Algebra II EOI Practice
PASS 1.1a: Convert expressions from radical notations to
rational exponents and vice versa.
1. Which expression is
1.1a equivalent to 3 a 2 
a.
3
a2
b.
2
a3
5. Which expression is the
simplified form of 7 x14 y35
1.1a
a. x2 y5
b. x7 y 28
c. x7 y5
d. x2 y 7
1
a6
c.
d. a6
6. Which expression is the
x5
simplified form of 5 15 
y
1.1a
2. Which expression is
1.1a
equivalent to
3
8x 6 
a. 2
b. 2x
c. 2x 2
d. 2x3
a.
x
y3
b.
x3
y5
c.
5
d.
x
5 y3
3. Which expression is
1.1a
3
4
equivalent to 16 
a. 4
b. 8
c. 12
d. 32
x
y3
7. Which expression is
1.1a
4. Which expression is
1.1a
equivalent to
1 
equivalent to a 2 b  
a. 2
b. 2
c. 2 2
d. 6
a. ab3
b. ab3
c. 3 a 2b4
d. 4 a2b3
Moore Public Schools
Algebra II EOI Practice
1
 

2 
Algebra II EOI Practice
8. Which expression is
equivalent to 6 a 2b3
11. What expression equals
1.1a
1.1a
4
1
a. a2b3
6
b. a3b2
a. 4 4 x
b. 4 4 4x
c.
4x
d. 4x
1
c. a3b 2
d.
1 1
a 3b 2
9. Which expression is
1.1a
3
equivalent to 25 2 
a. 125
b. 75
c. 15
d. 5
10. Which of the following is
not equal to 4 x8
1.1a
a. x2
b.
3
x6
4
c. x 8
d.
8
x4
Moore Public Schools
Algebra II EOI Practice
64 x 16 x4 
2
Algebra II EOI Practice
PASS 1.1b: Add, subtract, multiply, divide, and simplify radical
expressions and expressions containing rational exponents.
1. Which expression is equal
5. Which expression is equivalent
1.1b
1.1b
1

to 8 24  3 8 
to 83   


a.    
c. 4 12  
20
a.
3
b. 8 3   
d. 4 6   
b. 4
1
62
c.
1
d. 2412
1
1
6. What is 6 2  6 4 
1.1b
2. A rectangular shelf is
540 inches by 40 inches. Find
the area of the shelf.
1.1b
1
1
a. 68
c. 36 6
b.
a. 12 150 square inches
b. 12 6 square inches
c. 2000 square inches
1
36 8
d.
3
64
7. What is 5 4  5 8
1.1b
d. 60 6 square inches
a. -2
b. 2
3. What is the distance from point X to
point Z to point W?
c. -3
d. 3
1.1b
8. What is the simplified form of
4
1.1b
162
c. 34 2
d. 2 3 3
a. 3 2
b. 33 2
a. 15 2
b. 34
c. 43
d. 8 2
1.1b
4. A rectangular walkway is 6 11
1.1b
meters wide and 10 11 meters
long. What is the perimeter of
the walkway?
a.
b.
c.
d.
e.
16 11 meters
32 11 meters
60 11 meters
660 meters
Moore Public Schools
Algebra II EOI Practice

1

1




9. What is 3 53   4  53  
 
 
a.
1
353
b.
1
73
 1
 
 
 1
d. 12  53 
 
 
c.
3
7  53 
Algebra II EOI Practice
10. Simplify. 5x2 18 y  2 32 x4 y
13. If x and y are real numbers,
1.1b what is the simplified radical
1.1b
a. 13x 30 y
c. 3x 14 y
b. 13x 2 2 y
d. 7 x2 2 y
11. Multiply.
1.1b

2 34 5


form of x y
a. y 5 x 2
c. y 5 x2
b. y x5
d. y x5
14. What is the sum of
a. 4 3  8 15  16 5
b. 68 16 15
1

and 

3 25
 
a.
2
21
c.
2
33
b.
7
30
d.
11
90
c. 92  16 15
d. 92  16 15
15. The area of a square is 2 2  
1.1b
What is the length of a side of
the square?
12. Which expression is equivalent
14

to
2 5
1.1b
a.
2 1
c. 2 2 1
b.
2 1
d. 2 2 1
c. 56  14 5
b. 28 14 5 d. 56  14 5
Moore Public Schools
Algebra II EOI Practice

1
5 5
2
1.1b
a. 28  14 5
2
4
Algebra II EOI Practice
PASS 1.2a: Divide polynomial expressions by lower degree polynomials.


1. Divide x3  2x2  x  2 by  x 1 .
1.2a
a. x2  3x
c. x2  3x  2
b. x2  2x  3
d. x2  3x  2
6. What is the remainder when
4x3  2x2 10x 1 is divided by
1.2a
 x   
c. 119
d. 155
a. 61
b. 5
2. Use synthetic division to
simplify the expression below.
4 x3  x 2  117
x3
1.2a
7. What is the result of dividing
x3  6x  7 by x  2
1.2a
a. x2  2 x  2 
11
x2
b. 4x2 13x 156 d. 4x2 13x  39
b. x2  2 x  2 
3
x2
3. Use the Rational Roots
Theorem to give all possible
rational roots of the polynomial
equation 2x5  4x4  3x 10  0.
c. x2  2 x  2 
3
x2
d. x2  2 x  2 
11
x2
a. 4x 17 x  39 c. 4x 17 x  24
2
2
1.2a
1 5
a. 1, 2, 5, 10,  , 
2 2
b. 1, 2, 5, 10
c. 0, 1
d. 10
8. What is the result of dividing
3x3  7 x2  5 by x  1
1.2a
4. Find the quotient of
1.2a
x 2  6 x  5   x  5 


a. x  6 x
b. x  1
c. x  6x 1
d. x2  5x
5. Find the value of k that makes
1.2a
 x  4  a factor of
x3  kx2  33x  36.
a. -4
b. 4
Moore Public Schools
Algebra II EOI Practice
c. 2
d. 10
5
a. 3x2 10 x 10 
15
x 1
b. 3x2 10 x 10 
15
x 1
c. 3x2  4 x  4 
9
x 1
d. 3x2  4 x  4 
9
x 1
Algebra II EOI Practice
9. What expression is equal to
 4 y5  3 y 2 
12. What is the quotient when
6 x 2  7 x  2 is divided by
1.2a
5 y2

a. 4 y  2 y
5
1.2a
2x  1
a. 6 y 9  3 y 3  1
2
b. 6 y 4  3 y 2  1
4

b. y 3 
5

c.
5 3 5
y 
4
3
d.
4 3 
y 
5

c. 6 y 9  3 y 3
d. 6 y 4  3 y 2
13. A rectangular prism has a
volume of 8x3 14x2  x  2 and a
height of 2 x  1 Which
expression represents the area of
the base of the prism?
10. When 18 y12  9 y 6  3 y3 is divided
1.2a
by 3y 3 , the quotient is
1.2a
a. 6 y 9  3 y 3  1
b. 6 y 4  3 y 2  1
a. 4 x 2  5 x  2
c. 6 y 9  3 y 3
b. 4 x 2  5 x  2
d. 6 y 4  3 y 2
c. 4 x 2  9 x  4
d. 4 x 2  9 x  5
11. Which expression is equal to
1.2a
4 x 2 14 x3 11x



7 22 x 18 x 4
a.
3 3
x
4
b.
2
x
5
c.
1 4
x
4
d.
2
x
9
Moore Public Schools
Algebra II EOI Practice
6
Algebra II EOI Practice
PASS 1.2b: Add, subtract, multiply, divide, and simplify rational
expressions, including complex fractions.
1. Multiply and simplify.
5x2  25x x2  6 x  9
.

x2  2 x 15
30 x2
4. Simplify the complex fraction.
5
2
x
7
7
y
1.2b
a.
x3
6 x3
x x
6x
4
b.
c.
1.2b
x 3
6x
a.
2
d. none of the above
b.
2. Divide and simplify .
20 x3
4 x2

2
x3 x2 16 x  8x  16
5xy   2 xy 
14 xy
5 y  2 xy
7 x  7 xy
c.
7 xy
14 xy
d.
5 x  7 xy
2 y  7 xy
1.2b


5. Simplify.
1.2b
5x2  25x x2  6 x  9

x2  2 x 15
30 x2
a.
5 x  4
x2  x  4
c.
5
x2
a.
x3
6 x3
c.
x 3
6x
b.
5 x  4
x2  x  4
d.
 x  4
x2  x  4
b.
x4  x2
6x
d.
6 x2 19 x  9
31x2  2 x 15
6. Simplify.
3. Add and simplify the
1.2b
2x
2

expression. 2
x  36 5x  30
a.
b.
12 x 12
5 x  6
c.
1.2b
12 x 12
5 x  6
4  3 x  3
3x  3
d.
5  x  6  x  6 
5  x  6 x  6 
Moore Public Schools
Algebra II EOI Practice
6
4
 2
x  4 x 16
a.
10
c.
2
 x  4 x  4
6 x  20
 x  4 x  4
b.
6 x  24
x4 x4
10
x  x 12
d.
7. What is the sum
1.2b
7
a.
7 x2
7x
b.
3x 2  4 x
7x
2
3x 2  4 x 
7x 7x
c.
d.
3x 2  4 x
7 x2
3x 2  4 x
49 x2
Algebra II EOI Practice
8. What is the sum
1.2b
a.
x2  4
3x 2  x  2 
x2  4
b.
3x  x  2 
4
x


3x 2 3x 2  6 x
11. What is the simplified form of
x2  4 x  8
3x 2  x  2 
c.
x2  4 x  8
d.
3x  x  2 
9. What is the difference
1.2b
x4  1 
2
x  6 x  9 x2  9
a.
x 2  x  15
2
 x  3  x  3
b.
x  x  15
2
 x  3  x  3
x2  3x 18 
x2  36
1.2b
a.
x2
x6
c.
x3
x6
b.
x 3
x6
d.
x3
x6
12. What is the product
x2  3x 10 x 1


x2  6 x  5 x2  4
1.2b
c.
x 2  15
2
 x  3  x  3
d.
x  15
2
 x  3  x  3
2
a. x  2
b.
2
1
x2
c. x  2
d.
1
x2
13. What is the quotient
x2  5x  6
x

6

  x2   x  8 
1.2b
10. What is the simplified form of
the following complex fraction?
6
x2
1
3

4 x2
1.2b
24
a.
x3
b.
6
x5
Moore Public Schools
Algebra II EOI Practice
a. x 1
b.
6
c.
4 x 11
d.
x 8
x6
c.
x6
x 8
d. x 
14. What is the product
x2  7 x  44 x2 7 x  72


x2   x 16 x2   x  99
1.2b
24
x  14
8
a.
x
x2
c.
x4
x2
b.
x2
x4
d.
x 11
x9
Algebra II EOI Practice
15. Which expression is equal to
4 x2 14 x3 x



7  x 18x4
a.
b.
3 3
x
4
2
x
5
c.
d.
1.2b
1 4
x
4
2 2
x
9
16. What is the product of
x2  2 x  3 x2  25


x2   x  5 x2  x 12
b.
x 5
x
c.
x 3
x4
d.
x 5
x 
17. What is the quotient of
x2  4
x2  x  2


x2   x  3 x2   x  3
c.
x2
x3
b.
x2
x 1
d.
x 3
x 
c.
6 x2
x2  4 x  5
b.
5x
2x  4
d.
5x2  4
x2  4 x  5
a.
3x  
x  x
c.
3x  13
x2  x  6
b.
11x  7
x2  x  6
d.
11x  13
x2  x  6
2
21. What is the sum of
x 1
3x
and

x3
x4
1.2b
x
x 
5x2 3x
x 2  4 x 
20. What is the simplified form of
the following?
x  5 x 1

x 3 x  2
 x  3 x 1
 x  3 x 1
a.
a.
1.2b
1.2b
a.
3x
2x

x 1 x  5
19. Simplify:
1.2b
1.2b
18. Simplify the following
expression.
x2  4
x 2  3x  2
x2  9
x2  4 x  3
a.
3x 2  3x
 x    x  4 
c.
2  2 x  1 x  2
 x  3 x  4
b.
4x 1
2x 1
d.
x2  5x  4
 x  3 x  4
1.2b
a.
b.
x 3
x
x3
x 1
Moore Public Schools
Algebra II EOI Practice
c.
d.
22. What is the simplified
1.2b
equivalent of 2  x 
a.
1
3  2x
c.
x2  5x  
3 x
b.
x2  x  3
3 x
d.
x2  5x  
3 x
x2
x 3
 x     x  3
 x    x  1
9
1

3 x
Algebra II EOI Practice
PASS 1.3b: Add, subtract, multiply, divide, and simplify expressions involving
complex numbers.
1. Which is equivalent to
  i     i 
1.3b
a. 2  3i
b. 2  7i
c.
d.

