ALGEBRA I (COMMON CORE)
The University of the State
REGENTS HIGH SCHOOL E
Wednesday, June 17, 2015- 1:1
INATION
to 4:15p.m., only
9ev
Student Name: ------------------~~~~~~~~~-----------------e.....
.,.,
The possession or use of any communications device 's strictly prohibited when taking this
examination. If you have or use any communications devic , no matter how briefly, your examination
will be invalidated and no score will be calculated for you.
Print your name and the name of your schoo on the lines above.
A separate answer sheet for Part I has be n provided to you. Follow the
instructions from the proctor for completing the s dent information on your answer
sheet.
This examination has four parts, with a total f 37 questions. You must answer
all questions in this examination. Record your ans ers to the Part I multiple-choice
questions on the separate answer sheet. Write y ur answers to the questions in
Parts II, III, and IV directly in this booklet. Allwor should be written in pen, except
graphs and draWings, which ~hould be done in pen il. Clearly indicate the necessary
steps, including appropriate formula substitutio s, diagrams, graphs, charts, etc.
Utilize the information provided for each ques ·on to determine your answer.
Note that diagrams are not necessarily drawn to cale.
The formulas that you may need to answer so e questions in this examination
are found at the end of the examination. This shee is perforated so you may remove
it from this booklet.
Scrap paper is not permitted for any part of is examination, but you may use
the blank spaces in this booklet as scrap paper. A perforated sheet of scrap graph
paper is provided at the end of this booklet for any question for which graphing may
be helpful but is not required. You may remove his sheet from this booklet. Any
· work done on this she~t of scrap graph paper ' not be scored.
When you have completed the examination, yo must sign the statement printed
at the end of the answer sheet, indicating that you ad no unlawful knowledge of the
questions or answers prior to the examination t.nd that you have neither given
nor received assistance in answering any of the q estions during the examination.
Your answer sheet cannot be accepted if you fail o sign this declaration.
·
Notice ...
A graphing calculator and a straightedge (ruler) must be available for you to use while taking this
examination.
DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.
(3l::I08 NOV\IV\108) I Vl::IB3E>1V
Part I
Answer all24 questions in this part. Each correct answer will receive 2 credits. No partial
credit will be allowed. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For each statement or question, choose the
word or expression that, of those given, best completes the statement or answers the question.
Record your answers on your separate answer sheet. [48]
1 The cost of airing a commercial on television is modeled by the
function C(n) = liOn + 900, where n is the number of times the
commercial is aired. Based on this model, which statement is true?
yr}
The commercial costs $0 to produce and $110 per airing up to
$900.
j!l)
The commercial costs $110 to produce and $900 each time it is
aired .
•
The commercial costs $900 to produce and $110 each time it is
aired.
Use this space for
computations.
(A) The commercial costs $1010 to produce and can air an unlimited
number of times.
2 The graph below represents a jogger's speed during her 20-minute
jog around her neighborhood.
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6
8
10
12
14
Time (in minutes)
16
18
Which statement best describes what the jogger was doing during
the 9-12 minute interval of her jog?
(] ) She was standing still.
(2) She was increasing her speed.
(3) She was decreasing her speed.
•
She was jogging at a constant rate.
Algebra I (Common Core) -June '15
[2]
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Use this space for
computations.
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3 If the area of a rectangle is expressed as
9y2, then the product
of the length and the width of the rectangle could be expressed as
x4 -
+ 3y)
3y)(x 2 + 3y)
(1) (x- 3y)(x
(3) (x 2
-
t1
(4) (x 4
+ y)(x- 9y)
(x 2
-
3y)(x 2
-
(~ f t- 3 y) \.X .. :> 7
3y)
·
4 Which table represel}Js a function?
X
4
f(x)
9
1~ I : I : I : I : I
•
(1)
X
f(x)
l
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-1
\/>\
1
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1
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f(x)
1
I -1
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(2)
(4)
5 Which inequality is represented in the graph below?
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(7} y < -3x + 4
Algebra I (Common Core) -June '15
(3) y ?:. -4x - 3
5#f y < -4x- 3
[3]
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(. y > -3x
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[OVER]
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6 Mo's farm stand sold a total of 165 pounds o£ apples anq peaches.
