ALGEBRA 2/TRIGONOMETRY
The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA 2/TRIGONOMETRY
Wednesday, Janum-y 23, 2013- 1:15 to 4:15p.m., only
Student
~, bo I
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 he invalidated and no score will he 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 he written in pen,
except for 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 hooklet.
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.
Al:ll311\10N081tll/G V'tl838lV'
Part I
Answer all27 questions in this part. Each correct answer will receive 2 credits. No partial credit
will be allowed. 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
an&wer sheet. (54]
1 What is
Use this space for
computations.
equation of the graph shown below?
y
X
(1) y =
C0
y=
+
(1) (2,3)
(5,0)
Algebra 2ffrigonometry- January '13
-5,10)
( -4,9)
[2]
3 The relationship between t, a student's test scores, and d,
the student's success in college, is modeled by the equation
d = 0.48t + 75.2. Based on this linear regression model, the correlation
coefficient could be
(1) between -1 and 0
Use this space for
computations.
(3) equal to -1
@between 0 and 1
(4) equal to 0
4 What is the common ratio of the geometric sequence shown below?
-2, 4, -8, 16, ...
l
(1)
(2) 2
©V-2
(4) -6
5 Given the relation {(8,2), 6)6), (7,5), (k,4)}, which value of k will
result in the relation not being a function?
(1) 1
3
(2) 2
4
6 Which expression is equivalent to (9x 2y6 )
@ 3x~3
(2)
3xy3
Algebra 2/frlgonometry- January '13
"J/1
?
q ( j
3
(3)
(4)
r}
----
xy3
I
xy3
>xyJ
3
[3]
[OVER]
Use this space for
computations.
7 In a certain high school, a survey revealed the mean amount of bottled
water consumed by students each day was 153 bottles with a
standard deviation of 22 bottles. Assuming the survey represented a
normal distribution, what is the range of the number of bottled
waters that approximately 68.2% of the students drink?
(1) 131-164
x:!:cJ
142-164
@ 131-175
142-175
!- J-~
I
I~ 1 -)I
- 2)8?
8 What is the fourth term in the binomial expansion
448x5
@ -448x
X<( ~) (
5
~
-448x 4
(2) 448x4
3
b
e;:
X
~xs-
/
} } ~{lj)
9 Which value of k satisfies the equation 83k + 4 =
-2
-1
(2)
9
~
(
_14
4
l
~k-+1). ~
0
'l
J-
CJ }Cf
~/k~ ~
~ I/'
10 There are eight people in a tennis club. Which expression can
~e 5
used to find the number of different ways they can place first,
second, and third in a tournament?
@
Algebra 2ffrigonometry- January '13
[4]
11 If sin A =
1
, what is the value of cos 2A?
s~A _:- l -l ) h"A
I
~
7
(3) - -
2
(1)
( e)
3
9
'I
(2) 2
Use this space for
computations.
I - J-{ ~)
l -{
/?
<>.CJ
12 In the interval 0°
< x
< 360°, tan x is undefined when x equals
(1) 0° and goo
(3) 180° and 270°
{0 goo and 270°
(2) goo and 180°
13 If f(x) =
what are its domain and range?
@domain: {xl
{yiO:::::;; y < 3}
±3}; range: {yiO < y < 3}
<
domain: {x
=I=
x
orx > 3}; range: {yly =I= 0}
domain: {x!x:::::;;
(4) domain: {xlx
14 \;v'hen
<@
+ 3x + 2x 2
=I=
< 3}; range:
3}; range: {yly > 0}
2x, the difference is
4 is subtracted from
5x
+
+4
-x
Algebra 2/frigonometry- January '13
3
-
+x-4
2
2x + 5x + 4
[51
[OVER]
15 In the diagram below, the length of which line segment is equal to
the exact value of sin 9?
