INTEGRATED ALGEBRA
The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
INTEGRATED ALGEBRA
Wednesday, June 1, 2016 Student Name: _ _ _ _
1:15 to 4:15 p.m., only
----"=5-=--t-'--"=0=0::::.....:::-e_=--{y)~~O""'==~~S"""'O...· "-'°'"-----"~-----
School Name: _ _ _ _ _
""3j~(Y\~f\~r?~-=----C)-'·_Q~b=~---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 39 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.
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.
DO NOT OPEN mis EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.
V'l::l8381V' 03..LV'l::IP3..LNI
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]
Use this space for
computations.
1 A line of best fit has been drawn on the scatter plot below.
y
The relationship between these variables can be described as
having
(1) a negative correlation
(2) no correlation
c::J3)
J
a positive correlation
(4) zero correlation
q() eS r~~ ()_,
2 The amount of money spent at a parking met'er varies directly with
the amount of time spent parked in the parking space. Noah spent
$1.50 to pa1.fil}_.minutes. How m~ny minute~ can he park forJ.4.0o.?
Ii
(1) 667
(2) 360
(©": 24:9)
:;
o)-*
lo pe::.: Y:;:-f-
(4) 135
-
,()-0
ti\
/,5'-0
rt\~
60
(1) 5
(2) 6
H~e.t-
(3) 1
~
Cl..~t<:e.l'
4,~o
1:.
'I
3 An athlete has wie blue jersex and one oraug;t:. jersex, as well as_L
9ifferent colors of pa$. He also has...~ different colors of helmeU.,
How mwx, distinct uniforms consisting of v.ne helmes, ,2E~jer~W'
and..~p~..Eai_! of pants does the athlete have?
re.!Se.t
90
f'J'..
Z'fO
-µ-V-
::-bO"I--
()
.t
'~+: l
.cJ.o~.:eS ~o,ce,.s
0~ w~w::.\ 2
Integrated Algebra -June '16
[2]
4 Given:
A = {0,1,2,3,4}
B = {0,2,3,5, 7}
c = {0,2,4,6,8}
A
2 3
13
0 x 2. 3
(3) {0,2,3,4}
c_
)( 2
02) {o,2D
(4) {0,1,2,3,4,5,6,7,8}
i
t<;X;'. :£ ;<.
.~
What is the intersection of sets A, B, and C?
(1) {O}
y
;<
;< \
4
~
5r~ 11 x
ix ('~.x-'18
1
!
\ ( ." +.._~-u._\; "~
0
5 The equation y = x2
+ 3x
- 18 is graphed on the set of axes below.
y
Based on this graph, what are the roots of the equation
x2 + 3x - 18 = O?
(1) -3 and 6
(2) 0 and -18
Integrated Algebra -June '16
6[3and-6)
(4) 3and-18
[3]
[OVER]
(x: Yi)
Use this space for
computations.
6 What is an equation of the line that passes through (-2,3) and
t ~e.e..k \../'
(6, -1 ?
x 'I..
~~.. I'~
~7 \:S~T
c...o-'c...-
'I:: ~
(Y)
x.
7 If each member of the data set {2,2,3,5,8} is multiplied by 2, which
chan es will take lace in the mean median, and mosk_9f the data?
1 The mean, median, and mode will be multiplied by 2.
(2) The median will remain the same; the mean and mode will be
multiplied by 2.
(3) The mode will remain the same; the mean and median will be
multiplied by 2.
~ .\--Z
'Y
-2.
5
0
z
2
t
Lt
D
-1
b
~
v
(4) The mean will remain the same; the median and mode will be
multiplied by 2.
z) s)
[ 21
{!, tf
1
'!)'
6 J JD, llJ~,...J:2~~-=---;__.......,_
____
_-- ..------........
8 Which characteristic of a cat is qualitative?
(1) age
.:It0 ~
~-) color
':J
f fi!_a.. r S
' \ i'C)
.
.
(3) length·" :fl:. 0 .(:..
(
4) weight
~~+·
-
0-
('\
:tr 0-t'n
\
""-.2 ......
-/
i 1'.C:...~S ft a:.
I{j o
(2) 2
r1 \.A.. 'IV\.
e
r
I,.
J
C..c..
.
\.A-~~ ,,4t_,.....
