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Regents January 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 An example of an equation is
  (1) 2x2 - 4x + 12              (3) 4(x + 6)(x - 2)
  (2) |x - 6|                    (4) 2x = x2 + 3
Answer: 4

2.
2 The greatest common factor of 3m2n + 12mn2 is
  (1) 3n                      (3) 3mn
  (2) 3m                      (4) 3mn2
Answer: 3

3.
3 Jeremy is hosting a Halloween party for 80 children. He will give each
  child at least one candy bar. If each bag of candy contains 18 candy bars,
  which inequality can be used to determine how many bags, c, Jeremy
  will need to buy?

Answer: 1


4.
4 Which statement regarding biased sampling is false?
  (1) Online sampling is biased because only the people who happen
      to visit the web site will take the survey.
  (2) A radio call-in survey is biased because only people who feel
      strongly about the topic will respond.
  (3) A survey handed to every third person leaving a library is biased
      because everyone leaving the library was not asked to
      participate.
  (4) Asking for experts to take a survey is biased because they may
      have particular knowledge of the topic.
Answer: 3

5.
5 Which relation is not a function?
  (1) {(2,4), (1,2), (0,0), (-1,2), (-2,4)}
  (2) {(2,4), (1,1), (0,0), (-1,1), (-2,4)}
  (3) {(2,2), (1,1), (0,0), (-1,1), (-2,2)}
  (4) {(2,2), (1,1), (0,0), (1,-1), (2,-2)}
Answer: 4

6.
6 What is an equation of the line that passes through the point
  (-2,-8) and has a slope of 3?
  (1) y = 3x - 2              (3) y = 3x + 2
  (2) y = 3x - 22             (4) y = 3x + 22
Answer: 1

7.
7 A figure consists of a square and a semicircle, as shown in the
  diagram below.
If the length of a side of the square is 6, what is the area of the
shaded region?

Answer: 2

8.
8 The box-and-whisker plot shown below represents the number of
  magazine subscriptions sold by members of a club.
Which statistical measures do points B, D, and E represent,
respectively?
(1) minimum, median, maximum
(2) first quartile, median, third quartile
(3) first quartile, third quartile, maximum
(4) median, third quartile, maximum
Answer: 3

9.
9 What is the slope of a line represented by the equation 2y = x - 4?

Answer: 2

10.
10 What is the solution of the system of equations below?
                            2x + 3y = 7
                             x+y=3
   (1) (1,2)                      (3) (4,-1)
   (2) (2,1)                      (4) (4,1)
Answer: 2


11.
11 The graph below illustrates the number of acres used for farming in
   Smalltown, New York, over several years.
Using a line of best fit, approximately how many acres will be used
for farming in the 5th year?
(1) 0                          (3) 300
(2) 200                        (4) 400
Answer: 2

12.
12 When 16x3 - 12x2 + 4x is divided by 4x, the quotient is
   (1) 12x2 - 8x                 (3) 4x2 - 3x
   (2) 12x2 - 8x + 1             (4) 4x2 - 3x + 1
Answer: 4

13.
13 The width of a rectangle is 4 less than half the length. If ℓ represents
   the length, which equation could be used to find the width, w?

Answer: 3

14.
14 Which data can be classified as quantitative?
   (1) favorite stores at which you shop
   (2) U.S. Representatives and their home states
   (3) sales tax rate in each New York county
   (4) opinion of a freshman on the color of Paul’s shirt
Answer: 3

15.
15 Two cubes with sides numbered 1 through 6 were rolled 20 times.
   Their sums are recorded in the table below.
What is the empirical probability of rolling a sum of 9?

Answer: 2

16.
16 What is the vertex of the graph of the equation y = 3x2 + 6x + 1?
   (1) (-1,-2)                    (3) (1,-2)
   (2) (-1,10)                    (4) (1,10)
Answer: 1

17.
17 The length and width of a rectangle are 48 inches and 40 inches. To
   the nearest inch, what is the length of its diagonal?
   (1) 27                         (3) 88
   (2) 62                         (4) 90
Answer: 2

18.
18 Which graph represents the solution set of 2x - 5 < 3?

