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Algebra I (Common Core) - New York Regents June 2014 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 When solving the equation 4(3x2 + 2) - 9 = 8x2 + 7, Emily wrote
  4(3x2 + 2) = 8x2 + 16 as her first step. Which property justifies
  Emily’s first step?
  (1) addition property of equality
  (2) commutative property of addition
  (3) multiplication property of equality
  (4) distributive property of multiplication over addition
Answer: 1

2.
2 Officials in a town use a function, C, to analyze traffic patterns.
  C(n) represents the rate of traffic through an intersection where
  n is the number of observed vehicles in a specified time interval.
  What would be the most appropriate domain for the function?

Answer: 4

3.
3 If A = 3x2 + 5x - 6 and B = -2x2 - 6x + 7, then A - B equals
  (1) -5x2 - 11x + 13         (3) -5x2 - x + 1
  (2) 5x2 + 11x - 13          (4) 5x2 - x + 1
Answer: 2


4.
4 Given: y + x > 2
         y ≤ 3x - 2
  Which graph shows the solution of the given set of inequalities?

Answer: 2

5.
(1) 8.25   (3) 19.25
(2) 8.89   (4) 44.92
Answer: 1

6.
6 The table below shows the average yearly balance in a savings
  account where interest is compounded annually. No money is
  deposited or withdrawn after the initial amount is deposited.
                  Year        Balance, in Dollars
                     0               380.00
                    10               562.49
                    20               832.63
                    30              1232.49
                    40              1824.39
                    50              2700.54
  Which type of function best models the given data?
  (1) linear function with a negative rate of change
  (2) linear function with a positive rate of change
  (3) exponential decay function
  (4) exponential growth function
Answer: 4

7.
7 A company that manufactures radios first pays a start-up cost, and
  then spends a certain amount of money to manufacture each radio.
  If the cost of manufacturing r radios is given by the function
   c(r) = 5.25r + 125, then the value 5.25 best represents
  (1) the start-up cost
  (2) the profit earned from the sale of one radio
  (3) the amount spent to manufacture each radio
  (4) the average number of radios manufactured
Answer: 3

8.
8 Which equation has the same solution as x2 - 6x - 12 = 0?
  (1) (x + 3)2 = 21            (3) (x + 3)2 = 3
  (2) (x - 3)2 = 21            (4) (x - 3)2 = 3
Answer: 2

9.
9 A ball is thrown into the air from the edge of a 48-foot-high cliff so
  that it eventually lands on the ground. The graph below shows the
  height, y, of the ball from the ground after x seconds.
For which interval is the ball’s height always decreasing?
(1) 0 ≤ x ≤ 2.5                 (3) 2.5 < x < 5.5
(2) 0 < x < 5.5                 (4) x ≥ 2
Answer: 3

10.
10 What are the roots of the equation x2 + 4x - 16 = 0?
   (1) 2 ± 2 √5                   (3) 2 ± 4 √5
   (2) -2 ± 2 √5                  (4) -2 ± 4 √5
Answer: 2

11.
11 What is the correlation coefficient of the linear fit of the data shown
   below, to the nearest hundredth?
(1) 1.00   (3) -0.93
(2) 0.93   (4) -1.00
Answer: 3

12.
12 Keith determines the zeros of the function f(x) to be -6 and 5.
   What could be Keith’s function?
   (1) f(x) = (x + 5)(x + 6)    (3) f(x) = (x - 5)(x + 6)
   (2) f(x) = (x + 5)(x - 6)    (4) f(x) = (x - 5)(x - 6)
Answer: 3

13.
13 Given:    L=    √2
             M =3 √3
             N = √16
             P=    √9
   Which expression results in a rational number?
   (1) L + M                     (3) N + P
   (2) M + N                     (4) P + L
Answer: 3

14.
14 Which system of equations has the same solution as the system
   below?
                         2x + 2y = 16
                          3x - y = 4
   (1) 2x + 2y = 16            (3) x + y = 16
       6x - 2y = 4                 3x - y = 4
   (2) 2x + 2y = 16            (4) 6x + 6y = 48
       6x - 2y = 8                 6x + 2y = 8
Answer: 2

15.
15 The table below represents the function F.
           x        3        4         6           7    8
          F(x)      9        17       65        129    257
   The equation that represents this function is
   (1) F(x) = 3x                  (3) F(x) = 2x + 1
   (2) F(x) = 3x                  (4) F(x) = 2x + 3
Answer: 3

16.
16 John has four more nickels than dimes in his pocket, for a total of
   $1.25. Which equation could be used to determine the number of
   dimes, x, in his pocket?
   (1) 0.10(x + 4) + 0.05(x) = $1.25
   (2) 0.05(x + 4) + 0.10(x) = $1.25
   (3) 0.10(4x) + 0.05(x) = $1.25
   (4) 0.05(4x) + 0.10(x) = $1.25
Answer: 2

17.
             
