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1.
I
ff
Bat
ch:
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Facul
t
yI
D:
MAS
I
f
Dat
e:
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Dept
.ofMat
hemat
i
cs
t
hen
(
A)onl
ywhenm =n
(
C)onl
ywhenm =–n
2.
Funct
i
on
(
B)onl
ywhen
(
D)f
oral
l
m andn
t
hent
hepossi
bl
esetofv
al
uesofxandyar
e
(
A)
(
B)
(
C)
and
(
D)
and
3. LetSbet
hesetofal
l
t
r
i
angl
esand bet
hesetofposi
t
i
v
er
eal
number
s.Thent
he
f
unct
i
on,
,
wher
e
i
s:
(
A)i
nj
ect
i
v
ebutnotsur
j
ect
i
v
e
(
B)sur
j
ect
i
v
ebutnoti
nj
ect
i
v
e
(
C)i
nj
ect
i
v
easwel
l
assur
j
ect
i
v
e
(
D)nei
t
heri
nj
ect
i
v
enorsur
j
ect
i
v
e
4.
I
f
and
,
t
hendomai
nof
i
s:
5.
6.
7.
(
A)
(
B)
(
C)
(
D)
I
f
and
i
st
hei
nv
er
seof
t
heng’
(
x)i
sequal
t
o
(
A)
(
B)
(
C)
(
D)noneoft
hese
I
f
v
al
ueoff
(
1)i
sequal
t
o
(
A)1
(
C)0
Let
andi
ff(
x)i
snotaconst
antf
unct
i
on,
t
hent
he
(
B)2
(
D)–1
,
wher
ef
(
x)andg(
x)ar
er
eal
v
al
uedf
unct
i
ons.Foral
l
possi
bl
ev
al
uesof
(
A)
(
B)
(
C)
8.
Let
(
D)
domai
nof
i
s[
–5,
7]
,
domai
nof
i
s[
–6,
1]andr
angeofh(
x
)i
s
t
hesameasdomai
noff
(
x)
,
t
henv
al
ueofki
s
9.
(
A)
(
B)
(
C)1
(
D)noneoft
hese
Let
(
wher
e[
.
]denot
est
hegr
eat
esti
nt
egerf
unct
i
on)
,
t
hen
(
A)Rangeoffi
s{
–1,
1}
(
B)fi
sanev
enf
unct
i
on
(
C)fi
sanoddf
unct
i
on
(
D)
exi
st
s,
f
orev
er
yi
nt
egern
10. Let
beaone–onemappi
ngsucht
hatonl
yoneoft
hef
ol
l
owi
ngt
hr
ee
st
at
ement
si
st
r
ueandr
emai
ni
ngt
woar
ef
al
se:
(
A)
(
B)
(
C)
(
D)
t
hen
11. Thei
mageoft
hei
nt
er
v
al
[
–1,
3]undert
hemappi
ngspeci
f
i
edbyt
hef
unct
i
on
i
s:
(
A)
(
B)
(
C)
(
D)
12. I
f
t
henv
al
ueof
(
A)0
(
C)–1
13. Let
i
s:
(
B)1
(
D)
,
wher
e‘
a’
i
saposi
t
i
v
er
eal
numbernotequal
t
o1andF(
x
)i
san
oddf
unct
i
on.Whi
choft
hef
ol
l
owi
ngst
at
ement
si
st
r
ue?
(
A)G(
x)i
sanoddf
unct
i
on
(
B)G(
x)i
sanev
enf
unct
i
on
(
C)G(
x)i
snei
t
herev
ennoroddf
unct
i
on
(
D)Whet
herG(
x)i
sanoddorev
enf
unct
i
ondependsont
hev
al
ueof‘
a’
.