6. Which is equivalent form of
2

3 i
1.3b
2i
2  i

2. Which is equivalent to
3
1.3b
1  2i  
a. 11  2i
b. 13 10i
c. 13  2i
d. 1  8i
a.
 i
4
c.
 i
4
b.
 i
5
d.
 i
5
7. What it the product of the
1.3b
complex numbers
  i  and   i  
a. 8
b. 10
3. Which is equivalent to
  i    i 
1.3b
c. 9  i
d. 10  6i
8. Which is equivalent to
3   3
1.3b
a.  4  19i
b. 16  19i
c. 6  29i
d. 6 10i
4. If i  1 what is the value
of i 4
1.3b
c. i
d. i
a. 3i
b.  3i
c. 9
d. 9i
9. Which is equivalent to
1.3b
c. 1
d. 1
5. If i  1 then 4i  6i  
a.
 i
5
c.
b.
  i
5
d.
5i

1  3i
 i
5

 i
4
10. What it the sum of
   i  and   i 
1.3b
1.3b
a. 48
b. 24
Moore Public Schools
Algebra II EOI Practice
c. 24
d. 48
a.  4  4i
b. 1
10
c. 5
d. 5  4i
Algebra II EOI Practice
1  5i
is expressed in
1 i
a  bi form, a equals what?
11. When
1.3b
15. Which expression is equal
1.3b
c. 3
d. 5
a. 3
b. 6
a.
b.
c.
d.
12. Which of the following
expressions shows the
simplified form of
7  2  81 
1.3b


a. 5  9i
b. 0
c. 9  9i
d. 9  9i
13. Express  6  3i  in a  bi
1.3b
form.
2
a. 45  36i
b. 27  36i
c. 45  36i
d. 27  36i
14. The number 8i can best be
classified as ______.
1.3b
a. real
b. rational
Moore Public Schools
Algebra II EOI Practice
to
c. irrational
d. pure
imaginary
11
8
8
4
4
8


24  3 8 
3  24
3 3 8
12  24
6 3 8
Algebra II EOI Practice
PASS 2.1a: Recognize the parent graphs of polynomial, exponential,
and logarithmic functions and predict the effects of transformations
on the parent graphs, using various methods and tools which may
include graphing calculators.
2.1a
3. Which could be the graph of
2
1
y  2   x  3 
2
a.
1. Which of the following is most
likely the equation graphed above?
2.1a
a. y   x  2   1
2
c. y   x  2   2
2
b. y  5  x 1  2 d. y   x  2  1
2
2
b.
c.
2. Which equation most likely represents
the function shown by the graph?
2.1a
b.
c.
d.

 x  1 1

2
y   x  1  2

2
y   x  2 1

2
y   x  1  2
a. y 
2
Moore Public Schools
Algebra II EOI Practice
d.
12
Algebra II EOI Practice
2.1a
4. Which is the graph of
2
y   x  2  
7. Which of the following sentences is true
2
about the graph of y  3 x  5  1 and
2.1a
y  3 x  5  1
2
a. Their vertices are maximums.
b. The graphs have the same shape
with different vertices.
c. The graphs have different
shapes with different vertices.
d. One graph has a vertex that is a
maximum, while the other graph
has a vertex that is a minimum.
5. If the graph of a parabola that
opens upward is shifted 2 units to
the right and 3 units down, how is
the axis of symmetry affected?
2.1a
a. There is no effect on the axis of
symmetry.
8. Which graph illustrates a vertical
transformation?
2.1a
b. It is shifted 2 units to the right.
c. It is shifted 2 units to the left.
d. It is shifted 3 units down.
6. Which of the following most accurately
describes the translation of the graph
2
y   x  3  2 to the graph of
2.1a
y   x  2   2
2
a. up 4 and 5 to the right
b. down 2 and 2 to the right
c. down 2 and 3 to the left
d. up 4 and 2 to the left
Moore Public Schools
Algebra II EOI Practice
13
Algebra II EOI Practice
9. Which function is the graph of
f  x    x 2 translated horizontally 5 units
to the left?
2.1a
12. Which function is represented
by the graph?
2.1a
 
a. g  x    x2  5
b. g  x     x  5
2
c. g  x   5x 2
1
d. g  x   x2  5
5
10. Given the parent function
p  x   x2 , what translations
occur in the graph of
a.
b.
y   x3  2
y  x3  2
c.
d.
y   x3  2
y  x3  2
2.1a
13. Which graph is the reflection
of y  10 x about the line y  x
2.1a
p  x    x  7   3
2
a. right 7 units, up 3 units
b. down 7 units, left 3 units
c. left 7 units, up 3 units
d. right 7 units, down 3 units
11. Which of the following
results in the graph of
f  x   x3 being expanded
vertically by a factor of 3?
2.1a
a. f  x   x3  3


b. f  x   x3
c. f  x   x3

d. f  x    x3

Moore Public Schools
Algebra II EOI Practice
14
Algebra II EOI Practice
14. If the graph of f  x  is
16. Which function is graphed?
2.1a
2.1a
which of the following is
the graph of f   x  
a. f  x   4  0.3
b. f  x   4  0.3
x
x 2
c. f  x   4  0.3  2
x
d. f  x   4  0.3
x 2
17. Which function is graphed?
2.1a
15. If the graph of f  x  is
2.1a
which of the following is the graph
of  f  x  
a. f  x   2  0.5
b. f  x   2  0.5
x1
x
c. f  x   2  0.5 1
x
d. f  x   2  0.5 1
x
Moore Public Schools
Algebra II EOI Practice
15
Algebra II EOI Practice
18. Which of the following
diagrams is a reasonable
graph of y  2x3
2.1a
20. If the function y  2 x is replaced
2.1a
by y  2 x , then the new graph
can be described as a reflection
of y  2 x
a. in the y-axis
b. in the x-axis
c. in the line y  x
d. in the line y  x
19. To slide the graph of the
equation y  3x two units
right, the equation must be
altered. What is the new
equation?
2.1a
a. y  3x  2
b. y  3x2
c. y  3x  2
d. y  3x2
Moore Public Schools
Algebra II EOI Practice
16
Algebra II EOI Practice
no restrictions
PASS 2.1b: Add, subtract, multiply, andd.divide
functions using
function notation.
1. Let f  x   4 x 2 and g  x   3  x .
2.1b
Which of the following
function operations gives the
new function h  x   4 x3 12 x 2 ?
a.
b.
c.
d.
f
f
f
f
g
g
g
g
5. If f  x  
x2  4
, find f  1 
x2
2.1b
a. 1
b. 3
c. 3
d. 5
6. Find f  x  h  for the function
2.1b
f  x   3x 2  5 x .
a. 3x2  3h2  5x  5h
2. If f  x   4 x  5 and g  x   5 x ,
2.1b
b. 3x2  6xh  h2  5x  5h
What is the rule of  f  g   x  ?
a.
b.
c.
d.
c. 3x2  6xh  3h2  5x  5h
x 5
9x  5
d. 3x2  6xh  3h2  5x  5h
20x2  25x
x 5
7. Find 4 p  a   p  a  3 for
2.1b
3. What are the domain
2.1b
 f 
restrictions on    x  if
g
f  x   6 x 2  4 and g  x   2 x  6 ?
a.
b.
c.
d.
a. 5a2 16a  5
b. 5a2 10a  27
x3
x 3
x  12
no restrictions
4. What are the domain
restrictions on  f  g   x if
f  x   x3 and g  x   2 x  4 ?
2.1b
c. 5a2 10a  27
d. 2a2  4a 13
x2  6 x  3
, find g  2  
x4
8. If g  x  
2.1b
a.
a. x  4
b. x  2
c. x  1
Moore Public Schools
Algebra II EOI Practice
p  x   x2  2x  6 .
b.
17
8
1
2
9
1
2
c.
17
2
d. 19
1
2
Algebra II EOI Practice
11. If f  x   3x then f  2  equals
9. If f  x   x2  2 x 1 and
2.1b
g  x   3 x 1 , which is an
2
2.1b
equivalent form of f  x   g  x 
a.
1
9
a. x2  4x  2
b.
6
b. 4x2  2x  4
c.
9
d.
9
c. 4x2  8x  4
d. 10x2  20x 10
10. If the graph below is the
2.1b
graph of y  f  x  what is the
value of f 1 ?
12. If f  x   x  and g  x    2 , which
2.1b
a.
graph corresponds to the function
 fg  x  
a. line R
c. line T
b. line S
d. line U
1
b. 1
c.
1
2
13. If f  x   x 2  2 and g  x    x  2 ,
2.1b
2
d. 2
Moore Public Schools
Algebra II EOI Practice
18
what is the value of  f  g   1 
a.  7
c. 1
b. 1
d. 7
Algebra II EOI Practice
PASS 2.1c: Combine functions by composition.
1. Which expression represents
2.1c
f  g  x   if f  x   x 2 1 and
5. If f  x   x2  1 and g  x   2 x
2.1c
g  x   x  3
a.
b.
c.
d.
a.
b.
c.
d.
x3  3x2  x  3
x2  6 x  8
x2  x  2
x2  8
2.1c
g  x    x , what is the value



a.
b.
a. 19
b. 12
c. 13
d. 14
b.
1
x
1
x2
2.1c
c. 7
d. 11
c.
1
x 1

6
0
24
30
2
1
d. 2  1
x
8. If f  x    x and g  x   x  4
2.1c

x2  4
x2  5
x2   x  5
x2  4 x  4
19

what is the value of f g 3 ?
a. 2
b. 6
c. 2
d. 6
find  f g   x  
Moore Public Schools
Algebra II EOI Practice

then f g 3 is
a.
b.
c.
d.
4. If f  x   x 2  1 and g  x   x  2
a.
b.
c.
d.
63
5
7. If f  x   x  3 and g  x   x3
1
3. If f  x   x 2  1 and g  x   ,
2.1c
x
find  f g   x  
a. x 

what is g h  4 
2
of g f  2 
2.1c
2 x2  2
4 x2 1
x2   x  4
2 x2 1
6. If g  x   x and h  x   x3 1
2. When f  x   2 x and
2.1c
find  f g   x  
Algebra II EOI Practice
9. If f  x   5  2 x and g  x   x  3 
2.1c


what is the value of f g 3 ?
a. 
b. 
c. 1
d. 5
10. If f  x   3x 2 and g  x   2x 
2.1c
what is the value of  f g  8 
a.  
b. 
c. 16
d. 144


11. If f g  x   2 x 1 how might
2.1c
f  x  and g  x  be defined?
a.
f  x    x 1 and g  x    2 x 1
b. f  x    x 1 and g  x    2 x  1
c.
f  x    2 x 1 and g  x    x 1
d. f  x    2 x  1 and g  x    x 1
Moore Public Schools
Algebra II EOI Practice
20
Algebra II EOI Practice
PASS 2.1d: Use algebraic, interval, and set notations to specify the
domain and range of functions of various types.
1. What is the domain of the
function 5,1   6 2   7 3 

2.1d

5. Which graph illustrates a
quadratic relation whose domain
2.1d
is all real numbers?
a. 5 6 7
b. 5 61
c. 1 2 3
d. 1 2 3 5 6 7
2. The relation
2.1d
3 4  x5 6 7 is
a function. What values, if any,
may x not assume?
a.
b.
c.
d.
4 or 5
3 or 7
3 or 6
4 or 6
3. Give the range of
2.1d
f   2,3 ,  1,3 ,  1,5 and tell


if f is a function.
6. For what values of x will the
function f  x   x  4 be real?
2.1d


b.  x x  0
c.  x x  4
d.  x x  4
a. 21 f is a function.
a. x x  0
b. 21 f is not a function.
c. 3 5 f is a function.
d. 3,5 f is not a function.
2.1d
4. If the domain of y    x2 is
2, 1 1 3 what is the range?
7. What is the domain of
3
f  x 
x 1
2.1d
a. 1 2 7


c.
x x  1


d.
x x  1
b. 6  3 3,11
a. x x  1
d. 11  3 3,6
b. x x  1
c. 7  2  1,1
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Algebra II EOI Practice
21
Algebra II EOI Practice
8. What is the domain of
2.1d
11. Which is not the graph of a
2.1d
function?
f  x   3x  7

