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The Regents High School Examination for Algebra II held on August 16, 2018. instructions for the exam, as well as various algebraic problems that students are expected to solve. The problems cover topics such as equations, functions, roots, inverse functions, and graphs.
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The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA II
Thursday, August 16, 2018 - 12:30 to 3:30 p.m., only
N}1· <:::' ~ l I Student Name: / · (',. ) .) t>t) ti
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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.
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.
Notice ... A graphing calculator and a straightedge (ruler) must be available for you to use while taking this examination.
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]
\0) 14.
·-.~··--"'-" 2 A researcher randomly divides 50 bean plants int two groups He puts one group by a window to receive natur ig and the second group under artificial light. He records the growth of the plants weekly. Which data collection method is described in this situation? ~ observational study (J_g)}· controlled experiment
(3) survey (4) systematic sample
in a polynomial expression?
(2) f(x) - g(x)
Algebra II - Aug. '
'A j(x) • g(x) U,9 f (x) -7- g(x)
Use this space for computations.
6 Given f (x) = ~ x + 8, which equation represents the inverse, g(x)?
Use this space for computations. (1) g(x) = 2x - 8 (3) g(x) = - ~x + 8 /""- (~ g(x) = 2x - 16 (4) g(x) = -2x^1 - 16 x~fyt<g
Jx ::- y+/
7 The value(s) of x that satisfy ~x 2 .;- 4x - 5 ~ 2x - 10 are y : )-.x - j {; (1) {5} @2>{5, 1} x '---l.;x-5 ~ trx L -YDx-rt 06 (2) {7} (4) {3, 5, 7} 3 ;(L- )~ y fl D) '/ 0
x L_ J):x +3s ~ o
&-7)(x-s] ~ o 8 Stephanie found that the number of white-winged cross bills in an area can be represented by the formula C = 550(1.0B)t, where t represents the number of years since 2010. Which equation correctly represents the number of white-winged cross bills in terms of the monthly rate of population growth? .1.... (1) c = 550(1.00643)t (3) c = 550(1.00643) 12 @c = 550(l.00643)^12 t (4) c = 550(L00643)t + 12
(/,OD()+9 1 L ~ /.0'
9 The roots of the equation 3x 2 + 2x = -7 are 3 j L. f )-y f 7 ~ 6
(1) -2, - ~ <8>- ~ ± 2iys
(2) - ~ ,1 (4) - ~ ± vp
--J t 1 J~--4 (~) lj_
)-lJ)
Algebra II - Aug. '
10 The average depreciation rate of a new boat is approximately 8% per
is a recursive formula representing the value of the boat n years after it was purchased? Cf)Jo tft/V,
Use this space for computations.
(1) an= 75,000(0.08t (3) an= 75,000(l.08t qyo ~+ h (2) ao :'.: 75,00~ ® ao :'.: 75, ~n -= (.0.9:) .. _. ·) an - 0.92(an - i) (';1 /j ) ) _'I_ ~J /}1 ) +,/)I vv. lv{
11 Given cos 8 = 275 , where 8 is an angle in standard position terminating
in quadrant IV, and sin 2 8 + cos 2 8 = 1, what is the value of tan 8?
(1) - 24 25
(3) 24 25 ({;
12 F (^) or x > 0 , wh. h IC express10n.^ IS.^ eqmv.^ al ent t o ~ w;^ •^ Jl ?.
(1) x 3 G x 3
(2) x 2 (4) x^10
Algebra II - Aug. '18 [5]
1-- X -Y
~ ;x,
:L !l- y c; ·x-~
16 Which sketch best represents the graph of x = 3Yp
y y
y y
Algebra II - Aug. '18 [7]
Use this space for computations.
17 The graph below represents national and New York State average gas prices.
·---!. .., ... _ .........-v~.,,,,,.,,,,.,,,_, L--·· l __ ~>Y' !
