ALGEBRA I (COMMON CORE)
The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
algebra I (Common Core)
Wednesday, August 17, 2016 — 8:30 to 11:30 a.m., only
Student Name:______________________________________________________________
School Name:_______________________________________________________________
The possession or use of any communications device is strictly prohibited when taking this examination.
If you have or use any communications device, 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 school on the lines above.
A separate answer sheet for Part I has been provided to you. Follow the
instructions from the proctor for completing the student information on your
answer sheet.
This examination has four parts, with a total of 37 questions. You must answer
all questions in this examination. Record your answers to the Part I multiple-choice
questions on the separate answer sheet. Write your answers to the questions
in Parts II, III, and IV directly in this booklet. All work should be written in pen,
except for graphs and drawings, which should be done in pencil. 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.
The formulas that you may need to answer some questions in this examination
are found at the end of the examination. This sheet is perforated so you may
remove it from this booklet.
Scrap paper is not permitted for any part of this 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 this sheet from this booklet.
Any work done on this sheet of scrap graph paper will not be scored.
When you have completed the examination, you must sign the statement printed
at the end of the answer sheet, indicating that you had no unlawful knowledge of
the questions or answers prior to the examination and that you have neither given
nor received assistance in answering any of the questions during the examination.
Your answer sheet cannot be accepted if you fail to 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.
ALGEBRA I (COMMON CORE)

Part I
Answer all 24 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 graph below shows the distance in miles, m, hiked from a camp
in h hours.
6
Miles (m)
5
4
3
2
1
0
1
2
4
3
Hours (h)
5
6
Which hourly interval had the greatest rate of change?
(1) hour 0 to hour 1
(3) hour 2 to hour 3
(2) hour 1 to hour 2
(4) hour 3 to hour 4
2 The solution of an equation with two variables, x and y, is
(1) the set of all x values that make y 5 0
(2) the set of all y values that make x 5 0
(3) the set of all ordered pairs, (x,y), that make the equation true
(4) the set of all ordered pairs, (x,y), where the graph of the equation
crosses the y-axis
3 Which statistic can not be determined from a box plot representing
the scores on a math test in Mrs. DeRidder’s algebra class?
(1) the lowest score
(2) the median score
(3) the highest score
(4) the score that occurs most frequently
Algebra I (Common Core) – Aug. ’16
[2]
Use this space for
computations.

4 Which chart could represent the function f(x) 5 22x 1 6?
x
f(x)
x
f(x)
0
6
0
8
2
10
2
10
4
14
4
12
6
18
6
14
(1)
Use this space for
computations.
(3)
x
f(x)
x
f(x)
0
4
0
6
2
6
2
2
4
8
4
–2
6
10
6
–6
(2)
(4)
5 If f(n) 5 (n 2 1)2 1 3n, which statement is true?
(1) f(3) 5 22
(3) f(22) 5 215
(2) f(22) 5 3
(4) f(215) 5 22
6 The table below shows 6 students’ overall averages and their averages
in their math class.
Overall Student
Average
92
98
84
80
75
82
Math Class
Average
91
95
85
85
75
78
If a linear model is applied to these data, which statement best describes
the correlation coefficient?
(1) It is close to 21.
(3) It is close to 0.
(2) It is close to 1.
(4) It is close to 0.5.
Algebra I (Common Core) – Aug. ’16
[3]
[OVER]

Use this space for
computations.
7 What is the solution to 2h 1 8 . 3h 2 6?
(1) h , 14
(3) h . 14
(2) h , 14
(4) h . 14
5
5
8 Which expression is equivalent to 36x2 2 100?
(1) 4(3x 2 5)(3x 2 5)
(3) 2(9x 2 25)(9x 2 25)
(2) 4(3x 1 5)(3x 2 5)
(4) 2(9x 1 25)(9x 2 25)
9 Patricia is trying to compare the average rainfall of New York to that
of Arizona. A comparison between these two states for the months of
July through September would be best measured in
(1) feet per hour
(3) inches per month
(2) inches per hour
(4) feet per month
10 Which function defines the sequence 26, 210, 214, 218, …, where
f (6) 5 226?
(1) f(x) 5 24x 2 2
(3) f(x) 5 2x 1 32
(2) f(x) 5 4x 2 2
(4) f(x) 5 x 2 26
11 Which function has the greatest y-intercept?
(1) f(x) 5 3x
(2) 2x 1 3y 5 12
(3) the line that has a slope of 2 and passes through (1,24)
f(x)
(4)
x
Algebra I (Common Core) – Aug. ’16
[4]

