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

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Part I
    Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial
credit will be allowed. 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.
1 The owner of a small computer repair business has one employee,
  who is paid an hourly rate of $22. The owner estimates his weekly
  profit using the function P(x) = 8600 - 22x. In this function, x
  represents the number of
  (1) computers repaired per week
  (2) hours worked per week
  (3) customers served per week
  (4) days worked per week
Answer: 2

2.
2 Peyton is a sprinter who can run the 40-yard dash in 4.5 seconds.
  He converts his speed into miles per hour, as shown below.

Answer: 2

3.
3 Which equation has the same solutions as 2x2 + x - 3 = 0?
  (1) (2x - 1)(x + 3) = 0       (3) (2x - 3)(x + 1) = 0
  (2) (2x + 1)(x - 3) = 0       (4) (2x + 3)(x - 1) = 0
Answer: 4


4.
4 Krystal was given $3000 when she turned 2 years old. Her parents
  invested it at a 2% interest rate compounded annually. No deposits or
  withdrawals were made. Which expression can be used to determine
  how much money Krystal had in the account when she turned 18?
(1) 3000(1 + 0.02)16   (3) 3000(1 + 0.02)18
(2) 3000(1 - 0.02)16   (4) 3000(1 - 0.02)18
Answer: 1

5.
5 Which table of values represents a linear relationship?
x      f(x)     x      f(x)
−1         −3   −1         −3
 0         −2    0         −1
 1          1    1          1
 2          6    2          3
 3         13    3          5
     (1)             (3)
x      f(x)     x      f(x )
−1         ½    −1         −1
 0         1     0          0
 1         2     1          1
 2         4     2          8
 3         8     3         27
     (2)             (4)
Answer: 3

6.
6 Which domain would be the most appropriate set to use for a
  function that predicts the number of household online-devices in
  terms of the number of people in the household?
  (1) integers                 (3) irrational numbers
  (2) whole numbers            (4) rational numbers
Answer: 2

7.
Answer: 1

8.
8 The value in dollars, v(x), of a certain car after x years is represented
  by the equation v(x) = 25,000(0.86)x. To the nearest dollar,
  how much more is the car worth after 2 years than after 3 years?
  (1) 2589                          (3) 15,901
  (2) 6510                          (4) 18,490
Answer: 1

9.
9 Which function has the same y-intercept as the graph below?

Answer: 4

10.
10 Fred is given a rectangular piece of paper. If the length of Fred’s
   piece of paper is represented by 2x - 6 and the width is represented
   by 3x - 5, then the paper has a total area represented by
(1) 5x - 11          (3) 10x - 22
(2) 6x2 - 28x + 30   (4) 6x2 - 6x - 11
Answer: 2

11.
11 The graph of a linear equation contains the points (3,11) and (-2,1).
   Which point also lies on the graph?
   (1) (2,1)                       (3) (2,6)
   (2) (2,4)                       (4) (2,9)
Answer: 4

12.
12 How does the graph of f(x) = 3(x - 2)2 + 1 compare to the graph
   of g(x) = x2?
(1) The graph of f(x) is wider than the graph of g(x), and its vertex
    is moved to the left 2 units and up 1 unit.
(2) The graph of f(x) is narrower than the graph of g(x), and its vertex
    is moved to the right 2 units and up 1 unit.
(3) The graph of f(x) is narrower than the graph of g(x), and its vertex
    is moved to the left 2 units and up 1 unit.
(4) The graph of f(x) is wider than the graph of g(x), and its vertex is
    moved to the right 2 units and up 1 unit.
Answer: 2

13.
13 Connor wants to attend the town carnival. The price of admission to
   the carnival is $4.50, and each ride costs an additional 79 cents.
   If he can spend at most $16.00 at the carnival, which inequality can
   be used to solve for r, the number of rides Connor can go on, and
   what is the maximum number of rides he can go on?
(1) 0.79 + 4.50r ≤ 16.00; 3 rides
(2) 0.79 + 4.50r ≤ 16.00; 4 rides
(3) 4.50 + 0.79r ≤ 16.00; 14 rides
(4) 4.50 + 0.79r ≤ 16.00; 15 rides
Answer: 3

