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The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA II
Wednesday, January 24, 2018 — 1:15 to 4:15 p.m., only
Student Name: _________________________________________________________
School Name: ________________________________________________________________
DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.
Notice… A graphing calculator and a straightedge (ruler) must be available for you to use while taking this examination.
II ALGEBRA
The possession or use of any communications device is strictly prohibited when taking this examination. If you have or use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for you.
II
ALGEBRA
Print your name and the name of your school on the lines above. A separate answer sheet for Part I has been provided to you. Follow the instructions from the proctor for completing the student information on your answer sheet. This examination has four parts, with a total of 37 questions. You must answer all questions in this examination. Record your answers to the Part I multiple-choice questions on the separate answer sheet. Write your answers to the questions in Parts II, III, and IV directly in this booklet. All work should be written in pen, except graphs and drawings, which should be done in pencil. 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. The formulas that you may need to answer some questions in this examination are found at the end of the examination. This sheet is perforated so you may remove it from this booklet. Scrap paper is not permitted for any part of this examination, but you may use the blank spaces in this booklet as scrap paper. A perforated sheet of scrap graph paper is provided at the end of this booklet for any question for which graphing may be helpful but is not required. You may remove this sheet from this booklet. Any work done on this sheet of scrap graph paper will not be scored. When you have completed the examination, you must sign the statement printed at the end of the answer sheet, indicating that you had no unlawful knowledge of the questions or answers prior to the examination and that you have neither given nor received assistance in answering any of the questions during the examination. Your answer sheet cannot be accepted if you fail to sign this declaration.
Algebra II – Jan. ’18 [2]
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 ]
Use this space for 1 The operator of the local mall wants to find out how many of the computations. mall’s employees make purchases in the food court when they are working. She hopes to use these data to increase the rent and attract new food vendors. In total, there are 1023 employees who work at the mall. The best method to obtain a random sample of the employees would be to survey (1) all 170 employees at each of the larger stores (2) 50% of the 90 employees of the food court (3) every employee (4) every 30th employee entering each mall entrance for one week
2 What is the solution set for x in the equation below?
x 1 1 x
(1) {1} (3) {1,0} (2) {0} (4) {0,1}
3 For the system shown below, what is the value of z?
y 2 x 14 3 x 4 z 2 3 x y 16
(1) 5 (3) 6 (2) 2 (4) 4
Algebra II – Jan. ’18 [4]
8 For a given time, x , in seconds, an electric current, y , can be represented by y 2.5(1 2.7.10 x ). Which equation is not equivalent?
(1) y 2.5 2.5(2.7.10 x )
(2) y 2.5 2.5((2.7 2 ).05 x )
(3) y 2.5 2.5( _____^1 2.7 .10 x )
(4) y 2.5 2.5(2.7^2 )(2.7 .05 x )
9 What is the quotient when 10 x^3 3 x^2 7 x 3 is divided by 2 x 1? (1) 5 x^2 x 3 (3) 5 x^2 x 3 (2) 5 x^2 x 3 (4) 5 x^2 x 3
10 Judith puts $5000 into an investment account with interest compounded continuously. Which approximate annual rate is needed for the account to grow to $9110 after 30 years? (1) 2% (3) 0.02% (2) 2.2% (4) 0.022%
11 If n a^5 and m a , where a 0, an expression for __ mn could be
(1) a
__^5 (^2) (3) ^3 a 2
(2) a^4 (4) a^3
Use this space for computations.
Algebra II – Jan. ’18 [5] [OVER]
12 The solutions to x 3 _____ x ^4 1 5 are
(1) __^32 ____ 217 (3) __^32 ____ 233
(2) __^32 ____ 217 i (4) __^32 ____ 233 i
13 If ae bt^ c , where a , b , and c are positive, then t equals
(1) ln( ___ abc ) (3) ln (^) (__ (^) ac )
b
(2) ln(___ cb a ) (4) ln (^) (__ (^) ac )
ln b
14 For which values of x , rounded to the nearest hundredth , will
| x^2 9| 3 log 3 x? (1) 2.29 and 3.63 (3) 2.84 and 3. (2) 2.37 and 3.54 (4) 2.92 and 3.
15 The terminal side of θ, an angle in standard position, intersects the
unit circle at P ( ^13 , _ 3 ^8 ). What is the value of sec θ?
(1) 3 (3) __^13
(2) ____^3 8 ^8 (4) ___ 3 ^8
16 What is the equation of the directrix for the parabola 8( y 3) ( x 4) 2? (1) y 5 (3) y 2 (2) y 1 (4) y 6
Use this space for computations.
Algebra II – Jan. ’18 [7] [OVER]
20 The results of simulating tossing a coin 10 times, recording the number of heads, and repeating this 50 times are shown in the graph below.
