Algebra 2 TIE’s
1. Which represents the expression below?
8x2  8
10 x 2  10 x
4  4x
5x2  5x
x+1
1 –x
1
–x – 1
1–x
-1
-1/2
1/2
2. Which represents the expression below?
8x2  8
10 x 2  10 x
4x  4
5x2  5x
x+1
x–1
1
–x – 1
1–x
-1
-1/2
1/2
3. Which represents the expression below?
8x2  8
10 x 2  10 x
4x2  4
5x2  5x
x+1
1 –x
1
–x – 1
1–x
-1
-1/2
1/2
4. Identify which of the following are factors of this polynomial.
5 x 4  7 x3  2 x 2
x
5.
x–1
5x - 2
x2
5x +2
x4
Identify which of the following are factors of this polynomial.
18x2  120 x  150
6
3x+5
3x-5
X+1
2
x-5
6. Simplify each expression. Drag the expressions to the empty fraction bar below. Be
sure you are answering in the most simplified form.
3
3

3(3v  1) 2v
Choices: 6v
(3v + 1)
2v
3
(6v - 18)
(3 - 7v)
(3 + 7v)
(3v - 1)
7. Simplify each expression. Drag the expressions to the empty fraction bar below Be
sure you are answering in the most simplified form.
3p
3p
p5
Choices:
(p – 4)
(p + 2)
8.
-3p
(p + 4)
(p + 5)
-6p
(p – 5)
2
Perform following operation, drag correct answer into the empty space:
(8  7i)(7  i) 
49  57i
63  41i
63  41i
27  3i
9. Which of the following binomials added together will represent the sum of 10i – 15?
3i-4
12i  3
4i-10
3i-1
-13i2-15
i2
10.
Identify all that are equivalent to 11i11 .
0  11i
11.
0  11i
11  0i
0i  11
Which of the following functions is linear?
f ( x)  2 x
f ( x)  x  18
f ( x)  x 2  13
f ( x)  4 x  7
2
f ( x)   x  11
3
12.
What is (are) the solution(s) to 8x  6  2 x ? ________ _________
1
13.
Solve 2 x - 1 = 5
3

14.
State the property used in each step for the following equation
3(x – 2) + 5x = 10
3x – 6 + 5x = 10
5x + 3x – 6 = 10
8x – 6 = 10
8x = 16
x=2
Given
____________________
____________________
Simplify
____________________
Division Property of Equality
Commutative Property of Addition
Inverse Property of
Addition
Identity Property of Addition
Addition Property of Equality
Distributive Property
Associative Property of Addition
15. Circle the radical expression(s) that simplify to 4x 2 y ? More than one answer may be
correct
3
8x 2 y 4
x 3 12 x5 y 6
8x3 y 3
16x 4 y 2
2 x 4 x2 y 2
3
64x 6 y 3
16. Circle the graph(s) that show a function where the Domain : (, )
More than one answer may be correct.
17. Choose all of the following that are equivalent to -1:
i 32
i6
i
i12
i3
18. Choose all of the following that illustrate the associative property?
53  35
3   4  6  3  4  6
 4  2  9  4  2  9
2  x  3  2 x  6
 a  b  c  c   a  b
19. The steps used to simply an expression are shown. Identify the missing property
that shows each step.
STEPS
JUSTIFICATION
43  2i   6i
GIVEN
12  8i  6i
12  8i  6i 
12  14i

Simplify
Properties:
Distributive Property
Commutative Property of Addition
Associative Property of Addition
Inverse Property of
Addition
Identity Property of Addition
Closure Property of Addition
20. What is the domain of this function?
f  x  x  3 1
21. Which of the following function(s) have the same x – intercepts?
f  x  3 x  2
f  x   x2  4
f  x   2x  2
f  x   x 4  16
f  x  x  2
22. Indicate the intervals where the graph of f  x    x  1  x  1 is only decreasing
2
2
throughout the interval.
  x  1
1  x  0
0  x 1
1 x  
  x  
23. The steps used to simply an expression are shown. Identify the missing property
that shows each step.
STEPS
JUSTIFICATION
a   2   a 
Given
a   a   2
 a   a   2
02
2
Properties:
Identity
PPPrProperty
24. Which of the following function(s) have the same domains?
I
f  x  3 x  2
II
f  x   1/ x
III
f  x   2x  2
IV
f  x  x  2
V
f  x  x  2
25. Indicate the intervals where the graph is only increasing throughout the interval.
I
  x  1
II
1  x  1
III
1 x  
IV
2 x
V
2  x  2
VI
  xx22