14.
14 Corinne is planning a beach vacation in July and is analyzing the
   daily high temperatures for her potential destination. She would like
   to choose a destination with a high median temperature and a small
   interquartile range. She constructed box plots shown in the diagram
   below.
Which destination has a median temperature above 80 degrees and
the smallest interquartile range?
(1) Ocean Beach              (3) Serene Shores
(2) Whispering Palms         (4) Pelican Beach
Answer: 4

15.
What is the y-intercept of this equation and what does it represent?
(1) 0.98, the percent of money in the account initially
(2) 0.98, the percent of money in the account after x years
(3) 5000, the amount of money in the account initially
(4) 5000, the amount of money in the account after x years
15 Some banks charge a fee on savings accounts that are left inactive
   for an extended period of time. The equation y = 5000(0.98)x
   represents the value, y, of one account that was left inactive for a
   period of x years.
Answer: 3

16.
16 The equation for the volume of a cylinder is V = πr2h. The positive
   value of r, in terms of h and V, is
Answer: 1

17.
17 Which equation has the same solutions as x2 + 6x - 7 = 0?
   (1) (x + 3)2 = 2              (3) (x - 3)2 = 16
   (2) (x - 3)2 = 2              (4) (x + 3)2 = 16
Answer: 4

18.
18 Two functions, y = |x - 3| and 3x + 3y = 27, are graphed on the
   same set of axes. Which statement is true about the solution to the
   system of equations?
   (1) (3,0) is the solution to the system because it satisfies the equation
       y = |x - 3|.
   (2) (9,0) is the solution to the system because it satisfies the equation
       3x + 3y = 27.
   (3) (6,3) is the solution to the system because it satisfies both equations.
   (4) (3,0), (9,0), and (6,3) are the solutions to the system of equations
       because they all satisfy at least one of the equations.
Answer: 3

19.
Answer: 4

20.
Answer: 3

21.
21 An astronaut drops a rock off the edge of a cliff on the Moon.
   The distance, d(t), in meters, the rock travels after t seconds can be
   modeled by the function d(t) = 0.8t2. What is the average speed,
   in meters per second, of the rock between 5 and 10 seconds after
   it was dropped?
   (1) 12                           (3) 60
   (2) 20                           (4) 80
Answer: 1

22.
22 When factored completely, the expression p4 - 81 is equivalent to
   (1) (p2 + 9)(p2 - 9)
   (2) (p2 - 9)(p2 - 9)
   (3) (p2 + 9)(p + 3)(p - 3)
   (4) (p + 3)(p - 3)(p + 3)(p - 3)
Answer: 3

23.
23 In 2013, the United States Postal Service charged $0.46 to mail a
   letter weighing up to 1 oz. and $0.20 per ounce for each additional
   ounce. Which function would determine the cost, in dollars, c(z), of
   mailing a letter weighing z ounces where z is an integer greater
   than 1?
   (1) c(z) = 0.46z + 0.20         (3) c(z) = 0.46(z - 1) + 0.20
   (2) c(z) = 0.20z + 0.46         (4) c(z) = 0.20(z - 1) + 0.46
Answer: 4

24.
24 A polynomial function contains the factors x, x - 2, and x + 5.
   Which graph(s) below could represent the graph of this function?
(1) I, only    (3) I and III
(2) II, only   (4) I, II, and III
Answer: 1


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. 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.
25 Ms. Fox asked her class “Is the sum of 4.2 and √2 rational or irrational?” Patrick answered that
   the sum would be irrational.
State whether Patrick is correct or incorrect. Justify your reasoning.
Answer:
(25)   [2] Correct is stated and a correct justification is given.


26.
26 The school newspaper surveyed the student body for an article about club membership. The table
   below shows the number of students in each grade level who belong to one or more clubs.
                                  1 Club     2 Clubs     3 or More Clubs
                        9th         90          33               12
                        10th        125         12               15
                        11th        87          22               18
                        12th        75          27               23
   If there are 180 students in ninth grade, what percentage of the ninth grade students belong to
   more than one club?
Answer:
(26)   [2] 25, and correct work is shown.


27.
27 A function is shown in the table below.
                                              x    f(x)
                                             –4     2
                                             –1     –4
                                              0     –2
                                              3     16
   If included in the table, which ordered pair, (-4,1) or (1,-4), would result in a relation that is
   no longer a function? Explain your answer.
Answer:
(27)   [2] (-4,1), and a correct explanation is given.