Based on the results of the simulation, which statement is false? (1) Five heads occurred most often, which is consistent with the theoretical probability of obtaining a heads. (2) Eight heads is unusual, as it falls outside the middle 95% of the data. (3) Obtaining three heads or fewer occurred 28% of the time. (4) Seven heads is not unusual, as it falls within the middle 95% of the data.
21 What is the inverse of f ( x ) 6( x 2)?
(1) f ^1 ( x ) 2 __ 6 x
(2) f ^1 ( x ) 2 __ 6 x
(3) f ^1 ( x ) _________ 6( x^1 2)
(4) f ^1 ( x ) 6( x 2)
0 1 2 3 4 5 6 7 8 9
2
4
6
8
10
12
14
0 10 Number of Heads
Frequency
Use this space for computations.
Algebra II – Jan. ’18 [8]
22 Brian deposited 1 cent into an empty non-interest bearing bank account on the first day of the month. He then additionally deposited 3 cents on the second day, 9 cents on the third day, and 27 cents on the fourth day. What would be the total amount of money in the account at the end of the 20th day if the pattern continued? (1) $11,622,614.67 (3) $116,226,146. (2) $17,433,922.00 (4) $1,743,392,200.
23 If the function g ( x ) ab x^ represents exponential growth, which statement about g ( x ) is false? (1) a 0 and b 1 (3) The asymptote is y 0. (2) The y -intercept is (0, a ). (4) The x -intercept is ( b ,0).
24 At her job, Pat earns $25,000 the first year and receives a raise of $1000 each year. The explicit formula for the n th term of this sequence is a (^) n 25,000 ( n 1)1000. Which rule best represents the equivalent recursive formula? (1) a (^) n 24,000 1000 n (3) a 1 25,000, a (^) n a (^) n 1 1000 (2) a (^) n 25,000 1000 n (4) a 1 25,000, a (^) n a (^) n 1 1000
Use this space for computations.
26 A runner is using a nine-week training app to prepare for a “fun run.” The table below represents the amount of the program completed, A , and the distance covered in a session, D , in miles.
Based on these data, write an exponential regression equation, rounded to the nearest thousandth , to model the distance the runner is able to complete in a session as she continues through the nine-week program.
A __^49 __^59 __^69 __^89
D 2 2 2.25 3 3.
Algebra II – Jan. ’18 [10]
Algebra II – Jan. ’18 [11] [OVER]
27 A formula for work problems involving two people is shown below. __^1 t 1 ^
__^1 t 2 ^
__^1 t (^) b
t 1 the time taken by the first person to complete the job t 2 the time taken by the second person to complete the job t (^) b the time it takes for them working together to complete the job
Fred and Barney are carpenters who build the same model desk. It takes Fred eight hours to build the desk while it only takes Barney six hours. Write an equation that can be used to find the time it would take both carpenters working together to build a desk.
Determine, to the nearest tenth of an hour , how long it would take Fred and Barney working together to build a desk.
Algebra II – Jan. ’18 [13] [OVER]
30 Consider the function h ( x ) 2sin (3 x ) 1 and the function q represented in the table below.
Determine which function has the smaller minimum value for the domain [2,2]. Justify your answer.
x q (x) –2 – –1 0 0 0 1 – 2 0
31 The zeros of a quartic polynomial function h are 1, 2, and 3. Sketch a graph of y h ( x ) on the grid below.
Algebra II – Jan. ’18 [14]
33 Given: f ( x ) 2 x^2 x 3 and g ( x ) x 1 Express f ( x ) • g ( x ) (^) [ f ( x ) g ( x )] as a polynomial in standard form.
Algebra II – Jan. ’18 [16]
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 ]
Algebra II – Jan. ’18 [17] [OVER]
34 A student is chosen at random from the student body at a given high school. The probability that the student selects Math as the favorite subject is __^14. The probability that the student chosen is a junior is 116 ___ 459. If the probability that the student selected is a junior or that the student chooses Math as the favorite subject is ___ 10847 , what is the exact probability that the student selected is a junior whose favorite subject is Math?
Are the events “the student is a junior” and “the student’s favorite subject is Math” independent of each other? Explain your answer.
Algebra II – Jan. ’18 [19] [OVER]
36 The graph of y f ( x ) is shown below. The function has a leading coefficient of 1.
Write an equation for f ( x ).
The function g is formed by translating function f left 2 units. Write an equation for g ( x ).
50
–2 2
y
x
37 The resting blood pressure of an adult patient can be modeled by the function P below, where P ( t ) is the pressure in millimeters of mercury after time t in seconds. P ( t ) 24cos(3π t ) 120
On the set of axes below, graph y P ( t ) over the domain 0 ≤ t ≤ 2.
Question 37 is continued on the next page.
90
t
P(t)
1
Algebra II – Jan. ’18 [20]
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 done in pencil. [ 6 ]