She sold apples for $1.75 per pound and peaches for $2.50 per
pound. If she made $337.50, how many pounds of peaches did she
sell?
(1) 11
.) 65
(2) 18
(4) 100
Use this space for
computations.
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Algebra I (Common Core) -June '15
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7 Morgan can~ wrestling at,._age 5 in Division 1. He remains in that
division until his !!ext odd birthd:ry when he is required to move up
to the next division level. Which graph correctly represents this
information?
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8 Which statement is not always true?
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• The product of two irratio.nal numbers is rational.
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..(3) The sum of a rational number and an irrational number is irrational. ~
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}47 The product of a nonzero rational number and an irrational ~'. \ vY o.· •.l
Jf) The sum of two rational numbers is rational.
1
r
number is irrational.
9 The graph of the function f(x) = .Jx
+4
is shown below.
tt(x)
The domain of the function is
(1) {xlx
> 0}
(2) {xlx > 0}
(3) {x lx
tfj
> -4}
{xlx > -4}
c::
10 What are the zeros of the functionf(x)
= x2
-
(1) -10 and 3
(3) -15 and 2
(2) 10 and -3
tJ
13x- 30~
15 and -2
:0
0
Algebra I (Common Core)- June '15
[5]
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p.
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Use this space for
computations.
11 Joey enlarged a 3-inch by 5-inch photograph on a copy machine.
He enlarged it four times. The table below shows the area of the
photograph after each enlargement.
I
Enlargement
Area (square inches)
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r
,
0
1
2
3
4
15
18.8
23.4
29.3
36.6
3.B
4,b
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73
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(1) 4.3
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(2) 4.5
(4) 6.0
5.4
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12 Which equation(s) represent the graph below?
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y = (x
+ 2)(x 2
y = (x - 3)(x2
y = (x -
-
~~z_)
4x - 12)
+x
- 2)
1)(x2 - 5x -
6)
2-er ~S
_z> ~>-2.
&- 0('!'*2:)
3 ) -2
(~-3) (}+~ lx-\)
(l-1)
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y
,'2..)
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(1) I, only
(3) I and II
•
(4) II and III
II, only
Algebra I (Common Core)- June '15
/
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What is the average rate of change of the area from the original
photograph to the fourth enlargement, to the nearest tenth?
[6]
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computations.
13 A laboratory technician studied the population growth of a colony of
bacteria. He recorded the number of bacteria every other day, as
shown in the partial table below.
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t (time, in days)
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'2
f(t) (bacteria)
25
15,625
4
9,765,625
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.
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Which function would accurately model the technician's data?
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. ~
= 25t+ 1
f(t)
j14'J(t)
~ (3- x)(2 + x)
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+ 5, at which value of x isf(x) < g(x)?
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14 Which quadratic function has the largest maximum_ ? ..-.-··)
\)
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h(x)
(
~f(t) = 25t
= 25t
'/,
.)
q
\3
[OVER]
Use this space for
computations.
16 Beverly did a study this past spring using data she collected from a
cafeteria. She recorded data weekly for ice cream sales and soda sales.
Beverly found the line of best fit and the correlation coefficient,
as shown in the diagram below. '
Beverly's Cafeteria Study
•
'C
0
en
cu
"8
en
0
U)
c:
cu
Ir =
0
.961
Ice Cream Bars Sold
Given this information, which statement(s) can correctly be concluded?
I. Eating more ice cream c e a person to become thirsty.
II. Drinking more sod ca es person to become hungry.
III. There is a strong carr lation between ice cream sales and soda sales.
(1) I, only
(3) I and III
•
(4) II and III
III, only
c..:
it)
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17 The function V(t) = 1350(1.017l represents the value V(t), in dollars, /
of a comic book t years after its purchase. The yearly rate of
appreciation of the comic book is
/ -f-
(1) 17%
(3) 1.017%
•
(4) 0.017%
1.7%
, ol7
Algebra I (Common Core)- June '15
[8]
6
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7
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'(\e~f>oo'
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e~n by completing the
18 When directed to solve a quadratic
2
- ~)
square, Sam arrived at the equation (x
= 1;.
