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Algebra I (Common Core) - New York Regents June 2015 Exam

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1.
                                               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 cost of airing a commercial on television is modeled by the
  function C(n) = 110n + 900, where n is the number of times the
  commercial is aired. Based on this model, which statement is true?
  (1) The commercial costs $0 to produce and $110 per airing up to
      $900.
  (2) The commercial costs $110 to produce and $900 each time it is
      aired.
  (3) The commercial costs $900 to produce and $110 each time it is
      aired.
  (4) The commercial costs $1010 to produce and can air an unlimited
      number of times.
Answer: 3

2.
2 The graph below represents a jogger’s speed during her 20-minute
  jog around her neighborhood.
Which statement best describes what the jogger was doing during
the 9–12 minute interval of her jog?
(1) She was standing still.
(2) She was increasing her speed.
(3) She was decreasing her speed.
(4) She was jogging at a constant rate.
Answer: 4

3.
3 If the area of a rectangle is expressed as x4 - 9y2, then the product
  of the length and the width of the rectangle could be expressed as
  (1) (x - 3y)(x + 3y)           (3) (x2 - 3y)(x2 - 3y)
  (2) (x2 - 3y)(x2 + 3y)         (4) (x4 + y)(x - 9y)
Answer: 2


4.
4 Which table represents a function?

Answer: 3

5.
5 Which inequality is represented in the graph below?
(1) y ≥ -3x + 4   (3) y ≥ -4x - 3
(2) y ≤ -3x + 4   (4) y ≤ -4x - 3
Answer: 1

6.
6 Mo’s farm stand sold a total of 165 pounds of apples and 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                        (3) 65
  (2) 18                        (4) 100
Answer: 3

7.
7 Morgan can start wrestling at age 5 in Division 1. He remains in that
  division until his next odd birthday when he is required to move up
  to the next division level. Which graph correctly represents this
  information?

Answer: 1

8.
8 Which statement is not always true?
  (1) The sum of two rational numbers is rational.
  (2) The product of two irrational numbers is rational.
  (3) The sum of a rational number and an irrational number is irrational.
  (4) The product of a nonzero rational number and an irrational
      number is irrational.
Answer: 2

9.
Answer: 4

10.
10 What are the zeros of the function f(x) = x2 - 13x - 30?
   (1) -10 and 3                 (3) -15 and 2
   (2) 10 and -3                 (4) 15 and -2
Answer: 4

11.
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.
What is the average rate of change of the area from the original
photograph to the fourth enlargement, to the nearest tenth?
(1) 4.3                      (3) 5.4
(2) 4.5                      (4) 6.0
Answer: 3

12.
12 Which equation(s) represent the graph below?
(1) I, only    (3) I and II
(2) II, only   (4) II and III
Answer: 2

13.
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.

Answer: 2

14.
14 Which quadratic function has the largest maximum?

Answer: 3

15.
Answer: 1

16.
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.
Given this information, which statement(s) can correctly be concluded?
I.   Eating more ice cream causes a person to become thirsty.
II. Drinking more soda causes a person to become hungry.
III. There is a strong correlation between ice cream sales and soda sales.
(1) I, only                       (3) I and III
(2) III, only                     (4) II and III
Answer: 2

17.
Answer: 2

18.
Answer: 4

19.
Answer: 2

20.
20 The table below shows the annual salaries for the 24 members of a
   professional sports team in terms of millions of dollars.
The team signs an additional player to a contract worth 10 million
dollars per year. Which statement about the median and mean is
true?
(1) Both will increase.
(2) Only the median will increase.
(3) Only the mean will increase.
(4) Neither will change.
Answer: 3

21.
Answer: 1

22.
22 A pattern of blocks is shown below.
If the pattern of blocks continues, which formula(s) could be used
to determine the number of blocks in the nth term?
(1) I and II    (3) II and III
(2) I and III   (4) III, only
Answer: 3

23.
23 What are the solutions to the equation x2 - 8x = 24?

Answer: 1

24.
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               (4) 750 < p < 1500
Answer: 4


25.
                                              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 = |x - 3| on the set of axes below.
Explain how the graph of y = |x - 3| has changed from the related graph y = |x|.
Answer: MODEL ANSWER GIVEN BELOW


26.
26 Alex is selling tickets to a school play. An adult ticket costs $6.50 and a student ticket costs $4.00.
   Alex sells x adult tickets and 12 student tickets. Write a function, f(x), to represent how much
   money Alex collected from selling tickets.
Answer: MODEL ANSWER GIVEN BELOW


27.
27 John and Sarah are each saving money for a car. The total amount of money John will save is given
   by the function f(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
   saved? Explain how you arrived at your answer.
Answer: MODEL ANSWER GIVEN BELOW


28.
Answer: MODEL ANSWER GIVEN BELOW


29.
29 Dylan invested $600 in a savings account at a 1.6% 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.
Answer: MODEL ANSWER GIVEN BELOW


30.
30 Determine the smallest integer that makes -3x + 7 - 5x < 15 true.
Answer: MODEL ANSWER GIVEN BELOW


31.
31 The residual plots from two different sets of bivariate data are graphed below.
Explain, using evidence from graph A and graph B, which graph indicates that the model for the
data is a good fit.
Answer: MODEL ANSWER GIVEN BELOW


32.
32 A landscaper is creating a rectangular flower bed such that the width is half of the length.
   The area of the flower bed is 34 square feet. Write and solve an equation to determine the width
   of the flower bed, to the nearest tenth of a foot.
Answer: MODEL ANSWER GIVEN BELOW


33.
                                             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.
Determine and state whether you agree with Albert. Justify your answer.
Answer: MODEL ANSWER GIVEN BELOW


34.
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.
Determine the difference in salary, in dollars, for an employee who works 52 hours versus one
who works 38 hours.
Determine the number of hours an employee must work in order to earn $445. Explain how you
arrived at this answer.
Answer: MODEL ANSWER GIVEN BELOW


35.
35 An on-line electronics store must sell at least $2500 worth of printers and computers per day.
   Each printer costs $50 and each computer costs $500. The store can ship a maximum of 15 items
   per day.
   On the set of axes below, graph a system of inequalities that models these constraints.
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.
Answer: MODEL ANSWER GIVEN BELOW



36.
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.
Write an exponential equation that models these data.
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.
Would it be reasonable to use this model to predict the number of downloads past one year?
Explain your reasoning.
Answer: MODEL ANSWER GIVEN BELOW


37.
                                             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]
Determine the vertex of y = h(x). Interpret the meaning of this vertex in the context of the problem.
The goal post is 10 feet high and 45 yards away from the kick. Will the ball be high enough to
pass over the goal post? Justify your answer.
Answer: MODEL ANSWER GIVEN BELOW



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