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GPS ALGEBRA EOCT REVIEW PACKET
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GPS ALGEBRA
SAMPLE EOCT TEST – STUDY GUIDE
CROSSROADS
1
GPS ALGEBRA EOCT REVIEW PACKET
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1. Use the table of values to determine the function represented.
X
-2
-1
0
1
2
A)
B)
1.
2.
A)
B)
3.
g(x)
2
1
0
1
2
g ( x)
g ( x)
x
x
g ( x)
x
D) g ( x )
x3
C)
2
Given the graph below, which of the following are true?
I)
f(x) is increasing on the interval 1 x 3 .
II)
f(x) has exactly 2 zeros from 1 x 5 .
III)
f(x) is decreasing on the interval 0 x 2 .
IV)
f(x) has a local maximum at (3,0).
A) I and II
C) I and IV
B) I and III
D) I, II, and IV
Which of these are characteristics of the parent function of an absolute value equation?
I.
The parent function on an absolute value equation has the vertex at (0,0)
II.
The parent function of an absolute value equation opens downward.
III.
The parent function of an absolute value equation has the y-axis as its line of symmetry.
I and II only
C) II and III only
I and III only
D) I, II, and III
Which type of function would have a constant rate of change?
A) Linear
B) Quadratic
C) Cubic
D) square root
GPS ALGEBRA EOCT REVIEW PACKET
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Find the 25th term of the sequence 7, 11, 15, 19, 23, ….
A) 103
C) 107
B) 104
D) 111
5. What is a recursive rule for the sequence 2, 6, 10, ….?
4.
6.
A) an
2(3)n
B) a1
2, an
Add (6 x 4
A)
B)
1
3an
1
C) a1
2, an
an
D) a1
3, an
2 an
4
1
1
2 x3 9 x 7) to ( 12 x 4 6 x 3 21x 32)
6x8 4x6 12x2 25x
6x4 4x3 30x 25
6x4 4x3 12x 25
D) x( 6 x 7 4 x 5 12 x 25)
C)
For the sequence: 1, 6, 11, 16, …., the 50th term would be:
A) 56
C) 246
B) 251
D) 256
8. Al Gone went on a long trip. The graph below represents the relationship between distance
and time. During what interval was Al’s average rate of travel the fastest?
7.
A) 0 to 6
B) 6 to 8
C) 8 to 11
D) 11 to 16
GPS ALGEBRA EOCT REVIEW PACKET
9.
4
Simplify.
(7a 3b)(2a b)
A) 14a2
B) 14a2
14a2 6ab 3b2
D) 14a2 3b2
ab 3b2
13ab 3b2
10. Which is equivalent to
C)
3x 5 y
?
7 14 x
6 x2 5 y
C)
14 x
3x 2 5 y
D)
14 x
8y
21
x2
B)
14
A)
y)2 ( x
11. Simplify: ( x
A) 2y
B) 4 xy
2y
2
y)2
C) 4xy
D) 0
12. Tom is going to dinner at a pasta restaurant. He is allowed to choose one of three pastas, one
of 4 sauces, and one of three meats. How many different pasta dishes can he make?
A) 7
C) 24
B) 10
D) 36
13. Given a spinner with 8 equal sections numbered 1 through 8, what is the probability that you would
spin an even number in the first spin and a number less than 4 in the second spin?
1
16
1
B)
8
3
C)
16
1
D)
33
A)
14. Given a bag of 3 marbles, 5 blue marbles, and 4 green marbles, find the probability of drawing 2 red
marbles at once.
1
16
1
B)
16
1
C)
16
1
D)
16
A)
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15. Given a standard deck of 52 cards, find the probability of drawing 2 clubs.
1
16
1
B)
16
1
C)
16
1
D)
16
A)
16. Is the graph a function?
A. yes
B. no
C. cannot be determined
18. Give the interval over which the graph is decreasing.
A. All real numbers
B. 9 x 9
C. 10 x 5
D. 2 x 6
19. What is the domain of the graph?
A. All real numbers
B.
9, 8, 7,...9
C. 9 x 9
D. 10 x 5
20. Which one is of the following represents the graph f ( x)
x
A
D
B
C
21. Which one is of the following represents the graph f ( x)
A
B
C
x2
D
GPS ALGEBRA EOCT REVIEW PACKET
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22. Which one is of the following represents the graph f ( x)
A
B
C
D
23. Which one is of the following represents the graph f ( x)
A
B
x3
C
x
D
24. What is the maximum value of the function?
(1, 0)
B. (6,0)
C. (4,8)
D. (8,4)
A.
