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Algebra I (Common Core) - New York Regents August 2014 Exam

    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]

Formats Worksheet / Test Paper Quiz Review
: Multiple choice

Your Performance  

1.

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

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2.

2 A satellite television company charges a one-time installation fee and
  a monthly service charge. The total cost is modeled by the function
  y = 40 + 90x. Which statement represents the meaning of each part
  of the function?
  (1) y is the total cost, x is the number of months of service,
      $90 is the installation fee, and $40 is the service charge per
      month.
  (2) y is the total cost, x is the number of months of service,
      $40 is the installation fee, and $90 is the service charge per
      month.
  (3) x is the total cost, y is the number of months of service,
      $40 is the installation fee, and $90 is the service charge per
      month.
  (4) x is the total cost, y is the number of months of service,
      $90 is the installation fee, and $40 is the service charge per
      month.

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3.

3 If 4x2 - 100 = 0, the roots of the equation are
  (1) -25 and 25                 (3) -5 and 5
  (2) -25, only                  (4) -5, only

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4.

                                                                          U
4 Isaiah collects data from two different companies, each with four
  employees. The results of the study, based on each worker’s age and
  salary, are listed in the tables below.
             Company 1                      Company 2
       Worker’s       Salary          Worker’s       Salary
        Age in          in             Age in          in
        Years         Dollars          Years         Dollars
          25          30,000              25          29,000
          27          32,000              28          35,500
          28          35,000              29          37,000
          33          38,000              31          65,000
  Which statement is true about these data?
  (1) The median salaries in both companies are greater than $37,000.
  (2) The mean salary in company 1 is greater than the mean salary in
      company 2.
  (3) The salary range in company 2 is greater than the salary range in
      company 1.
  (4) The mean age of workers at company 1 is greater than the mean
      age of workers at company 2.

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5.

5 Which point is not on the graph represented by y = x2 + 3x - 6?
  (1) (-6,12)                   (3) (2,4)
  (2) (-4,-2)                   (4) (3,-6)

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6.

6 A company produces x units of a product per month, where C(x)
  represents the total cost and R(x) represents the total revenue for the
  month. The functions are modeled by C(x) = 300x + 250 and
  R(x) = -0.5x2 + 800x - 100. The profit is the difference between
  revenue and cost where P(x) = R(x) - C(x). What is the total profit,
  P(x), for the month?
  (1) P(x) = -0.5x2 + 500x - 150
  (2) P(x) = -0.5x2 + 500x - 350
  (3) P(x) = -0.5x2 - 500x + 350
  (4) P(x) = -0.5x2 + 500x + 350

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7.

7 What is one point that lies in the solution set of the system of
  inequalities graphed below?
(1) (7,0)   (3) (0,7)
(2) (3,0)   (4) (-3,5)

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8.

8 The value of the x-intercept for the graph of 4x - 5y = 40 is

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9.

9 Sam and Jeremy have ages that are consecutive odd integers.
  The product of their ages is 783. Which equation could be used to
  find Jeremy’s age, j, if he is the younger man?
  (1) j2 + 2 = 783              (3) j2 + 2j = 783
  (2) j2 - 2 = 783              (4) j2 - 2j = 783

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10.

10 A population that initially has 20 birds approximately doubles every
   10 years. Which graph represents this population growth?

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11.

11 Let f be a function such that f(x) = 2x - 4 is defined on the domain
   2 ≤ x ≤ 6. The range of this function is
   (1) 0 ≤ y ≤ 8                   (3) 2 ≤ y ≤ 6
   (2) 0 ≤ y < ∞                   (4) -∞ < y < ∞

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12.

12 Which situation could be modeled by using a linear function?
   (1) a bank account balance that grows at a rate of 5% per year,
       compounded annually
   (2) a population of bacteria that doubles every 4.5 hours
   (3) the cost of cell phone service that charges a base amount plus
       20 cents per minute
   (4) the concentration of medicine in a person’s body that decays by
       a factor of one-third every hour

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13.

13 Which graph shows a line where each value of y is three more than
   half of x?

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14.

14 The table below shows the average diameter of a pupil in a person’s
   eye as he or she grows older.
                        Age     Average Pupil
                      (years)   Diameter (mm)
                        20           4.7
                        30           4.3
                        40           3.9
                        50           3.5
                        60           3.1
                        70           2.7
                        80           2.3
   What is the average rate of change, in millimeters per year, of a
   person’s pupil diameter from age 20 to age 80?
   (1) 2.4                        (3) -2.4
   (2) 0.04                       (4) -0.04

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15.

15 Which expression is equivalent to x4 - 12x2 + 36?
   (1) (x2 - 6)(x2 - 6)          (3) (6 - x2)(6 + x2)
   (2) (x2 + 6)(x2 + 6)          (4) (x2 + 6)(x2 - 6)

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16.

16 The third term in an arithmetic sequence is 10 and the fifth term is 26.
   If the first term is a1, which is an equation for the nth term of this
   sequence?
   (1) an = 8n + 10                  (3) an = 16n + 10
   (2) an = 8n - 14                  (4) an = 16n - 38

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17.

17 The graph of the equation y = ax2 is shown below.
(1) wider and opens downward
(2) wider and opens upward
(3) narrower and opens downward
(4) narrower and opens upward

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18.

18 The zeros of the function f(x) = (x + 2)2 - 25 are
   (1) -2 and 5                   (3) -5 and 2
   (2) -3 and 7                   (4) -7 and 3

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19.

19 During the 2010 season, football player McGee’s earnings, m, were
   0.005 million dollars more than those of his teammate Fitzpatrick’s
   earnings, f. The two players earned a total of 3.95 million dollars.
   Which system of equations could be used to determine the amount
   each player earned, in millions of dollars?
   (1) m + f = 3.95                (3) f - 3.95 = m
       m + 0.005 = f                   m + 0.005 = f
   (2) m - 3.95 = f                (4) m + f = 3.95
       f + 0.005 = m                   f + 0.005 = m

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20.

      
(1) 4   (3) 8
(2) 6   (4) 11

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21.

21 The table below shows the number of grams of carbohydrates, x, and
   the number of Calories, y, of six different foods.
                   Carbohydrates (x)       Calories (y)
                            8                  120
                           9.5                 138
                           10                  147
                            6                   88
                            7                  108
                            4                   62
   Which equation best represents the line of best fit for this set of data?
   (1) y = 15x                       (3) y = 0.1x - 0.4
   (2) y = 0.07x                     (4) y = 14.1x + 5.8

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22.

22 A function is graphed on the set of axes below.

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23.

23 The function h(t) = -16t2 + 144 represents the height, h(t), in feet, of
   an object from the ground at t seconds after it is dropped. A realistic
   domain for this function is
   (1) -3 ≤ t ≤ 3                    (3) 0 ≤ h(t) ≤ 144
   (2) 0 ≤ t ≤ 3                     (4) all real numbers

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24.

24 If f(1) = 3 and f(n) = -2f(n - 1) + 1, then f(5) =
   (1) -5                         (3) 21
   (2) 11                         (4) 43

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