3' ( 2A + 3W =
(1) 1
~
\o.A..f\.($l ..Si.
9 What is the value of A in the following system of equations?
I ( 6A
f\
.......
12.)
- 5W = 8 )
~
:=!!?"
-=7:
=
6 A }- 9 w
3b
[6 A - s w == f3)
.
14- 0 ;::
(4) 9
-2.8
\:~f;)Jfo \.
U;'~
2 Ii +5r;) ,;: ; I z
/\ .+ 3 (z.) ~ 1'2
2n
z:A 4- b ;;. \:?
Integrated Algebra -June '16
[4]
2A
A
;; b
=3
\ )..,"
\
10 A cell phone company is conducting a survey to determine the cell
phone features that its customers use. Which survey is least biased?
(1) The company conducts the survey on teenagers.
(2) The company conducts the survey on all age groups.
e company conducts the survey on retired females.
(4) The company conducts the survey on middle-aged males.
~y=-~x+4
y=2x+4
->
+y = 5
-x + y = 4
;'; x
y=-'?<.-1-
y:= x.+ 'f
(1) {(-3,-2),(-1, -2),(0,- l),(l,O)}
(2) {(-2,3),(0,4),(3, -2),(4,2)}
((3) {(2, -2),(l,4),(2,5),(3,6p
(4) {(-2,4),(1,l),(2,4),(3,9)}
Integrated Algebra -June '16
Use this space for
computations.
Use this space for
computations.
13 A system of inequalities is graphed on the set of axes below.
The coordinates of a point in the solution of this system of
inequalities are
(3) (-2,-1)
(1) (4,7)
(2) (1,-4)
---------·
.
~(3~)
--.-.
----·-·-- ~ ....
.
h ~... tJ
ad
14 The axis of s mmetry and the vertex of
~
(1) x ,= 2 and (2,6)
/(t-
...
...,...-.~~---",....•--------- ·~----
=
2 -
4x
n
·~
0-?<-1..S
C:::: JO .
10 are
_
+
nd (-2,6)
C.."f..\J
5/"",..,e],J -
R
~~~
.. - -- (
15 What is the slope of the line whose equation is 4x = 3(y
~
(2) ~
4
(3)
-~
(4)
3
4
l/x
+ 8)?
=='
s( y+~)
4t:;3j~Z~
L.JX-29- :::.~f
3l.I
Integrated Algebra - June '16
[6]
.b
Z0-
e
>/""""" e..: 7 ..
0
~~Y E/, ~I ·~J-e_ G._At cL-'-L-e.5 w ~~~ ~~ '2G\__~ ~"
Y
~ R~- 0-~' l oC- Sy.,_V'-~'7 oloe..s V"\o\:- \:>~ '""""
x
--
-
--
2lt) -
/( :::::: z_
x- ~
-::
~
v1
'-'
8
Y=-3X-
5b1?~
"'\
2
~~,.
c/,.eJc ;_ _g "'"?I..·~~ c.-
2 and (2,6)
v,_,~\\,.._
_ ~ _ -{-ti) '1
-
16 The students in Ms. Glenn's math class earned the grades shown
~t
{)j
f(\o-.-;<.
below. jV\1'./"\
~
I
t
I
/,:::.
rJ.,
Use this space for
computations.
65, 70, 70,80,80,82,88,88,90,90,95
Which box-and-whisker plot represents these data?
ft2
.
I
60
Ill
I
I
70
j
60
.ff
60
I
I
70
80
/!_
I I~
90
I~ t
r
80
90
100
I
•
100
I
•
I
•
~
I
I
70
60
100
90
80
(4)
+ fz x
17 When translated into symbols, "~than ~r" is
-5
1
(1) 3 - -x
2
1
-x-3
2
(3) 3
(4)
< ~x
~x<3
18 An example of }lil algebraic expression is
~ 6x - 2/~
y;tf' 3x + t.;{jj-10
Integrated Algebra - June '16
,r4 (x (4) 3x2
.
4)(x - 1
-
~
lOx - 3
[7]
[OVER]
Use this space for
computations.
19 Which equation could be used to find the measure of one acute
angle in the right triangle shown below?
........
B
,
/"" I
}
I
12
7
A
f'f> o +'"t:-1'\..~e..
