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Algebra I (Common Core) - New York Regents August 2015 Exam

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1.
                                             Part I
    Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial
credit will be allowed. Utilize the information provided for each question to determine your
answer. Note that diagrams are not necessarily drawn to scale. For each statement or question,
choose the word or expression that, of those given, best completes the statement or answers
the question. Record your answers on your separate answer sheet. [48]
1 Given the graph of the line represented by the equation
  f(x) = -2x + b, if b is increased by 4 units, the graph of the new
  line would be shifted 4 units
  (1) right                      (3) left
  (2) up                         (4) down
Answer: 2

2.
2 Rowan has $50 in a savings jar and is putting in $5 every week. Jonah
  has $10 in his own jar and is putting in $15 every week. Each of them
  plots his progress on a graph with time on the horizontal axis and
  amount in the jar on the vertical axis. Which statement about their
  graphs is true?
  (1) Rowan’s graph has a steeper slope than Jonah’s.
  (2) Rowan’s graph always lies above Jonah’s.
  (3) Jonah’s graph has a steeper slope than Rowan’s.
  (4) Jonah’s graph always lies above Rowan’s.
Answer: 3

3.
3 To watch a varsity basketball game, spectators must buy a ticket at
  the door. The cost of an adult ticket is $3.00 and the cost of a
  student ticket is $1.50. If the number of adult tickets sold is
  represented by a and student tickets sold by s, which expression
  represents the amount of money collected at the door from the
  ticket sales?
  (1) 4.50as                     (3) (3.00a)(1.50s)
  (2) 4.50(a + s)                (4) 3.00a + 1.50s
Answer: 4


4.
4 The graph of f(x) is shown below.
Which function could represent the graph of f(x)?
(1) f(x) = (x + 2)(x2 + 3x - 4)
(2) f(x) = (x - 2)(x2 + 3x - 4)
(3) f(x) = (x + 2)(x2 + 3x + 4)
(4) f(x) = (x - 2)(x2 + 3x + 4)
Answer: 1

5.
5 The cost of a pack of chewing gum in a vending machine is $0.75.
  The cost of a bottle of juice in the same machine is $1.25. Julia has
  $22.00 to spend on chewing gum and bottles of juice for her team and
  she must buy seven packs of chewing gum. If b represents the number
  of bottles of juice, which inequality represents the maximum number
  of bottles she can buy?
  (1) 0.75b + 1.25(7) ≥ 22       (3) 0.75(7) + 1.25b ≥ 22
  (2) 0.75b + 1.25(7) ≤ 22       (4) 0.75(7) + 1.25b ≤ 22
Answer: 4

6.
6 Which graph represents the solution of y ≤ x + 3 and y ≥ -2x - 2?

Answer: 3

7.
7 The country of Benin in West Africa has a population of 9.05 million
  people. The population is growing at a rate of 3.1% each year.
  Which function can be used to find the population 7 years from now?

Answer: 3

8.
8 A typical cell phone plan has a fixed base fee that includes a certain
  amount of data and an overage charge for data use beyond the plan.
  A cell phone plan charges a base fee of $62 and an overage charge
  of $30 per gigabyte of data that exceed 2 gigabytes. If C represents
  the cost and g represents the total number of gigabytes of data,
  which equation could represent this plan when more than
  2 gigabytes are used?
  (1) C = 30 + 62(2 - g)          (3) C = 62 +30(2 - g)
  (2) C = 30 + 62(g - 2)          (4) C = 62 + 30(g - 2)
Answer: 4

9.
9 Four expressions are shown below.
                        I     2(2x2 - 2x - 60)
                        II    4(x2 - x - 30)
                        III   4(x + 6)(x - 5)
                        IV    4x(x - 1) - 120
  The expression 4x2 - 4x - 120 is equivalent to
  (1) I and II, only               (3) I, II, and IV
  (2) II and IV, only              (4) II, III, and IV
Answer: 3

