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Algebra II Regents High School Examination, June 18: Algebraic Equations and Functions, Study notes of Algebra

The Algebra II Regents High School Examination held on June 18, 2018. The examination covers various topics related to algebraic equations and functions, including solving systems of linear equations, graphing functions, and identifying functions. Students are required to write their answers directly in the booklet and follow specific instructions for completing the examination.

What you will learn

  • What is the solution set of the equation x^2 + 3 = x?
  • Which expression can be rewritten as (x + 1)(x - 1)?
  • Given the equation d = 5cos(~t) + 9, what is the depth of the water at the marker at time t?

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ALGEBRA
The
University
of
the
State
of
New
York
REGENTS
HIGH
SCHOOL
EXAMINATION
ALGEBRA
II
Thursday, June 14, 2018 -1:15 to 4:15 p.m., only
Student
Name:
/VJ
{ ·
[s
b6
]
School
Name:
__
~_M__._A__.P
_________
_
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
p~rt
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.
DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.
II
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Download Algebra II Regents High School Examination, June 18: Algebraic Equations and Functions and more Study notes Algebra in PDF only on Docsity!

ALGEBRA

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION

ALGEBRA II

Thursday, June 14, 2018 - 1:15 to 4:15 p.m., only

Student Name: /VJ { · [s b6 ]

School Name: ~M.A.P_________ _

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 p~rt 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.

DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.

II Vl::l83E>lV

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 The graphs of the equations y = x 2 + 4x - 1 and y + 3 = x are

Use this space for computations. drawn on the same set of axes. One solution of this system is (1) (-5, -2) ® (-1,-4)

(3) (1,4) (4) (-2,-1) yr~; - I

Y',~ 4- x

xl-tlf~ - I ~

y-i-- t J)( J-)-?

{x r;}){x +J) t;

. X"' -J.,-) 2 Which statement is true about the graph of f(x) = ( ~)? ..Ql The graph is always increasing. lJ,p~f )A.1, QgJ The graph is always decreasing. (3) The graph passes through (1,0). (4) The graph has an asymptote, x = 0.

(1) 3

(2) 17 2

Algebra II -June '

(4) x2 - 9 x(x -3)

~(j~y

[2]

x-

0

0

Use this space for 7 The function N(t) = lOOe -o.o^23 t models the number of grams in a computations. sample of cesium-137 that remain after t years. On which interval is the sample's average rate of decay the fastest? JJ [ID) -/JU) Q) [1,101 (3) [15,251 I b _l ,,:. -J, _oJ (2) [10,20] (4) [1,30]

W(J-->),.. μ(Is)"-. -/ (^) 4 b fJ{}o)-ftJOo) ~ -/.l.J

~)~fS rv ,. Fb-}D (^1) .8 Which expression can be rewritten as (x + 1)(x - 1)? Al{J _D:'_ • ){))

t(i\ (x + 3)2 - 16 !v '/ - 1-1 ..~ -/ b 4- ~(2) (x + 3) 2 - lO(x + 3) - 2(x + 3) + 20 'D-l 1 '

( x - 1 )( x 2 - 6x - 7) (^3 ) (x+l)

( x + 7)( x 2 + 4x + 3) (4) (x+3)

9 What is the solution set of the equation ~ - x ~ 3 = x : 3?

(1) {3}

(2) { ~}

Algebra II - June '

(3) {-2,3}

@J{-1, ~} ,,,---~^ ~ k .:y Xt-}

ft x J- ~ J-)( f- t:,

lfxi- -J-~ -b t D

Jxi.. ...-x -J ,,, b

{-μ-3) lxn) ,, o

X> -r,-

[4]

10 The depth of the water at a marker 20 feet from the shore in a bay is depicted in the graph below.

d

t

If the depth, d, is measured in feet and time, t, is measured in hours

since midnight, what is an equation for the depth of the water at the marker? (1) d = 5cos( ~t) + 9

(2) d = 9cos( ~t) + 5

(3) d = 9sin(~t) + 5

@d ~ 5sin( ~t) + 9

q

d~

11 On a given school day, the probability that Nick oversleeps is 48% and the probability he has a pop quiz is 25%. Assuming these two

Use this space for computations.

events are independent, what is the probability that Nick oversleeps ) .. J and has a pop quiz on the same day? Pl Q l Q ~ ('(OJ #fJ{Q) (1) 73% ~ 23%. q Ii p (2) 36% ~ 12% ; • 4 w- .. J 5

-,; 11~

12 If x - 1 is a factor of x^3 - kx 2 + 2x, what is the value of k?

(1) 0 @2) (2) 2 (4) -

Algebra II - June '18 [5]^ [OVER]

16 A 4th degree polynomial has zeros -5, 3, i, and -i. Which graph could represent the function defined by this polynomial?

y (^) y

5 x

(1) (^) (3)

y (^) y

(4)

17 The weights of bags of Graseck's Chocolate Candies are normally

distributed with a mean of 4.3 ounces and a standard deviation of 0.05 ounces. What is the probability that a bag of these chocolate candies weighs less than 4.27 om1ces? (1) 0. @0.

Algebra II - June '

[7]

Use this space for computations.

