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Regents June 2014 Exam

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                                             Part I
    Answer all 30 questions in this part. Each correct answer will receive 2 credits. No partial
credit will be allowed. For each question, write on the separate answer sheet the numeral
preceding the word or expression that best completes the statement or answers the question. [60]

1.
1 The product of 6x3y3 and 2x2y is
  (1) 3xy2                      (3) 12x5y4
  (2) 8x5y4                     (4) 12x6y3
Answer: 3

2.
2 Which set of data is qualitative?
  (1) laps swum in a race
  (2) number of swimmers on the team
  (3) swimmers’ favorite swimsuit colors
  (4) temperature in Fahrenheit of the water in a pool
Answer: 3

3.
3 It takes a snail 500 hours to travel 15 miles. At this rate, how many
  hours will it take the snail to travel 6 miles?
  (1) 0.18                        (3) 150
  (2) 5.56                        (4) 200
Answer: 4


4.
4 The equation y = ax2 + bx + c is graphed on the set of axes below.
Based on the graph, what are the roots of the equation
ax2 + bx + c = 0?
(1) 0 and 5              (3) 1 and 5
(2) 1 and 0              (4) 3 and -4
Answer: 3

5.
5 When solving for the value of x in the equation 4(x - 1) + 3 = 18,
  Aaron wrote the following lines on the board.
                     [line 1]     4(x - 1) + 3 = 18
                     [line 2]          4(x - 1) = 15
                     [line 3]            4x - 1 = 15
                     [line 4]                4x = 16
                     [line 5]                   x=4
  Which property was used incorrectly when going from line 2 to line 3?
  (1) distributive                (3) associative
  (2) commutative                 (4) multiplicative inverse
Answer: 1

6.
6 What is the solution of 4x - 30 ≥ -3x + 12?
  (1) x ≥ 6                    (3) x ≥ -6
  (2) x ≤ 6                    (4) x ≤ -6
Answer: 1

7.
7 A local government is planning to increase the fee for use of
  a campsite. If a survey were taken, which group would be most biased
  in their opposition to the increase?
  (1) teachers                   (3) postal workers
  (2) soccer players             (4) campers
Answer: 4

8.
8 An example of an algebraic equation is

Answer: 3

9.
9 What is the value of x in the solution of the system of equations 
  3x + 2y = 12 and 5x - 2y = 4?
  (1) 8                          (3) 3
  (2) 2                          (4) 4
Answer: 2

10.
10 What is the slope of a line that passes through the points (-2,-7)
   and (-6,-2)?

Answer: 2


11.
11 Which notation is equivalent to the inequality -3 < x ≤ 7?
   (1) [-3,7]                    (3) [-3,7)
   (2) (-3,7]                    (4) (-3,7)
Answer: 2

12.
12 What is the value of the expression 3a2 - 4|a| + 6 when a = -3?
   (1) -24                       (3) 21
   (2) -9                        (4) 45
Answer: 3

13.
13 Which relation is a function?
   (1) {(2,1), (3,1), (4,1), (5,1)}
   (2) {(1,2), (1,3), (1,4), (1,5)}
   (3) {(2,3), (3,2), (4,2), (2,4)}
   (4) {(1,6), (2,8), (3,9), (3,12)}
Answer: 1

14.
14 When 6x2 - 4x + 3 is subtracted from 3x2 - 2x + 3, the result is
   (1) 3x2 - 2x                  (3) 3x2 - 6x + 6
   (2) -3x2 + 2x                 (4) -3x2 - 6x + 6
Answer: 2

15.
15 The lengths of the sides of a right triangle can be
   (1) 9, 12, 15                   (3) 5, 5, 10
   (2) 8, 10, 13                   (4) 4, 5, 6
Answer: 1

16.
16 Which equation represents a line that is parallel to the y-axis?
   (1) x = 5                       (3) y = 5
   (2) x = 5y                      (4) y = 5x
Answer: 1

17.
17 In right triangle ABC shown below, AC = 12, BC = 16, and
   AB = 20.


Answer: 4

18.
18 Three times the sum of a number and four is equal to five times
   the number, decreased by two. If x represents the number, which
   equation is a correct translation of the statement?
   (1) 3(x + 4) = 5x - 2        (3) 3x + 4 = 5x - 2
   (2) 3(x + 4) = 5(x - 2)      (4) 3x + 4 = 5(x - 2)
Answer: 1

19.
19 What is the equation of the line that passes through the point (3,-7)
   and has a slope of -4/3 ?

Answer: 2

20.
20 Which parabola has an axis of symmetry of x = 1?