Which equation
could have been the original equation given to Sam?
r)/ x2 + 5x + 7
,)(1·
~2
x -
= 0
J21x 2 + 5x + 3 = 0
/
\
"-"'-)
5x
x2 - 5x
•
+7=
+3=
-7
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19 The distance a free falling object has traveled can be modeled by the
equation d
=
~ at 2 , where a is acceleration due to gravity and tis
the amount of time the object has fallen. What is t in terms of a and d?
(1) t
•
t
=
-1¥
(3)t=e:t
=P!
(4) t
=
(2:t
20 The table below shows the annual salaries for the 24 members of a
profes~sional sports team in terms of millions of dollars.
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0.5
0.5
0.6
0.7
0.75
0.8
1.0
1.0
1.1
1.25
1.3
1.4
':1' 1.4
1.8
2.5
3.7
3.8
4
4.2
4.6
5.1
6
6.3
7.2
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cr
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..-v The team signs an additional player to a contract worth 10 million
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dollars per year. Which statement about the median and mean is
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true?
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(1) Both will increase.
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Algebra I (Common Core)- June '15
[9]
[OVER]
Use this space for
21 A student is asked to solve the equation 4(3x The student's solution to the problem starts as .
1) 2 -
17 = 83.
(2x~0 ._ =~
4(3x - 1) 2 = 100
(3x- 1)2 = 25
"31-\ ::
A correct next step in the solution of the problem is
IJ
3x - 1 = ±5
(3) 9x 2
(4) 9x 2
(2) 3x - 1 = ±25
22 A pattern of blocks is shown below.
-
1 = 25
6x + 1 = 5
'2.
-"(af
3
r" •
k ~
"\J_.
--fet,.,. \
computations.
a~$$
Term 1
Term2
Term 3
Term4
If the pattern of blocks continues, which formula(s) could be used
to determine the number of blocks in the nth term?
I
an= n
II
+4
/
III
a1 = 2
an= an-
(1) I and II
(2) I and III
Algebra I (Common Core)- June '15
1
+4
/
an= 4n- 2
0
II and III
(4) III, only
[10]
.± tj
23 What are the solutions to the equation x2
= 4 :±: 2Vl0
•
X
(2)
X=
-4 :±: 2Vl0
-
8x
=
Use this space for
computations .
24?
= 4 :±: 2V2
(3)
X
(4)
X=
-4 :±: 2V2
~ ';~,)._
24 Natasha is planning a school celebration and wants to have live music
and food for everyone who attends. She has found a band that will
charge her $750 and a caterer who will provide snacks and drinks for
$2.25 per person. If her goal is to keep the average cost per person
between _$2.75 and $3.25, how many people, p, must attend?
(1) 225 < p < 325
(3) 500 < p < 1000
(2) 325 < p < 750
•
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Algebra I (Common Core)- Jnne '15
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[OVER]
S
Part II
Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer. Note that
diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical
answer with no work shown will receive only 1 credit. All answers should be written in pen,
except for graphs and drawings, which should be done in pencil. [16]
25 Graph the function y =
lx - 31 on the set of axes below.
y
Explain how the graph of y
= lx- 31 has changed from the related graph y = lxl.
Tte _:ra-pl
Jr~'h
~~
Algebra I (Common Core)- June '15
[12]
26 Alex is selling tickets to a school play. An adult ticket costs $6.50 and a student ticket costs $4.00.
Alex sells ~~dl1!! tick~§ and 12 student tickets. Write a function, j(x), to represent how much
money Alex collected from selling tickets.
~
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-/y,l
'··
Algebra I (Common Core)- June '15
[13]
[OVER]
27 John and Sarah are each saving money for a car. The total amount of money John will save is given
by the function j(x) = 60 + 5x. The total amount of money Sarah will save is given by the
function g(x) = x2 + 46. After how many weeks, x, will they have the same amount of money
------
_1!1Ylld? Explain how you arrived at your a n ' w /
fh e_
f r " b)e_""'
fl ( x)
w
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k:
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28 If the difference (3x 2 - 2x
written in standard form?