/0
~.t
..anA =
C;;:o..__
:_______
(2) tan A
s-'J_
'Z~"' L
=
yr'sinC
1;
·
,
t
r:o_;'l ft ::. 0 ppo~ ~
e...J,:':..; ~ .,:t·
I
=
(1) [-5,6]
-
_\. · '· . . .,.,
~,ve ~,-;-:;- ~ X
i_\
(-
\->~ \Ac.\~eA -
~
,L
A =
800(~
;t1 A = 80o(l +R!J~
·
=
b
::-r
6_1
•
<
Q...,._\es;
6}?
c'-'-'"eJ f"<-'"-~ee> do
.
, ~-'
-L
\
\.
\"""-C... '-"-" ~
~.S' r- ~
#
bq
e:
A = 800(1 +
(2) -3
/L.r.
/f~
(\
<-
1aaO
-<./
(4) 0
~· ~ l I~~ ~\L .JSol-·ko""' S<Z.J
x<-3
I
(3) 3
I · i. ·
-3 -z
Integrated Algebra - June '16
\
_
E?(~i\ e.~,o..\. t;-re:.-h.;>+"'-.
(\
\-\ :::.
x
('\(_
y
p
=Bw
-t
~
\ ..\;-- ' )
A;; etx:(i+.01s'/
----~----__..::---------
> - 2"X+b
>6
- S-"X+ZJ(-3
--Z.l>
-3
~reJ oa.re~e.ses
c = \. 8~ro ::: ... o\B
t ==- 3
~ 50\ve..
[8]-
'
'
+ 6?
-~x
-sX
-3,X
;n
,.,J-
lV\C...\...-!~ ~E!....~
.01~
-S'°>\-s
~
\\
\h_e_
l---a...re_ Go
L-
;al_ A = 800(~018)3
22 Which value of xis a solution of -5x - 3 > -2x
d-4 ~
a.
l 'Z
'J )
~.,...."\~
,olo
21 Robert invests $800 in an account at 1.8% interest compouftded
annually. He will make no deposits or withdrawals on this account
for 3 years. Which formula could be used to find the balance, A, in
the account after the 3 years?
A
0·05"·~
1.,,.... io-,,O \....,._
oN'\. \ " "
(3) [ -5,6)
(4) (-5,6)
~
.,·V\.e... .fl.~
C. ~
+.:,_"'- :=: ~"---\;s-t J..
~"''"" ,'.)..,... "
~ 1.,....1 f'" h_,.. -s "- lJ: <' ~ 3 111 f.J\..)
1 • ...,. e (J.' ~~.(4) ·
, . e::;...> •
c:..."T'~
>,.i
.
1;
20 Which inteival notation describes the set S = {xj-5 < x
-
\
:::. ~'j,.~e,_.f'. - o
\r,. 1 Y° e- t· ~,..,,.,.. --.S .._.
Dt'lt
yl cos A = 1~
o
I/)
i
Df po.J' 1-«
C
i~
0
:::;;>
. ,o_c:e......
...,,
i ~ c s. ', \.··:7C.,. - ..-..<s .e...
v-'iP'o ·-~-
-
)
'7"
-:s
76...r3
7
c:..
~
9
_j_
-3
-3
Use this space for
computations.
2
23 Given W = VR t , which expression can be used to represe~ in
w = vZ.-1:_
terms of W, R, and V?
~
(3)
w
(2)
w -v2
R
R
\<w=\/~f
(4) WR-V 2
RV 2
Qw
1
,-- \-. 1r /Z_e..I\~ IL
v
=i
L
24 The long_est side of a right trian~ is 25. If one of the other sides i~------"2..--,.-'Z.,--·..-···
5, which measure is the length of the missing side?
~<: S"
Q.., Z. -\- 'b .,;: <....
(1)
&J26
_
(3) 30
Gi ur/6 ~
(4)
!).
-
'2-
~
0...., ....
~·
60
s-"" " zS "Z.
a..... .\- Z.S""
:::.
6 ?.S'
.:::..6()0
0 6 oo
D- ~ J\~ Jr'
Cl.- :::-
25 Which statement is correct?_Gi)
,)11{ (2lA )(-3b c) ~ -Ob
5
2
6m 3t 8 _ -3t 5
---2m5t3
m2
5/
.