24. What is the domain of the function?
A. 1
x
B. 1 x
C. 0 x
D. 0 x
1
7
7
8
8
2
3
4
25. Draw the next shape.
26. Write a closed form rule for the number of dots in the pattern of figures above.
A. tn
n 3, for n 1, 2,3,...
B. tn
2n, for n 1, 2,3,...
C. tn
2n 1, for n 1, 2,3,...
D. tn
n 2, for n 1, 2,3,...
GPS ALGEBRA EOCT REVIEW PACKET
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27. If this pattern continues how many dots will be in the 100th figure?
A. 100
B. 101
C. 199
200
E. 201
D.
28. The table below represents the amount of your gross pay based on how many hours you work. Use the
table to find a function that will show your gross pay based on the numbers of hours you work.
x
f(x)
f ( x)
B. f ( x)
C. f ( x)
D. f ( x)
A.
0
0
1
8.50
2
17
3
25.50
4
34
5
42.5
6
51
7
59.50
7x
8.5x
17 x
8x
29. The diagram represents the dimensions of a box. Which expression represents the volume of the figure
below?
3x3
3
B. 5x
3
C. 3x
3
D. 5x
A.
2
2
6 x2
6 x2
x 2
x
x 2
30. Given f ( x )
x 2 , describe the transformation f ( x)
4x2.
A. Stretches vertically by 4
B. Shrinks vertically by 4
C. Shifts 4 units up
D. Shifts 4 units down
31. Given f ( x)
x , describe the transformation f ( x)
A. Stretches vertically by 3
B. Shrinks vertically by 3
C. Shifts 3 units up
D. Shifts 3 units down
x 3
GPS ALGEBRA EOCT REVIEW PACKET
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32. There are five points in a plane, buy no three points are collinear. How many different straight lines that
pass through two of the points are possible?
A. 2
B. 10
C. 15
D. 20
33. Danny has 3 identical color cubes. Each of the 6 faces on the color cubes is a different color. He also has
2 fair coins. What is the total number of possible outcomes if Danny rolls all three cubes OR flips both
coins?
A. 22
B. 144
C. 220
D. 864
34. There are 14 students in a mathematics competition. The students with the greatest number of points
will be first place winner, and the student with the second greatest number of points will be the second
place winner. How many different ways can the 14 students finish in first place and second place?
A. 27
B. 91
C. 182
D. 196
35. You have 9 red crayons, 4 blue crayons, 7 purple crayons, and 5 black crayons in a basket. A student
reaches into basket and randomly selects a crayon. What is the probability that the crayon will be either
black or blue?
A.
4
16
B.
9
25
C.
13
25
D.
9
16
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36. There are 6 red apples, 4 yellow apples, and 2 green apples in a bucket. Maria will choose 2 apples at
random without replacement. What is the probability that Maria will choose a red apple and then a
green apple?
5
121
6
B.
121
1
C.
11
1
D.
12
A.
37. There are 6 red apples, 4 yellow apples, and 2 green apples in a bucket. Maria will choose 2 apples at
random without replacement. What is the probability that Maria will choose a red apple and then a
green apple?
5
121
6
B.
121
1
C.
11
1
D.
12
A.
38. The table shows the probability of each possible sum when two cubes with faces numbered 1 through 6
are rolled and the numbers showing on each face are added.
Sum
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
5
4
3
2
1
Probability 1
36
36
36
36
36
36
36
36
36
36
36
You are playing a game in which you get 10 points when the sum is a perfect square. You get 5 points if
the sum is a prime number. You get 0 points if the sum is a number which is neither a prime nor a
perfect square.
What is the expected value, to the nearest 0.1, for one roll of the two number cubes?
A. 4.0 points
B. 4.1 points
C. 4.2 points
D. 4.3 points
GPS ALGEBRA EOCT REVIEW PACKET
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39. The table shows the average high temperature, in ˚F, recorded in Atlanta, GA, and Austin, TX, over a sixday period.
Day
1 2 3 4 5 6
Temperature in Atlanta 85 88 83 79 81 85
Temperature in Austin 80 86 82 80 93 89
Which conclusion can be drawn?
A. The median temperature over the six-year period was the same for both cities, but the interquartile range
is greater for Austin than Atlanta.
B. The mean temperature of Atlanta was higher than the mean temperature in Austin, and the interquartile
range is greater for Austin than Atlanta.
C. The mean temperature of Austin was higher than the mean temperature in Atlanta, but the median
temperature of Austin was lower.