Aug Oct Dec Feb Apr Jun Aug 2014 2014 2014 2015 2015 2015 2015
Kev
expression best approximates the^ national average^ x^ months from August 2014? (I) G(x + C)
~ G(x-C) ~G(x)-C
18 Data for the students enrolled in a local high school are shown in the Venn diagram below.
If a student from the high school is selected at random, what is the probability that the student is a sophomore given that the student is enrolled in Algebra II? 85 (I) 210 I::'\ 85 :::.!) 295
Algebra II -Aug. '
85 (3 ) 405 85 (4) 1600
[8]
Use this space for computations.
v ())d-,)
23 The parabola described by the equation y = 1 ~ (x - 2) 2 + 2 has the
(1) (2,-1) (2) (2,2)
i~ (2,3) ®(2,5)
24 A fast-food restaurant analyzes data to better serve its customers. After its analysis, it discovers that the events D, that a customer uses the drive-thru, and F, that a customer orders French fries, are independe121 The following data are given in a report: -- P(F) = 0. P(F n D) = 0.
Given this information, P(FID) is (1) 0. (2) 0.
Algebra II - Aug. '
Use this space for compt1tions. 7 ~,~ 5 JJ,_
' I { J-,J.)
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.
25 Over the set of integers, factor the expression x 4 - 4x 2 - 12.
_(x}-r) Ci1' J-)
Algebra II - Aug. '18 [11]^ [OVER]
27 The world population was 2560 million people in 1950 and 3040 million in 1960 and can be modeled by the function p(t) = 2560e0·017185t, where tis time in years after 1950 and p(t) is the population in millions. Determine the average rate of change of p(t) in millions of people per year, from 4 < t < 8. Round your answer to the nearest hundredth.
pl't)-pl4)_
F, '-!
28 The scores of a recent test taken by 1200 students had an approximately normal distribution with a mean of 225 and a standard deviation of 18. Determine the number of students who scored between 200 and 245.
/)00, (^) , -7-',· ·o'·
Algebra II - Aug. '18 [13]^ [OVER]
29 Algebraically solve for x:
-3 + l_ = _£ - 1 x+3 2 6 2
.-&CxH)(~ -ft I ~ b)
I~ f y{/+1J) ,.(,(y
/¥ + 11- f"'1:x ,,C,x ,.}F ~b
y1- -}x ;, o
j(;<-Q :; {)
Jl·-0,
Algebra II -Aug. '18 [14]
31 Solve the following system of equations algebraically.
Algebra II - Aug. '
x^2 + y^2 = 400
x1-t (~-f8) 1-~ ~ oo
I f7Qlt ~ ~+(X) XL1-xL-)bX o.
'J-y1- - 5 bx f- }8 ~ ~, o
x'J,- -7-W t-Jq;--o
6-19 (X-)f) ~()
xs JI) l-b
y-· l~-J-F
', -lb
In--, -
y )b-J-?
~ -} )",_
()(:>, -)J)
32 Some smart-phone applications contain «in-app" purchases, which allow users to purchase special content within the application. A random sample of 140 users found that 35 percent made in-app purchases. A simulation was conducted with 200 samples of 140 users assuming 35 percent of the samples make in-app purchases. The approximately normal results are shown below.
25-
20-
15-
10-
5
0 I
Mean= 0. SD= 0.
Considering the middle 95% of the data, determine the margin of error, to the nearest hundredth, for the simulated results. In the given conJxt, explain what this value represents..
} (O.OL/~ ~o_07Jl/~-;O.,O?
U5-(! VS /"10 [ f htp
;)7 -^11 ~lb
/n- o;jf I
Algebra II -Aug. '18 [17] [OVER]
34 Evaluatej(-1) givenj(x) = 2x^4 - x^3 -35x 2 + 16x + 48. Explain what your answer tells you about
x + 1 as. a. factor. .·· .... - l L.J_ _ f - } _S. J C, _;.?
1 #^ -^ ~^ i~^.^ -1^3 3 f^ ¥ X·r '~) Lt. tot·. - ,,-. .-1_ .. ---
o{ j(x} :;._ >((~l't·~D 0
Algebraically find the remaining zeros of j(x).
Algebra II - Aug. '
d- x ~ ·1J'j1-. - }). y I-~~ 7 ()
x:J.( Jx-~) -) ( u-?) -,Q
(:< ~· .~ I&) ( ) A - 3) .._ ()
(~t~){x·^ )^ (Jx-3);
. ·
-~ lf
35 Determine, to the nearest tenth of a year, how long it would take an investment to double at a
). -; Q._
o·~ 5 f
f1cf9.
Algebra II -Aug. '18 [20]