14. S1:I
ff
(
x)i
si
ncr
easi
ngf
unct
i
ont
hen
i
sal
soi
ncr
easi
ngf
unct
i
on
S2:I
ff
(
x)i
sconst
antf
unct
i
on,
t
hen
i
sal
soaconst
antf
unct
i
on
–1
S3:I
fgr
aphoff
(
x)andf (
x)ar
ei
nt
er
sect
i
ngt
hent
heyal
way
si
nt
er
sectont
hel
i
ne
S4:
Thei
nv
er
seof
(
A)TTTF
(
C)FFFT
i
s
(
B)TFFT
(
D)TFTT
15. S1:
I
fgofi
sone–onet
henbot
hfandgmustbeone–one
S2:
Gr
aphoft
hecur
v
e
l
i
esi
nf
our
t
hquadr
ant
S3:
I
fgofi
sont
of
unct
i
ont
henfmaynotbeont
o
S4:
I
fgofi
sbi
j
ect
i
v
et
henbot
hfandgmustbebi
j
ect
i
v
e
(
A)TTTF
(
B)FFFF
(
C)TTTT
(
D)FTTF
16. S1:
def
i
nedas
i
sanoddandont
of
unct
i
on.
S2:
Foral
l
r
eal
v
al
uesofxandyt
her
el
at
i
on
S3:
I
f
and
S4:
I
f
(
A)TTFF
(
C)TFTF
r
epr
esent
syasaf
unct
i
onofx.
t
henf=g
,
t
hen
(
B)TFFT
(
D)FTTF
17. S1:
Af
unct
i
oni
si
nv
er
t
i
bl
ei
f
fi
ti
sone–one
S2:
Letfandgbet
wof
unct
i
ons
sucht
hatgofi
sone–onet
henfmustbeone–one
S3:
Fundament
al
per
i
odofsi
n{
x}i
s1.Wher
e r
epr
esentf
r
act
i
onal
par
tf
unct
i
ons.
S4:
I
f
(
A)TTFF
(
C)FTTF
i
sanoddf
unct
i
onst
hen
(
B)TTFT
(
D)FTTT
18. Consi
dert
hef
ol
l
owi
ngst
at
ement
s:
S1:
Numberofsol
ut
i
onsof
i
st
wo
S2:
i
ssur
j
ect
i
v
ef
unct
i
on
S3:
Al
l
basi
ci
nv
er
set
r
i
gonomet
r
i
cf
unct
i
onar
eper
i
odi
c
S4:
Domai
nof
i
s
St
at
e,
i
nor
der
,
whet
her
(
A)TTFF
(
C)FTTF
ar
et
r
ueorf
al
se
(
B)TTFT
(
D)FTTT
19. Let
andg:
c Dbef
unct
i
onsf
orwhi
chcomposi
t
ef
unct
i
ongofi
sdef
i
ned:
S1:
I
feachoffandgi
sone–one,
t
hengofi
sone–one
S2:
I
feachoffandgi
sont
o,
t
hengofi
sont
o
S3:
I
fB=Candgofi
sone–one,
t
hengmaynotbeone–one
S4:
I
fB=Candgofi
sont
o,
t
henfmaynotbeont
o
(
A)FTFF
(
B)TTFF
(
C)TFTT
(
D)TTTT
Sect
i
onI
I:Mul
t
i
pl
eCor
r
ectAnswerTy
pe
20. Whi
choft
hef
ol
l
owi
ngf
unct
i
onsar
eper
i
odi
c?
(
A)
(
B)
(
C)
(
D)
21. Thegr
aphoft
hef
unct
i
on
gr
aphcor
r
ect
?
(
wher
e[
.
]denot
esgr
eat
esti
nt
egerf
unct
i
on)
i
sasshowni
nt
hef
i
gur
e.Thenwhi
choneoft
hef
ol
l
owi
ng
(
A)
(
B)
(
C)
(
D)
22.
,
wher
e[
.