D. The mean and median temperatures of Atlanta were higher than the mean and median temperatures of
Austin.
40. The table shows the scores of four students on the first four math quizzes.
Student
Quiz Scores
Mean Score
Anna
80,90,75,75 80
Jim
100,70,80,70 80
Stacy
92,78,68,82 80
Ted
71,84,84,81 80
Which student had the least mean absolute deviation on the quiz scores?
A. Anna
B. Jim
C. Stacy
D. Ted
41. The heights, in inches, of five girls were 66,64,68,70, and 65. A sixth girl joined the class. The mean
height of the six girls in the class was 66 inches and the mean absolute deviation was 2 inches. What was
the height of the sixth girl who joined the class?
A. 63 inches
B. 64 inches
C. 65 inches
D. 66 inches
42. A train travels at a rate of (4x+5) miles per hour. How many miles can it travel at a rate of (x-1) hours?
A. 3x-4 miles
B. 5x-4 miles
C. 4x²+x-5 miles
D. 4x²-9x-5 miles
GPS ALGEBRA EOCT REVIEW PACKET
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43. Which binomial expansion represents the volume of the box?
x2
3
B. x
3
C. x
4
D. x
A.
8x 16
12x2 48x 64
768x2 192x 4
12x3 96x2 256x 256
x 4
x 4
x 4
44. What is the product of the expression represented by the model below?
A. 3x 11
B.
3
x
x
30
3
6
5
2
x 768x 192x 4
4
3
D. x 12x
96x2 256x 256
C.
x
x
45. Which expression represents the area of a rectangle given that the length is
3d 9?
A. 7
B. 12
C.
4
3(d 3) 2
7d 3
D. 2
d 9
46. Which expression is equivalent to 3
27 x
3
9 x
B.
9
3
C.
9 x
3
D.
27 x
A.
9
?
27 x
4d 12
and the width is
d2 9
GPS ALGEBRA EOCT REVIEW PACKET
47. What value of x makes the equation
12
x 3 7 true?
A. 4
B. 10
C. 16
D. 21
48. A right isosceles triangle has a hypotenuse with length of 4 y. Which expression represents the length of
one of the legs of the triangle?
A. 2y
B. 4y
C. y 2
D. 2 y 2
50. Match the graph with the corresponding function.
A. f ( x)
1.___
x B. f ( x)
x C. f ( x)
2.___
x 2 D. f ( x)
x 3 E. f ( x)
3.___
1
F. f ( x)
x
4.___
5.___
x
6.___
51. Match the graph with the corresponding function.
A. f ( x)
1.___
x B. f ( x)
x C. f ( x)
2.___
x 2 D. f ( x )
3.___
x 3 E. f ( x)
4.___
x
5.___
52. Match the graph with the corresponding function.
A. f ( x)
1.___
x 2 B. f ( x)
2.___
x
3 C. f ( x )
3.___
x 2 7 D. f ( x)
4.___
x 3 1 E. f ( x)
5.___
1
F. f ( x)
x
6.___
x 3
GPS ALGEBRA EOCT REVIEW PACKET
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53. Match the graph with the corresponding function.
A. f ( x) x 6 4 B. f ( x) x 4 3 C. f ( x) x 1 7 D. f ( x) x 2 E. f ( x) x 2 1 F. f ( x) x 3 2
1.___
2.___
54. Draw in the graphs.
1. f ( x) x
2. f ( x) x
Distance from Home (miles)
1.___
2.___
3.___
3. f ( x) x2
3.___
4.___
4. f ( x) x3
4.___
5.___
E.
f ( x)
5.___
6.___
x
F. f ( x)
x2
6.___
55. Which statement best describes what is being modeled by this graph?
Wyatt’s Jog
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Time in minutes
A. Wyatt started from a standstill, gradually picking up speed, jogged at a constant rate for 4 minutes,
gradually slowed down, and stopped.
B. Wyatt began jogging at a constant rate and increased his pace steadily until coming to a complete stop
after jogging for 11 minutes.
C. Wyatt jogged at a steady pace for 4 minutes, took a 4-minute break, walked at a steady pace for 3
minutes, and stopped.
D. Wyatt jogged uphill for 4 minutes, jogged on a flat surface for 4 minutes, jogged downhill for 3 minutes,
and stopped.
56. Heather is taking a turn in playing a game.
- If she answers the first question correctly, she is awarded 2 points.
- If she answers the second question correctly, she is awarded 4 points.
- If she answers the third question correctly, she is awarded 6 paints.
If this pattern continues and Heather answers all of the questions correctly, which function can be used
to calculate the total number of points awarded?