7
3
a.  x x  


3
7
b.  x x   


3
7
c.  x x  


7
3
d.  x x   

9. Find the domain of the function
graphed.
2.1d
a.
b.
c.
d.
x 3
x3
x3
all real numbers
12. Give the domain and range of
the function f 
2.1d

a.
b.
c.
d.
Moore Public Schools
Algebra II EOI Practice

f   2,2 ,  1,1 , 0,0    2,2 
10. Determine which relation is a
2.1d
function.
22
Domain: 1 2
Range : 2, ,0,2
Domain: 21 0,2
Range : 0,1,2
Domain: 21 0,2
Range : 1,2
Domain: 01
Range : 2,2
Algebra II EOI Practice
13. The domain of f  x  is
2.1d
1 0 2
If f  x   2 x  3 what is the
range?
1
is
x 3
defined for all real numbers except
when x is
15. The function of f  x  
2.1d
a. 1 0 1
a. 3
b.   2 0,4
b. 3
c. 1 0 5
c. 
d. 1 3,7
d. 0
14. Which of the following tables
shows a possible domain and
range generated by
x
g  x    1
2
1
3
16. Which intervals correctly define
the domain?
3x  4
f  x  2
x  12 x  32
2.1d
2.1d
a.  8 and  8, 4 and  4, 
b.   4 and  4,8 and 8,  
8
8
c.     and   ,1 and 1, 
3

 3 
d.  4 and  4,3 and 3, 
Moore Public Schools
Algebra II EOI Practice
23
Algebra II EOI Practice
PASS 2.1e: Find and graph the inverse of a function, if it exists.
1. What is the inverse of the
equation y  3x  2
2.1e
a. y 
x
3
b. y  3x  2
5. What is the inverse of the
function y  2  7 x
2.1e
c. y  2 x  3
a. y 
x
7
c. y 
d. y  x
b. y 
 x
7
d. y   x  2
2. Given:
2.1e
set A  1,2 ,  2,3 , 3,4 ,  4,5


x
7
6. The inverse function of
 2,6 ,  3,4, 7, 5 is
2.1e
If the inverse of the set is A1 ,
which statement is true?


6,2,  4, 3,  5,7
b.  6, 2 ,  4,3 , 5,7 
c.  2,6 , 3,4 ,  7, 5
d.  2, 6 ,  3, 4 ,  7,5
a.
a.
b.
c.
d.
1
Aisnot a function and A is a function.
A isa function and A1 is not a function.
A and A1 are not functions.
A and A1 are functions.
3. Which equation defines a
function whose inverse is not a
function?
7. If  3,1 is in the function f  x  
which of the following points will
be in the function f 1  x  
2.1e
a. y  3x  2
c. y  x
b. y   x
d. y  2
2.1e
a. 1,  3
x
b.  3,1
4. What restriction can be made to
the domain of f  x   1  x 2 so that
2.1e
f 1  x  will be a function?
a. x  0
c. x  2
b. x  1
d. 1  x  1
Moore Public Schools
Algebra II EOI Practice
c.
3, 1
d.
 1,3
1
8. What is f 1  x  when f  x    2 
x
2.1e
24
a.
1
x2
c. x  2
b.
1
x2
d. x 
1
2
Algebra II EOI Practice
9. If the function y  x is replaced by
x  y  then the new graph can be
described as a reflection of y  x
2.1e
11. The domain of a linear function is
2.1e
 x : x  0 and the range is
 y : y  5 What are the domain
and range of the inverse?
a. in the y  axis
a.
b. in the line y   x
c. in the line y  x
b.
d. in the line y  x
10. Which graph is the graph of
2.1e
f  x   x  1 and its inverse?
c.
d.
Domain:  y : y  0
Range :  x : x  5
Domain:  x : x  0
Range:  y : y  5
Domain:  x : x  5
Range:  y : y  0
Domain:  x : x  5
Range :  y : y  0
12. The graph of y   x2  2 is the solid
2.1e
graph below. Which dashed graph
is its inverse?
a.
b.
c.
d.
Moore Public Schools
Algebra II EOI Practice
25
a
b
c
None of the above
Algebra II EOI Practice
13. The inverse of the function
y  x2  9 x  0 is
2.1e
a. y  x  9
b. y   x  9
c. y  x  9
d. y   x  9
Moore Public Schools
Algebra II EOI Practice
26
Algebra II EOI Practice
PASS 2.2a: Model a situation that can be described by a system of
equations or inequalities and use the model to answer questions about
the situation.
1. A landscape company is having a
tree sale. Five Maple trees and 6
Ash trees are on sale for $83.
Nine Maple trees and 11 Ash trees
are on sale for $151. What is the
cost of an Ash tree?
2.2a
a. $7
c. $8
b. $14
d. $16
2. Which system of equations
2.2a represents the following
situation?
3. One Internet provider has a
monthly rate of $11.95 and a
connection fee of $2.55 per hour.
Another company’s monthly rate is
$20, plus $1.85 per hour. Both
companies would charge the same
amount for connecting to the
Internet each month for
2.2a
c. 10 hours
b. 7.3 hours
d. 11.5 hours
4. Hunter’s time for the 100-meter
freestyle event was 57.9 seconds.
His time for the second half of the
race was 4.7 seconds slower than
his time for the first half. What
was Hunter’s time for the first
half?
2.2a
Mrs. Stevens bought 3
containers of yogurt and 5 oranges
for $2.79. The next week she
bought 4 containers of yogurt and
7 oranges for $3.81, paying the
same price.
x  y  8
a. 


3x  5 y  2.79
 x  y  2.79
b. 

 x  y   
a. 1.8 hours
a. 31.3 s
c. 21.9 s
b. 26.6 s
d. 36 s
5. Which of the following systems
is shown in the graph?
2.2a
3x  5 y  2.79

4 x   y  81
c. 
5 x  3 y  2.79
d. 

4 x   y  
Moore Public Schools
Algebra II EOI Practice
27
a.
2 y  4 x  4
2 y  x  3
b.
2 y  4 x  4
2y  x  3
c.
2 y  4 x  4
2y  x  3
d.
2 y  4 x  4
2 y  x  3
Algebra II EOI Practice
6. Which graph is the solution to the
2.2a
system?
8. Mario recorded the temperature
every two hours beginning at
8:00 A.M. until 6:00 P.M. for two
consecutive days in January. The
data are represented in the graph.
At what time was the temperature
the same on the two days?
2.2a
y  x  

 y  x  3
a. 10:00 A.M
c. 2:00 P.M
b. 12:00 P.M
d. 4:00 P.M
9. Let M equal the first number and N
equal the second number. The sum
of the two numbers is 36, and the
second number is three less than
one-half of the first. Which pair of
equations would be suitable for
finding the numbers?
2.2a
7. Which linear system is
represented by the graph?
2.2a
a. M  N  36,
1
M N 3
2
b. 2  M  N   36,
1
N M 3
2
 y   x  4
a. 
 y   x
 y  x  4
c. 
 y   x
c. 2  M  N   36,
1
M  N   3
2
 y   x  4
b. 
 y   x
 y   x  4
d. 
 y   x
d. 2M   N  36,
1
M N 3
2
Moore Public Schools
Algebra II EOI Practice
28
Algebra II EOI Practice
10. The perimeter of a rectangle is 120 12. Jennie purchased 3 packages of
2.2a
2.2a
cm. Twice the width is 15 cm less
the cheaper soda and 4 packages
than the length. Which pair of
of the more expensive soda for a
equations will determine the length
total of $57. Rob purchased 7
and width?
packages of the cheaper soda and
11 packages of the more
expensive soda for a total of
a. 2L  2W  W  15  L
$148. How much was the
cheaper package of soda?
b. L  W  W  15  L
c. 2L  2W  W  15  L
a. $4.33
c. $7.00
d. L  W  W  15  L
b. $4.20
d. $9.00
11. At a student bake sale cakes sold
2.2a
for $4 each and pies sold for $5
each. The students sold a total of
75 cakes and pies and made $340.
Which pair of equations would
determine the number of each
dessert sold?
a. x  y   4 x  5 y  340
13. A shopper purchased 4 boxes of
2.2a
Sugarburst cereal and 3 boxes of
Nutragood cereal for $40.75.
Another shopper purchased 1 box
of Sugarburst and 4 boxes of
Nutragood for $27.25. How
much more expensive is a box of
Sugarburst than a box of
Nutragood?
b. x  y  340 4 x  5 y  
c. x  y  340 4 x  5 y  
d. x  y   4 x  5 y  340
Moore Public Schools
Algebra II EOI Practice
29
a. $2.75
c. $1.67
b. $0.35
d. $1.00
Algebra II EOI Practice
14. Which set of constraints
describes the number of batches
of each type of cookie that
Danielle can make?
2.2a
15. What is the system of restrictions
for the shaded area?
2.2a
x   y  8

x  2 y  12
a. 
x  0
y  0

y  x 3

 x  2
a. 
3
x


2

 y  x  2
2 x  y  8

 x  3 y  12
b. 
x  0
y  0

y  x 3

 x  2
b. 
3
x


2

 y  x  2
2 x   y  8

x  y  12
c. 
2 x  2 y
y  0

2 x   y  12

 x  y  8
d. 
x  0
y  0

y  x 3

 x  2
c. 
3
x  2

 y  x  2
y  x 3

 x  2
d. 
3
x  2

 y  x  2
Moore Public Schools
Algebra II EOI Practice
30
Algebra II EOI Practice
PASS 2.2b: Solve systems of linear equations and inequalities using
various methods and tools which may include substitution, elimination,
matrices, graphing, and graphing calculators.
1. Solve the system by graphing.
x y 8
3x  y  0
2.2b
2. Solve the system of equations.
2x  y  
x  2 y  3
2.2b
a.
b.
c.
d.
 1,  2
1,  2
1, 2 
 2, 3
3. How many solutions does the
2.2b system have?
2 x  y  

4 x  2 y 14  0
a.
b.
c.
d.
0
1
2
infinite
4. Which ordered pair is a solution to
the system?
4 y  12 x 

 y  3x  4
2.2b
a.
b.
c.
d.
Moore Public Schools
Algebra II EOI Practice
31
1, 1
 0,  8
8, 0
no solution
Algebra II EOI Practice
5. What is true about the lines of
the system?
 y  4 x 

 y  5x  3
2.2b
a.
b.
c.
d.
The lines intersect.
The lines coincide.
The lines are parallel.
The lines are perpendicular.
6. Solve the system for x and y  .
2.2b
 x  y  
2 x  3 y  5
a.
b.
c.
d.
8. Using the elimination method, what
can you multiply the first equation
by in order to eliminate x 
 x   y 

8x  5 y  9
2.2b
 2,  3
 2, 3
8,  3
 3,  2 
a.
b.
c.
d.
4
4
5
3
9. Which expression can be
2.2b
substituted for y in the top equation
x   y  
of the system
to solve
x y 3
the system by substitution?
a. 3  x
b. x  3
7. Which ordered pair is a solution to
the system?
4
1
c.  x 
3
3
2.2b
d. 3x  9
a.
b.
c.
d.
1, 3
 5, 3
 3, 1
 3, 5
Moore Public Schools
Algebra II EOI Practice
10. You want to eliminate x by
2.2b
x  y  
addition in the system
.
3x   y  20
If you multiply each side of the top
equation by 3, by which number
would you multiply each side of
the bottom equation?
a. 2
b. 
c. 3
d. 3
32
Algebra II EOI Practice
11. What does d equal in the solution
of the system?
2c  d  
5c  2d  4
Use the graph below for questions
14 and 15.
2.2b
a. 2
b. 3
c. 3
d. 2
12. For which system are there
infinitely many solutions?
2.2b
a.
3x   y  7
 x  10 y  14
b.
x  y  7
 x  10 y  15
c.
3x  y  8
x  y  10
d.
14. Which system of inequalities is
shown?
2.2b
1
3
x
a.
2
2
y   x  4
y
1
3
x
b.
2
2
y   x  4
y
1
3
x
c.
2
2
y   x  4
y
2x  y  1
y  2x  3
1
3
x
d.
2
2
y   x  4
y
13. What does x equal in the solution
of the system?
2.2b
x y
 