10.
10 Last week, a candle store received $355.60 for selling 20 candles.
   Small candles sell for $10.98 and large candles sell for $27.98.
   How many large candles did the store sell?
   (1) 6                          (3) 10
   (2) 8                          (4) 12
Answer: 2

11.
11 Which representations are functions?
(1) I and II    (3) III, only
(2) II and IV   (4) IV, only
Answer: 2

12.
Answer: 3

13.
13 The zeros of the function f(x) = 3x2 - 3x - 6 are
   (1) -1 and -2                 (3) 1 and 2
   (2) 1 and -2                  (4) -1 and 2
Answer: 4

14.
14 Which recursively defined function has a first term equal to 10 and
   a common difference of 4?
   (1) f(1) = 10                  (3) f(1) = 10
       f(x) = f(x - 1) + 4            f(x) = 4 f(x - 1)
   (2) f(1) = 4                   (4) f(1) = 4
       f(x) = f(x - 1) + 10           f(x) = 10 f(x - 1)
Answer: 1

15.
15 Firing a piece of pottery in a kiln takes place at different
   temperatures for different amounts of time. The graph below shows
   the temperatures in a kiln while firing a piece of pottery after the
   kiln is preheated to 200ºF.
During which time interval did the temperature in the kiln show the
greatest average rate of change?
(1) 0 to 1 hour                (3) 2.5 hours to 5 hours
(2) 1 hour to 1.5 hours        (4) 5 hours to 8 hours
Answer: 1

16.
Answer: 2

17.
Answer: 2

18.
18 Alicia has invented a new app for smart phones that two companies
   are interested in purchasing for a 2-year contract.
   Company A is offering her $10,000 for the first month and will
   increase the amount each month by $5000.
   Company B is offering $500 for the first month and will double their
   payment each month from the previous month.
   Monthly payments are made at the end of each month. For which
   monthly payment will company B’s payment first exceed company A’s
   payment?
   (1) 6                          (3) 8
   (2) 7                          (4) 9
Answer: 3

19.
19 The two sets of data below represent the number of runs scored by
   two different youth baseball teams over the course of a season.
                   Team A: 4, 8, 5, 12, 3, 9, 5, 2
                   Team B: 5, 9, 11, 4, 6, 11, 2, 7
   Which set of statements about the mean and standard deviation is
   true?
   (1) mean A < mean B
       standard deviation A > standard deviation B
   (2) mean A > mean B
       standard deviation A < standard deviation B
   (3) mean A < mean B
       standard deviation A < standard deviation B
   (4) mean A > mean B
       standard deviation A > standard deviation B
Answer: 1

20.
20 If Lylah completes the square for f(x) = x2 - 12x + 7 in order
   to find the minimum, she must write f(x) in the general form
   f(x) = (x - a)2 + b. What is the value of a for f(x)?
   (1) 6                          (3) 12
   (2) -6                         (4) -12
Answer: 1

21.
21 Given the following quadratic functions:
Which statement about these functions is true?
(1) Over the interval -1 ≤ x ≤ 1, the average rate of change for n(x)
    is less than that for g(x).
(2) The y-intercept of g(x) is greater than the y-intercept for n(x).
(3) The function g(x) has a greater maximum value than n(x).
(4) The sum of the roots of n(x) = 0 is greater than the sum of the
    roots of g(x) = 0.
Answer: 4

22.
22 For which value of P and W is P + W a rational number?

Answer: 2

23.
23 The solution of the equation (x + 3)2 = 7 is

Answer: 3

24.
24 Which trinomial is equivalent to 3(x - 2)2 - 2(x - 1)?
   (1) 3x2 - 2x - 10             (3) 3x2 - 14x + 10
   (2) 3x2 - 2x - 14             (4) 3x2 - 14x + 14
Answer: 4


25.
                                            Part II
    Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. 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. [16]
25 Each day Toni records the height of a plant for her science lab. Her data are shown in the table
   below.
The plant continues to grow at a constant daily rate. Write an equation to represent h(n),
the height of the plant on the nth day.
Answer: MODEL ANSWER GIVEN BELOW


26.
26 On the set of axes below, graph the inequality 2x + y > 1.