A.
fCn)
= n 2 +2n
2
B. !(n)=n +n
c.j(n)=n 2 +2
D.
s~ 7
v
2
!Cn)=n +1
These are the first four steps of a dot pattern.
• •
• •
• • •
• •
• • •
• • • ••
• • •
• • • • •
•••••••
Step]
Step 2
Step J
•
• •
• • •
• • • •
• •
• •
• • •
• • • •
• • • • •
Step 4
The pattern continues. Which function represents the number of dots in Stepn?
A. f(n)=n 2 +n-5
B. f(n)=n 2 +n+3
C. fen) = n2
+ 5n-1
2
D. f(n)=n +2n+2
--------
-
The first term in this sequence is -3.
~
a
-3
44
23
60
/I
Which function represents the sequence?
A. fen) = n 2
-
4
3
B. f(n)=n -4
C. !(n)=-n 3 +4
D. f(n)=-n 2 +4
----------- ---
5
121
~"
~.
A squirrel in a tree dropped an acorn 48 feet to the ground. The number of seconds, t, it
took the acorn to reach the ground is modeled by this equation.
-16t 2 +48= 0
How many seconds did it take the acorn to reach the ground?
-.J
A.
B. 3
C.r
D. 32
60<
.. 1
An,art tea~her painted a.rectangular picture on the art room wall. Then she enlarged it
by mcreasmg both the Width and the length by x feet. This equation can be solved to
find x, the number of feet the art teacher increased each dimension of her picture.
Xl
+7x-18=O
The area of the enlarged picture was 35 square feet. Which dimensions could be for the
picture before it was enlarged?
A.
B.
C.
D.
3 feet by 6 feet
5 feet by 3 feet
7 feet by 5 feet
9 feet by 2 feet
---
bo' •
Breanne is rowing a boat at a rate of 5 miles per hour. She can row 7 miles downstream,
with the current, in the same amount of time it takes her to row 3 miles upstream,
against the current. This equation can be used to find the speed of the current in the
stream.
7
5+c
3
5-c
What is the speed of the current in the stream?
A.
B.
C.
D.
2 miles
3 miles
4 miles
5 miles
per hour
per hour
per hour
per hour
----_
.
16
-6j..
What value of x makes this equation true?
4
1
x
2x
-+-=8
A.
B.
c.
D.
,.
,
bj.
_.. The base of a triangle is represented by E inches. The height is 4 inches. The area of
the triangle is 18 square inches.
What is the value of x?
A. 9
B. 18
C. 36
D. 81
6V-.
The equation .j3x + 4 = 5 compares the areas of two congruent triangles. What is
the value of x?
A. 1
B. 3
C.?
D. 25
------
---- -------
ir.
The graph of the function f(x)
= x 3 + X Z + 4 is shown on this coordinate plane.
,
y
20
15
10
c
""'"
/
-4
-3/
-1
:7 Il~
I
J
-
I 2 3 4
x
/15
1
1
20
T
Which statement best describes the behavior of the function within the interval
x=-3 tox = O?
A.
B.
C.
D.
From
From
From
From
left to
left to
left to
left to
right,
right,
right,
right,
the
the
the
the
function
function
function
function
rises only.
falls and then rises.
rises and then falls.
falls, rises, and then falls.
66.
.' : ,~'What is the formula for the function with a graph the same as the graph obtained by
- reflecting the graph of y = .J-x across the x-axis?
A.
B.
C.
D.
.
-
--_.
y=-h
y=-E
y=h
y=E
.
---_.
67.
1
The vertex of the quadratic function g(x) is located at (4, 2). An x-intercept of g(x) is
located at (5, 0). What is the y-intercept of g(x)?
A.
B.
C.
D.
(0, -30)
(0,-14)
(0, -4)
(0,3)
--
--
...
_-.-------.
17
/8
:8
The quadratic function f(x) has these characteristics:
•
•
The vertex is located at (8, - 2).
The range is -2 S:. f(x) < co.
Which function could be f (x)?
f(X)=~X2_8X+30
A.
1 2
3
B. !(x)=2x -8x+ 1
C.
!(X)=_~X2
+8x-34
1 2
6
D. !(x)=-2x -2x+
i.e;;I .
v
Use this graph of the function g(x) to answer the question.
Which statement about the real solutions of g(x) is true?
A. g(x) has
B. g(x) has
C. g(x) has
D. g(x) has
no real solutions.
exactly one real solution.
two real solutions that are rational.
two real solutions that are irrational.
