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Algebra I (Common Core) - New York Regents January 2016 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 In the function f(x) = (x - 2)2 + 4, the minimum value occurs
  when x is
  (1) -2                      (3) -4
  (2) 2                       (4) 4
Answer: 2

2.
2 The graph below was created by an employee at a gas station.
Which statement can be justified by using the graph?
(1) If 10 gallons of gas was purchased, $35 was paid.
(2) For every gallon of gas purchased, $3.75 was paid.
(3) For every 2 gallons of gas purchased, $5.00 was paid.
(4) If zero gallons of gas were purchased, zero miles were driven.
Answer: 2

3.
3 For a recently released movie, the function y = 119.67(0.61)x models
  the revenue earned, y, in millions of dollars each week, x, for several
  weeks after its release.
  Based on the equation, how much more money, in millions of dollars,
  was earned in revenue for week 3 than for week 5?
  (1) 37.27                       (3) 17.06
  (2) 27.16                       (4) 10.11
Answer: 3


4.
4 Given the following expressions:
Which expression(s) result in an irrational number?
(1) II, only                   (3) I, III, IV
(2) III, only                  (4) II, III, IV
Answer: 1

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

6.
6 Michael borrows money from his uncle, who is charging him simple
  interest using the formula I = Prt. To figure out what the interest
  rate, r, is, Michael rearranges the formula to find r. His new formula
  is r equals

Answer: 3

7.
7 Which equation is equivalent to y - 34 = x(x - 12)?
  (1) y = (x - 17)(x + 2)       (3) y = (x - 6)2 + 2
  (2) y = (x - 17)(x - 2)       (4) y = (x - 6)2 - 2
Answer: 4

8.
8 The equation A = 1300(1.02)7 is being used to calculate the amount
  of money in a savings account. What does 1.02 represent in this
  equation?
  (1) 0.02% decay                (3) 2% decay
  (2) 0.02% growth               (4) 2% growth
Answer: 4

9.
9 The zeros of the function f(x) = 2x2 - 4x - 6 are
  (1) 3 and -1                   (3) -3 and 1
  (2) 3 and 1                    (4) -3 and -1
Answer: 1

10.
10 When (2x - 3)2 is subtracted from 5x2, the result is
   (1) x2 - 12x - 9               (3) x2 + 12x - 9
   (2) x2 - 12x + 9               (4) x2 + 12x + 9
Answer: 3

11.
                                                                            Use this space for
11 Joe has a rectangular patio that measures 10 feet by 12 feet. He wants    computations.
   to increase the area by 50% and plans to increase each dimension by
   equal lengths, x. Which equation could be used to determine x?
   (1) (10 + x)(12 + x) = 120       (3) (15 + x)(18 + x) = 180
   (2) (10 + x)(12 + x) = 180       (4) (15)(18) = 120 + x2
Answer: 2

12.
12 When factored completely, x3 - 13x2 - 30x is
   (1) x(x + 3)(x - 10)          (3) x(x + 2)(x - 15)
   (2) x(x - 3)(x - 10)          (4) x(x - 2)(x + 15)
Answer: 3

13.
13 The table below shows the cost of mailing a postcard in different years.
   During which time interval did the cost increase at the greatest
   average rate?
(1) 1898–1971   (3) 1985–2006
(2) 1971–1985   (4) 2006–2012
Answer: 4

14.
14 When solving the equation x2 - 8x - 7 = 0 by completing the square,
   which equation is a step in the process?
   (1) (x - 4)2 = 9               (3) (x - 8)2 = 9
   (2) (x - 4)2 = 23              (4) (x - 8)2 = 23
Answer: 2

15.
15 A construction company uses the function f(p), where p is the number
   of people working on a project, to model the amount of money it spends
   to complete a project. A reasonable domain for this function would be
   (1) positive integers
   (2) positive real numbers
   (3) both positive and negative integers
   (4) both positive and negative real numbers
Answer: 1

16.
16 Which function is shown in the table below?

Answer: 4

17.
Answer: 1

18.
18 Which recursively defined function represents the sequence
   3, 7, 15, 31, …?
   (1) f(1) = 3, f(n + 1) = 2 f(n) + 3
   (2) f(1) = 3, f(n + 1) = 2 f(n) - 1
   (3) f(1) = 3, f(n + 1) = 2f(n) + 1
   (4) f(1) = 3, f(n + 1) = 3f(n) - 2
Answer: 3

19.
19 The range of the function defined as y = 5x is
   (1) y < 0                      (3) y ≤ 0
   (2) y > 0                      (4) y ≥ 0
Answer: 2

20.
20 The graph of y = f(x) is shown below.
What is the graph of y = f(x + 1) - 2?