17 If f(x) = (1/3)x + 9, which statement is always true?
            
   (1) f(x) < 0                    (3) If x < 0, then f(x) < 0.
   (2) f(x) > 0                    (4) If x > 0, then f(x) > 0.
Answer: 4

18.
18 The Jamison family kept a log of the distance they traveled during a
   trip, as represented by the graph below.
During which interval was their average speed the greatest?
(1) the first hour to the second hour
(2) the second hour to the fourth hour
(3) the sixth hour to the eighth hour
(4) the eighth hour to the tenth hour
Answer: 1

19.
19 Christopher looked at his quiz scores shown below for the first and
   second semester of his Algebra class.
   Semester 1:   78, 91, 88, 83, 94
   Semester 2:   91, 96, 80, 77, 88, 85, 92
   Which statement about Christopher’s performance is correct?
   (1) The interquartile range for semester 1 is greater than the
       interquartile range for semester 2.
   (2) The median score for semester 1 is greater than the median
       score for semester 2.
   (3) The mean score for semester 2 is greater than the mean score
       for semester 1.
   (4) The third quartile for semester 2 is greater than the third
       quartile for semester 1.
Answer: 3

20.
20 The graph of y = f(x) is shown below.
Which point could be used to find f(2)?
(1) A                         (3) C
(2) B                         (4) D
Answer: 1

21.
21 A sunflower is 3 inches tall at week 0 and grows 2 inches each week.
   Which function(s) shown below can be used to determine the
   height, f(n), of the sunflower in n weeks?
         I. f(n) = 2n + 3
        II. f(n) = 2n + 3(n - 1)
       III. f(n) = f(n - 1) + 2 where f(0) = 3
   (1) I and II                    (3) III, only
   (2) II, only                    (4) I and III
Answer: 4

22.
22 A cell phone company charges $60.00 a month for up to 1 gigabyte
   of data. The cost of additional data is $0.05 per megabyte. If d
   represents the number of additional megabytes used and c
   represents the total charges at the end of the month, which linear
   equation can be used to determine a user’s monthly bill?
   (1) c = 60 - 0.05d             (3) c = 60d - 0.05
   (2) c = 60.05d                 (4) c = 60 + 0.05d
Answer: 4

23.
                                               
23 The formula for the volume of a cone is V = (1/3)πr2 h. The radius, r,
                                               
   of the cone may be expressed as

Answer: 1

24.
24 The diagrams below represent the first three terms of a sequence.
Assuming the pattern continues, which formula determines an,
the number of shaded squares in the nth term?
(1) an = 4n + 12            (3) an = 4n + 4
(2) an = 4n + 8             (4) an = 4n + 2
Answer: 2


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 Draw the graph of y = √x - 1 on the set of axes below.

Answer: MODEL ANSWER GIVEN BELOW
(25)   [2] A correct graph is drawn.


26.
26 The breakdown of a sample of a chemical compound is represented by the function p(t) = 300(0.5)t,
   where p(t) represents the number of milligrams of the substance and t represents the time, in years.
   In the function p(t), explain what 0.5 and 300 represent.
Answer: MODEL ANSWER GIVEN BELOW
(26)   [2] Correct explanations are made, such as 0.5 is the rate of decay and 300 is the
           initial amount.


27.
27 Given 2x + ax - 7 > -12, determine the largest integer value of a when x = -1.
Answer: MODEL ANSWER GIVEN BELOW
(27)   [2] 2, and correct work is shown.


28.
28 The vertex of the parabola represented by f(x) = x2 - 4x + 3 has coordinates (2,-1). Find the
   coordinates of the vertex of the parabola defined by g(x) = f(x - 2). Explain how you arrived at
   your answer.
   [The use of the set of axes below is optional.]

Answer: MODEL ANSWER GIVEN BELOW
(28)   [2] (4,-1), and a correct explanation is given.