3 4
x y
 0
6 12
15. Which point is a solution to the
2.2b
system in the graph?
a.
b.
c.
d.
a. 6
b. 12
c. 12
d. 
Moore Public Schools
Algebra II EOI Practice
33
 0,  2 
 ,  
 0, 0 
none of these
Algebra II EOI Practice
16. Solve the following system of
equations.
2x  y  
x   y  3
2.2b
a.
b.
c.
d.
 5,  3
 ,  
 3, 5
 5, 3
17. Which quadrants contain the
solutions to this system of
inequalities?
 y  2 x  

3 y  x  
2.2b
a.
b.
c.
d.
19. Which set of constraints
produced the shaded feasible
region?
2.2b
y  6  x

a.  x  
y  2

quadrants I and IV
quadrants II and III
quadrants III and IV
quadrants II, III, and IV
x  y  6

b.  x   2
y 

18. The corners of a triangle are
2.2b
 2, 1   4, 4  and  6, 2   Which
system of inequalities describes
the interior of the triangle?
4 y  x  2

a. 3 y   x 
y  8 x

2 y  x

c. 2 y  x  
y  8 x

4 y  x  2

b. 2 y  x  
y  8 x

2 y  x

d. 3 y   x 
y  8 x

Moore Public Schools
Algebra II EOI Practice
c.
x  6  y

x  
y  2

x  y  8
x  y  6

d. 

x  2
 y  1
34
Algebra II EOI Practice
PASS 2.2c: Use either one quadratic equation and one linear equation
or two quadratic equations to solve problems.
1. What is the solution to the
following system?
 x  4 2  y  

2

 x  4    y  1  
2.2c
a.
b.
c.
d.
3. What is one solution to the
following system?
2
2
 x  y  
 2

2 x  3 y  
2.2c
 
b.   2 5, 5 
c.  2 2,  1
d.  5, 2 5 
1, 4 
 , 
 , 3
 4,  1
2. Which graph represents the
2.2c following system?
  x 2  y  2 2



 9
4
 x 2  y  

a. 1, 2 2
4. The graphs of the equation y  x 2
2.2c
and y  2 x intersect in two points,
one of which is the origin. What
are the coordinates of the other
point?
a.
b.
c.
d.
 , 1
1, 2 
 2, 4 
 4, 2 
5. Which is a point of intersection of
the equations y  x and
2.2c
y  x 2  x  1
a.
b.
c.
d.
Moore Public Schools
Algebra II EOI Practice
35
 , 
 0, 0 
1, 0 
 1, 0 
Algebra II EOI Practice
6. The graphs of the equations
y  x 2  5 x  6 and x  y  6 are drawn
on the same set of axes. At which
point do the graphs intersect?
2.2c
a.
b.
c.
d.
 5, 1
 3, 3
 4, 2 
 2, 4 
7. The graphs of the equations
2.2c
x 2  y 2  4 and y   are drawn
on the same set of axes. What is
the total number of points common
to both graphs?
a.
b.
c.
d.
1
2
3
4
8. If the graphs of the equations
2.2c
x 2  y 2   and y  x are drawn
on the same set of axes, what is
the total number of points common
to both graphs?
a.
b.
c.
d.
9. This is a portion of the graph of a
2.2c system of equations. Which is most
likely the solution set for the
system?
 2.1, 3.4  2, 3
b.  3, 2    2.1, 3.4 
c.  2, 3   3, 2 
d.  2.1, 3.4    3, 2 






10. Which is the solution set for the
following system of equations?
 y  x 


 y   x  3  
2.2c
0
1
2
3

b. 
c. 
a.
d.
Moore Public Schools
Algebra II EOI Practice

a.
36




6.4, 7.4     0.6, 1.6 

4,  3    2,  3

4,  3   1, 0 
 0.6, 1.6  6.4, 7.4
Algebra II EOI Practice
PASS 2.3 a: Solve quadratic equations by graphing, factoring,
completing the square and quadratic formula.
1. Choose the solution set for
x 2  16  0
2.3a
4. Choose the solution set for
3x 2   x  15  0
2.3a
 4
b.  4 4
a.
5

a.   3, 
3

 2  i 41 
b. 

3




c. 0 4
d. 4
 5 
c.   3
 3 
  2  i 41 
d. 

3


2. Choose the solution set for
2
 3x  1  0
2.3a
1 
a.  , 1
3 
  1
b.  1, 
3

5. What are solutions to
x 2  x  16  0
2.3a
 1
c.  
 3
d.  1
3. Which is a solution to
2.3a
2 x 2   x  3  0
a.
b.
c.
d.
12  4 5
62 5
62 5
12  4 5

6. What are solutions to

2.3a
 y  3    0
a. x  3
a.
b.
c.
d.
b. x  

1
2

d. x  3
c. x 
Moore Public Schools
Algebra II EOI Practice

37
y  12 or y   6
y  12 or y  6
y  12 or y   6
y  12 or y  6
Algebra II EOI Practice
7. What are solutions to
x 2  x  4  0
2.3a
11. What value of k will make
x 2  kx     a perfect-square
trinomial?
2.3a
a. x  1 or x   4
b. x  1 or x  
3i 7
2
3 7
d. x 
2
a.
b.
c.
d.
c. x 
12. What are the roots of the quadratic
equation y 2   y  3  0
2.3a
8. The height of a right triangle is 5
units more than twice its base. If
the area of the triangle is 21 square
units, what is its height?
a.
3  3
2
b.
3 3
2
c.
3  21
2
d.
3  21
2
2.3a
a.
b.
c.
d.
6
9
3
18
7
units
2

5  193
units
4
5  193
units
2
12units
9. What are the solutions to
4x     x 2
2.3a
13. Which set of numbers represent
the solutions to the equation
w2 3w  
2.3a
a.
b.
c.
d.
x  4i or x   2
x   4 or x  2
x  4 or x  2i
x  4 or x  2
a.
b.
c.
d.
10. Fill in the blank to make the
2.3a
expression x2  x  
a perfect-square trinomial?
a.
b.
c.
d.
2x
10
20
25
Moore Public Schools
Algebra II EOI Practice
38
8, 6
16,  3
3, 16
8, 6
Algebra II EOI Practice
14. The base of a triangle is 6 inches
shorter than its altitude. What is
the length of the base if the area
of the triangle is 56 square
inches?
2.3a
a.
b.
c.
d.
17. Which apparently is a graph of a
quadratic function that has no real
zeros?
2.3a
8 inches
14 inches
26 inches
20 inches
15. If x 2  x  c is a perfect-square
2.3a
trinomial, what is the value of c ?
a.
b.
c.
d.
5
10
25
50
16. If x 2  x  c is a perfect-square
2.3a
trinomial, what is the value of c ?
1
2
a.
1
8
c.
b.
1
4
d. 1
18. Which of the following equations
are you solving if the quadratic
formula you have is
2.3a
x
a.
b.
c.
d.
Moore Public Schools
Algebra II EOI Practice
39
6 
 6
3x 2  6 x  7  0
3x 2  6 x  7  0
3x 2  6 x  7  0
3x 2  6 x  7  0
2
 4  3 7 
2  3

Algebra II EOI Practice
PASS 2.3 b: Graph a quadratic function
c.and identify the x- and yintercepts and maximum or minimum value, using various methods
and tools which may include a graphing calculator.
1.
2.3b
Which graph has x-intercepts of
1, 0 and 5, 0  ?
3. What is the vertex of the graph of
1

y   x  2   6
4
2.3b
a.  0, 7 
b.  2, 6 
c.  2,  6 
d.  4, 7 
4. What is the vertex of the graph of
2.3b
y  4  x  x  5 
a.  2,  6 
b. 1,  5
c.
d.
 1, 5
 2, 36
5. What is the vertex of the graph of
2.3b
y  3x 2  x  13
a.  2, 1
b.  2, 1
c.  2,  1
d.  0, 13
6. What is the axis of symmetry of the
1
graph of y    x  2  x  6  
2
2.3b
a. x  6
b. x  2
2. Which gives the equation for the
axis of symmetry in the graph of
f  x   x 2  4 x  5
7. Which is true of the graph of the
parabola whose equation is
y  x 2   x  8
2.3b
a. x  2
c. x 
4
5
b. x  2
d. x 
4
5
Moore Public Schools
Algebra II EOI Practice
c. x  2
d. x  6
2.3b
a.
b.
c.
d.
40
The x  intercepts are at x  2 and x  4
There are no x  intercepts.
The x  intercepts are at x  4 and x  2
The only x  intercept is at x  4.
Algebra II EOI Practice
8. What is the y  intercept of the graph
2.3b
of the equation y  x 2   x  3
a. 1
b. 2
13. The parabola y   x 2   x  1
2.3b
will have
a.
b.
c.
d.
c. 3
d. 2
9. What is the y  intercept of the
2.3b
parabola whose equation is
y  x 2   x  5
a minimum of 2
a minimum of 5
a maximum of 5
a maximum of 2
14. Which is an equation of the
parabola that intersects the
x  axis at the points  2, 0  and
 5, 0  
2.3b
a. 5
c. 
b. 3
d.
7
2
7
2
a.
b.
c.
d.
10. What is the y  intercept of the
parabola whose equation is
y  x 2   x  6
2.3b
a. 6
b. 1
c. 1
d. 6
11. What are the coordinates of the
minimum point of a parabola
whose equation is
y  x 2  3
15. Which is an equation of the
2.3b
parabola that intersects the
x  axis at the points  , 0  and
 5, 0  
2.3b
a.  3, 12 
b.  1, 2 
c.
d.
a.
b.
c.
d.
a.
b.
c.
d.
 3, 0
 0, 3
12. The parabola y   x 2   x  14
2.3b
will have
y  x 2   x 
y  x 2   x 
y  x 2   x 
y  x 2   x 
16. Which of the following best
describes the graph of a quadratic
equation with one real root?
2.3b
a minimum at  2,  6 
a.
b.
c.
d.
a minimum at  2, 10 
a minimum at 10,  6 
a maximum at  2,  6 
Moore Public Schools
Algebra II EOI Practice
y  x 2   x 
y  x 2   x 
y  x 2  x  
y  x 2  x  
41
It has 2 x  intercepts
It does not cross the x  axis.
Its vertex lies on the x  axis.
Its vertex lies on the y  axis.
Algebra II EOI Practice
2.3b
17. Two factors of a polynomial,
P  x   are  x  6  and  x  3 
Which is a zero of P  x  
19. Which statement best
describes these two functions?
f  x   x2  x  6
2.3b
g  x    3x 2  3x  5
a. 6
b. 3
c. 1
d.  3
18. Which equation most likely
2.3b
represents the function shown by
the graph?
a. They have no common points.
b. They have the same x  intercepts
c. The maximum of f  x 
is the same as the minimum of g  x .
d. The maximum of g  x 
is the same as the minimum of f  x .
20. Which statement best
2.3b
describes these two functions?
f  x   x2  x  
g  x    3x 2  3x  
 x  1  1

2
y   x  1  

2
y   x    1

2
y   x  1  
a. y 
b.
c.
d.
a. The maximum of f  x 
is less than the minimum of g  x  .
b. The minimum of f  x 
is less than the maximum of g  x  .
c. The maximum of f  x 
is greater than the minimum of g  x  .
d. The minimum of f  x 
is greater than the maximum of g  x .

