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Regents August 2012 Exam

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    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]
Part I
1.
1 A system of equations is graphed on the set of axes below.
The solution of this system is
(1) (0,4)                        (3) (4,2)
(2) (2,4)                        (4) (8,0)
Answer: 3

2.
2 A cell phone can receive 120 messages per minute. At this rate, how
  many messages can the phone receive in 150 seconds?
  (1) 48                         (3) 300
  (2) 75                         (4) 18,000
Answer: 3

3.
Answer: 3


4.
4 The scatter plot shown below represents a relationship between
  x and y.
This type of relationship is
(1) a positive correlation     (3) a zero correlation
(2) a negative correlation     (4) not able to be determined
Answer: 1

5.
Answer: 2

6.
6 Jason’s part-time job pays him $155 a week. If he has already saved
  $375, what is the minimum number of weeks he needs to work in
  order to have enough money to buy a dirt bike for $900?
  (1) 8                          (3) 3
  (2) 9                          (4) 4
Answer: 4

7.
Answer: 3

8.
8 The scatter plot below shows the profit, by month, for a new
  company for the first year of operation. Kate drew a line of best fit,
  as shown in the diagram.
Using this line, what is the best estimate for profit in the 18th month?
(1) $35,000                      (3) $42,500
(2) $37,750                      (4) $45,000
Answer: 3

9.
9 Which statement illustrates the additive identity property?

Answer: 1

10.
10 Peter walked 8,900 feet from home to school.
                         1 mile ϭ 5,280 feet
   How far, to the nearest tenth of a mile, did he walk?
   (1) 0.5                         (3) 1.6
   (2) 0.6                         (4) 1.7
Answer: 4


11.
(1) exponential growth and 12%
(2) exponential growth and 88%
(3) exponential decay and 12%
(4) exponential decay and 88%
Answer: 3

12.
12 The length of a rectangle is 15 and its width is w. The perimeter of
   the rectangle is, at most, 50. Which inequality can be used to find
   the longest possible width?

Answer: 2

13.
13 Craig sees an advertisement for a car in a newspaper. Which
   information would not be classified as quantitative?
   (1) the cost of the car    (3) the model of the car
   (2) the car’s mileage      (4) the weight of the car
Answer: 3

14.
14 What are the coordinates of the vertex and the equation of the axis
   of symmetry of the parabola shown in the graph below?

Answer: 4

15.
Answer: 2

16.
16 The rectangular prism shown below has a length of 3.0 cm, a width
   of 2.2 cm, and a height of 7.5 cm.
What is the surface area, in square centimeters?
(1) 45.6                       (3) 78.0
(2) 49.5                       (4) 91.2
Answer: 4

17.
Answer: 4

18.
(1) narrower and open downward
(2) narrower and open upward
(3) wider and open downward
(4) wider and open upward
Answer: 2

19.
Answer: 3

20.
Answer: 1


21.
21 Given:

Which statement is false?
Answer: 3

22.
Answer: 4

23.
23 In a given linear equation, the value of the independent variable
   decreases at a constant rate while the value of the dependent
   variable increases at a constant rate. The slope of this line is
   (1) positive                  (3) zero
   (2) negative                  (4) undefined
Answer: 2

24.
24 The volume of a cylindrical can is 32π cubic inches. If the height of
   the can is 2 inches, what is its radius, in inches?
   (1) 8                           (3) 16
   (2) 2                           (4) 4
Answer: 4

25.
Answer: 3

26.
Answer: 3

27.
27 The total score in a football game was 72 points. The winning team
   scored 12 points more than the losing team. How many points did
   the winning team score?
   (1) 30                         (3) 54
   (2) 42                         (4) 60
Answer: 2

28.
28 What is the perimeter of the figure shown below, which consists of
   an isosceles trapezoid and a semicircle?

Answer: 1

29.
Answer: 4

30.
Answer: 3


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]

Answer: MODEL ANSWER GIVEN BELOW


32.
Answer: MODEL ANSWER GIVEN BELOW


33.

Answer: MODEL ANSWER GIVEN BELOW


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 following cumulative frequency histogram shows the distances swimmers completed in a
   recent swim test.
Based on the cumulative frequency histogram, determine the number of swimmers who swam
between 200 and 249 yards.
Answer: MODEL ANSWER GIVEN BELOW
3


35.
Determine the number of swimmers who swam between 150 and 199 yards.
Answer: MODEL ANSWER GIVEN BELOW
0


36.
Determine the number of swimmers who took the swim test.
Answer: MODEL ANSWER GIVEN BELOW
20


37.
Ashley measured the dimensions of a rectangular prism to be 6 cm by 10 cm by 1.5 cm. The actual
dimensions are 5.9 cm by 10.3 cm by 1.7 cm. Determine the relative error, to the nearest thousandth,
in calculating the volume of the prism.
Answer: MODEL ANSWER GIVEN BELOW
[3] 0.129, and appropriate work is shown.


38.
Solve the following system of equations algebraically for all values of x and y.

Answer: MODEL ANSWER GIVEN BELOW
[3] x ϭ Ϫ3, y ϭ Ϫ5 and x ϭ 3, y ϭ 7 or (Ϫ3,Ϫ5) and (3,7), and appropriate
    algebraic work is shown.


39.
                                           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]
A company is running a contest and offering a first, second, and third prize. First prize is a choice
of a car or $15,000 cash. Second prize is a choice of a motorbike, a trip to New York City, or $2,000
cash. Third prize is a choice of a television or $500 cash.
If each prize is equally likely to be selected, list the sample space or draw a tree diagram of all
possible different outcomes of first, second, and third prizes.
Answer: MODEL ANSWER GIVEN BELOW
A correct tree diagram or sample space is shown,


40.
Determine the number of ways that all three prizes selected could be cash.
Answer: MODEL ANSWER GIVEN BELOW
1


41.
Determine the number of ways that none of the three prizes selected could be cash.
Answer: MODEL ANSWER GIVEN BELOW
2


42.
Answer: MODEL ANSWER GIVEN BELOW
54


43.
Answer: MODEL ANSWER GIVEN BELOW
23


44.
On the set of axes below, graph the following system of inequalities.

Answer: MODEL ANSWER GIVEN BELOW


45.

Answer: MODEL ANSWER GIVEN BELOW



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