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Regents August 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 What is the product of 3a2b and -2ab3?
  (1) a 2b3                   (3) -6a2b3
  (2) a3b4                    (4) -6a3b4
Answer: 4

2.
2 The value of the expression |-20| - |6| is
  (1) 26                         (3) -14
  (2) 14                         (4) -26
Answer: 2

3.
3 When 9x2 - 100 is factored, it is equivalent to (3x - b)(3x + b).
  What is a value for b?
  (1) 50                        (3) 3
  (2) 10                        (4) 100
Answer: 2


4.
4 Which equation represents the line that passes through the points
  (1,1) and (-2,7)?

Answer: 2

5.
5 The graph below represents the parabolic path of a ball kicked by
  a young child. What are the vertex and the axis of symmetry for
  the parabola?
(1) vertex: (3,8); axis of symmetry: x = 3
(2) vertex: (3,8); axis of symmetry: y = 3
(3) vertex: (8,3); axis of symmetry: x = 3
(4) vertex: (8,3); axis of symmetry: y = 3
Answer: 1

6.
6 Which relationship can best be described as causal?
  (1) The alarm goes off and the sun rises.
  (2) The car is moving slowly and the driver is singing.
  (3) The snow is falling and the stores run out of snow shovels.
  (4) The birds are chirping and the rain is coming down.
Answer: 3

7.
7 In a class, which data can be classified as qualitative?
  (1) age of students              (3) shoe size of students
  (2) weight of students           (4) hair color of students
Answer: 4

8.
8 Given the following:
        A = {Charles, Kyle, Nakim, Jade}
        B = {Charles, Jade, Alicia, Kyle}
        C = {Kyle, Nakim, Jade, Dylan}
  What is the intersection of sets A, B, and C?
  (1) {Kyle, Nakim}              (3) {Jade, Nakim}
  (2) {Charles, Kyle}            (4) {Jade, Kyle}
Answer: 4

9.
Answer: 1

10.
10 If Rosa’s age is represented by R, which inequality represents the
   statement “Rosa is at most 29 years old”?
   (1) R < 29                     (3) R ≤ 29
   (2) R > 29                     (4) R ≥ 29
Answer: 3


11.
11 What is the slope of a line passing through points (-7,5) and (5,-3)?

Answer: 2

12.
12 A positive correlation always exists on a scatter plot when
   (1) y remains unchanged as x increases
   (2) y changes randomly as x increases
   (3) y decreases as x increases
   (4) y increases as x increases
Answer: 4

13.
13 A sandwich consists of one type of meat, one type of condiment, and
   one type of cheese. The possible choices are listed below:
            Meat: beef, chicken, turkey
            Condiment: ketchup, mustard, mayonnaise
            Cheese: American, cheddar, provolone, mozzarella
   In the sample space of all the possible different sandwiches consisting
   of one type of meat, one type of condiment, and one type of cheese,
   how many sandwiches do not include provolone cheese?
   (1) 27                           (3) 3
   (2) 9                            (4) 36
Answer: 1

14.
14 The graph of the equation y = x2 is shown below.
Which statement best describes the change in this graph when the
coefficient of x2 is multiplied by 4?
(1) The parabola becomes wider.
(2) The parabola becomes narrower.
(3) The parabola will shift up four units.
(4) The parabola will shift right four units.
Answer: 2

15.
15 A parking lot is 100 yards long. What is the length of 3/4 of the
   parking lot, in feet?
(1) 300   (3) 75
(2) 225   (4) 25
Answer: 2

16.
16 What is the solution of the equation
(1) 1   (3) 3
(2) 5   (4) 14
Answer: 3

17.
17 The expression
is undefined when x is

Answer: 2

18.
18 In right triangle JKL in the diagram below, KL = 7, JK = 24, JL = 25,
   and ∠K = 90°.
Which statement is not true?

Answer: 2

19.
19 A teacher asked the class to solve the equation 3(x + 2) = 21.
   Robert wrote 3x + 6 = 21 as his first step. Which property did he use?
   (1) associative property         (3) distributive property
   (2) commutative property         (4) zero property of addition
Answer: 3

20.
20 If the roots of a quadratic equation are -4 and 2, the equation is
   equivalent to
   (1) (x + 4)(x - 2) = 0         (3) (x + 4)(x + 2) = 0
   (2) (x - 4)(x + 2) = 0         (4) (x - 4)(x - 2) = 0
Answer: 1


21.
21 Kelsey scored the following points in her first six basketball games:
   22, 14, 19, 22, 8, and 17. What is the relationship between the measures
   of central tendency of these data?
   (1) mode > median > mean          (3) mean > median > mode
   (2) median > mode > mean          (4) mode > mean > median
Answer: 1

