D
F all 20 14
NC F inal Ex am
R
EL
EA
SE
Math I I I
Public Schools of North Carolina
State Board of Education
Department of Public Instruction
Raleigh, North Carolina 27699-6314
Copy right ã 20 14 by the North Carolina Department of Public Instruction. A ll rights reserv ed.
Student Booklet
Released Items
M ATH I I I — R ELEASED I TEM S
A
512
B
511
C
256
D
81
D
2
A boar
di
smadeupof9 squar
es. A cer
t
ai
nnumberofpenni
esi
spl
acedi
neach
squar
e, f
ol
l
owi
ngageomet
r
i
csequence. Thef
i
r
stsquar
ehas1 penny, t
hesecond
has2 penni
es, t
het
hi
r
dhas4 penni
es, et
c. Whenever
ysquar
ei
sf
i
l
l
ed, how many
penni
eswi
l
lbeusedi
nt
ot
al
?
Letf(x) = 14x3 + 28x2 !46x andg(x) = 2x + 7. Whi
chi
st
hesol
ut
i
onsett
ot
he
equat
i
on 1 f(x) = g(x)?
12
B
{3, 1, 2}
C
{ 2, 1, 3}
D
{1, 5, 11}
EL
EA
{ 3, 0, 1}
Theequat
i
on2x
2x2 !5x
5x = 12 i
sr
ewr
i
t
t
eni
nt
hef
or
m of2(x !p)2 + q = 0. Whati
s
t
heval
ueofq?
A
167
16
B
71
8
C
25
8
D
25
16
R
3
A
SE
1
1
Got
ot
henextpage.
M ATH I I I — R ELEASED I TEM S
4
A boxwi
t
hanopent
opwi
l
lbeconst
r
uct
edf
r
om ar
ect
angul
arpi
eceofcar
dboar
d.
x
Thepi
eceofcar
dboar
di
s8 i
ncheswi
deand12 i
nchesl
ong.
x
Theboxwi
l
lbeconst
r
uct
edbycut
t
i
ngoutequalsquar
esofsi
dex at
eachcor
nerandt
henf
ol
di
ngupt
hesi
des.
B
0< x < 6
C
0< x < 8
D
0< x < 12
SE
0< x < 4
EL
EA
Af
unct
i
oni
sshownbel
ow.
f (x)
3
­ x 2 d
2x f
or x
d2
°
2x
°2 1
f
or 3
x
® 3
°
° 2x 5
f
or x t 4
¯x 7
4
Whati
st
heval
ueoft
heexpr
essi
on f ( 3) 2f (1) f (4)?
A
101
36
B
32
9
C
4
D
22
R
5
A
D
Whati
st
heent
i
r
edomai
nf
ort
hef
unct
i
onV(x) t
hatgi
vest
hevol
umeoft
heboxas
af
unct
i
onofx?
2
Got
ot
henextpage.
M ATH I I I — R ELEASED I TEM S
8
B
y = ex !9 !3
C
y = x2 + 5x + 6
D
y = 3x5 + 4x3 !11x !6
Whi
chexpr
essi
oni
sequi
val
entt
o
A
T cos2 T
si
n2 B
T si
cos2 n2 T
C
2
D
1
si
n4 T cos4 T , wher
n2 T
e si
si
n2 T cos2 T
D
y =l
og(x) + 100
2
cosT ?
SE
A
EL
EA
7
ckl
yasx i
ncr
eases?
Whi
chf
unct
i
ongoest
oposi
t
i
ve f mostqui
Thedi
amet
erofaci
r
cl
ei
s8 cent
i
met
er
s. A cent
r
alangl
eoft
heci
r
cl
ei
nt
er
cept
san
ar
cof12 cent
i
met
er
s. Whati
st
her
adi
anmeasur
eoft
heangl
e?
A
3
2
B
3
C
4
D
8S
R
6
3
Got
ot
henextpage.
M ATH I I I — R ELEASED I TEM S
Whati
st
heval
ueofx i
nt
het
r
i
angl
ebel
ow?
10
cm
9
B
5 3 cm
C
10 cm
D
15 cm
EL
EA
5 3 cm
2
Tocompl
et
el
ycoveraspher
i
calbal
l
, abal
lcompanyusesat
ot
alar
eaof36 squar
e
mum vol
umet
hebal
lcanhave?
i
nchesofmat
er
i
al
. Whati
st
hemaxi
(Not
e:Sur
f
acear
eaofaspher
e= 4Sr 2. Vol
umeofaspher
e= 4 Sr 3. )
3
R
10
A
SE
x
D
60°
A
ci
nches
27S cubi
B
ci
nches
36 S cubi
C
36 cubi
ci
nches
S
D
27 cubi
ci
nches
S
4
Got
ot
henextpage.