29.
                                                                  
29 On the set of axes below, draw the graph of the equation y = -(3/4)x + 3.
                                                                 
                                                                     
Is the point (3,2) a solution to the equation? Explain your answer based on the graph drawn.
Answer: MODEL ANSWER GIVEN BELOW
(29)   [2] A correct graph is drawn, no, and a correct explanation that is based on the
           graph is given.


30.
30 The function f has a domain of {1, 3, 5, 7} and a range of {2, 4, 6}.
   Could f be represented by {(1,2), (3,4), (5,6), (7,2)}?
   Justify your answer.
Answer: MODEL ANSWER GIVEN BELOW
(30)   [2] Yes, and a correct justification is given.


31.
31 Factor the expression x4 + 6x2 - 7 completely.
Answer: MODEL ANSWER GIVEN BELOW
(31)   [2] (x2 + 7)(x + 1)(x - 1) and correct work is shown.


32.
32 Robin collected data on the number of hours she watched television on Sunday through Thursday
   nights for a period of 3 weeks. The data are shown in the table below.
                                Sun      Mon       Tues      Wed      Thurs
                    Week 1       4         3        3.5        2         2
                    Week 2      4.5        5        2.5        3        1.5
                    Week 3       4         3         1        1.5       2.5
   Using an appropriate scale on the number line below, construct a box plot for the 15 values.

Answer: MODEL ANSWER GIVEN BELOW
(32)   [2] A correct box plot with Min = 1, Q1 = 2, Q2 = 3, Q3 = 4, Max = 5 is drawn.



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 Write an equation that defines m(x) as a trinomial where m(x) = (3x - 1)(3 - x) + 4x2 + 19.
Solve for x when m(x) = 0.
Answer: MODEL ANSWER GIVEN BELOW
(33)   [4] m(x) = x2 + 10x + 16 or an equivalent trinomial equation and -8 and -2,
           and correct work is shown.


34.
34 A rectangular garden measuring 12 meters by 16 meters is to have a walkway installed around it
   with a width of x meters, as shown in the diagram below. Together, the walkway and the garden
   have an area of 396 square meters.
Write an equation that can be used to find x, the width of the walkway.
Describe how your equation models the situation.
Determine and state the width of the walkway, in meters.
Answer: MODEL ANSWER GIVEN BELOW
(34)   [4] (12 + 2x)(16 + 2x) = 396 or an equivalent equation, a correct description is
           given, and correct work is shown to find 3.


35.
35 Caitlin has a movie rental card worth $175. After she rents the first movie, the card’s value is
   $172.25. After she rents the second movie, its value is $169.50. After she rents the third movie,
   the card is worth $166.75.
   Assuming the pattern continues, write an equation to define A(n), the amount of money on the
   rental card after n rentals.
Caitlin rents a movie every Friday night. How many weeks in a row can she afford to rent a movie,
using her rental card only? Explain how you arrived at your answer.
Answer: MODEL ANSWER GIVEN BELOW
(35)   [4] A(n) = 175 - 2.75n, correct work is shown to find 63, and a correct explanation
           is given.


36.
36 An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to care for each
   dog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on Wednesday.
   Write an equation to represent the possible numbers of cats and dogs that could have been at the
   shelter on Wednesday.
Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’s
numbers possible? Use your equation to justify your answer.
Later, Pat found a record showing that there were a total of 22 cats and dogs at the shelter on
Wednesday. How many cats were at the shelter on Wednesday?
Answer: MODEL ANSWER GIVEN BELOW
(36)   [4] 2.35c + 5.50d = 89.50 or an equivalent equation, no, and a correct justification
           is written, and correct work is shown to find 10.



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. The answer should
be written in pen. [6]

37.
37 A company is considering building a manufacturing plant. They determine the weekly production
   cost at site A to be A(x) = 3x2 while the production cost at site B is B(x) = 8x + 3, where x
   represents the number of products, in hundreds, and A(x) and B(x) are the production costs, in
   hundreds of dollars.
   Graph the production cost functions on the set of axes below and label them site A and site B.
State the positive value(s) of x for which the production costs at the two sites are equal.
Explain how you determined your answer.
If the company plans on manufacturing 200 products per week, which site should they use?
Justify your answer.

Answer: MODEL ANSWER GIVEN BELOW
(37)   [6] Both functions are graphed and labeled correctly, 3, and a correct explanation
           is given, and site A and a correct justification is given.


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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