22.
22 Sheba opened a retirement account with $36,500. Her account grew
   at a rate of 7% per year compounded annually. She made no deposits
   or withdrawals on the account. At the end of 20 years, what was the
   account worth, to the nearest dollar?
   (1) $87,600                    (3) $141,243
   (2) $130,786                   (4) $1,483,444,463
Answer: 3

23.
23 Which equation represents a vertical line?
   (1) y = -x                     (3) x = y
   (2) y = 12                     (4) x = 12
Answer: 4

24.
24 Byron has 72 coins in his piggy bank. The piggy bank contains only dimes
   and quarters. If he has $14.70 in his piggy bank, which equation can be
   used to determine q, the number of quarters he has?
   (1) 14.70 + 0.25q = 72
   (2) 0.10(q - 72) + 0.25q = 14.70
   (3) 0.10(72 - q) + 0.25q = 14.70
   (4) 0.10q + 0.25(72 - q) = 14.70
Answer: 3

25.
25 Which graph represents the equation y = |x - 2|?

Answer: 4

26.
26 If ax + 3 = 7 - bx, what is x expressed in terms of a and b?

Answer: 3

27.
27 Which equation represents a line that is parallel to the line whose
   equation is y = -3x?

Answer: 3

28.
28 What is the result when 6x2 - 13x + 12 is subtracted from
   -3x2 + 6x + 7?
   (1) 3x2 - 7x + 19         (3) 9x2 - 7x + 19
   (2) 9x2 - 19x + 5         (4) -9x2 + 19x - 5
Answer: 4

29.
29 What is the solution set of the equation
(1) {-6,-4}   (3) {6,-4}
(2) {-6,4}    (4) {6,4}
Answer: 2

30.
30 Which set of integers is included in (-1,3]?
   (1) {0,1,2,3}                  (3) {-1,0,1,2,3,4}
   (2) {-1,0,1,2}                 (4) {-2,-1,0,1,2,3}
Answer: 1


31.
                                               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 Using his data on annual deer population in a forest, Noj found the following information:
                                     25th percentile: 12
                                     50th percentile: 15
                                     75th percentile: 22
                                     Minimum population: 8
                                     Maximum population: 27
     Using the number line below, construct a box-and-whisker plot to display these data.

Answer: MODEL ANSWER GIVEN BELOW
[2] A correct box-and-whisker plot with a correct scale is drawn and labeled.


32.
32 The diagram below consists of a square with a side of 4 cm, a semicircle on the top, and an
   equilateral triangle on the bottom. Find the perimeter of the figure to the nearest tenth of
   a centimeter.

Answer: MODEL ANSWER GIVEN BELOW
[2] 22.3, and correct work is shown.


33.
33 A thermos in the shape of a cylinder is filled to 1 inch from the top of the cylinder with coffee.
   The height of the cylinder is 12 inches and its radius is 2.5 inches. State, to the nearest hundredth
   of a cubic inch, the volume of coffee in the thermos.
Answer: MODEL ANSWER GIVEN BELOW
[2] 215.98, 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 The top of a lighthouse, T, is 215 feet above sea level, L, as shown in the diagram below. The
     angle of depression from the top of the lighthouse to a boat, B, at sea is 26º. Determine, to the
     nearest foot, the horizontal distance, x, from the boat to the base of the lighthouse.

Answer: MODEL ANSWER GIVEN BELOW
[3] 441, and correct work is shown.


35.
35 There are six apples, five oranges, and one pear in John’s basket. His friend takes three pieces of
   fruit at random without replacement. Determine the probability that all three fruits taken are
   apples.
Answer: MODEL ANSWER GIVEN BELOW


36.
36 Express
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 On the set of axes below, solve the following system of inequalities graphically.
                                               y + 3 < 2x
                                             -2y ≤ 6x - 10
     State the coordinates of a point in the solution set.

Answer: MODEL ANSWER GIVEN BELOW
[4] Both inequalities are graphed and shaded correctly, at least one is labeled, and
    coordinates of a point in the solution set are stated.


38.
38 The actual side of a square tile is 4 inches. The manufacturers allow a relative error of 0.025 in
   the area of a tile. Two machines are used to cut the tiles. Machine A produces a square tile with
   a length of 3.97 inches. Machine B produces a square tile with a length of 4.12 inches. Determine
   which machine produces a tile whose area falls within the allowed relative error.
Answer: MODEL ANSWER GIVEN BELOW
[4] Machine A and correct work is shown.


39.
39 Solve the following system of equations algebraically:
                                         y = x2 - 6x + 9
                                          y = -9x + 19
Answer: MODEL ANSWER GIVEN BELOW
[4] (-5,64) and (2,1) or equivalent, and correct algebraic work is shown.



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