26.
Identify the equation of the horizontal and vertical asymptotes of p  x  
Horizontal
Asymptote
Vertical
Asymptote
Solutions:
y=2
x=2
1
x=1
y=
2
y=3
27.
x=
3
2
Which of the following function(s) have the same range?
I
f  x   3x  7
II
f  x  3 x  2
III
f  x  x 1
IV
f  x  x
2x  3
x 1
28. Indicate the intervals where the graph is only decreasing throughout the interval.
I
  x  1
II
1  x  1
III
1 x  3
IV
3 x 
V
2  x  2
VI

2
2  xx
  x  2
29.
Identify the equation of the horizontal and vertical asymptotes of
2x  5
p  x 
3x  1
Horizontal
Asymptote
Vertical
Asymptote
Solutions:
y=
1
y=
2
y=
3
3
x=
1
3
x=
2
2
x=
3
3
3
2
30. Which of the following function(s) have the same range?
I
f  x  x  4
II
f  x   x2  4
III
f  x   x4
IV
f  x   x3  4
V
f  x  x  4
31.
Indicate the intervals where the graph is only increasing throughout the interval.
I
  x  2
II
2  x  1
III
1  x  1
IV
1 x  2
V
2 x
VI

 xx  2
32.
Directions: Click on the area that should be shaded.
y  x  3
1.
+11
+10
+9
+8
+7
+6
+5
+4
+3
+2
+1
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
+1
+2
+3
+4
+5
+6
+7
+8
+9
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
33. Click and drag the appropriate characteristic to the correct box.
Discriminant of
Type of Solution
the equation
for
Characteristics of graph
ax2  bx  c  0
y  ax2  bx  c
ax2  bx  c  0
0
-13
20
one real solution
no x-intercepts
two real solution
one x-intercept
no real solution
two x-intercepts
+10 +11
34. Click on the solution(s) to the system of equations whose graphs are shown below.
+11
+10
+9
+8
+7
+6
+5
+4
+3
+2
+1
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10 +11
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
35. Determine the number of solutions for the system of quadratic equations below.
x2  5x  7  0
2 x2  2 x  3  0
Answer _____
36. Which ordered pairs are solutions to the inequality y >
(5, 1 )
(0, 0 )
(3, 0 )
(5, 3 )
(3, 5 )
(4, -1 )
|x–3|+2?
37. What value of x makes
3
- 7 = 8 true?
38. Select the region that represents the solution to the inequality
y>
|x+4|-1
39. Select the appropriate characteristics of the graph of y  2 x  1  3
Vertex
1,  3
 1,3
Direction of
opening
Transformation
UP
DOWN
Dilation by 2
Dilation by -2
Slope of sides
m  2
m
1
2
 1,  3
1,3
Dilation by 1/2
Dilation by -1/2
m  1
m  3
40. Identify all the solutions to the systems. (Estimate to the nearest tenth.)
41. List all of the solutions to the function:
42. Select all of the functions below that have the same end behavior as the function
shown above.
a.
b.
d.
e.
43. Label the mean and three standard deviations:
c.
f.
44. Indicate the intervals where the graph of
f  x    2 x3  3x2  12 x  6
Directions: Click on a box to choose
each interval you want to select. You
must select all correct intervals.
is only decreasing throughout the interval.
45. Identify the equation of the horizontal asymptote
and the equation of the vertical asymptote of
3x  2
f  x 
x 1
Directions: Click and drag each selected
equation to the correct box.
46. Identify each function with the same range as
g  x   x  5
47. Circle the zero(s) of the function graphed below.
9 y
8
7
6
5
4
3
2
1
-1
-9-8 -7 -6 -5-4 -3 -2 -1
-2
-3
-4
-5
-6
-7
-8
-9
1 2 3 4 5 6 7 8 9
x
Directions: Click on a box to choose
each interval you want to select. You
must select all correct functions.
48. Circle the zero(s) of the function graphed below.
4 y
3
2
1
-1
-9-8 -7 -6 -5-4 -3 -2 -1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
x
1 2 3 4 5 6 7 8 9
49. Circle the zero(s) of the function graphed below.
9 y
8
7
6
5
4
3
2
1
-1
-9-8 -7 -6 -5-4 -3 -2 -1
-2
-3
-4
-5
-6
-7
-8
-9
x
1 2 3 4 5 6 7 8 9
50. Circle the turning point(s) of the function graphed below.
9 y
8
7
6
