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Regents January 2015 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 If A = {1, 2, 3, 4, 5, 6, 7, 8} and B = {2, 4, 6, 8, 10, 12}, the
  intersection of sets A and B is
(1) {10, 12}       (3) {1, 3, 5, 7}
(2) {2, 4, 6, 8}   (4) {1, 2, 3, 4, 5, 6, 7, 8, 10, 12}
Answer: 2

2.
2 What is the value of n in the equation 0.2(n - 6) = 2.8?
(1) 8   (3) 20
(2) 2   (4) 44
Answer: 3

3.
3 The expression
is equivalent to
(1) -4x2y3   (3) -4x9y4
(2) -4x3y3   (4) -4x3y2
Answer: 4


4.
4 Which situation is represented by bivariate data?
  (1) A student lists her algebra quiz grades for one month.
  (2) A wrestler records his weight before each match.
  (3) A musician writes down how many minutes she practices her
      instrument each day.
  (4) An ice cream vendor tracks the daily high temperature and how
      many ice cream bars he sells each day.
Answer: 4

5.
5 A cylinder has a circular base with a radius of 3 units and a height of
  7 units. What is the volume of the cylinder in cubic units?

Answer: 3

6.
6 The graph of f(x) is shown below.
Based on this graph, what are the roots of the equation f(x) = 0?
(1) 1 and -5                   (3) 2 and -9
(2) -1 and 5                   (4) -1 and -5 and 5
Answer: 2

7.
7 Jose wants to ride his bike a total of 50 miles this weekend. If he
  rides m miles on Saturday, which expression represents the number
  of miles he must ride on Sunday?
(1) m - 50   (3) 50 - m
(2) m + 50   (4) 50m
Answer: 3

8.
8 Four students are playing a math game at home. One of the math
  game questions asked them to write an algebraic equation.
Brandon wrote: 3(5x - 0)
William wrote: 7 < 2(6 + x)
Alice wrote: 15x
Kayla wrote: 11 = 2x + 3
Which student wrote an algebraic equation?
(1) Brandon                  (3) Alice
(2) William                  (4) Kayla
Answer: 4

9.
9 A student spent 15 minutes painting a 2-foot by 3-foot bulletin board.
  To the nearest tenth of a minute, how long did it take the student to
  paint 1 square foot?
  (1) 0.4                         (3) 2.5
  (2) 1.5                         (4) 3.5
Answer: 3

10.
10 What is an equation of the line that passes through the points (2,1)
   and (6,-5)?

Answer: 2


11.
Answer: 3

12.
12 In the box-and-whisker plot below, what is the 2nd quartile?
(1) 25   (3) 45
(2) 30   (4) 50
Answer: 2

13.
13 The length of a rectangle is three feet less than twice its width. If x
   represents the width of the rectangle, in feet, which inequality
   represents the area of the rectangle that is at most 30 square feet?
(1) x(2x - 3) ≤ 30   (3) x(3 - 2x) ≤ 30
(2) x(2x - 3) ≥ 30   (4) x(3 - 2x) ≥ 30
Answer: 1

14.
14 Which set is a function?
   (1) {(3,4), (3,5), (3,6), (3,7)}   (3) {(6,7), (7,8), (8,9), (6,5)}
   (2) {(1,2), (3,4), (4,3), (2,1)}   (4) {(0,2), (3,4), (0,8), (5,6)}
Answer: 2

15.
15 The weights of 40 students were recorded. If the 75th percentile of
   their weights was 140 pounds, what is the total number of students
   who weighed more than 140 pounds?
   (1) 10                         (3) 30
   (2) 20                         (4) 4
Answer: 1

16.
16 What is the slope of the line represented by the equation 4x + 3y = 7?

Answer: 4

17.
Answer: 1

18.
18 In ABC below, the measure of ∠A = 90°, AB = 6, AC = 8, and
   BC = 10.
Which ratio represents the sine of ∠B?