Q..;...:::,
\0
~
2
i
t-
3
- - XlJ S"
'V
26 What value of x would make the expression 2x ~ 1 undefined?
(1) 0
~
~
.
-:Pe
1
2x+ \
2
ve_fl"2
a2 -
(2) (a - 4b)(a -4b)
Integrated Algebra - June '16
""X
(I
et"
~~o..n.l
'
.
;;-\
- \
-Z:.
-"·
= ti_"""'~J ~ _~ J
+ 8b)
v-
(4) (a -Bb)(a - Bb)
Q.
[9]
-- ze.\D,
=0
)(
.:
l6b is equivalent to " '2 _·i_ "'I.
27 Written in factored form, the binomial
(a - 4b)(a + 4b)~
(3) (a - 8b)(a
@
~r
,
e_{\IC>M I f\ Q;..
;f
1)\
r · " w~e..-A.'fhll.
i
l)...f'Oe:!.' ""e_cJ.
J-
(3) - 1
(4)
~l~
{} -;J-,; ,,J ~~\~"
0
~
~ J(,b2 .::-~..}l/-bX'o..-t.!b)
[OVER]
Use this space for
computa!ion~.
28 A spinner is divided into three equal regions, as shown in the
diagram below. Ray spun the spinner six times and recorded his
results: red, blue, blue, green, red, red.
{_ e> ....:t'tC.D ,,._ e_~..)
I
theof12.-i"" '~
}
ProW~ l'. +
Red
'\.
QJ
C
Pro~J;J ..~
z
~
--
--
~
z.
z_
-1-
fa=--
G-re..e.-..
\
C:.: Mf e.n~
--:--
131 ~e_
·
6
b
Which statement is true about the outcomes of b~1:!.e in Ray's
experiment?
·-
~he
empirical probability was less than the theoretical
yrobability.
,ftJ The empirical probability was greater than the theoretical
-·--------------:=:
robability.
(3) The empirical and theoretical probabilities were equ ·""".-The empirical and theoretical probabilities were unrelated.
F~~---·_j__...J6~--\:--_;0:;;..._I_
29 Liem is 6 feet 2 inches, Eli is 5 feet 9 inches, Faith is 6 feet, and
Simon is ~-feet 4 inches. In yards, what is the total of their heights?$
~_ )
(3) 22:
(2) 712.
36
(4) 23.!.
30 The sum of
(l)
4
(1)2~+~)
:a and ~~ is
3x
5a
(2 ) 3x
6a
Integrated Algebra - June '16
@
(4)
1.;..,, 0
-.r-...
~
4
_:J.,.._'2;2~:.:--.r-,-~~,V'\-,r-
23 -f+ 3~(\. j
7 yas 2. o+ 3 ,·,..,
1yJsfJflf- 27i,.,
7ff 1J'"
0J/. 0 I(\
s:. . fl:~
2x 2
6a2
[10]
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 I credit. All answers should be written in pen, except for graphs and drawi;:p"ngs,
which should be done in pencil. [6]
1
TV\~~
~
31 Jim calculated the area of a triangle to be 51.75 cm 2 . The actual area of the triangle is~ cm 2
Find the relative error in Jim's calculation of the area to the nearest thousandth.
\(Le_\-~::~~)
Pe_lj-;_,e_ i:;..,f
L 7~- 53. 2.Y
--
s-s.zY.
-
-...
Integrated Algebra -June '16
[11]
[OVER]
32 A 12 foot ladder is placed against a wall. The ladder makes an angle of 73° with the floor.
Determine, to the nearest tentg ofa foot, how high up the wall the ladder will reach.
5
'
'I/\
73°;;;
Integrated Algebra - June '16
><_
\ 'Z-
[12]
33 On the set of axes below, draw the graph of the function y = 3x. Include the interval - 2 < x < 2.
y
_5'-J~
L
_dee z
-z.
• /\I I
,..-
Integrated Algebra - June '16
[13]
[OVER]
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 I credit. All answers should be written in pen, except for graphs and drawings,
which should be done in pencil. [9 J
34 Ryan bought three bags of mixed tulip bulbs at a local garden store. The first bag contained
7 yellow bulbs, 8 red bulbs, and 5 white bulbs. The second bag contained 3 yellow bulbs, 11 red
bulbs, and 6 white bulbs. The third bag contained 13 yellow bulbs, 2 red bulbs, and 5 white bulbs.