28.
28 Subtract 5x2 + 2x - 11 from 3x2 + 8x - 7. Express the result as a trinomial.
Answer:
(28)   [2] -2x2 + 6x + 4 or equivalent trinomial, and correct work is shown.


29.
29 Solve the equation 4x2 - 12x = 7 algebraically for x.
Answer:


30.
30 Graph the following function on the set of axes below.
f(x) =      |x|, -3 ≤ x < 1
              4,  1 ≤ x ≤ 8

Answer:
(30)   [2] A correct graph is drawn.


31.
31 A gardener is planting two types of trees:
       Type A is three feet tall and grows at a rate of 15 inches per year.
       Type B is four feet tall and grows at a rate of 10 inches per year.
   Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:


32.
32 Write an exponential equation for the graph shown below.
Explain how you determined the equation.
Answer:
(32)   [2] y = 0.25(2)x or an equivalent equation is written, and a correct explanation is
           given.



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. 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.
33 Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob
   spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total of $27.50
   for four bags of popcorn and two drinks.
   Write a system of equations that can be used to find the price of one bag of popcorn and the price
   of one drink.
Using these equations, determine and state the price of a bag of popcorn and the price of a drink,
to the nearest cent.
Answer:
(33)   [4] A correct system of equations is written, popcorn = 5.75, drink = 2.25 and
           correct work is shown.


34.
34 The graph of an inequality is shown below.
a) Write the inequality represented by the graph.
b) On the same set of axes, graph the inequality x + 2y < 4.
c) The two inequalities graphed on the set of axes form a system. Oscar thinks that the point (2,1)
   is in the solution set for this system of inequalities. Determine and state whether you agree
   with Oscar. Explain your reasoning.
Answer:
(34)   [4] y ≥ 2x - 3, a correct graph, and disagree, and a correct explanation is written.


35.
35 A nutritionist collected information about different brands of beef hot dogs. She made a table
   showing the number of Calories and the amount of sodium in each hot dog.
                             Calories per     Milligrams of Sodium
                             Beef Hot Dog      per Beef Hot Dog
                                  186                  495
                                  181                  477
                                  176                  425
                                  149                  322
                                  184                  482
                                  190                  587
                                  158                  370
                                  139                  322
   a) Write the correlation coefficient for the line of best fit. Round your answer to the nearest
      hundredth.
b) Explain what the correlation coefficient suggests in the context of this problem.
Answer:
(35)   [4] 0.94 and a correct explanation is written.


36.
36 a) Given the function f(x) = -x2 + 8x + 9, state whether the vertex represents a maximum or
      minimum point for the function. Explain your answer.
b) Rewrite f(x) in vertex form by completing the square.
Answer:
(36)   [4] Maximum is stated, a correct explanation is written, and f(x) = -(x - 4)2 + 25,
           and correct work is shown using completing the square.



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.
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]

37.
37 New Clarendon Park is undergoing renovations to its gardens. One garden that was originally a
   square is being adjusted so that one side is doubled in length, while the other side is decreased
   by three meters.
   The new rectangular garden will have an area that is 25% more than the original square garden.
   Write an equation that could be used to determine the length of a side of the original square
   garden.
Explain how your equation models the situation.
Determine the area, in square meters, of the new rectangular garden.
Answer:
(37)   [6] (x - 3)(2x) = 1.25x2 or an equivalent quadratic in one variable is written, a cor-
           rect explanation is written, 80, and correct work is shown.


38.
                            High School Math Reference Sheet
1 inch = 2.54 centimeters     1 kilometer = 0.62 mile    1 cup = 8 fluid ounces
1 meter = 39.37 inches        1 pound = 16 ounces        1 pint = 2 cups
1 mile = 5280 feet            1 pound = 0.454 kilogram   1 quart = 2 pints
1 mile = 1760 yards           1 kilogram = 2.2 pounds    1 gallon = 4 quarts
1 mile = 1.609 kilometers     1 ton = 2000 pounds        1 gallon = 3.785 liters
                                                         1 liter = 0.264 gallon
                                                         1 liter = 1000 cubic centimeters

Answer:


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