M ATH I I I — R ELEASED I TEM S
11
Af
ar
merwant
st
obuybet
ween90and100acr
esofl
and.
x
Hei
si
nt
er
est
edi
nar
ect
angul
arpi
eceofl
andt
hati
s1,500yar
dsl
ong
and300yar
dswi
de.
x
Thepi
eceofl
andi
sbei
ngsol
dasonecompl
et
euni
tf
or$87,000.
I
ft
hef
ar
merdoesnotwantt
ospendmor
et
han$900anacr
e, doest
hel
andmeet
2
al
lofhi
sr
equi
r
ement
s? (1 acr
e§ 43,560f
t
)
13
B
No, t
hepr
i
cei
sl
ow enough, butt
her
ei
st
oomuchl
and.
C
No, t
hepr
i
cei
sl
ow enough, butt
her
ei
snotenoughl
and.
D
No, t
heamountofl
andsat
i
sf
i
eswhatheneeds, butt
hepr
i
cei
st
oohi
gh.
SE
D
Yes, t
heamountofl
andsat
i
sf
i
eshi
sneeds, andt
hepr
i
cei
sl
ow enough.
EL
EA
Ar
epor
t
erwant
st
oknow t
heper
cent
ageofvot
er
si
nt
hest
at
ewhosuppor
t
bui
l
di
nganew hi
ghway. Whati
st
her
epor
t
er
"
spopul
at
i
on?
A
t
henumberofpeopl
ewhol
i
vei
nt
hest
at
e
B
t
hepeopl
ewhower
ei
nt
er
vi
ewedi
nt
hest
at
e
C
al
lvot
er
sover25 year
sol
di
nt
hest
at
e
D
al
lel
i
gi
bl
evot
er
si
nt
hest
at
e
R
12
A
I
nasetoft
estscor
est
hatar
enor
mal
l
ydi
st
r
i
but
ed, at
estscor
eof76 i
s
3 st
andar
ddevi
at
i
onsbel
ow t
hemean. A scor
eof88 i
s1 st
andar
ddevi
at
i
on
abovet
hemean. Whati
st
hemeanoft
hedat
a?
A
79
B
82
C
84
D
85
5
Got
ot
henextpage.
MATH III — RELEASED ITEMS
Thi
si
st
heend oft
heMat
h III Rel
eased It
ems.
Di
r
ect
i
ons:
1.Lookbackoveryouranswer
sf
ort
het
estquest
i
ons.
2.Makesur
eal
lyouranswer
sar
eent
er
ed on t
heanswersheet
.Onl
ywhati
s
ent
er
ed on youranswersheetwi
l
lbescor
ed.
3.Putal
lofyourpaper
si
nsi
deyourt
estbookand cl
oset
het
estbook.
4.Pl
aceyourcal
cul
at
oron t
op oft
het
estbook.
5.St
ayqui
et
l
yi
n yourseatunt
i
lyourt
eachert
el
l
syou t
hatt
est
i
ng i
s
f
i
ni
shed.
6.Remember
,t
eacher
sar
enotal
l
owed t
odi
scussi
t
emsf
r
om t
het
estwi
t
h
you,and you ar
enotal
l
owed t
odi
scusswi
t
h ot
her
sanyoft
het
est
quest
i
onsori
nf
or
mat
i
on cont
ai
ned wi
t
hi
nt
het
est
.
6
M ATH I I I — R ELEASED I TEM S
Mat
h III
RELEASED It
ems1
Fal
l2014
AnswerKey
Type2
Key
3
Per
centCor
r
ect
St
andar
d
1
MC
B
51%
CCSS.Mat
h.Cont
ent
.HSA.SSE.B.4
2
MC
B
41%
CCSS.Mat
h.Cont
ent
.HSA.REI
.D.11
3
MC
B
30%
CCSS.Mat
h.Cont
ent
.HSA.REI
.B.4.A
4
MC
A
28%
CCSS.Mat
h.Cont
ent
.HSF.I
F.B.5
5
MC
D
22%
6
MC
B
22%
7
MC
D
21%
CCSS.Mat
h.Cont
ent
.HSF.TF.C.8
8
MC
B
15%
CCSS.Mat
h.Cont
ent
.HSF.TF.A.1
9
MC
D
61%
CCSS.Mat
h.Cont
ent
.HSG.SRT.B.5
10
MC
C
38%
CCSS.Mat
h.Cont
ent
.HSG.MG.A.3
MC
D
36%
CCSS.Mat
h.Cont
ent
.HSG.MG.A.3
12
MC
D
76%
CCSS.Mat
h.Cont
ent
.HSS.I
C.A.1
13
MC
D
49%
CCSS.Mat
h.Cont
ent
.HSS.I
D.A.4
SE
CCSS.Mat
h.Cont
ent
.HSF.I
F.A.2
CCSS.Mat
h.Cont
ent
.HSF.LE.A.3
EL
EA
R
11
D
It
em Number
1
M ATH I I I — R ELEASED I TEM S
1
Theser
el
easedi
t
emswer
eadmi
ni
st
er
edt
ost
udent
sdur
i
ngapr
evi
oust
estadmi
ni
st
r
at
i
on. Thi
s
sampl
esetofr
el
easedi
t
emsmaynotr
ef
l
ectt
hebr
eadt
hoft
hest
andar
dsassessedand/
ort
he
r
angeofi
t
em di
f
f
i
cul
t
yf
oundont
heNC Fi
nalExam. Addi
t
i
onali
t
emsmayber
evi
ewedat
. Addi
t
i
onal
ht
t
p:
/
/
www.ncpubl
i
cschool
s.or
g/
account
abi
l
i
t
y/
commonexams/
r
el
easedf
or
ms/
i
nf
or
mat
i
onaboutt
heNC Fi
nalExam i
savai
l
abl
ei
nt
heAssessment Specification f
oreachexam
.