Answer: 4

19.
19 The equations 6x + 5y = 300 and 3x + 7y = 285 represent the
   money collected from selling gift baskets in a school fundraising
   event. If x represents the cost for each snack gift basket and
   y represents the cost for each chocolate gift basket, what is the cost
   for each chocolate gift basket?
(1) $20   (3) $30
(2) $25   (4) $54
Answer: 3

20.
20 Which equation represents the axis of symmetry of the graph of the
   equation y = x2 + 4x - 5?
   (1) x = -2                     (3) y = -2
   (2) x = 4                      (4) y = 4
Answer: 1


21.
Answer: 4

22.
22 Last year, Nick rode his bicycle a total of 8000 miles. To the
   nearest yard, Nick rode an average of how many yards per day?
(1) 22    (3) 1659
(2) 236   (4) 38,575
Answer: 4

23.
23 The set of integers is not closed for
   (1) division                     (3) addition
   (2) multiplication               (4) subtraction
Answer: 1

24.
24 A model rocket is launched into the air from ground level.
   The height, in feet, is modeled by p(x) = -16x2 + 32x, where x is
   the number of elapsed seconds. What is the total number of seconds
   the model rocket will be in the air?
(1) 1   (3) 0
(2) 2   (4) 16
Answer: 2

25.
25 The diagram below shows the path a bird flies from the top of
   a 9.5-foot-tall sunflower to a point on the ground 5 feet from the
   base of the sunflower.
To the nearest tenth of a degree, what is the measure of angle x?
(1) 27.8                       (3) 58.2
(2) 31.8                       (4) 62.2
Answer: 1

26.
26 Which set of numbers represents the lengths of the sides of a right
   triangle?
   (1) {7, 24, 25}                (3) {10, 12, 14}
   (2) {9, 16, 23}                (4) {14, 16, 18}
Answer: 1

27.
27 How many different seven-letter arrangements of the letters in the
   word HEXAGON can be made if each letter is used only once?
   (1) 28                         (3) 720
   (2) 49                         (4) 5040
Answer: 4

28.
28 Three students each rolled a wooden cube with faces painted red,
   white, and blue. The color of the top face is recorded each time the
   cube is rolled. The table below shows the results.
If a fourth student rolled the cube 75 times, based on these
experimental data, approximately how many times can the cube be
expected to land with blue on top?
(1) 25                       (3) 35
(2) 30                       (4) 40
Answer: 2

29.
29 Dominick graphs the equation y = a | x| where a is a positive
   integer. If Gina multiplies a by -3, the new graph will become
(1) narrower and open downward
(2) narrower and open upward
(3) wider and open downward
(4) wider and open upward
Answer: 1

30.
30 Mr. Suppe recorded the height, in inches, of each student in his
   class. The results are recorded in the table below.
Which cumulative frequency histogram represents the data?

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]
31 As shown in the diagram below, a ladder 12 feet long leans against a wall and makes an angle of
   72º with the ground.
Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder.
Answer: MODEL ANSWER GIVEN BELOW
[2] 3.7, and correct work is shown.


32.
32 Carla bought a dress at a sale for 20% off the original price. The sale price of the dress was $28.80.
   Find the original price of the dress, in dollars.
Answer: MODEL ANSWER GIVEN BELOW
[2] 36, and correct work is shown.


33.
33 The probability that a student owns a dog is 1/3. The probability that the same student owns
   a dog and a cat is 2/15 . Determine the probability that the student owns a cat.
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 A DVD costs twice as much as a music CD. Jack buys 2 DVDs and 2 CDs and spends $45.
   Determine how much one CD costs, in dollars. [Only an algebraic solution can receive full credit.]
Answer: MODEL ANSWER GIVEN BELOW
[3] 7.50 or equivalent and correct work is shown.


35.
35 Noj has the following test scores:
                                        76, 84, 69, 74, 91
   His teacher will allow him to retake the test on which he scored lowest. Noj wants an average of
   at least 82. Determine the least number of additional points Noj must score on the retest.
Answer: MODEL ANSWER GIVEN BELOW
[3] 16 and correct work is shown.


36.
36 Graph y < x and x > 5 on the axes below.
State the coordinates of a point in the solution set.
Answer: MODEL ANSWER GIVEN BELOW
[3] Correct graphs are drawn and at least one is labeled, and coordinates of a point
    within the solution set are found.


37.
Part IV
Find the cost, in dollars, of paving the area if the Rock Solid Concrete Company charges $8.95
per square foot.
    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 The Rock Solid Concrete Company has been asked to pave a rectangular area surrounding a
   circular fountain with a diameter of 8 feet, as shown in the diagram.
Find the area, to the nearest square foot, that must be paved.
Answer: MODEL ANSWER GIVEN BELOW
[4] 490 and 4385.50 and correct work is shown.


38.
38 Solve the following system of equations algebraically:
y = x2 + 5x - 17
   y=x-5
Answer: MODEL ANSWER GIVEN BELOW
[4] (2,-3) and (-6,-11) or equivalent, and correct algebraic work is shown.


39.
39 Perform the indicated operations and express the result in simplest form:

Answer: MODEL ANSWER GIVEN BELOW



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