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Regents August 2013 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. Record your answers on your separate answer sheet. [60]

1.
1 Which situation describes a negative correlation?
  (1) the amount of gas left in a car’s tank and the amount of gas used
      from it
  (2) the number of gallons of gas purchased and the amount paid for
      the gas
  (3) the size of a car’s gas tank and the number of gallons it holds
  (4) the number of miles driven and the amount of gas used
Answer: 1

2.
Answer: 1

3.
3 Which event is certain to happen?
  (1) Everyone walking into a room will have red hair.
  (2) All babies born in June will be males.
  (3) The Yankees baseball team will win the World Series.
  (4) The Sun will rise in the east.
Answer: 4


4.
4 Noj is 5 years older than Jacob. The product of their ages is 84.
  How old is Noj?
  (1) 6                         (3) 12
  (2) 7                         (4) 14
Answer: 3

5.
5 Marie currently has a collection of 58 stamps. If she buys s stamps
  each week for w weeks, which expression represents the total
  number of stamps she will have?

Answer: 2

6.
6 Given:
What is the complement of set B within set A?
(1) {3, 5, 7}                 (3) {1, 3, 5, 7}
(2) {3, 5, 7, 19}             (4) {1, 3, 5, 7, 19}
Answer: 4

7.

Answer: 1

8.
8 Which graph does not represent the graph of a function?

Answer: 3

9.
Answer: 1

10.

Answer: 2


11.
Answer: 2

12.
12 The box-and-whisker plot below represents a set of grades in
   a college statistics class.
Which interval contains exactly 50% of the grades?
(1) 63–88                     (3) 75–81
(2) 63–95                     (4) 75–88
Answer: 4

13.
13 An art studio has a list of information posted with each sculpture that
   is for sale. Each entry in the list could be classified as quantitative
   except for the
   (1) cost                         (3) artist
   (2) height                       (4) weight
Answer: 3

14.

Answer: 2

15.
15 Using the substitution method, Ken solves the following system of
   equations algebraically.
Which equivalent equation could Ken use?

Answer: 1

16.
Answer: 4

17.

Answer: 3

18.
18 Which equation is true?

Answer: 2

19.
(1) commutative   (3) distributive
(2) associative   (4) multiplicative inverse
Answer: 1

20.
20 Monique has three sons who play football, two sons who play baseball,
   and one son who plays both sports. If all of her sons play baseball or
   football, how many sons does she have?
   (1) 5                            (3) 3
   (2) 6                            (4) 4
Answer: 4


21.

Answer: 4

22.
Answer: 4

23.
Answer: 3

24.
24 A cube, with faces numbered 1 to 6, is rolled, and a penny is tossed
   at the same time. How many elements in the sample space consist
   of an even number and a tail?
   (1) 12                          (3) 3
   (2) 2                           (4) 4
Answer: 3

25.
25 If the volume of a cube is 8 cubic centimeters, what is its surface
   area, in square centimeters?
   (1) 32                         (3) 12
   (2) 24                         (4) 4
Answer: 2

26.
26 A designer created a garden, as shown in the diagram below. The
   garden consists of four quarter-circles of equal size inside a square.
   The designer put a fence around both the inside and the outside of
   the garden.

Answer: 1

27.
27 Mr. Taylor raised all his students’ scores on a recent test by five
   points. How were the mean and the range of the scores affected?
   (1) The mean increased by five and the range increased by five.
   (2) The mean increased by five and the range remained the same.
   (3) The mean remained the same and the range increased by five.
   (4) The mean remained the same and the range remained the same.
Answer: 2

28.
Answer: 3

29.
29 Which ratio represents the cosine of angle A in the right triangle
   below?

Answer: 1

30.
Answer: 2


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 A jogger ran at a rate of 5.4 miles per hour. Find the jogger’s exact rate, in feet per minute.
                                        1 mile = 5,280 feet
Answer: MODEL ANSWER GIVEN BELOW
[2] 475.2, and correct work is shown.


32.
Answer: MODEL ANSWER GIVEN BELOW


33.
33 Adrianne invested $2000 in an account at a 3.5% interest rate compounded annually. She made
   no deposits or withdrawals on the account for 4 years. Determine, to the nearest dollar, the
   balance in the account after the 4 years.
Answer: MODEL ANSWER GIVEN BELOW
[2] 2295, 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 Miller’s Department Store is having a sale with a 25% discount on mattresses.
   If the sales tax rate is 8%, how much change will Frank receive from $800 if he purchases a
   mattress regularly priced at $895 during this sale?
Answer: MODEL ANSWER GIVEN BELOW
[3] 75.05, and correct work is shown.


35.
35 The difference between two numbers is 28. The larger number is 8 less than twice the smaller
   number. Find both numbers.
   [Only an algebraic solution can receive full credit.]
Answer: MODEL ANSWER GIVEN BELOW
[3] 36 and 64, and correct algebraic work is shown.


36.
36 Janis measures the dimensions of the floor in her rectangular classroom for a rug. Her measurements
   are 10.50 feet by 12.25 feet. The actual measurements of the floor are 10.75 feet by 12.50 feet.
   Determine the relative error in calculating the area, to the nearest thousandth.
Answer: MODEL ANSWER GIVEN BELOW
[3] 0.043, and correct work is shown.


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, graph the following system of equations. Using the graph, determine
   and state all solutions of the system of equations.


Answer: MODEL ANSWER GIVEN BELOW


38.
Answer: MODEL ANSWER GIVEN BELOW


39.
39 A bottle contains 12 red marbles and 8 blue marbles. A marble is chosen at random and not
   replaced. Then, a second marble is chosen at random.
   Determine the probability that the two marbles are not the same color.
Answer: MODEL ANSWER GIVEN BELOW


40.
Determine the probability that at least one of the marbles is red.
Answer: MODEL ANSWER GIVEN BELOW




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