l
ocat
edatht
t
p:
/
/
www.ncpubl
i
cschool
s.or
g/
account
abi
l
i
t
y/
commonexams/
speci
f
i
cat
i
ons/
2
Thi
sNC Fi
nalExam cont
ai
nsonl
ymul
t
i
pl
echoi
ce(
MC)i
t
ems.
3
R
EL
EA
SE
D
Per
centcor
r
ecti
st
heper
cent
ageofst
udent
swhoanswer
edt
hei
t
em cor
r
ect
l
ydur
i
ngt
he
Spr
i
ng2014admi
ni
st
r
at
i
on.
2
M ATH I I I — R ELEASED I TEM S
St
andar
d Descr
i
pt
i
ons
Onl
yst
andar
ddescr
i
pt
i
onsaddr
essedbyt
her
el
easedi
t
emsi
nt
hi
sbookl
etar
el
i
st
edbel
ow.
A compl
et
el
i
stofst
andar
dsf
orEngl
i
shLanguageAr
t
sandMat
hemat
i
csmayber
evi
ewedat
.
ht
t
p:
/
/
www.cor
est
andar
ds.or
g/
r
eadt
hest
andar
ds/
CCSS.
Mat
h.
Cont
ent
.
HSA.
SSE.
B.
4 (Hi
gh School
:Al
gebr
a)
Seei
ngSt
r
uct
ur
ei
nExpr
essi
ons:Wr
i
t
eexpr
essi
onsi
nequi
val
entf
or
mst
osol
vepr
obl
ems.
Der
i
vet
hef
or
mul
af
ort
hesum ofaf
i
ni
t
egeomet
r
i
cser
i
es(whent
hecommonr
at
i
oi
snot1),
anduset
hef
or
mul
at
osol
vepr
obl
ems. Forexampl
e,cal
cul
at
emor
t
gagepayment
s.
SE
D
CCSS.
Mat
h.
Cont
ent
.
HSA.
REI.
B.
4.
A (Hi
gh School
:Al
gebr
a)
Reasoni
ngwi
t
hEquat
i
onsandI
nequal
i
t
i
es:Sol
veequat
i
onsandi
nequal
i
t
i
esi
nonevar
i
abl
e.
Sol
vequadr
at
i
cequat
i
onsi
nonevar
i
abl
e:Uset
hemet
hodofcompl
et
i
ngt
hesquar
et
o
2
hathast
he
t
r
ansf
or
m anyquadr
at
i
cequat
i
oni
nx i
nt
oanequat
i
onoft
hef
or
m (x
(x –p) = q t
samesol
ut
i
ons. Der
i
vet
hequadr
at
i
cf
or
mul
af
r
om t
hi
sf
or
m.
EL
EA
CCSS.
Mat
h.
Cont
ent
.
HSA.
REI.
D.
11 (Hi
gh School
:Al
gebr
a)
Reasoni
ngwi
t
hEquat
i
onsandI
nequal
i
t
i
es:Repr
esentandsol
veequat
i
onsandi
nequal
i
t
i
es
gr
aphi
cal
l
y. Expl
ai
nwhyt
hexcoor
di
nat
esoft
hepoi
nt
swher
et
hegr
aphsoft
heequat
i
ons
y = f(x) andy = g(x)) i
nt
er
sectar
et
hesol
ut
i
onsoft
heequat
i
onf(x) = g(x);f
i
ndt
hesol
ut
i
ons
appr
oxi
mat
el
y,e.g.,usi
ngt
echnol
ogyt
ogr
apht
hef
unct
i
ons,maket
abl
esofval
ues,orf
i
nd
successi
veappr
oxi
mat
i
ons. I
ncl
udecaseswher
ef(x)
f
and/
org(x) ar
el
i
near
,pol
ynomi
al
,r
at
i
onal
,
absol
ut
eval
ue,exponent
i
al
,andl
ogar
i
t
hmi
cf
unct
i
ons.