2
Moore Public Schools
Algebra II EOI Practice
42
Algebra II EOI Practice
PASS 2.3 c: Model a situation that can be described by a quadratic
function and use the model to answer questions about the situation.
1. The length of a rectangle is 8 feet
4. A young girl standing on a cliff is
2.3c
longer than its width. If the area of
throwing stones up into the air so
the rectangle is 65 square feet, what
that they land in the ocean below.
is the length of the rectangle?
The height  h in meters  of the
stones above the ocean is related to
a. 79 feet
c. 11 feet
the time  t in seconds  after
b. 13 feet
d. 17 feet
it has been thrown, by the function
h  t 2  t   What was the
2. An object’s height is given by
maximum height reached by the
2.3c
h  t   16t 2  32t   where t is the
stones?
time in seconds after the object is
released. Find the time(s) when
a. 40.5 m
c. 36.5 m
the object is 22 feet in the air.
b. 20 m
d. 40 m
2.3c
a.
b.
c.
d.
2 and 4 seconds
1 second
1 and 3 seconds
3 seconds
5. You have 32 m of fencing to
2.3c enclose a rectangular garden. If one
side of the garden will be the side of
a barn, what is the maximum area
that the enclosure can contain?
3. A worker finds a ball on the roof of
a building as he is doing some
repairs. he tosses the ball up and
off the roof so that its height
 h in meters  above the ground is
related to time  t in seconds  after
it has been tossed, by the function
h  t 2  4t   What was the
maximum height reached by the
ball?
a.
b.
c.
d.
2.3c
a. 36 m
b. 32 m
Moore Public Schools
Algebra II EOI Practice
128 m2
64 m 2
222 m2
256 m 2
6. You have 42 m of fencing to
2.3c enclose a rectangular garden. If one
side of the garden will be the side of
a barn, what is the maximum area
that the enclosure can contain?
c. 36.5 m
d. 42 m
a.
b.
c.
d.
43
420 m 2
216 m 2
220.5 m2
440.5 m2
Algebra II EOI Practice
7. If the area of a rectangular field is
9. The revenue, R at a bowling alley is
2
2.3c
given by the equation
x  x  2800 square feet, which

of the following could be the length
R
x 2   x   where x is the

of the field?

number of frames bowled. What is
a.  x  560  feet
the maximum amount of revenue
the bowling alley can generate?
b.  x  70  feet
c.  x  700  feet
a. $800
c. $1,800
d.  x   feet
b. $1,200
d. $2,400
2.3c
8. A model rocket is launched into the
air. Its path can be modeled using a
quadratic equation. What is the best
way to determine when the toy
rocket reaches the highest point in
its flight?
2.3c
a. Graph the equation and find its
y  intercept.
b. Graph the equation and find its
minimum.
c. Graph the equation and find the
x  intercepts.
d. Graph the equation and find its
maximum.
Moore Public Schools
Algebra II EOI Practice
44
Algebra II EOI Practice
PASS 2.4: Identify, graph, and write the equations of the conic sections
(circle, ellipse, parabola, and hyperbola).
1. Which equation is most likely
represented by the ellipse shown?
3. Which graph best represents
2
2
 x      y    4
2.4
x y
a.
 1
16 4
x2 y 2
c.

1
4 16
x2 y 2

1
b.
4
2
x2 y 2
d.

1
16 4
2.4
2. Which equation is graphed?
2.4
a.
b.
c.
d.
9 y 2  16 x 2  144
9 x 2  y 2  144
 y 2  9 x 2 4
9 x 2  y 2 4
Moore Public Schools
Algebra II EOI Practice
45
Algebra II EOI Practice
4. Which describes the graph of
x2 y 2

 1
4 16
7. Which is the standard form of the
equation where the point (3, -6) is
on a circle whose center is the
origin?
2.4
a. Parabola
b. Circle
2.4
c. Ellipse
d. Hyperbola
a.
b.
c.
d.
5. Which equation is graphed?
2.4
x 2  y 2  
x2  y 2  
3x 2   y 2 
x2  y 2  
8. What is the equation of the ellipse
2.4
with center at (0, 0), vertex at
(0, 3), and co-vertex at (-2, 0)?
a.
b.
c.
d.
x 2  y 2  16
x 2  y 2  16
x2  y 2  4
x2  y 2  4
x2 y 2
c. 
1
4 9
x2 y 2
b.

1
2 3
x2 y 2
d. 
1
3 2
9. Which equation is graphed?
6. Which is the standard form of the
2.4
equation where the point (-2, 4) is
on a circle whose center is the
origin?
a.
b.
c.
d.
x2 y 2
a.

1
9
4
2.4
x 2  y 2  20
x2  y 2  
x 2  y 2  
x2  y 2  
a.
b.
c.
d.
Moore Public Schools
Algebra II EOI Practice
46
y 2  6 x 2  
36 x 2  y 2  36
 y 2  x 2  36
x 2   y 2  36
Algebra II EOI Practice
10. What is the standard form of the
hyperbola with foci at  0,  5
and vertices at  0,  2  
13. Which of the following is an
equation of the ellipse with foci at
 2, 4  and  6, 4 and vertices at
 , 4 and  4, 4  ?
2.4
2.4
y2 x2
 1
21 4
x2 y2

1
b.
21 4
y2 x2
 1
c.
4 21
x2 y2

1
d.
4 21
a.
a.
b.
c.
11. What is the standard form of the
hyperbola with foci at   4, 0 
and vertices at  3, 0  
2.4
d.
 x  
2
 y  

2
 y  

2
 y  

2
 y  

2


20
 x  
2


20
 x  
2


20
 x  

2
36

14. What conic does the equation
y 2  x 2  6 y  12 x  28  0 represent?
2.4
y 2 x2
a.
 1
9 7
b.
x2 y 2

1
7 9
y 2 x2
c.
 1
7 9
d.
a.
b.
c.
d.
x2 y 2

1
9 7
12. Which of the following is an
2.4
equation of the circle whose
center is at  3, 6  and the diameter
is 8?
a.
b.
c.
d.
 x  3   y  6  
2
2
 x  3   y  6 
2
2
 x  3   y  6 
2
2
 x  3   y  6 
2
parabola
circle
ellipse
hyperbola
15. What conic does the equation
x 2  y 2  4 x  6 y  9  0 represent?
2.4
a.
b.
c.
d.
2
parabola
circle
ellipse
hyperbola
16. What is the equation of a circle
with the center at the origin and a
radius of 4 units?
2.4
a. x  y  4
c. x 2  y 2  16
b. x  y  4
x2 y 2

1
d.
4
4
2
Moore Public Schools
Algebra II EOI Practice
47
2
Algebra II EOI Practice
17. If the equation y  x 2  2  0 were
20. If the equation 3x 2  2 y 2  6 were
2.4
2.4
graphed in the standard coordinate
graphed in the standard coordinate
plane, the graph would be which of
plane, the graph would be which of
the following?
the following?
a.
b.
c.
d.
circle
ellipse
parabola
hyperbola
a.
b.
c.
d.
18. In the coordinate plane, which of
2.4
the following is the equation of an
ellipse with its center at the origin,
vertices of (4, 0) and (-4, 0), and
convertices of (0, 3) and (0, -3)?
21. Which equation represents an
2.4
ellipse?
a. 25 x 2  16 y 2  400
b. x 2  y 2  400
c. xy  400
x2 y 2
a.

1
3
4
d. x 2  y 2  400
x2 y 2
b.

1
4
3
c.
d.
2
2
2
2
circle
ellipse
parabola
hyperbola
22. When drawn on a set of axes,
which equation is an ellipse?
x
y

1
9 16
2.4
a.
b.
c.
d.
x
y

1
16 9
19. What is the equation of a circle
with the center at (-1, 3) and a
radius of 6 units?
2 x 2  y  12
2 x 2  y 2  12
2 x 2  2 y 2  12
2 x 2  y 2  12
2.4
23. An equation of a hyperbola is
2.4
a. ( x  1)2  ( y  3)2  36
a. x 2  y 2  16
b. x  y  16
x2 y 2
b.

 36
1
9
c. x 2  y 2  16
d. 2 x 2  y 2  16
c. x 2  y 2  36
d. ( x  1)2  ( y  3)2  36
Moore Public Schools
Algebra II EOI Practice
48
Algebra II EOI Practice
24. What is the equation of the ellipse
below?
26. What is the equation of the
hyperbola below?
2.4
2.4
y2
a. x 
1
5
2
a.
b.
c.
d.
x2 y 2
b.

1
25 25
c.
x2
 y2  1
5
9 x 2  4 y 2  36
9 x 2  4 y 2  36
9 x 2  4 y 2  36
4 x 2  9 y 2  36
27. Which of the following equations
represents an ellipse with xintercepts 4 and y-intercepts 9?
2.4
x2
d.
 y2  1
25
a.
x2 y 2

1
16 81
x2 y 2
b.

1
9
4
25. What is the equation of the
2.4
hyperbola below?
c.
x2 y 2

1
4
9
x2 y 2
d.

1
2
3
28. Which description best fits the
equation?
2
2
4  x  1  2  y  2   12
2.4
a.
b.
c.
d.
x2  y 2  1
y 2  x2  1
y 2  x2  4
xy  2
Moore Public Schools
Algebra II EOI Practice
a.
b.
c.
d.
49
a translated ellipse
an ellipse in standard position
a translated hyperbola
a translated circle
Algebra II EOI Practice
29. What equation is represented by
the graph?
31. Which equation of a hyperbola,
has vertices  0,  3 and foci
 0,  5 
2.4
2.4
a.
b.
c.
d.
y 2 x2

1
9 256
9 y 2  256 x 2  1
16 y 2  9 x 2  144
16 x 2  9 y 2  1
32. What equation is represented by
the graphed hyperbola?
2.4
x2
a.
 y2  1
16
y2
b. x 
1
16
2
y2
c.
 x2  1
16
x2
d. y   1
16
2
30. The coordinate of the center of the
2.4
hyperbola,
2 x 2  3 y 2  8 x  12 y  0 is:
a.
b.
c.
d.
a.
b.
 2, 2
 4, 6 
 2, 2 
 2,  2 
c.
d.
Moore Public Schools
Algebra II EOI Practice
50
 x  3
2
2
2
4
2
 x  3

2
 x  3

2
1
1

2
 y  
 x  3

1

4
 y  
2

4
 y  
 y  

2

1
Algebra II EOI Practice
PASS 2.5a: Graph exponential and logarithmic functions.
1. Which graph represents the
2.5a following function?
1 
y  log  x 
2 
3. What is the equation of the
2.5a function graphed below?
a.
b.
c.
d.
y  ex
y  e3x
y  e3x
y  log 3 x
4. Which graph represents the
function y  2 ln x ?
2.5a
2. Which graph represents the
2.5a
1
equation y  log x
2
Moore Public Schools
Algebra II EOI Practice
51
Algebra II EOI Practice
5. Which graph represents the
1
function y     x 
2
2.5a
A
C
8. Which of the following equations
could be represented by the
graph below?
2.5a
B
a. y  log 2 x
b. y  log x 2
D
c. y  2 x
d. y  2 x
9. The graph of the y  log x
lies in Quadrants
2.5a
a. I and IV
b. III and IV
6. Which is the graph of y  e x 
c. II and III
d. I and II
2.5a
10. What is the equation of the
graph below?
2.5a
a. y  2 x  3
b. y  2 x  
7. The graph of the equation y  x
2.5a
lies in Quadrants
a. I and II
b. I and IV
Moore Public Schools
Algebra II EOI Practice
c. II and III
d. III and IV
52
c. y  2 x  3
1
d. y   3
x
Algebra II EOI Practice
PASS 2.5b: Apply the inverse relationship between exponential
and logarithmic functions to convert from one form to another.
1. What is the base in log5   2 
2.5b
a. 25
b. 52
2. Write
2.5b
6. Which of the following is equivalent
2.5b
to log 4 64 x 
c. 5
d. 2
1