5
4
3
2
1
-1
-9-8 -7 -6 -5-4 -3 -2 -1
-2
-3
-4
-5
-6
-7
-8
-9
1 2 3 4 5 6 7 8 9
x
51. Circle the turning point(s) of the function graphed below.
4 y
3
2
1
-1
-9-8 -7 -6 -5-4 -3 -2 -1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
x
1 2 3 4 5 6 7 8 9
52. Circle the turning point(s) of the function graphed below.
9 y
8
7
6
5
4
3
2
1
-1
-9-8 -7 -6 -5-4 -3 -2 -1
-2
-3
-4
-5
-6
-7
-8
-9
x
1 2 3 4 5 6 7 8 9
53. Which of the following are solutions of the following polynomial function?
f(x) = x4 + x3 – 4x2 – 12x
x = –3
x = –1
x=2
x = –2
x=1
x=0
54. Which of the following are x intercepts of the following polynomial function?
g(x) = x4 + 2x2 – 3
(–3,0)
(–1,0)
(1,0)
(3,0)
(0,0)
55. Which of the following are factors of the following polynomial function?
h(x) = x3 – 5x2 + 6x
(x – 2)
x
(x + 2)
(x –1)
(x+1)
(x - 3)
56. Which of the following functions has a solution of x = 3?
f(x) = x3 + 2x2 – 9x – 18
f(x) = x3 + 9x2 + 27x + 27
f(x) = 2x3 – 18x2 + 18x + 36
f(x) = x3 – 27
f(x) = 3x3 + 9x3 – 12x – 36
57. Which of the following functions has a zero at x = 1?
g(x) = 5x7 + 13x4 – 12x2 – 10
g(x) = x3 – 5x2 + 6x + 3
g(x) = 9x4 + 3x2 – 10x – 2
g(x) = x3 – 4x2 + 8x – 5
g(x) = x2 + 2x + 1
58. Circle the asymptotes of the following function.
f ( x) 
x = –1
x=1
2x  1
x 1
x=2
y=1
y=2
y=0
y=1
59. Circle the asymptotes of the following function.
x2  4 x  3
g ( x)  2
x  x  2
x = –1
x=1
x=2
60. Circle the asymptotes of the following function.
f ( x) 
x = –3
x  2
( x  3)( x  2)
x=2
x=3
y=0
y=2
x=2
y=4
61. Circle the asymptotes of the following function.
4 x2  4
g ( x)  2
x  4
x = –2
x = –1
x=1
62. Circle the asymptotes of the following function.
f ( x) 
x=1
x=2
2
 1
x  3
x=3
y=1
y=2
63. Circle the asymptotes of the following function.
g ( x) 
x = -3
x = -1
x=1
1
 1
x  3
x=3
y=1
64. Circle the asymptotes of the following function.
h( x ) 
x = -3
x = -2
5
 3
x  2
x=2
y = -3
y = -2
65. Which of the following relations represents a direct variation?
y  3x
y  x  3
y
 3
x
y 
x
3
y 
3
x
y 
x
4
66. Which of the following relations represents a direct variation?
y  x  4
y 
4
x
y
 4
x
y  4x
67. Which of the following relations represents an inverse variation?
y  2x
xy  2
2y  x
y 
2
x
y 
x
2
68. Which of the following relations represents an inverse variation?
y   5x
xy   5
5y  x
y 
5
x
y 
x
5
69. The graph summarizes the test scores for 22,000 students. The data is
normally distributed with   84 , and   2.4 . Shade the regions under the
curve where only the data for approximately the middle 14,960 students are
located.
76.8
79.2
81.6
84
86.4
88.8
91.2
70. The following graph summarizes the ages of death of 1,213 American Chestnut
Trees. The mean of the population is 3.2 years, and the standard deviation is
0.4 years. Shade the regions under the curve where approximately the 194
longest living trees are located.
2.0
2.4
2.8
3.2
3.6
4.0
4.4
71. The graph below summarizes the heart rates (beat per minute) for a
population of healthy students. The date is normally distributed with a mean
of 70 and a standard deviation of 9 beats per minute. Shade the regions under
the curve that are within
43
2
52
of the mean.
61
70
79
88
97
72. The graph summarizes the test scores of 25000 students. The data is normally
distributed with a mean of 83 and a standard deviation of 3.5.
Shade the regions under the curve where only the data for
approximately 3963 of the lowest scores are located.
A
C
B
72.5
76
D
79.5
E
83
F
86.5
H
G
90
93.5
73.
Identify the factors of the function graphed below:
 x  3
 x  3
 x 1
 x 1
 x  5
 x  5
f  x 
74. Identify the function(s) that have the same range as f  x   x  4  3 .
f  x    x  4  3
3
f  x    x  4  3
2
f  x  3 x  4  3
f  x    x  4  3
4
f  x  x  4  3