R
CCSS.
Mat
h.
Cont
ent
.
HSF.
IF.
A.
2 (Hi
gh School
:Funct
i
ons)
I
nt
er
pr
et
i
ngFunct
i
ons:Under
st
andt
heconceptofaf
unct
i
onandusef
unct
i
onnot
at
i
on. Use
f
unct
i
onnot
at
i
on,eval
uat
ef
unct
i
onsf
ori
nput
si
nt
hei
rdomai
ns,andi
nt
er
pr
etst
at
ement
st
hat
usef
unct
i
onnot
at
i
oni
nt
er
msofacont
ext
.
CCSS.
Mat
h.
Cont
ent
.
HSF.
IF.
B.
5 (Hi
gh School
:Funct
i
ons)
I
nt
er
pr
et
i
ngFunct
i
ons:I
nt
er
pr
etf
unct
i
onst
hatar
i
sei
nappl
i
cat
i
onsi
nt
er
msoft
hecont
ext
.
Rel
at
et
hedomai
nofaf
unct
i
ont
oi
t
sgr
aphand,wher
eappl
i
cabl
e,t
ot
hequant
i
t
at
i
ve
r
el
at
i
onshi
pi
tdescr
i
bes. Forexampl
e,i
ft
hef
unct
i
onh(n) gi
vest
henumberofper
sonhour
si
t
t
akest
oassembl
en engi
nesi
naf
act
or
y,t
hent
heposi
t
i
vei
nt
eger
swoul
dbeanappr
opr
i
at
e
domai
nf
ort
hef
unct
i
on.
CCSS.
Mat
h.
Cont
ent
.
HSF.
LE.
A.
3 (Hi
gh School
:Funct
i
ons)
Li
near
,Quadr
at
i
c,andExpondent
i
alModel
s:Const
r
uctandcompar
el
i
near
,quadr
at
i
c,and
exponent
i
almodel
sandsol
vepr
obl
ems. Obser
veusi
nggr
aphsandt
abl
est
hataquant
i
t
y
i
ncr
easi
ngexponent
i
al
l
yevent
ual
l
yexceedsaquant
i
t
yi
ncr
easi
ngl
i
near
l
y,quadr
at
i
cal
l
y,or
(mor
egener
al
l
y) asapol
ynomi
alf
unct
i
on.
3
M ATH I I I — R ELEASED I TEM S
CCSS.
Mat
h.
Cont
ent
.
HSF.
TF.
A.
1 (Hi
gh School
:Funct
i
ons)
Tr
i
gonomet
r
i
cFunct
i
ons:Ext
endt
hedomai
noft
r
i
gonomet
r
i
cf
unct
i
onsusi
ngt
heuni
tci
r
cl
e.
Under
st
andr
adi
anmeasur
eofanangl
east
hel
engt
hoft
hear
cont
heuni
tci
r
cl
esubt
endedby
t
heangl
e.
CCSS.
Mat
h.
Cont
ent
.
HSF.
TF.
C.
8 (Hi
gh School
:Funct
i
ons)
Tr
i
gonomet
r
i
cFunct
i
ons:Pr
oveandappl
yt
r
i
gonomet
r
i
ci
dent
i
t
i
es. Pr
ovet
hePyt
hagor
ean
2
2
i
dent
i
t
ysi
n (T) + cos(T) = 1andusei
tt
of
i
ndsi
n(T),cos(T),ort
an(T) gi
vensi
n(T),cos(T),or
t
an(T) andt
hequadr
antoft
heangl
e.
D
CCSS.
Mat
h.
Cont
ent
.
HSG.
SRT.
B.
5 (Hi
gh School
:Geomet
r
y)
Si
mi
l
ar
i
t
y,Ri
ghtTr
i
angl
es,andTr
i
gonomet
r
y:Pr
ovet
heor
emsi
nvol
vi
ngsi
mi
l
ar
i
t
y. Use
congr
uenceandsi
mi
l
ar
i
t
ycr
i
t
er
i
af
ort
r
i
angl
est
osol
vepr
obl
emsandt
opr
over
el
at
i
onshi
psi
n
geomet
r
i
cf
i
gur
es.
SE
CCSS.
Mat
h.
Cont
ent
.
HSG.
MG.
A.
3 (Hi
gh School
:Geomet
r
y)
Model
i
ngwi
t
hGeomet
r
y:Appl
ygeomet
r
i
cconcept
si
nmodel
i
ngsi
t
uat
i
ons. Appl
ygeomet
r
i
c
met
hodst
osol
vedesi
gnpr
obl
ems(e.g.,desi
gni
nganobj
ectorst
r
uct
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