Ryan combined the contents of these three bags into a single container. He randomly selected
one bulb, planted it, and then randomly selected another and planted that one. Determine if it
is giore likely that Ryan ,elanted a red bulb and then another red bulb, or planted a yellow bu!,9
and then a white bulb. Justify your answer.
- --==
•'·'
I
Ye\\ ow
I~~. .., (.U\;,.\e
~-~"
'
?
cg
s
3
\\
b
s
\3
2
\o\-0-\s
2.3
'7
Jh
60-~
.__,
\
~~
. ,. . . .- ·- . "6'-
...,_,.....,,,_,,...~
13~
-
Integrated Algebra - June '16
z.. '
[14]
-'-·
'\o\.o_t~
2-0
'
zo
zo
60
~
35 A particular jewelry box is in the shape of a rectangular prism. The box is advertised as having an
interior length of 20.3 centimeters, an interior width of 12. 7 centimeters, and an interior height
of 10.2 centimeters. However, when a customer measures the interior of the box, she finds that
the interior height is actually 6.3 centimeters. Upon further examination, she discovers that the
bottom of the interior of the box lifts up to reveal a hidden compartment. Find the volume of this
hidden compartment to the nearest cubic centimeter.
-
,
V==Xv.)k
V ~~o. "3)(\_z.7)Go.z-b.~
V =-(z_o,3)Qz.7)~·q)
\}
--
\DOS-.4S9
\f
Integrated Algebra - June '16
[15]
[OVER]
36 Solve algebraically for all values of x that satisfy the equation: x : 4
=
x
--
3
x~·-/\-\2
=O
-'fr'-1-'-I =J...
_!:L - -18 - "
Y.
c../ +"'2..
-t -
Integrated Algebra -June '16
[16]
(!.
~·
~2
Part IV
Answer all 3 questions in this part. Each cqrrect 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 On the set of axes below, jQ].ye_the following system of equations ggi_£hically for all values of
x and y. State the coordinates of all solutions.
5-l-ee I -
~--f bc-M .~--. .-f-i~~
.
1-
j~h ..·3 QQ..\c.J~,...
=
x 2 - 4x -
y
+ 3x = 1
~-L.spQ.c+__sr~l o..r-.~ c.o~1
S'+ 3 - P Io t- j ,..o-f lr
gep 4 - .Loler.4-/Q s~ \-~ o ~
Integrated Algebra - June '16
5 _
_ _
+
~-- Y_::__!_.!:,._\_
.ble...-ol u~......IU
y
[17]
x
[OVER]
.
.
38 Express m simplest form:
x 2 +5x +6
2
X -X-20
'2X-+4x.-J + Zx - 8
Integrated Algebra - June '16
[18]
39 The, lengt~ of a rectangle is ( 3.JB
+ 2) and the width is ( 2./2 + 1).
..
Express the perimeter of the rectangle in......,,.simplest radical form .
-Z (f+~)
2 ( s ~+ 2
p =-
~
==
p ==
P .=
2. ( 3
+-\J
+ z JZ
~JZ +2 1t- 232 +\)
:z_.(s-2SZ:+z.+-ZJ2:+\)
p :::. z.. ( bi SL 4- "2 Jz +· 2 +-'\)
.~ ~
2 (eJZ. :r-3)
fJ ::: Q: JZ" -+-kJ a_~ ~ e..r
Express
the~of the
rectangle in simplest radical form.
A :: 2w
.
A ; (3 J-a-4-~ {fa.~+-\)
A:: (jJB. 2Ji)4~J8·0+~·2JL)~(2·\)
A =~ JiI."") -+- (:3 .re) +- [l4 Ji'.) Jr~)
A = ~ •'1) +(sJlfJZ) +(<t rz) -+{2)
A = 2'\ .1r ~· z .rz) .\-(tt Jz) ~ Cz)
t+
{+
:=
:=.
Integrated Algebra -June '16
24 +- bsz:-
~b +-- \ 0
+- L\ 37 +- z
:S ~~ Q...C\S u..'.le....\
[19]