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+ 5)
- (x 2
+ 3x
- 2) is multiplied by ~ x2, what is the result,
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[OVER]
29 Dylan invested $600 in a savings account at a~ annual interest rate. He made no deposits or
withdrawals on the account for 2 years. The interest was compounded annually. Find, to the
nearest cent, the balance in the account after 2 years.
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30 Determ·me t he smallest integer that makes -3x
+ 7 - 5x < 15 true.
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[17]
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[OVER]
31 The residual plots from two different sets of bivariate data are graphed below.
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Graph A
Graph B
I
Explain, using evidence from graph A and graph B, which graph indicates that the model for the
data is a good fit.
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32 A landscaper is creating a rectangular flower bed such that the width is half of the lengt~.
The ~rea of the flower bed is 34 square feet. Write and solve an equation to determine th,;:_."~J!th_
of the flower bed, to the nearest tenth of a foot. ·
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[19]
[OVER]
Part III
Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer. Note that
diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical
answer with no work shown will receive only 1 credit. All answers should be written in pen,
except for graphs and drawings, which should be done in pencil. [16]
33 Albert says that the two systems of equations shown below have the same solutions.
First System
Second System
+ 9y = 48
12x + 5y = 21
8x
8x
+ 9y = 48
-8.5y =-51
Determine and state whether you agree with Albert. Justify your answer.
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[20]
34 The equation to determine the weekly earnings of an employee at The Hamburger Shack is given
by w(x), where x is the number of hours worked.
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W X
= 15(x- 40) + 400,
0 ::S
X>
< 40
40
X
Determine the difference in salary, in dollars, for an employee who works 52 hours versus one
who works 38 hours.
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Determine the number ofhoui'S an employee must work in order to earn $445. Explain how you
arrived at this answer.
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gebra I (Common Core) -June '15
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[21]
[OVER]
35 An on-line electronics store must sell at least $2500 worth of printers and computers per day.
Each -e:,inter costs $50 and each computer costs $500. The store can ship a maximum of 15 items
per day.
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On the set of axes below, graph a system of inequalities that models these constraints.
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Number of Printers
Determine a combination of printers and computers that would allow the electronics store to
meet all of the constraints. Explain how you obtained your answer.
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Algebra I (Common Core)- June '15
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[22]
36 An application developer released a new app to be downloaded. The table below gives the number
of downloads for the first four weeks after the launch of the app.
1
2
3
4
><
120
180
270
405
y
Number of Weeks
Number of Downloads
Write an exponential equation that models these data.
. x
j= Q_·0
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y :: 'BD L{. s)
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Use this model to predict how many downloads the developer would expect in the 26th week if
this trend continues. Round your answer to the nearest download.
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Would it be reasonable to use this model to predict the number of downloads past one year?
Explain your reasoning.
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Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate
the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.
Utilize the information provided for each question to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive only
· 1 credit. All answers should be written in pen, except for graphs and drawings, which should
be written in pencil. [6]
.
1
3 7 A football player attempts to kick a football over a goal post .. The path of the football can be
modeled by the function h(x) = - 2~ 5 x 2
+ ;
x, where xis the horizontal distance from the kick,
and h(x) is the height of the football above the ground, when both are measured in feet.
On the set of axes below, graph the function y = h(x) over the interval 0 < x < 150.
y
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()
10
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lfJ
{Jo
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/t>D 1ft> /2D /.5C> 1'/D /'S'D
~eanin'£ftlit~ertex in the context of the problem.
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t j ~\ 0~ k l e. f!o o+'b ~u
Determine the vertex of y = h(x). Interpret the
r
The goal post is 10 feet high and 45 xards away from the kick. Will the ball be high enough to
pass~:~gort:Jusj/iJUsw:r -ILe £)-foe-)) J oes
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Algebra I (Common Core) -June '15
[24]
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