Answer: MODEL ANSWER GIVEN BELOW


27.
27 Rachel and Marc were given the information shown below about the bacteria growing in a Petri
   dish in their biology class.
Rachel wants to model this information with a linear function. Marc wants to use an exponential
function. Which model is the better choice? Explain why you chose this model.
Answer: MODEL ANSWER GIVEN BELOW


28.
28 A driver leaves home for a business trip and drives at a constant speed of 60 miles per hour for
   2 hours. Her car gets a flat tire, and she spends 30 minutes changing the tire. She resumes driving
   and drives at 30 miles per hour for the remaining one hour until she reaches her destination.
   On the set of axes below, draw a graph that models the driver’s distance from home.

Answer: MODEL ANSWER GIVEN BELOW


29.
29 How many real solutions does the equation x2 - 2x + 5 = 0 have? Justify your answer.
Answer: MODEL ANSWER GIVEN BELOW


30.
30 The number of carbon atoms in a fossil is given by the function y = 5100(0.95)x, where
   x represents the number of years since being discovered.
   What is the percent of change each year? Explain how you arrived at your answer.
Answer: MODEL ANSWER GIVEN BELOW


31.
31 A toy rocket is launched from the ground straight upward. The height of the rocket above the
   ground, in feet, is given by the equation h(t) = -16t2 + 64t, where t is the time in seconds.
   Determine the domain for this function in the given context. Explain your reasoning.
Answer: MODEL ANSWER GIVEN BELOW


32.
32 Jackson is starting an exercise program. The first day he will spend 30 minutes on a treadmill.
   He will increase his time on the treadmill by 2 minutes each day. Write an equation for T(d),
   the time, in minutes, on the treadmill on day d.
   Find T(6), the minutes he will spend on the treadmill on day 6.
Answer: MODEL ANSWER GIVEN BELOW


33.
                                            Part III
    Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. 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. [16]

Answer: MODEL ANSWER GIVEN BELOW


34.
34 Solve for x algebraically:   7x - 3(4x - 8) ≤ 6x + 12 - 9x
   If x is a number in the interval [4,8], state all integers that satisfy the given inequality.
   Explain how you determined these values.
Answer: MODEL ANSWER GIVEN BELOW


35.
35 The volume of a large can of tuna fish can be calculated using the formula V = πr2h.
   Write an equation to find the radius, r, in terms of V and h.
   Determine the diameter, to the nearest inch, of a large can of tuna fish that has a volume of
   66 cubic inches and a height of 3.3 inches.
Answer: MODEL ANSWER GIVEN BELOW


36.
36 The table below shows the attendance at a museum in select years from 2007 to 2013.
State the linear regression equation represented by the data table when x = 0 is used to
represent the year 2007 and y is used to represent the attendance. Round all values to
the nearest hundredth.
State the correlation coefficient to the nearest hundredth and determine whether the data
suggest a strong or weak association.
Answer: MODEL ANSWER GIVEN BELOW


37.
                                            Part IV
     Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate
the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.
Utilize the information provided to determine your answer. Note that diagrams are not
necessarily drawn to scale. 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 written in pencil. [6]
37 A rectangular picture measures 6 inches by 8 inches. Simon wants to build a wooden frame for
   the picture so that the framed picture takes up a maximum area of 100 square inches on his wall.
   The pieces of wood that he uses to build the frame all have the same width.
   Write an equation or inequality that could be used to determine the maximum width of the pieces
   of wood for the frame Simon could create.
   Explain how your equation or inequality models the situation.
   Solve the equation or inequality to determine the maximum width of the pieces of wood used for
   the frame to the nearest tenth of an inch.
Answer: MODEL ANSWER GIVEN BELOW



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