1'1
7~
V
~7
·What are the solutions to the equation 289 =
(! x 3
)2
8 ?
A. x = -27 only
B. x = 750nly
C. x=-27andx=75
D. x = - 75 and x = 75
Which expression represents the sum of the first n multiples of 8?
8n
B. 8n 2
C. 4n 2 +4n
D. 8n 2 +8n
A.
72.
Alex started a business making bracelets. She sold 30 bracelets the first month. Her
goal is to sell 6 more bracelets each month than she sold the previous month.
If Alex meets her goal, what is the total number of bracelets she will sell in the first
12 months?
A. 378
B. 426
C. 498
D. 756
Which function is equivalent to f(x) = 2/x + 21 + I?
A. j(x) =
B. j(x) =
12x+5, if x2':-2
-2x-3, if x <-2
12x+5, if x 2': 1
-2x-3,
1-2X-5
2x+3:
C. j(x)=
D. j(x)=1-2X-5
2x+3:
if x <1
if x 2':-2
if x <-2
if x 2': 1
if x<l
to
7V-.
What is the function that results from multiplying f(x) =
2 units to the right?
l-X-2
'
x+2,
f(x) = l-X-2 '
x+2,
A. f(x)
B.
=
1-x+2,'
f(x) = 1
'
-x+2,
if x:S;
2
if x> 2
if x:S; 0
if x> 0
2
C. f(x) =
x-2
if x:S;
D.
x-2
if x> 2
if x :s; 0
if x> 0
7'>-:' This graph shows the two parts of a piecewise function.
For what value of x is the function NOT defined?
A. -1
B. 0
C.
D.
- - -
1
2
o.
.
----------
Ixl by -1 and shifting it
76.
:"
For which graph of a set of data is a linear function the best model?
A.
y
l
50
40
I ,' _
--j'-
•,
30 -'-+---1-!-'.
.
I
20
•
\0 _.... ~_!-
..
o
I.
'---'---'-~~~--1~'
X
10 20 30 40 50
B.
y
50+-.-l~~:
,I. :
40
3O···J_·J·
+.
j :
.L .,
!.
I
20··-1...!'···1!-··r······-L~·!1
.!
10- ..
o
L-...'-....L._ _L....--'-I""
X
10 20 30 40 50
c.
y
_ .....;--. r·--···__....., .._...•.•....- ...:
50 _.. ·~-t-----.-·-l
40 --_. -.--~-~.!. .~
I
30 _.•.-+
-+
•
! •
··+.-t·_·..-r·---,_..__.
20
10 - ....-i-.._.~_._:
i .":-
o'--'-----'----'---'-I~'
X
10 20 30 40 50
Y
D.
50 ..
40
30
20
I0 --l-~-L- --!l
0'-1-'-0-2....0---'-30--'40-5-0...' x
---------------
This graph plots the number of wins in the 2006 and 2007 seasons for a sample of
professional football teams.
Team Wins, 2006 and 2007
"'-"'-"',"--""
16
Q
0
14
'"e<:l 12
<lJ
1JJ
t
. 0
0
N
10
8
.S
'"c
:E
6
4
2
0
,·..····················T·-····
=~-1Ft=H=Hi
, ~ - . ,.....'j' ~, . _~~-,
-.
~
1+++·
-:±H:I-i~~t
2
4
6
8 10 12 14 16
Wins in 2006 Season
The linear regression model for these data is y = 1.10x - 2.29. Based on this model,
what is the predicted number of 2007 wins for a team that won 5 games in 2006?
A.3
B. 4
,_-~
~
C. 5
D. 6
---n
10,
This graph shows the expected income from sales vs. price per issue for a new
magazine.
Price vs. Expected
y
60
Income from Sales
'--1=~~:,-j-
Tool
50
40
30
20
10
o
2 3 4 5 6
Price (in dollars)
Which equation models these data?
A. y=-5.1x 2 +34.4x-3.0
B. y
= 5.1x 2 -
34.4x + 3.0
2
C. y=-34.4x +5.1x-3.0
D. y=34.4x 2 -5.lx+3.0
.
This graph shows the price of a new audio-visual component over time.
Price of New Audio-Visual
Component Over Time
Year
0
2
4
6
8
Median Price
(in dollars)
500
425
360
280
200
Which is the best explanation for why a linear model may not be appropriate for these
data?
A.
B.
C.
D.
The median price decreases over time.
The value of the median price cannot be negative.
The value of the median price cannot continue to decrease.
A quadratic model would be a better fit because the rate of decrease is decreasing.