
find:
( )
f 5x
61. If asked to find g(x)=0, what are you
really finding in relation to the graph?
Graph each of the following.
( ) = ! 41 x
63.
3x ! 2y + 8 > 0
65.
3y ! 9 x " 6
62.
f x
64.
2y ! 12 > 4y
66.
Graph an absolute value function that is reflected over the x-axis, vertically stretched
by a factor of 3, is shifted left 5 and up 4 units. Find the x intercepts if possible.
! 2 + 5
Write the equation or inequality for each of the following.
67.
68.