2
1
 81
9
a. 3x
c. 43 x
b. 3 x
d.
in logarithmic form.
1
x
4
7. Which of the following is equivalent
to log 5 125
2.5b
1
2
1

c. log81    
2

b. log 2 9  81
 1
d. log 1     81
9 2
a. log9 81  
a. 25
c. 3
1
3
d. 5
b.
3. Which of the following is equivalent 8. Which of the following is equivalent
2.5b
to 91.5  27 
x2 y3
to log 4 
z
a. log1.5 9  27
c. log 27 9  1.5
a. 6 log xy  4log z
b. log 9 1.5  27
d. log 9 27  1.5
b. 2 log x  log y  4log z
c. 2 log x  log y  4log z
4. Use natural logarithms to solve the
d. 2 log x  log y  4log z
3x
equation. 6e  8
2.5b
9. What is the condensed expression
2.5b
for 3log x  log 2 
a. x  0.811
c. x  0.096
2.5b
b. x  0.405
5. Simplify. 2ln e
d. x  0.231
x3
a. log
2
4
2.5b
a. 2
c. 8
b. 4
d. e8
Moore Public Schools
Algebra II EOI Practice
b. log 2x
53
c. log 2x3
3
x 3
d. log
2
Algebra II EOI Practice
10. What is the condensed expression
2.5b for 2 ln x  ln 3
15. What is y 
2.5b
 5  written in
x
logarithmic form?
a. 3ln x 2
c. ln 3x 2
2
b. ln
x
3
d. ln
a. x  log
3
x2
11. Which of the following is not
2.5b
correct?
a.
b.
c.
d.
log 2 4  log 2 9  log 2 36
log 2 18  log 2 18  log 2 36
log 2 3  log 2 12  log 2 36
log 2 6  log 2 6  log 2 36
b. b N  x
d. N b  x
b. log y 3  x
d. log 3 x  y
x
 5
 5
log 3 log 4
log 6  log 6
log 3   log 2
log 3   log 2
17. The expression
2.5b
13. Which equation is equivalent to
y  3x 
c. log 3 y  x
c. y  log
a.
b.
c.
d.
1
log  a   3log  b 
3
is equivalent to
3
2.5b
a. log y x  3
 5
16. The expression log 12 is equivalent
2.5b
to
12. Which is the equivalent
exponential form of log b N  x 
c. xb  N
y
b. y  log x
d. x  log y
2.5b
a. b x  N
 5
a. log
a
b3
c. log
a
3b3
3
b. log
a
3b
d. log

3
a  b3
18. If 3log3 7  x what is the value
14. The expression log 4x is equivalent 2.5b of x
2.5b
to
a. 4 log x
b. log x 4
c. log 4  log x
d.  log 4  log x 
Moore Public Schools
Algebra II EOI Practice
54
a. 7
c.
b. 37
d.
3
7
7
3

Algebra II EOI Practice
19. Which equation represents the
2.5b
solution for x in the formula
6 x  21
a. x 
log 6
log 21
c. x  log 21 log6
b. x 
log 21
log 6
d. x  log 21 log6
1
20. If log x    what is the value of x
3
2.5b
a. 8
b. 2
c.
1
3
21. If log x  
2.5b
2
d. 4
1
what is the value of x
2
a. 81
b. 4
3
1
2
Moore Public Schools
Algebra II EOI Practice
c. 3
d. 27
55
Algebra II EOI Practice
PASS 2.5c: Model a situation that can be described by an exponential
or logarithmic function and use the model to answer questions about
the situation.
1. The growth of an investment over
a period of time is shown in the
accompanying graph.
2.5c
4. About how much will $5000 be
worth 54 months from now if the
interest rate of 4% is compounded
once a year?
2.5c
a. $41,569
b. $10,800
c. $ 5,965
d. $ 1,965
5. The population of a town in 2000
was about 15,000. The annual rate
of increase for the past few years
was about 1.16%. Which
equation models this situation?
2.5c
The graph is best modeled by what
type of function?
a.
b.
c.
d.
a. y  15,000 1.16 
exponential
absolute value
logarithmic
trigonometric
2. If the population of a city was 2
2.5c
million in 2005 and growing at a
rate of 6.4%, what will the
population be in the year 2010?
b. y  1.0116 15,000 
x
d. y  15,000 1.0116 
x
c. y  15,000  x1.16 
6. The table below gives data about
the population of South Carolina
in ten-year intervals from 1900 to
1990.
2.5c
a. 2.5 million
b. 2.7 million
c. 10.64 million
d. 43.6 million
3. Given 100 bacteria, what was the
original population if it started
doubling every hour 4 hours ago?
2.5c
a. 0
b. 6.25
Which of the following could be an
exponential model for these data?
a. P  1.0111.30 
c. 12.5
d. 25
t
b. P  1.30 1.011
t 10
c. P  1.30 1.011
t
d. P  1.110 
Moore Public Schools
Algebra II EOI Practice
x
56
t
Algebra II EOI Practice
7. A population of animals in an
experiment increases over time, as
shown in the table. Using an
exponential model and the data,
what is the best estimate of the
number of animals in May?
2.5c
Time
Number of Animals
April
235
May
?
June
445
July
611
August
841
a. 296
b. 323
10. Which of the following is an
exponential decay function?
2.5c
a. f  x   4  2 
4
b. f  x   3  
3
11. If you deposit of $2000 in an
account that pays 6.5% annual
interest compounded
continuously, what is the
balance after 3 years?
a. $2,134.32
b. $5,835.96
2.5c
a. 547.5 ft.
b. 617.3 ft.
12. If the loudness of fizz in a can of
soda pop is represented by
 x 
F  4log  5   where x is
 10 
represented by the intensity of
sound, how loud is the fizz if
x  103 
a. 4 decibels
b. 8 decibels
Moore Public Schools
Algebra II EOI Practice
c. 16 decibels
d. 32 decibels
13. What is $600 invested at 9%
interest, compounded quarterly,
worth in 3 years?
2.5c
a. $301.78
b. $306.54
c. $2,415.90
d. $2,430.62
2.5c
c. 606 ft.
d. 695.9 ft.
9. An initial deposit of $212 is
placed in a bank account and left
to grow, with interest
compounded continuously. If the
account balance is $249.41 after
2.5 years, what will it be after 6
years?
x
1
c. f  x   5  
3
x
4
d. f  x   6  
5
2.5c
c. 387
d. 401
8. Over the past several months, the
water level of a lake has been
decreasing by 0.02% each week.
If the highest water level before
the decrease started was 618 ft,
what was the level at the end of 6
weeks?
x
x
2.5c
a. $640.50
b. $641
c. $309.33
d. $313.13
57
c. $762
d. $784
Algebra II EOI Practice
14. The population, P , of prairie dogs
2.5c
increases according to the
equation P  2,250ert , where t is
the number of years, and r is the
rate of growth. Which equation
solves for r?
15. r  2
This formula gives the annual
interest rate, r, required for your
money to double in x years. If it
takes 18 years for your money to
double, what was the
approximate annual interest rate?
a. 2%
b. 4%
t
 P 
ln 

 2,250 
 2,250 
ln 

P 

c. r 
t
d. r 
t
 2,250 
ln 

 P 
Moore Public Schools
Algebra II EOI Practice
1
2.5c
 P 
ln 
2,250 

a. r 
t
b. r 
1
 
x
58
c. 8%
d. 18%
Algebra II EOI Practice
PASS 2.6a: Solve polynomial equations using various methods and
tools which may include factoring and synthetic division.
1. What are the factors of a
polynomial function if its graph
has x  intercepts , at 1 0, and 4
2.6a
a.
b.
c.
d.
x  x  1  and  x  4 
x  x  1  and  x  4 
 x  1  and  x  4
 x  1  and  x  4
5. What are the solutions of
3x3   x 2  12 x  0
2.6a
a. 4  3 1
b. 4  1 0
6. Find the zeros of the function
y  x 4  x3  15x 2   x  56
2.6a
a.
b.
c.
d.
2. Which of the following is a zero of
2.6a
the function
f  x   x 3  x 2  14 x  24
a.  4
b.  3
c.  2
d. 
2 1 and 2 complex roots
  1   4
 1  4
no real solutions
7. The polynomial function
P  x   2 x 3  3x 2  4 could have a
zero at ? .
2.6a
3. Use synthetic division to find
P  2  for P  x   x3   x 2  4 x
2.6a
a. 
b. 
c. 1 0 4
d.   
a. 8
b. 3
c. 12
d. 
1
4
d. 2
c. 
8. Which of the following binomials
is not a factor of the
polynomial 2 x3  11x 2  18 x  9 
2.6a
4. Use the Rational Roots Theorem
to give all possible rational roots
of the polynomial equation
2 x5   x 4  x  10  0
2.6a
a.
b.
c.
d.
 5
        
 2
     
0, 

Moore Public Schools
Algebra II EOI Practice
a.  2 x  3
b.  x  3
c.  x 
d.  x  3
9. Given that one of the roots of the
following equation is 4, find the
other roots.
P  x   x3  6 x 2  5 x  12
2.6a
a. 3,  1
b. 3 1
59
c. 3, 1
d.  
Algebra II EOI Practice
10. What is the factored form of
x3  4 x 2  12 x
2.6a
14. Find the sum of the zeros of the
following polynomial function.
y  4 x3 x  6
2.6a
a. x  x  6  x  2 
a. 2
b. 1
b. x 2  x  4   12
c. x  x  6  x   
d.  3 x     x 2  4 
15. Which polynomial has zeros at 1,
2, and 4?
2.6a
a.  x  1 x  2  x  4   0
11 Which binomial is a factor of
2.6a
x3   x 2  12 x  12 
a. x  2
b. x  1
c. x  6
d. x  4
12. The graph below is related to the
polynomial expression that has
factors of:
2.6a
a.
b.
c.
d.
 x  3   x  2   x  1
x  x  2  x  3
 x  x  3 x 
 x  3   x  2   x  1
c. 1
d. 0
b. x 2  3x  2  0
c. x3  7 x 2  x    
d. x3  7 x 2  x    
16. A rectangular prism has a volume
of 120 cubic inches. The length
2.6a
of the prism is 5 inches, the width
is  x  2  inches, and the height is
 x  3 inches. What are the width
and height of the prism?
a.
b.
c.
d.
width: 3 in., height: 8 in.
width: 4 in., height: 6 in.
width: 6 in., height: 4 in.
width: 8 in., height: 3 in.
17. What are the solutions to the
following equation?
x3  x 2 0 x
2.6a
a. 0 2  5
b. 0 2 5
13. Which function has zeros of
2 and i?
2.6a
c. 0  2  5
d. 0  2 5
18. What is
 3x5  15x4  4 x3  11x2  9 x  2 
2.6a
a.
b.
c.
d.
y  x 2  2i  2
y  x3  3x 2  2 x  1
y  x3  2 x 2  x  
y  x3  2 x 2  x  
Moore Public Schools
Algebra II EOI Practice
divided by  x 2  5 x    
a.
b.
c.
d.
60
3x3  2 x  1
3x3  2 x 2  7
3x3  2 x2   x  
3x3  30 x 2  x  
Algebra II EOI Practice
PASS 2.6b: Sketch the graph of a polynomial function.
1. The graph of which function rises
on the right end?
2.6b
4. Which of the graphs represents the
following function?
y   x3   x 2  x  
2.6b
a. f  x   2 x 2  x  3
1
b. f  x   x3  x 2  2 x
2
c. f  x   x 4 
1
d. f  x   x 2  x  2
2
2. Which describes end behavior of
the graph of y   x3  2 x 2   x  
2.6b
a.
b.
c.
d.
rises on both ends
rises on right, falls on left
rises on left, falls on right
falls on both ends
3. Which represents the function
y  x 4  3x3   x  
2.6b
5. Find the product of the zeros of
the function
y  x3  4 x 2  7 x  10
2.6b
a. 
b. 
Moore Public Schools
Algebra II EOI Practice
61
c. 10
d. 10
Algebra II EOI Practice
6. Use the table of information to
2.6b
determine which of the following
would best describe g  x  
7. Which statement describes the
characteristics of the graph of
f  x    5 x 4  3x 2  x  
2.6b
a. The graph primarily increases in
the third quadrant and increases
in the first quadrant.
b. The graph primarily decreases
in the second quadrant and
increases in the first quadrant.
c. The graph primarily increases in
the third quadrant and decreases
in the fourth quadrant.
d. The graph primarily decreases
in the second quadrant and
decreases in the fourth quadrant.
g  x
Number of real
roots
Number of
complex roots
Relative
minimum?
Relative
maximum?
1
2
Yes
Yes
a. a parabola that opens upward
and has no x  intercept
b. a parabola that opens downward
and has two x  intercepts
c. a cubic that has one x  intercept
d. a cubic that has three
x  intercepts
Moore Public Schools
Algebra II EOI Practice
62
Algebra II EOI Practice
PASS 2.6c: Given a graph of a polynomial function, identify the x- and
y-intercepts, relative maximums and relative minimums, using various
methods and tools which may include a graphing calculator.
1.
4. Which graph represents the function
f  x    x  2  x  3 x  1 
2.6c
2.6c
This is a portion of the graph of a
polynomial function. Apparently
the function has a double zero a.
b.
c.
d.
between
between
between
between