[OVER]

18 The half-life of iodine-131 is 8 days. The percent of the isotope left d in the body d days after being introduced is I = 1oo(iJ8.

When this equation is written in terms of the number e, the base of the natural logarithm, it is equivalent to I = lOOid. What is the

~proximate value of the constant, k?

(]) -0.087 (3) -11.

19 The graph of y = log 2 x is translated to the right 1 unit and down 1 unit.

Use this space for computations.

The coordinates of the x-intercept of the translated graph are (1) (O,O) fg{ (2,0) (2) (1,0) ~ (3,0)

/0~ 1 Jx~1)-/ ' 0

Io J i & ~iJ ,, I

20 For positive values of x, which expression is equivalent to

.. c<i g ..3CS

V lbx-x 3 + V 8x~?

(1) 6W

G)hW

Algebra II -June '

(3) 4-ifx2+2V

(4) 4'\fx3+2W

[8]

x ,, ~ J-

,

x ~. 3

23 On average, college seniors graduating in 2012 could compute their growing student loan debt using the function D(t) = 29,400(1.068)t, where t is time in ~· Which expression is equivalent to 29,400(1.068/ and could be used by students to identify an approximate dai!v interest rate on their loans?

(1) 29,400(i.068 3 i^5 )' (3) 29,400( 1 + 0 3:8)'

(2) 29,400( 1 3~~^8 )

365t (^) ( 1 )365t @29,400 1.068 365

24 A manufacturing plant produces two different-sized containers of

Use this space for computations.

peanuts. One container weighs x ounces and the other weighs J JJ I / ' y pounds. If a gift set can hold one of each size container, which lD, / b 0 t-, expression represents the number of gift sets needed to hold 124 ounces?

124

(l) 16x + y

(2) x + 16y

Algebra II - June '

~ 124 ~ x + 16y

(4) 16x + y

[10]

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 A survey about television-viewing preferences was given to randomly selected freshmen and seniors at Fairport High School. The results are shown in the table below.

Favorite Type of Program Sports Reality^ Show^ Comedy Series Senior 83 110 67

Freshman 119 103 54

A student response is selected at random from^ "'} the results. State the exact probability the student response is from a freshman, given the student prefers to watch reality shows on television.

Algebra II - June '18 [11]^ [OVER]

27 Solve the equation 2x 2 + 5x + 8 = 0. Express the answer in a +bi form. JS - 61../·. _)q

::.illc; '.} - '-/ l )_ )lflj

Jl~)

Algebra II - June '18 [13]^ [OVER]

28 Chuck's Trucking Company has decided to initiate an Employee of the Month program. To determine the recipient, they put the following sign on the back of each truck.

How's My Driving? Call 1-555-DRIVING

The driver who receives the highest number of positive comments will win the recognition. Explain one statistical bias in this data collection method.

Algebra II - June '18 [14]

r;f 6)~

}tv1+n

30 The recursive formula to describe a sequence is shown below.

a 1 = 3 an= 1+2an_ (^1)

State the first four terms of this sequence.

Can this sequence be represented using an explicit geometric formula? Justify your answer.

N D, b-e ca u )c,, f 'J.e. yt > S l')o ( t> M 111 on 1'/t., f^1 IJ

Algebra II - June '

I ('" )

----· 7

[16]

31 The Wells family is looking to purchase a home in a suburb of Rochester with a 30-year mortgage that has an annual interest rate of 3.6%. The house the family wants to purchase is $152,500 and they will make a $15,250 down payment and borrow the remainder. Use the formula below to determine their monthly payment, to the nearest dollar.

Algebra II - June '

M=

P(f2)(1+12r

(1+:2r-

M = monthly payment P = amount borrowed r = annual interest rate n = total number of monthly payments

[17]

'}GD

. oJ6 ) --/L. )

[OVER]

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]

33 Solve algebraically for all values of x:

v' 6 - 2x + x = 2(x + 15) - 9

10- ]_x r x :=)>{I- 31.J -

[6-f;, ::: ¥ t J- I

b - } 'X 0 ¥ -i- + 9 J·{' + 9 11 l

X t. f ./ 1./-y /l/lS 1 0

~rJ4){x11s) -;D

x -]

Algebra II - June '18 [19]^ [OVER]

34 Joseph was curious to determine if scent improves memory. A test was created where better memory is indicated by higher test scores. A controlled experiment was performed where one group was given the test on scented paper and the other group was given the test on unscented paper. The summary statistics from the experiment are given below.

Scented Paper Unscented Paper x 23 18 sx 2.898 2.

Calculate the difference in means in the experimental test grades (scented - unscented).

A simulation was conducted in which the subjects' scores were rerandomized into two groups 1000 times. The differences of the group means were calculated each time. The results are shown below.

50

40

~ c 30 Q) :::J er LL^ ~ 20-

10

  • • •••••
  • •• •••••• ••••••••

Algebra II -June '

  • • -2 -1 2

I

samples = 1000 mean= 0. st. dev. = 1.

  • • ••• •
  • • •••••••
  • • ••••••••••
  • • ••••••••••••••••I I 4 5 Simulated Group Difference of the Means

Question 34 is continued on the next page.

[20]