Use this space for
computations.
y
(0, 1)
(0,-1)
(1) TO
@rs
(3) OR
(4) OS
16 The area of triangle ABC is 42. If AB = 8 and mLB = 61, the length
y~-::), {o.)( ?) )ihb}
d-...
ofBC is approximately
(1) 5.1
(2) 9.2
@
12.0
y}- ~ 5. 5 Ot_
(4) 21.7
0[
I 7 When factored completely, the expression 3x3
equivalentto
2
(1) (x - 16)(3x- 5)
(2) (x 2
@)
(4) (x
+ 16)(3x- 5)(3x + 5)
+ 4)(x- 4)(3x- 5)
+ 4)(x - 4)(3x 5)(3x -
Algebra 2ffrigonometry -January '13
.
-:
5x 2
+ 80 is
-/0 ()X ~S)
48x
xl.()x ,. . lJ)
/ 2.
r: ) ( 3 _>)
vr -l(y )( . cJ
{,X-t~) {x- t;) nx-7
5)
[6]
18 ~~~:::ex
sin (180
+
5/Yl ( 1rb tx )
5; rt JrD e~ sx f co> lf!J 'l J'hX
()
X -I ")hX
Use this space for
computations.
is equivalent to
sin x
'(2:)
-sin (90 -
sin (90-
-))rrx
19 The sum of
form, is
~6a 4 b 2
and
~+)~
( ~
r~
(lt (?t\,tl
'J(.
@J 4a~6ab 2
(1)
(2)
expressed in simplest radical
2a 2 b~2la 2 b
20 Which equation is represented by the graph below?
y
~y =
2 cos 3x
(2) y = 2 sin
Algebra 2ffrigonometry- January '13
2n:
3x
y
= 2 cos
y
. 2n:
= 2 sm3x
[7]
[OVER]
Use this space for
computations.
-f) _,X (-J-_x 1)J
21 The quantities p and q vary inversely. If p = 20 when q = -2, and
p =xwhenq = -2x + 2,thenxequals
).0{
@
and 5
(2) 20
19
(3)
(4)
and 4
-
l
4
~0
'l
-
)-x 7-- t d-x
1-:x.1- -J_X - \.fO ~ D
X
-x -){) D
(xtl]) Cx-SJ ';) D
-J2 secx =
22 What is the solution set of the equation
0° :5 X < 360°?
If% { 5
5 }
(1) {45°, 135°, 225°, 315°}
~ 13 °, 22 °
(2) {45°, 315°}
(4) {225°, 315°}
2 when
)_
fCX ;:::--
5
y """ . . l.f) 5
1 )-_
co>x _., -JEd-
23 The discriminant of a quadratic equation is 24. The roots are
b?-_ ~q,c_
(1) imaginary
(2) real, rational, and equal
(3) real, rational, and unequal
@D real, irrational, and unequal
24 How many different six-letter arrangements can be made using the
letters of the word "TATTOO"?
® 60
(3) 120
~)oo
~)no
Algebra 21Trigonometry- January '13
[8]
to
25 Expressed in simplest form, 2y _ 6
+
(l)
is equivalent to
-~y
@~
-54
(2y- 6)(6- 2y)
(2)
9
+ 62y
Use this space for
computations.
)y-
l.v-q
CJ
~~
~~-:5-H
- ~')
3
(4) - 2
-9
2y-6
26 If log 2 = a and log 3 = b, the expression log { is equivalent to
0
(1) 2b -a
@_)h-
(3) b2 - a+ 10
+1
(4)
a -1
27 The expression (x + i) 2
-
a
(3) -2
@4xi
(2) -2
q - Ia~ )D
{D9 sL
2b
(x - i) 2 is equivalent to
(1) 0
1o ~
+ 4xi
x;_ +Lx ( t i J.-
-
I0 ~
0 'LJ
(/o9IO flv1)j
J_lo~ ~J-b-{/+e>c)
)-b-~-1
-
(X 1-- ~x ,, f ; iJ
~XL
Algebra 2/frigonometry -January '13
[9]
[OVER}
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. 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.
28 Determine the sum of the first twenty terms of the sequence whose first five terms are 5, 14, 23,
and41.
(1.
~
Ut f\ <:.' ·' { V) - I
qi ~5
:: /70
q
;),_
(
(;:
,..,
~
')
j>S
Algebra 2ffrigonometry- January '13
[10]
29 Determine the sum and the product of the roots of 3x2 = llx - 6.
1x
Q ~) 3
--Jlxt6r:b
b~ /11 c ~b
c-u~:.