2 and 1

2 and 1
1 and 2
3 and 4
2. Which polynomial has solutions of
2 5, and  4
5. List all of the zeros of the
2.6c
polynomial function graphed.
2.6c
a.
b.
c.
d.
 x  2 x  5 x  4
 2 x  4 x  5 x  4 
 x   x  5 x  4
 2 x    x  5 x  4 
a.
b.
c.
d.
3. What are the relative maxima of
f  x   x 4  8 x 2  10
2.6c
a.
b.
c.
d.
 2  6  2,  6
 0, 10
 2 10  2, 10
no local maxima
Moore Public Schools
Algebra II EOI Practice
63
3,  3,  1, 1
3,  1, 9, 1
2, 0
3,  3,  1, 1,1
Algebra II EOI Practice
PASS 2.6d: Model a situation that can be described by a polynomial
function and use the model to answer questions about the situation.
1. Use the table of information to
3. The graph below is related to the
2.6d
2.6d
determine which of the following
polynomial expression that has
factors of:
would best describe g  x  
g  x
Number of real
roots
Number of
complex roots
Relative
minimum?
Relative
maximum?
1
2
Yes
Yes
a. a parabola that opens upward
and has no x  intercept
b. a parabola that opens downward
and has two x  intercepts
c. a cubic that has one x  intercept
d. a cubic that has three
x  intercepts
a.
b.
c.
d.
4. A brick falls from the top of a tall
building. The distance, in feet,
between the brick and the ground t
seconds after it falls is given by
d  16t 2  4t  446. How long after
the brick falls is it 390 feet from
the ground?
2.6d
2. A model rocket is launched into
the air. Its path can be modeled
using a quadratic equation. What
is the best way to determine when
the toy rocket reaches the highest
point in its flight?
2.6d
a. Graph the equation and find its
y  intercept
b. Graph the equation and find its
minimum.
c. Graph the equation and find its
x  intercepts
d. Graph the equation and find its
maximum.
Moore Public Schools
Algebra II EOI Practice
 x  3 ,  x  2  ,  x  1
x  x  2  ,  x  3
 x  x  3 x  1
 x  3 ,  x  2 ,  x  1
7
sec
4
9
b. sec
4
a.
c. 2 sec
d. 3 sec
5. Which function is graphed?
2.6d
a.
b.
c.
d.
64
x3  11x 2  34 x  24
 x3  11x 2  34 x  24
 x3  11x 2  34 x  24
x3  11x 2  34 x  24
Algebra II EOI Practice
PASS 2.7a: Solve rational equations.
1.
2.7a
3x
12
Solve.
 2
2
x 1 x 1
4.
2.7a
a. x  1, x  0
b. x  1, x  1
a. 2
c. x  2, x  5
b. 3
c. 4
d. x  2, x  1
d. 5
5.
2.
2.7a
Which of the following is the best
solution to the equation?
x9 x3

6
x
2.7a
What is the solution set of this
rational equation?
5
9 1


2x  2 2x 4
a. 6
a. x  2
b. x  2, or x  5
b.
3
c. x  5
c.
3, 6
d. x  3, or x  6
d.
3,  6
6.
3.
What is the value of x in this
rational equation?
2
3

x 1 x 1
Solve.
2.7a
x
1
1
 
x 1 2 x 1
2.7a
a. 1
a. 4
b. 0
b. 1
c. -1
d. no solution
Moore Public Schools
Algebra II EOI Practice
What is the value of x in this
rational equation?
4x  5
2x 
3
65
c.
1
2
d.
5
2
Algebra II EOI Practice
7.
2.7a
What is the solution set of this
rational equation?

10. Solve.
2.7a
3 1 1
 
x2 2 2 x
a. 3,  2
8.
3
2
b.
3
,1
2
b.
3, 2
c.
2, 3
3
c.  ,  1
2
d.
2, 3
d.
Solve.
2.7a
a. 
c.
3
7
d.
7
3
3
7
Solve.
2.7a
a. 
b.
7
4 x
4
x
x 1
7
3
b. 
9.
a.
x 1
2
2


x  1 2x  1 x  1
7x 3
 7
x 1 x
3
4
3
4
c. 
4
3
d. 
Moore Public Schools
Algebra II EOI Practice
66
2
,1
3
Algebra II EOI Practice
PASS 2.7b: Sketch the graph of a rational function.
1.
2.7b
Which equation has the graph
below?
a. y 
3
x2
c. y 
x
x2
2
b. y 
3x  1
b. y 
3
x2
d. y 
x
x2
d. y 
2.7b
Which equation might have the
graph shown below?
x 1
a. y 
3x  2
c. y 
2.
3.
2.7b
3x  2
x 1
3
x 1
4.
2.7b
What is the equation of the graph
below?
2
is to be
x
translated three units to the right
and four units downward. What
is the new equation?
The graph of y 
a. y 
a. y 
2
4
x3
2
4
x3
d. y 
2
4
x3
Moore Public Schools
Algebra II EOI Practice
 x  3 x  1
b. y   x  3 x  1
2
4
b. y 
x3
c. y 
3
c. y   x  3 x  1
d. y 
67
3
 x  3 x  1
Algebra II EOI Practice
5.
2.7b
6.
2.7b
Which of the graphs represent the
3
function y 
?
4x  1
a.
b.
c.
d.
7.
a.
c.
Which equation is represented by the
graph?
a. y 
2
x2
c. y 
2
x
b. y 
2
x
d. y 
2
x2
Moore Public Schools
Algebra II EOI Practice
Which of the graphs represent the
2
function y  ?
x
2.7b
68
b.
d.
Algebra II EOI Practice
PASS 2.7c: Given the graph of a rational function, identify the x- and
y-intercepts, asymptotes, using various methods and tools which may
include a graphing calculator.
1.
2.7c
What are the vertical asymptotes in the
2
graph of the function y  2 ?
x 1
a. x = 2
4.
2.7c
The following is a graph of
3
y
 3. What are the vertical and
x 1
horizontal asymptotes?
b. x = 2 and x = 1
c. x = 1 and x = -1
d. There are no vertical asymptotes
2.
2.7c
Determine the location of the horizontal
asymptotes in the graph of the function
3x  2
y
.
2x  1
a. x = -1; y = 3
a. y = 2
b. x = 0; y = 3
b. y = 1.5
c. x = 3; y = 0
c. y = 3
d. x = 1; y = 3
d. There are no horizontal
asymptotes
3.
2.7c
Which is the equation of the horizontal
asymptote for the rational function
3x 2
f  x  2
?
x  3x  4
5.
2.7c
a. 0 vertical asymptotes
a. x = 4
b. 1 vertical asymptote
b. x = 3
c. 2 vertical asymptotes
c. y = 3
d. 4 vertical asymptotes
d. y = 4
Moore Public Schools
Algebra II EOI Practice
How many vertical asymptotes does the
graph of this equation have?
x2
y 2
x 4
69
Algebra II EOI Practice
6.
2.7c
Below is a graph of a rational function,
f. Which is not a solution of the
equation f  x   0?
7.
2.7c
Which function is represented by this
graph?
2  x 2
a. f  x 
x
2  x 2
b. f  x 
x
c.
2  x2
d. f  x 
x
a. -2
b. -1
c. 1
d. 2
Moore Public Schools
Algebra II EOI Practice
2  x2
f  x
x
70
Algebra II EOI Practice
PASS 2.7d: Model a situation that can be described by a rational
function and use the model to answer questions about the situation.
1.
2.7d
Frank is planning to fly his plane on a
round-trip to an airfield 300 miles west.
There is a 20 mi/h wind blowing from
the east. Write the round-trip time t as
a function of Frank’s air speed r.
3.
2.7d
a. t  r   300  r  20   300  r  20 
A homeowner stocked his pond with
fish. The number of fish, F, increases
according to the equation below, where
t is the time in years. What is the
approximate number of fish after 10
years?
F
300
b. t  r  
 300  r  20 
r  20
2.
2.7d
c. t  r  
300
20r
a. 49 fish
d. t  r  
300
300