Use this space for
computations.
12 What is the product of 2x 1 3 and 4x2 2 5x 1 6?
(1) 8x3 2 2x2 1 3x 1 18
(3) 8x3 1 2x2 2 3x 1 18
(2) 8x3 2 2x2 2 3x 1 18
(4) 8x3 1 2x2 1 3x 1 18
13 The height of a rocket, at selected times, is shown in the table below.
Time (sec)
0
1
2
3
4
5
6
7
Height (ft)
180
260
308
324
308
260
180
68
Based on these data, which statement is not a valid conclusion?
(1) The rocket was launched from a height of 180 feet.
(2) The maximum height of the rocket occurred 3 seconds after
launch.
(3) The rocket was in the air approximately 6 seconds before hitting
the ground.
(4) The rocket was above 300 feet for approximately 2 seconds.
14 A parking garage charges a base rate of $3.50 for up to 2 hours, and
an hourly rate for each additional hour. The sign below gives the prices
for up to 5 hours of parking.
Parking Rates
2 hours
$3.50
3 hours
$9.00
4 hours
$14.50
5 hours
$20.00
Which linear equation can be used to find x, the additional hourly
parking rate?
(1) 9.00 1 3x 5 20.00
(3) 2x 1 3.50 5 14.50
(2) 9.00 1 3.50x 5 20.00
(4) 2x 1 9.00 5 14.50
Algebra I (Common Core) – Aug. ’16
[5]
[OVER]

Use this space for
computations.
15 Which function has a constant rate of change equal to 23?
y
x
y
0
2
1
5
2
8
3
11
x
(1)
(3)
{(1,5), (2,2), (3,�5), (4,4)}
(2)
2y � �6x � 10
(4)
16 Kendal bought x boxes of cookies to bring to a party. Each box contains
12 cookies. She decides to keep two boxes for herself. She brings
60 cookies to the party. Which equation can be used to find the number
of boxes, x, Kendal bought?
(1) 2x 2 12 5 60
(3) 12x 2 24 5 60
(2) 12x 2 2 5 60
(4) 24 2 12x 5 60
17 The table below shows the temperature, T(m), of a cup of hot chocolate
that is allowed to chill over several minutes, m.
Time, m (minutes)
0
2
4
6
8
Temperature, T(m)
(°F)
150
108
78
56
41
Which expression best fits the data for T(m)?
(1) 150(0.85)m
(3) 150(0.85)m 2 1
(2) 150(1.15)m
(4) 150(1.15)m 2 1
Algebra I (Common Core) – Aug. ’16
[6]

18 As x increases beyond 25, which function will have the largest value?
(1) f(x) 5 1.5x
(3) h(x) 5 1.5x2
(2) g(x) 5 1.5x 1 3
(4) k(x) 5 1.5x3 1 1.5x2
Use this space for
computations.
19 What are the solutions to the equation 3x2 1 10x 5 8?
(1)
2
and 24
3
(3)
4
and 22
3
(4) 2 4 and 2
3
(2) 2 2 and 4
3
20 An online company lets you download songs for $0.99 each after
you have paid a $5 membership fee. Which domain would be most
appropriate to calculate the cost to download songs?
(1) rational numbers greater than zero
(2) whole numbers greater than or equal to one
(3) integers less than or equal to zero
(4) whole numbers less than or equal to one
21 The function f(x) 5 3x2 1 12x 1 11 can be written in vertex form as
(1) f(x) 5 (3x 1 6)2 2 25
(3) f(x) 5 3(x 1 2)2 2 1
(2) f(x) 5 3(x 1 6)2 2 25
(4) f(x) 5 3(x 1 2)2 1 7
22 A system of equations is given below.
x 1 2y 5 5
2x 1 y 5 4
Which system of equations does not have the same solution?
(1) 3x 1 6y 5 15
(3) x 1 2y 5 5
2x 1 y 5 4 6x 1 3y 5 12
(2) 4x 1 8y 5 20
(4) x 1 2y 5 5
2x 1 y 5 4 4x 1 2y 5 12
Algebra I (Common Core) – Aug. ’16
[7]
[OVER]

23 Based on the graph below, which expression is a possible factorization
of p(x)?
p(x)
x
1
(1) (x 1 3)(x 2 2)(x 2 4)
(3) (x 1 3)(x 2 5)(x 2 2)(x 2 4)
(2) (x 2 3)(x 1 2)(x 1 4)
(4) (x 2 3)(x 1 5)(x 1 2)(x 1 4)
24 Milton has his money invested in a stock portfolio. The value, v(x), of
his portfolio can be modeled with the function v(x) 5 30,000(0.78)x,
where x is the number of years since he made his investment. Which
statement describes the rate of change of the value of his portfolio?
(1) It decreases 78% per year.
(2) It decreases 22% per year.
(3) It increases 78% per year.
(4) It increases 22% per year.
Algebra I (Common Core) – Aug. ’16
[8]
Use this space for
computations.