+~
;l3
)
ct
pvociucJ
30 If sec (a
r:.
0:
<
f:_,
3
+ 15) = esc (2a) find the smallest positive value of a, in degrees.
0
0
,
ot-11 +J-A ~ q0
3 C1f1 <;~? e{
)ci~~7S
0 1 d-S
Algebra 2ffrigonometry- January '13
[11]
[OVER]
31 The heights, in inches, of 10 high school varsity basketball players are 78, 79, 79, 72, 75, 71, 74,
74, 83, and 71. Find the interquartile range of this data s~t.
1 71
Algebra 21frigonometry -January '13
@7
lf
[12]
7tt 7 c;
~ 7 OJ
32 Solve the equation 6x2
;; t
2x
-
3
0 and express the answer in simplest radical form.
{)-}~ ~ lf( 6) {-~)
:/-(6)
J-:{7{:
~
I
i ;fift{ICf
-----1)--
~i Jki
)J-1 tt{tf
~
6
Algebra 2ffrigonometry- January '13
[13]
[OVER]
33 The number of bacteria present in a Petri dish can be modeled by the function N = 50e3t, where
N is the number of bacteria present in the Petri dish after t hours. Using this model, determine,
to the nearest hundredth, the number of hours it will take for N to reach 30,700.
1
50700Y~
--So
>u
(; llf ~ .f,
3t
t~, ()l Lf/ lht~
~"~
J.ltr
Algebra 2ffrigonometry - Jannary '13
[14]
34 Detennine the solution of the inequality 13
[The use of the grid below is optional.]
·~--)x 7
7
-
2x I > 7.
1-J-x ~. --7
~J-x
-J-x 2 Lf
X 3:. -)_
Algebra 2ffrigonometry- January '13
- -lD
L
) 2)
(15]
[OVER]
35 Convert 3 radians to degrees and express the answer to the nearest minute.
Algebra 2/Trigonometry- January '13
[16]
Part III
Answer all 3 questions in this part. Each correct 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]
36 Solve algebraically for all values of x:
log(x + 4 )(17x - 4)
2
(x tlt-) :~- /, 1/x-- lf
x)-+ h -rib -; n.x ~ Lf
0
(x-'i) cx~s) ~ 0
XJ- -Cf X fcf-0 --
X',Y)q
Algebra 2ffrigonometry - January '13
[17]
[OVER]
37 The data collected by a biologist showing the growth of a colony of bacteria at the end of each
hour are displayed in the table below.
Time, hour, (x)
Population (y)
I
0
1
2
3
4
250
330
580
800
1650
5
3000
Write an exponential regression equation to model these data. Round all values to the nearest
thousandth.
y~
JJS, 90J {J~bCJ))X
Assuming this trend continues, use this equation to estimate, to the nearest ten, the number of
bacteria in the colony at the end of 7 hours.
Algebra 2/frigonometry -January '13
[18]
38 As shown in the diagram below, fire-tracking station A is 100 miles due west of fire-tracking
station B. A forest fire is spotted at F, on a bearing 47° northeast of station A and 15° northeast
of station B. Determine, to the nearest tenth of a tnile, the distance the fire is from both
station A and station B. [N represents due north.]
F
N
100 miles
---r;-J
/{)
9ih
b~
_Q_
~
7'Y1 IDS
1() (),.
') ;' 'rJ }~
C\
}
Algebra 2/frigonometry -January '13
[19]
-
G{
,;
c; ~-~LfJ
JJ-S~ 7
[OVER}
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate fonnula substitutions, diagrams, graphs,
charts, etc. A correct numerical answer with no work shown will receive only 1 credit.
The answer should be written in pen.
+ llx
39 Solve algebraically for x:
~
1)_
r
..J
0
--}
,....,
_...
0
=
+3
-Ljyf3
J0x -)Lf:x:
1/
jSxV-)-)x J)D
1x --S"x-t:l
0 0x-~ LJc~o
0
q
:::-,
)\~
___
,
~Lf-)13:?-0
Algebra 2ffrigonometry- January '13
X)(
-~(J) f~