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Regents January 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 The number of hours spent on math homework during one week and
  the math exam grades for eleven students in Ms. Smith’s algebra
  class are plotted below.
Based on the plotted data, what is the correlation between the time
spent on homework and the exam grade?
(1) positive                   (3) no correlation
(2) negative                   (4) cannot be determined
Answer: 1

2.
2 A car uses one gallon of gasoline for every 20 miles it travels. If a
  gallon of gasoline costs $3.98, how much will the gas cost, to the
  nearest dollar, to travel 180 miles?
  (1) 9                           (3) 45
  (2) 36                          (4) 80
Answer: 2

3.
3 If Angelina’s weekly allowance is d dollars, which expression
  represents her allowance, in dollars, for x weeks?

Answer: 1


4.
4 What is the solution of the system of equations shown in the graph
  below?

Answer: 3

5.
Answer: 4

6.
Answer: 1

7.
7 In right triangle ABC shown below, what is the value of cos A?

Answer: 2

8.
8 A bag contains five green gumdrops and six red gumdrops. If Kim
  pulls a green gumdrop out of the bag and eats it, what is the
  probability that the next gumdrop she pulls out will be red?

Answer: 4

9.
9 Which graph represents a function?

Answer: 3

10.
10 The current population of a town is 10,000. If the population, P,
   increases by 20% each year, which equation could be used to find the
   population after t years?

Answer: 3


11.
(1) twice the sum of a number and four
(2) the sum of two times a number and four
(3) two times the difference of a number and four
(4) twice the product of a number and four
Answer: 1

12.
12 How many cubes with 5-inch sides will completely fill a cube that is
   10 inches on a side?
   (1) 50                          (3) 8
   (2) 25                          (4) 4
Answer: 3

13.
13 A school newspaper will survey students about the quality of the
   school’s lunch program. Which method will create the least biased
   results?
   (1) Twenty-five vegetarians are randomly surveyed.
   (2) Twenty-five students are randomly chosen from each grade
       level.
   (3) Students who dislike the school’s lunch program are chosen to
       complete the survey.
   (4) A booth is set up in the cafeteria for the students to voluntarily
       complete the survey.
Answer: 2

14.
(1) I    (3) III
(2) II   (4) IV
Answer: 3

15.
15 In the figure below, ABCD is a square and semicircle O has a radius
   of 6.

Answer: 3

16.
Answer: 2

17.
17 Which expression can be used to change 75 kilometers per hour to
   meters per minute?

Answer: 3

18.
Answer: 4

19.
Answer: 3

20.
Answer: 4


21.
Answer: 2

22.
Answer: 1

23.
Answer: 2

24.
Answer: 3

25.
25 A cube with faces numbered 1 through 6 is rolled 75 times, and the
   results are given in the table below.

Answer: 4

26.
26 Given:
(1) {9, 25, 81}           (3) {1, 4, 9, 25, 81, 100}
(2) {4, 9, 25, 81, 100}   (4) {4, 16, 36, 49, 64, 100}
Answer: 2

27.
Answer: 1

28.
Answer: 1

29.
29 Which statement is true about the data set 4, 5, 6, 6, 7, 9, 12?

Answer: 2

30.
(1) The graph becomes wider, and the y-intercept changes.
(2) The graph becomes wider, and the y-intercept stays the same.
(3) The graph becomes narrower, and the y-intercept changes.
(4) The graph becomes narrower, and the y-intercept stays the
    same.
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]

Answer: MODEL ANSWER GIVEN BELOW


32.
Answer: MODEL ANSWER GIVEN BELOW


33.

Answer: MODEL ANSWER GIVEN BELOW
[2] A correct graph is drawn that includes the given interval.


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 In a game, a player must spin each spinner shown in the diagram below once.
Draw a tree diagram or list a sample space showing all possible outcomes.
Answer: MODEL ANSWER GIVEN BELOW
[3] A correct tree diagram or sample space is shown


35.
Determine the number of outcomes that consist of a prime number and a letter in the word
“CAT.”
Answer: MODEL ANSWER GIVEN BELOW
6 is stated.


36.
The cost of three notebooks and four pencils is $8.50. The cost of five notebooks and eight
pencils is $14.50. Determine the cost of one notebook and the cost of one pencil.
[Only an algebraic solution can receive full credit.]
Answer: MODEL ANSWER GIVEN BELOW


37.
Wendy measures the floor in her rectangular bedroom for new carpeting. Her measurements are
24 feet by 14 feet. The actual measurements are 24.2 feet by 14.1 feet.
Determine the relative error in calculating the area of her bedroom. Express your answer as a
decimal to the nearest thousandth.
Answer: MODEL ANSWER GIVEN BELOW
[3] 0.015, and appropriate work is shown.


38.
                                           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]
Using the line provided, construct a box-and-whisker plot for the 12 scores below.
                         26, 32, 19, 65, 57, 16, 28, 42, 40, 21, 38, 10

Answer: MODEL ANSWER GIVEN BELOW


39.
Determine the number of scores that lie above the 75th percentile.
Answer: MODEL ANSWER GIVEN BELOW


40.
A metal pipe is used to hold up a 9-foot fence, as shown in the diagram below. The pipe makes
an angle of 48° with the ground.
Determine, to the nearest foot, how far the bottom of the pipe is from the base of the fence.
Answer: MODEL ANSWER GIVEN BELOW
8


41.
Determine, to the nearest foot, the length of the metal pipe.
Answer: MODEL ANSWER GIVEN BELOW
12,


42.
On the set of axes below, graph the following system of equations.

Answer: MODEL ANSWER GIVEN BELOW
Both equations are graphed correctly,


43.
Using the graph, determine and state the coordinates of all points in the solution set for the
system of equations.

Answer: MODEL ANSWER GIVEN BELOW
(0,4) and (3,7) are stated.



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