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 5 2 x 1 3 on the set of axes below.
y
x
Algebra I (Common Core) – Aug. ’16
[9]
[OVER]

26 Richard is asked to transform the graph of b(x) below.
b(x)
x
The graph of b(x) is transformed using the equation h(x) 5 b(x 2 2) 2 3. Describe how the graph
of b(x) changed to form the graph of h(x).
Algebra I (Common Core) – Aug. ’16
[10]

27 Consider the pattern of squares shown below:
Which type of model, linear or exponential, should be used to determine how many squares are in
the nth pattern? Explain your answer.
28 When multiplying polynomials for a math assignment, Pat found the product to be
24x 1 8x2 2 2x3 1 5. He then had to state the leading coefficient of this polynomial. Pat wrote
down 24. Do you agree with Pat’s answer? Explain your reasoning.
Algebra I (Common Core) – Aug. ’16
[11]
[OVER]

29 Is the sum of 3 2 and 4 2 rational or irrational? Explain your answer.
30 The graph below shows two functions, f(x) and g(x). State all the values of x for which f(x) 5 g(x).
y
g(x)
f(x)
x
Algebra I (Common Core) – Aug. ’16
[12]

31 Find the zeros of f(x) 5 (x 2 3)2 2 49, algebraically.
32 Solve the equation below for x in terms of a.
4(ax 1 3) 2 3ax 5 25 1 3a
Algebra I (Common Core) – Aug. ’16
[13]
[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 The data table below shows the median diameter of grains of sand and the slope of the beach for
9 naturally occurring ocean beaches.
Median Diameter of
Grains of Sand,
in Millimeters (x)
0.17
0.19
0.22
0.235 0.235
0.3
0.35
0.42
0.85
Slope of Beach,
in Degrees (y)
0.63
0.7
0.82
0.88
1.5
4.4
7.3
11.3
1.15
Write the linear regression equation for this set of data, rounding all values to the nearest
thousandth.
Using this equation, predict the slope of a beach, to the nearest tenth of a degree, on a beach with
grains of sand having a median diameter of 0.65 mm.
Algebra I (Common Core) – Aug. ’16
[14]

34 Shawn incorrectly graphed the inequality 2x 2 2y $ 8 as shown below.
y
x
Explain Shawn’s mistake.
Graph the inequality correctly on the set of axes below.
y
x
Algebra I (Common Core) – Aug. ’16
[15]
[OVER]

35 A drama club is selling tickets to the spring musical. The auditorium holds 200 people. Tickets
cost $12 at the door and $8.50 if purchased in advance. The drama club has a goal of selling
at least $1000 worth of tickets to Saturday’s show.
Write a system of inequalities that can be used to model this scenario.
If 50 tickets are sold in advance, what is the minimum number of tickets that must be sold at
the door so that the club meets its goal? Justify your answer.
Algebra I (Common Core) – Aug. ’16
[16]

36 Janice is asked to solve 0 5 64x2 1 16x 2 3. She begins the problem by writing the following
steps:
Line 1
Line 2
Line 3
0 5 64x2 1 16x 2 3
0 5 B2 1 2B 2 3
0 5 (B 1 3)(B 2 1)
Use Janice’s procedure to solve the equation for x.
Explain the method Janice used to solve the quadratic equation.
Algebra I (Common Core) – Aug. ’16
[17]
[OVER]

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 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 done
in pencil. [6]
37 For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased
18 juice boxes and 32 bottles of water, and spent $19.92. The other teacher purchased
14 juice boxes and 26 bottles of water, and spent $15.76.
Write a system of equations to represent the costs of a juice box, j, and a bottle of water, w.
Kara said that the juice boxes might have cost 52 cents each and that the bottles of water might have
cost 33 cents each. Use your system of equations to justify that Kara’s prices are not possible.
Question 37 is continued on the next page.
Algebra I (Common Core) – Aug. ’16
[18]

Solve your system of equations to determine the actual cost, in dollars, of each juice box and each
bottle of water.
Algebra I (Common Core) – Aug. ’16
[19]
[OVER]

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1 inch � 2.54 centimeters
1 meter � 39.37 inches
1 mile � 5280 feet
1 mile � 1760 yards
1 mile � 1.609 kilometers
1 kilometer � 0.62 mile
1 pound � 16 ounces
1 pound � 0.454 kilogram
1 kilogram � 2.2 pounds
1 ton � 2000 pounds
1 cup � 8 fluid ounces
1 pint � 2 cups
1 quart � 2 pints
1 gallon � 4 quarts
1 gallon � 3.785 liters
1 liter � 0.264 gallon
1 liter � 1000 cubic centimeters
Pythagorean
Theorem
a2 � b2 � c2
A � bh
Quadratic
Formula
x�
Circle
A � πr 2
Arithmetic
Sequence
an � a1 � (n � 1)d
Circle
C � πd or C � 2πr
Geometric
Sequence
a n � a 1r n � 1
General Prisms
V � Bh
Geometric
Series
Sn �
Cylinder
V � πr 2h
Radians
1 radian �
180
degrees
π
Sphere
V�
4 3
πr
3
Degrees
1 degree �
π
radians
180
Cone
V�
1 2
πr h
3
Exponential
Growth/Decay
A � A0ek(t � t0) � B0
Pyramid
V�
1
Bh
3
Triangle
A�
Parallelogram
1
bh
2
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High School Math Reference Sheet
Algebra I (Common Core) – Aug. ’16
[23]
�b �
b2 � 4ac
2a
a1 � a1r n
1�r
where r � 1

ALGEBRA I (COMMON CORE)
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ALGEBRA I (COMMON CORE)