Answer: 1

19.
19 Jonathan drove to the airport to pick up his friend. A rainstorm
   forced him to drive at an average speed of 45 mph, reaching the
   airport in 3 hours. He drove back home at an average speed of
   55 mph. How long, to the nearest tenth of an hour, did the trip home
   take him?
   (1) 2.0 hours                   (3) 2.8 hours
   (2) 2.5 hours                   (4) 3.7 hours
Answer: 2

20.
Answer: 3


21.
21 When x = 4, the value of 2x0 + x! is
   (1) 24                         (3) 26
   (2) 25                         (4) 28
Answer: 3

22.
22 Which graph represents the solution of 2y + 6 > 4x?

Answer: 3

23.
23 Which graph represents the exponential decay of a radioactive
   element?

Answer: 4

24.
24 Which fraction represents
expressed in simplest form?

Answer: 3

25.
Answer: 1

26.
26 Given:
                  U = {x|0 < x < 10 and x is an integer}
                  S = {x|0 < x < 10 and x is an odd integer}
   The complement of set S within the universal set U is
   (1) {0, 2, 4, 6, 8, 10}         (3) {0, 2, 4, 6, 8}
   (2) {2, 4, 6, 8, 10}            (4) {2, 4, 6, 8}
Answer: 4

27.
27 The roots of the equation 2x2 - 8x = 0 are
   (1) -2 and 2                  (3) 0 and -4
   (2) 0, -2, and 2              (4) 0 and 4
Answer: 4

28.
28 Which equation illustrates the multiplicative inverse property?

Answer: 3

29.
29 What is the result when 4x2 - 17x + 36 is subtracted from
   2x2 - 5x + 25?
   (1) 6x2 - 22x + 61        (3) -2x2 - 22x + 61
   (2) 2x2 - 12x + 11        (4) -2x2 + 12x - 11
Answer: 4

30.
30 Julie has three children whose ages are consecutive odd integers.
   If x represents the youngest child’s age, which expression represents
   the sum of her children’s ages?
   (1) 3x + 3                      (3) 3x + 5
   (2) 3x + 4                      (4) 3x + 6
Answer: 4


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.
32 The cumulative frequency table below shows the number of minutes 31 students spent text
   messaging on a weekend.
Determine which 10-minute interval contains the median. Justify your choice.
Answer: MODEL ANSWER GIVEN BELOW
[2] 71–80, and a correct justification is given.


33.
33 Kirsten invested $1000 in an account at an annual interest rate of 3%. She made no deposits or
   withdrawals on the account for 5 years. The interest was compounded annually. Find the balance
   in the account, to the nearest cent, at the end of 5 years.
Answer: MODEL ANSWER GIVEN BELOW
[2] 1159.27 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 Graph and label the functions y = |x| and y = |2x| on the set of axes below.
Explain how increasing the coefficient of x affects the graph of y = |x|.
Answer: MODEL ANSWER GIVEN BELOW
[3] Both equations are graphed correctly, and at least one is labeled. A correct
    explanation is given.


35.
35 Terry estimated the length of the edge of a cube to be 5 cm. The actual length of the side is
   5.2 cm. Find the relative error of the surface area of the cube, to the nearest thousandth.
Answer: MODEL ANSWER GIVEN BELOW
[3] 0.075, and correct work is shown.


36.
36 From the top of an apartment building, the angle of depression to a car parked on the street below
   is 38 degrees, as shown in the diagram below. The car is parked 80 feet from the base of the
   building. Find the height of the building, to the nearest tenth of a foot.

Answer: MODEL ANSWER GIVEN BELOW
[3] 62.5, 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, solve the following system of equations graphically for all values of
     x and y. State the coordinates of all the solutions.
                                          y = x2 + 4x - 5
                                            y = 2x + 3

Answer: MODEL ANSWER GIVEN BELOW
[4] Both equations are graphed correctly, and (-4,-5) and (2,7) are stated.


38.
38 Solve algebraically for all values of x:

Answer: MODEL ANSWER GIVEN BELOW
[4] -2 and 12, and correct algebraic work is shown.


39.
39 Doug has four baseball caps: one tan, one blue, one red, and one green. He also has three
   jackets: one blue, one red, and one white. Draw a tree diagram or list a sample space to show all
   possible outfits consisting of one baseball cap and one jacket.
   Find the number of Doug’s outfits that consist of a cap and a jacket that are different colors.
On Spirit Day, Doug wants to wear either green or white, his school’s colors. Find the number
of his outfits from which he can choose.
Answer: MODEL ANSWER GIVEN BELOW
[4] A correct tree diagram or sample space is shown, and 10 and 6 are stated.



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