Answer: 1

21.
21 Which pair of equations could not be used to solve the following
   equations for x and y?
                          4x + 2y = 22
                         -2x + 2y = -8
   (1) 4x + 2y = 22              (3) 12x + 6y = 66
       2x - 2y = 8                   6x - 6y = 24
   (2) 4x + 2y = 22              (4) 8x + 4y = 44
       -4x + 4y = -16                -8x + 8y = -8
Answer: 4

22.
22 The graph representing a function is shown below.
Which function has a minimum that is less than the one shown in the
graph?
(1) y = x2 - 6x + 7            (3) y = x2 - 2x - 10
(2) y = |x + 3| - 6            (4) y = |x - 8| + 2
Answer: 3

23.
23 Grisham is considering the three situations below.
   I.   For the first 28 days, a sunflower grows at a rate of 3.5 cm per day.
   II. The value of a car depreciates at a rate of 15% per year after it
       is purchased.
   III. The amount of bacteria in a culture triples every two days during
        an experiment.
   Which of the statements describes a situation with an equal difference
   over an equal interval?
   (1) I, only                       (3) I and III
   (2) II, only                      (4) II and III
Answer: 1

24.
24 After performing analyses on a set of data, Jackie examined the scatter
   plot of the residual values for each analysis. Which scatter plot
   indicates the best linear fit for the data?

Answer: 3


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 The function, t(x), is shown in the table below.
Determine whether t(x) is linear or exponential. Explain your answer.
Answer: MODEL ANSWER GIVEN BELOW


26.
26 Marcel claims that the graph below represents a function.
State whether Marcel is correct. Justify your answer.
Answer: MODEL ANSWER GIVEN BELOW


27.
27 Solve the equation for y.
                               (y - 3)2 = 4y - 12
Answer: MODEL ANSWER GIVEN BELOW


28.
28 The graph below shows the variation in the average temperature of Earth’s surface from 1950–2000,
   according to one source.
During which years did the temperature variation change the most per unit time? Explain how you
determined your answer.
Answer: MODEL ANSWER GIVEN BELOW


29.
29 The cost of belonging to a gym can be modeled by C(m) = 50m + 79.50, where C(m) is the total
   cost for m months of membership.
   State the meaning of the slope and y-intercept of this function with respect to the costs associated
   with the gym membership.
Answer: MODEL ANSWER GIVEN BELOW


30.
30 A statistics class surveyed some students during one lunch period to obtain opinions about
   television programming preferences. The results of the survey are summarized in the table below.
Based on the sample, predict how many of the school’s 351 males would prefer comedy. Justify
your answer.
Answer: MODEL ANSWER GIVEN BELOW


31.
31 Given that a > b, solve for x in terms of a and b:
                                        b(x - 3) ≥ ax + 7b
Answer: MODEL ANSWER GIVEN BELOW


32.
32 Jacob and Jessica are studying the spread of dandelions. Jacob discovers that the growth over
   t weeks can be defined by the function f(t) = (8) • 2t. Jessica finds that the growth function over
   t weeks is g(t) = 2t + 3.
   Calculate the number of dandelions that Jacob and Jessica will each have after 5 weeks.
   Based on the growth from both functions, explain the relationship between f(t) and g(t).
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 Let h(t) = -16t2 + 64t + 80 represent the height of an object above the ground after t seconds.
   Determine the number of seconds it takes to achieve its maximum height. Justify your answer.
   State the time interval, in seconds, during which the height of the object decreases. Explain your
   reasoning.
Answer: MODEL ANSWER GIVEN BELOW


34.
34 Fred’s teacher gave the class the quadratic function f(x) = 4x2 + 16x + 9.
   a) State two different methods Fred could use to solve the equation f(x) = 0.
   b) Using one of the methods stated in part a, solve f(x) = 0 for x, to the nearest tenth.
Answer: MODEL ANSWER GIVEN BELOW


35.
35 Erica, the manager at Stellarbeans, collected data on the daily high temperature and revenue
   from coffee sales. Data from nine days this past fall are shown in the table below.
State the linear regression function, f(t), that estimates the day’s coffee sales with a high
temperature of t. Round all values to the nearest integer.
State the correlation coefficient, r, of the data to the nearest hundredth. Does r indicate a strong
linear relationship between the variables? Explain your reasoning.
Answer: MODEL ANSWER GIVEN BELOW


36.
36 A contractor has 48 meters of fencing that he is going to use as the perimeter of a rectangular
   garden. The length of one side of the garden is represented by x, and the area of the garden is
   108 square meters.
   Determine, algebraically, the dimensions of the garden in meters.
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 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 The Reel Good Cinema is conducting a mathematical study. In its theater, there are 200 seats.
   Adult tickets cost $12.50 and child tickets cost $6.25. The cinema’s goal is to sell at least $1500
   worth of tickets for the theater.
   Write a system of linear inequalities that can be used to find the possible combinations of adult
   tickets, x, and child tickets, y, that would satisfy the cinema’s goal.
   Graph the solution to this system of inequalities on the set of axes on the next page. Label
   the solution with an S.
   Marta claims that selling 30 adult tickets and 80 child tickets will result in meeting the cinema’s
   goal. Explain whether she is correct or incorrect, based on the graph drawn.

Answer: MODEL ANSWER GIVEN BELOW



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