Answer: 1


21.
21 When factored completely, the expression 3x2 - 9x + 6 is equivalent to
   (1) (3x - 3)(x - 2)              (3) 3(x + 1)(x - 2)
   (2) (3x + 3)(x - 2)              (4) 3(x - 1)(x - 2)
Answer: 4

22.
22 The equation P = 0.0089t2 + 1.1149t + 78.4491 models the
   United States population, P, in millions since 1900. If t represents the
   number of years after 1900, then what is the estimated population
   in 2025 to the nearest tenth of a million?
   (1) 217.8                         (3) 343.9
   (2) 219.0                         (4) 356.9
Answer: 4

23.
23 Which graph represents an absolute value equation?

Answer: 2

24.
Answer: 3

25.
25 Which value of x is the solution of the equation 2(x - 4) + 7 = 3?
   (1) 1                          (3) 6
   (2) 2                          (4) 0
Answer: 2

26.
26 Given:
            M = {green, red, yellow, black}
            N = {blue, green, yellow}
   Which set represents M ʜ N?
   (1) {yellow}                    (3) {blue, red, black}
   (2) {green, yellow}             (4) {green, red, yellow, blue, black}
Answer: 4

27.
27 Which situation describes a correlation that is not a causal relationship?
   (1) the number of miles walked and the total Calories burned
   (2) the population of a country and the census taken every ten years
   (3) the number of hours a TV is on and the amount of electricity used
   (4) the speed of a car and the number of hours it takes to travel a
       given distance
Answer: 2

28.
28 A school offers three classes of math and two classes of science, all of
   which meet at different times. What is the total number of ways
   a student can take a math class and a science class?
   (1) 5                             (3) 8
   (2) 6                             (4) 9
Answer: 2

29.
(1) 3 and 7    (3) 3, only
(2) 3 and -3   (4) 9
Answer: 2

30.
Answer: 3


Part II
    Answer all 3 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. [6]

31.
31 A patio consisting of two semicircles and a square is shown in the diagram below. The length of
   each side of the square region is represented by 2x. Write an expression for the area of the entire
   patio, in terms of x and π.

Answer: MODEL ANSWER GIVEN BELOW


32.
32 Clayton is performing some probability experiments consisting of flipping three fair coins.
   What is the probability that when Clayton flips the three coins, he gets two tails and one head?
Answer: MODEL ANSWER GIVEN BELOW


33.
33 Ross is installing edging around his pool, which consists of a rectangle and a semicircle, as shown
   in the diagram below.
Determine the length of edging, to the nearest tenth of a foot, that Ross will need to go
completely around the pool.
Answer: MODEL ANSWER GIVEN BELOW
[2] 98.6, and correct work is shown.


34.
                                                Part III
    Answer all 3 questions in this part. Each correct answer will receive 3 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. [9]
  34 Solve the following system of equations algebraically for all values of x and y.
                                            y = x2 + 2x - 8
                                               y = 2x + 1
Answer: MODEL ANSWER GIVEN BELOW
[3] x = -3, y = -5, and x = 3, y = 7 or an equivalent answer, and correct
    algebraic work is shown.


35.
35 A storage container in the form of a rectangular prism is measured to be 12 inches by 8 inches
   by 4 inches. Its actual measurements are 11.75 inches by 7.75 inches by 4 inches. Find the
   relative error in calculating the volume of the container, to the nearest thousandth.
Answer: MODEL ANSWER GIVEN BELOW
[3] 0.054, and correct work is shown.


36.
36 Perform the indicated operations and express the answer in simplest radical form.

Answer: MODEL ANSWER GIVEN BELOW


37.
                                               Part IV
    Answer all 3 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. [12]
  37 During its first week of business, a market sold a total of 108 apples and oranges. The second
     week, five times the number of apples and three times the number of oranges were sold. A total
     of 452 apples and oranges were sold during the second week. Determine how many apples and
     how many oranges were sold the first week. [Only an algebraic solution can receive full credit.]
Answer: MODEL ANSWER GIVEN BELOW
[4] 64 apples and 44 oranges, and correct algebraic work is shown.


38.
38 On the set of axes below, solve the following system of inequalities graphically.
   Label the solution set S.
                                           2x + 3y < -3
                                            y - 4x ≥ 2

Answer: MODEL ANSWER GIVEN BELOW
[4] Both inequalities are graphed and shaded correctly, and at least one is labeled.
    The solution set is labeled S.


39.
39 During the last 15 years of his baseball career, Andrew hit the following number of home runs
   each season.
                      35, 24, 32, 36, 40, 32, 40, 38, 36, 33, 11, 20, 19, 22, 8
   State and label the values of the minimum, 1st quartile, median, 3rd quartile, and maximum.
Answer: MODEL ANSWER GIVEN BELOW
[4] A correct box-and-whisker plot is drawn, and minimum = 8, Q1 = 20,
    median = 32, Q3 = 36, and maximum = 40 are stated.


40.
Using the line below, construct a box-and-whisker plot for this set of data.

Answer:


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