r  20 r  20
c. 138 fish
b. 69 fish
If the surface area of the closed cylinder
is 25 square inches, which equation
represents the height of the cylinder in
terms of r?
d. 291 fish
4.
2.7d
SA  2 rh  2 r 2
25  2 r 2
a. h 
2 r
b. h 
25  2 r
2 r
The cost, C, in thousands of dollars, to
remove x percent of the trash left by a
tornado is modeled by the equation
450 x
C
. Approximately what
225  x
percent of trash will be removed if 100
thousand dollars are spent?
a. 41%
b. 50%
2
c. 59%
d. 64%
c. h  25  r
d. h  25  r
Moore Public Schools
Algebra II EOI Practice
19  3  2t 
1  0.05t
71
Algebra II EOI Practice
PASS 3.1a: Display data on a scatter plot.
1.
3.1a
George was comparing the heights of
11 of his classmates with their algebra
scores. Which of the following
scatterplots is most likely a
representation of that relationship?
2.
3.1a
a.
b.
c.
d.
Moore Public Schools
Algebra II EOI Practice
72
Nancy made a scatter plot of how much
money she had left at the end of each
day of her vacation. Which table best
represents the data in her scatter plot?
Algebra II EOI Practice
3.
3.1a
Which of the scatter plots shown below
suggests a strong negative correlation?
4.
3.1a
Which of the following scatterplots
shows a negative correlation?
a.
a. A
b. B
b.
c. C
d. D
c.
d.
Moore Public Schools
Algebra II EOI Practice
73
Algebra II EOI Practice
PASS 3.1b: Interpret results using a linear, exponential or quadratic
model/equation.
1. Which is most likely the equation for
3. The chart gives the average number of
3.1b
3.1b
the curve of best fit for the scatterplot
students per computer in public schools
below?
in America.
Students per
Year
computer
2000-01
20.0
2001-02
18.0
2002-03
16.0
2003-04
14.0
2004-05
10.5
2005-06
10.0
2006-07
7.8
2007-08
6.1
Assuming a linear relationship, which is
the best estimate for the number of
students per computer during 1999-2000?
1
a. y  x  2
2
1
b. y  x  4
8
a. 5.4
b. 10.8
c. y  x  2
c. 20.2
d. y  x  3
2.
3.1b
In 2000, sales at ABC Electronics
totaled 4.9 million dollars. During
2006, total sales amounted to 12.1
million. Assuming the growth in sales
is a linear relation, what total sales can
the company expect in 2011?
d. 21.9
4.
3.1b
a. The population started out large, decreased
in size, and then became large again.
b. The population is observed to increase at
a faster rate as time passes.
a. 16.9 million
b. 18.1 million
c. The population is observed to increase
steadily over time.
c. 24.2 million
d. 25.3 million
Moore Public Schools
Algebra II EOI Practice
Which of these observations would be
consistent with an exponential model of
population growth?
d. The population grew very quickly but
then declined.
74
Algebra II EOI Practice
5.
3.1b
A clothing manufacturer is funding a
study to determine the amount spent
annually on clothes, given a family’s
income. This table contains data
tracking the clothing purchases for
seven families.
Annual Income
$25,100
29,600
34,400
28,700
34,600
31,500
27,700
6.
3.1b
Annual Clothes
Expenditure
$3,800
4,200
5,000
3,900
4,700
4,500
4,200
Time
April
May
June
July
August
a. 296
b. 323
c. 387
Assuming a linear relationship,
approximately how much would you
expect a family with an annual income
of $33,000 to spend on clothes?
d. 401
a. 4,400
b. 4,600
c. 4,800
d. 5,000
Moore Public Schools
Algebra II EOI Practice
A population of animals in an
experiment increases over time, as
shown in the table. Using an
exponential model and the data, what is
the best estimate of the number of
animals in May?
75
Number of Animals
235
?
445
611
841
Algebra II EOI Practice
PASS 3.1c: Identify whether the model/equation is a curve of best fit
for the data, using various methods and tools which may include a
graphing calculator.
2.
3.1c
1.
3.1c
Which type of function would best fit
the data in this scatterplot?
a. y 
a. Linear
2
2
x
b. 4 y 2  x 2  4
b. Exponential
c. 4 y  x 2  8 x
c. Logarithmic
d. y  2 x  x 2
d. Quadratic
Moore Public Schools
Algebra II EOI Practice
Which equation most closely fits the
data in this scatterplot?
76
Algebra II EOI Practice
The table shows the number of students
enrolled in the advanced algebra program at
Fairoaks High School during the 6 years
since its initiation.
Year (x)
1
2
3
4
5
6
4.
3.1c
3.
3.1c
Which equation is nearest to the line of
best fit of the data in this scatterplot?
b. n  6 x  60
c. n  8x  58
1
b. y  x  1
2
c.
d. n  10 x  46
y  2x
d. y  x  2
Moore Public Schools
Algebra II EOI Practice
Which of the following equations most
closely describes the relationship
between n, the number of students
enrolled, and x, the number of years the
class has been in existence?
a. n  x  65
a. y  x
77
Number of Students
(n)
66
72
82
90
100
106
Algebra II EOI Practice
7.
3.1c
Suppose you are selling yearbooks for
ten days at your high school. You
record your sales for the first nine days.
Day
1
2
3
4
5
6
7
8
9
Books
Sold
15 22 34 37 57 61 78 89 113
Choose the best estimate for the equation
of the line of best fit and use the equation
to predict the number of yearbooks you
will sell on the tenth day.
5.
3.1c
a. y  11.75x  2.5; 115
Which line best fits the scatter plot
data?
b. y  7 x  15; 85
c.
b. 8  x  y
d. y  8 x  5; 85
c.
y 8 x
8.
d. 2 y  x  15
6.
3.1c
y  11.75x  2.5; 115
a. 2 y   x  8
3.1c
Year after
1900
Population
(millions)
The table shows the relationship
between calories and fat in fast-food
hamburgers.
Hamburger
A B C D E F G H
The table below gives data about the
population of South Carolina in tenyear intervals from 1900 to 1990.
t 0 10 20 30 40 50 60 70 80 90
P 1.3 1.5 1.7 1.7 1.9 2.1 2.4 2.6 3.1 3.5
Which of the following could be an
exponential model for this data?
I
Fat (grams) 46 30 27 26 13 20 25 13 26
Calories 720 530 510 500 305 410 440 320 590
Which equation best models the
relationship of fat, x, and calories, y?
a. P  1.0111.30 
t
b. P  1.30 1.011
t 10
y  15 x  30
c. P  1.30 1.011
b. y  13x  20
d. P  1.17 1.110 
a.
c.
t
y  24 x  8
d. y  28 x
Moore Public Schools
Algebra II EOI Practice
78
t
Algebra II EOI Practice
PASS 3.3: Identify and use arithmetic and geometric sequences and
series to solve problems.
1.
3.3
Driving a piling into a harbor bottom, a
pile driver sinks the piling 24 inches on
the first stroke, 18 inches on the second
stroke, and 13 1 inches on the third
4.
3.3
2
stroke. If the sequence is continued,
how far will the piling be driven down
on the 5th stroke?
5.
a. 1
3.3
1
in.
2
b. 1,050
d.
15,250
Which of the following sets represents
an arithmetic sequence?
d. {1, 16, 36, 64, 100, …}
6.
3.3
Is the sequence arithmetic? If so, what
is the common difference?
-0.5, 3.5, 7.5, …
a. no.
7.
3.3
b. yes, 3.0
3.3
5,250
c. {3,  5, 7,  9, 11, …}
19
d. 7
in.
32
3.
c.
b. {1, 3, 9, 27, 81, …}
c. 6 in.
3.3
a. 25,250
a. {2, 11, 20, 29, 38, …}
1
b. 4 in.
2
2.
What is the sum of the first 100 positive
multiples of 5?
If an  6   n  1 5, then a7 
a. 31
c.
40
b. 36
d.
42
Find the sum of the first 6 terms of the
series: 2 – 6 + 18 – 54 + …
c. yes, 3.5
a. 122
c.
1094
d. yes, 4.0
b.  364
d.
 40
8.
What is the sum of the first five terms
of an arithmetic series if the first term is
6 and the common difference is  2?
3.3
Find the value of k that makes the
sequence arithmetic.
13, k ,  3, 2, ...
a. 10
c.
25
a. 5
c.
5
b. 20
d.
14
b.  8
d.
 10
Moore Public Schools
Algebra II EOI Practice
79
Algebra II EOI Practice
9.
3.3
Find the sum of the multiples of 6 from
18 to 312, inclusive.
a. 50
c. 5616
b. 52
d. 8250
13. A new pair of sneakers cost $70 now.
3.3
Assuming an annual 8% price increase,
what is the cost of the shoes 5 years
from now?
10. A pile of bricks has 85 bricks in the
3.3
bottom row, 81 bricks in the second
row up, 77 in the third, and so on up to
the top row that contains only 1 brick.
How many bricks are in the 12th row?
a. 41
c. 49
b. 45
d. 56
c. $105,000
b. $12,500
d. $122,500
12. Suppose you put $1.50 in a jar at the
3.3
end of one week. One week later you
put in $2.00. At the end of the third
week you deposit $2.50 and continue to
add 50¢ to the previous week’s deposit
thereafter. What is your weekly deposit
at the end of the 27th week?
a. $15.00
c. $15.50
b. $14.50
d. $231.00
Moore Public Schools
Algebra II EOI Practice
c. $89.38
b. $88.18
d. $95.23
14. A forest fire covers twice the amount of
3.3
forest as it did 3 days ago. If the fire
covered 300 square miles 3 days ago
and it continues to grow at the same
rate, how many square miles will it
cover 12 days from now?
11. A new business has $10,000 in sales the
3.3
first year. Sales are expected to
increase by a constant amount each
year. What is this constant yearly
increase in sales if the total sales for the
first 5 years is $500,000?
a. $45,000
a. $102.85
80
a. 9,600
c. 3,200
b. 4,800
d. 6,400
Algebra II EOI Practice
Answer Key
Pass 1.1a
Pass 1.1b
Pass 1.2a
Pass 1.2b
1.
b
1.
a
1.
b
1.
c
2.
c
2.
d
2.
d
2.
a
3.
b
3.
d
3.
a
3.
d
4.
d
4.
b
4.
b
4.
b
5.
a
5.
b
5.
d
5.
c
6.
a
6.
d
6.
a
6.
c
7.
c
7.
b
7.
c
7.
b
8.
d
8.
c
8.
d
8.
c
9.
a
9.
c
9.
d
9.
c
10.
c
10.
d
10.
a
10.
d
11.
c
11.
c
11.
d
11.
d
12.
b
12.
a
12.
b
13.
a
13.
a
13.
d
14.
b
14.
c
15.
b
15.
d
16.
a
17.
b
18.
c
19.
a
20.
b
21.
c
22.
c
Moore Public Schools
Algebra II EOI Practice
81
Algebra II EOI Practice
Pass 1.3b
Pass 2.1a
Pass 2.1b
Pass 2.1c
1.
d
1.
d
1.
b
1.
b
2.
a
2.
b
2.
b
2.
a
3.
a
3.
b
3.
a
3.
d
4.
c
4.
c
4.
d
4.
c
5.
c
5.
c
5.
c
5.
b
6.
b
6.
a
6.
c
6.
a
7.
b
7.
b
7.
a
7.
c
8.
a
8.
c
8.
b
8.
a
9.
b
9.
b
9.
c
9.
d
10.
d
10.
a
10.
b
10.
b
11.
a
11.
c
11.
a
11.
d
12.
c
12.
a
12.
d
13.
d
13.
c
13.
b
14.
d
14.
a
15.
a
15.
b
16.
c
17.
d
18.
a
19.
b
20.
a
Moore Public Schools
Algebra II EOI Practice
82
Algebra II EOI Practice
Pass 2.1d
Pass 2.1e
Pass 2.2a
Pass 2.2b
1.
a
1.
a
1.
c
1.
b
2.
c
2.
d
2.
c
2.
b
3.
d
3.
c
3.
d
3.
a
4.
a
4.
a
4.
b
4.
d
5.
a
5.
a
5.
c
5.
a
6.
c
6.
a
6.
c
6.
a
7.
b
7.
a
7.
b
7.
c
8.
d
8.
b
8.
b
8.
a
9.
c
9.
c
9.
a
9.
b
10.
d
10.
b
10.
c
10.
b
11.
b
11.
c
11.
a
11.
b
12.
b
12.
a
12.
c
12.
a
13.
d
13.
a
13.
d
13.
d
14.
b
14.
b
14.
c
15.
a
15.
b
15.
d
16.
b
16.
d
17.
a
18.
b
19.
b
Moore Public Schools
Algebra II EOI Practice
83
Algebra II EOI Practice
Pass 2.2c
Pass 2.3a
Pass 2.3b
Pass 2.3c
1.
d
1.
b
1.
a
1.
b
2.
d
2.
c
2.
b
2.
b
3.
b
3.
a
3.
b
3.
a
4.
c
4.
c
4.
d
4.
d
5.
a
5.
c
5.
b
5.
a
6.
c
6.
b
6.
c
6.
c
7.
a
7.
b
7.
c
7.
b
8.
c
8.
d
8.
c
8.
d
9.
c
9.
b
9.
a
9.
c
10.
c
10.
d
10.
a
11.
d
11.
d
12.
d
12.
a
13.
c
13.
c
14.
a
14.
a
15.
c
15.
c
16.
b
16.
c
17.
a
17.
b
18.
b
18.
b
19.
d
20.
b
Moore Public Schools
Algebra II EOI Practice
84
Algebra II EOI Practice
Pass 2.4
Pass 2.5a
Pass 2.5b
1.
d
16.
c
1.
c
1.
c
2.
d
17.
c
2.
c
2.
c
3.
b
18.
d
3.
b
3.
d
4.
d
19.
a
4.
d
4.
c
5.
b
20.
b
5.
a
5.
c
6.
c
21.
a
6.
b
6.
a
7.
a
22.
b
7.
a
7.
c
8.
c
23.
c
8.
c
8.
d
9.
a
24.
d
9.
a
9.
a
10.
c
25.
a
10.
a
10.
c
11.
d
26.
b
11.
b
12.
d
27.
a
12.
a
13.
c
28.
d
13.
c
14.
d
29.
c
14.
c
15.
b
30.
a
15.
a
31.
c
16.
d
32.
d
17.
a
18.
a
19.
b
20.
a
21.
a
Moore Public Schools
Algebra II EOI Practice
85
Algebra II EOI Practice
Pass 2.5c
Pass 2.6a
Pass 2.6b
Pass 2.6c
1.
a
1.
b
1.
d
1.
c
2.
b
2.
a
2.
c
2.
d
3.
b
3.
b
3.
a
3.
b
4.
c
4.
a
4.
b
4.
b
5.
d
5.
c
5.
d
5.
d
6.
c
6.
b
6.
c
7.
b
7.
d
7.
c
8.
b
8.
c
9.
d
9.
a
10.
b
10.
c
11.
d
11.
a
12.
b
12.
d
13.
d
13.
d
14.
a
14.
d
15.
b
15.
c
16.
a
17.
a
18.
a
Moore Public Schools
Algebra II EOI Practice
86
Algebra II EOI Practice
Pass 2.6d
Pass 2.7a
Pass 2.7b
Pass 2.7c
1.
c
1.
c
1.
c
1.
c
2.
d
2.
d
2.
b
2.
b
3.
d
3.
c
3.
a
3.
c
4.
c
4.
d
4.
a
4.
d
5.
c
5.
c
5.
d
5.
a
6.
d
6.
a
6.
a
7.
c
7.
d
7.
c
8.
a
9.
a
10.
a
Moore Public Schools
Algebra II EOI Practice
87
Algebra II EOI Practice
Pass 2.7d
Pass 3.1a
Pass 3.1b
Pass 3.1c
1.
d
1.
b
1.
d
1.
d
2.
b
2.
d
2.
b
2.
c
3.
d
3.
d
3.
d
3.
b
4.
a
4.
c
4.
b
4.
c
5.
b
5.
c
6.
b
6.
b
7.
a
8.
c
Moore Public Schools
Algebra II EOI Practice
88
PASS
2.1a:
Recogniz
e the
Pass 3.3
parent
graphs 1.
d
of
d
polynomi2.
al,
a
exponent3.
ial, and 4.
a
logarith
mic
5.
a
functions
6.
b
and
predict
7.
b
the
effects of8.
b
transfor
mations 9.
d
on the
parent 10. b
graphs,
11. a
using
various 12. b
methods
and tools13. d
which
14. b
may
include
graphing
calculato
rs..
Moore Public Schools
Algebra II EOI Practice
Algebra II EOI Practice
89