]denot
et
hegr
eat
esti
nt
egerf
unct
i
on,
hasf
undament
al
per
i
od
f
or
(
A)
(
B)
(
C)
(
D)
23. Letf
(
x)bear
eal
v
al
uedf
unct
i
ondef
i
nedon:
sucht
hat
wher
e
[
x]=t
hegr
eat
esti
nt
eger .Then
(
A)fi
smany–oneandi
nt
of
unct
i
on
(
C)f(
x)=0f
oronl
yt
wor
eal
v
al
ues
(
B)f(
x)=0f
ori
nf
i
ni
t
enumberofv
al
uesofx
(
D)noneoft
hese
24. I
f
i
sgi
v
enf
unct
i
on,
t
henwhi
choft
hef
ol
l
owi
ngar
ecor
r
ect
:
(
A)f(
x)i
samany–oneandi
nt
of
unct
i
on
(
B)fi
smanyoneont
of
unct
i
on
(
C)r
angeoffi
s
(
D)r
angeoffi
s
25. Whi
choft
hef
ol
l
owi
ngpai
r
(
s)off
unct
i
onsar
ei
dent
i
cal
?
(
A)
(
B)
(
C)
(
D)
wher
esgn(
.
)
,
{
.
}denot
essi
gnum,
gr
eat
esti
nt
egerand
f
r
act
i
onal
par
tf
unct
i
onr
espect
i
v
el
y
)
26. I
f
f
or
i
si
nv
er
t
i
bl
e,
wher
e{
.
}and[
.
]r
epr
esent
f
r
act
i
onpar
tandgr
eat
esti
nt
egerf
unct
i
onsr
espect
i
v
el
y
,
t
hen
(
A)
(
B)
(
C)
(
D)
27. Rangeof
i
s
i
s
(
A)
(
B)
(
C)
(
D)noneoft
hese
Sect
i
on–I
I
I:Asser
t
i
onandReasonTy
pe
Foreach2838quest
i
onsopt
i
onsar
easf
ol
l
owi
ng(
A)St
at
ement1i
st
r
ue,
St
at
ement2i
st
r
ue,
St
at
ement2i
scor
r
ectexpl
anat
i
onofSt
at
ement1
(
B)St
at
ement1i
st
r
ue,St
at
ement2i
st
r
ue,St
at
ement2i
snotcor
r
ectexpl
anat
i
onof
St
at
ement1
(
C)St
at
ement1i
st
r
ue,
St
at
ement2i
sf
al
se
(
D)St
at
ement1i
sf
al
se,
St
at
ement2i
st
r
ue
28. St
at
ement–1: cannotbeexpr
essedast
hesum ofev
enandoddf
unct
i
on
St
at
ement–2: i
snei
t
herev
ennoroddf
unct
i
on
29. St
at
ement–1:
I
f
t
hen
St
at
ement–2:
Theder
i
v
at
i
v
eofanoddf
unct
i
oni
sev
enandv
i
ce–v
er
sa
30. St
at
ement–1Thei
nv
er
seofast
r
i
ct
l
yi
ncr
easi
ngexponent
i
al
f
unct
i
oni
sal
ogar
i
t
hmi
c
f
unct
i
ont
hati
sst
r
i
ct
l
ydecr
easi
ng.
St
at
ement–2
i
si
nv
er
seofex
31. St
at
ement–1Fundament
al
per
i
odof
i
s
St
at
ement–2I
ft
heper
i
odoff
(
x)i
sT1andt
heper
i
odofg(
x)i
sT2,
t
hent
hef
undament
al
per
i
odof
i
st
heLC.
M.ofT1andT2
32. St
at
ement–1:
I
faf
unct
i
on
i
ssy
mmet
r
i
cabout
St
at
ement–2:
I
f
,
t
hen
t
hen
33. St
at
ement–1:
i
sper
i
odi
cand
i
sal
soper
i
odi
c
St
at
ement–2:
I
ft
heder
i
v
at
i
v
eofaf
unct
i
oni
sper
i
odi
c,
t
hent
hef
unct
i
onwi
l
l
al
sobe
per
i
odi
c
34. St
at
ement–1:
f
unct
i
on
St
at
ement–2:
i
sper
i
odi
c
i
sper
i
odi
ci
f
i
sper
i
odi
c
35. St
at
ement–1:
Thef
unct
i
on,
cannotat
t
ai
nt
hev
al
ue
St
at
ement–2:
Thedomai
nof
36. St
at
ement-1:
Rangeof
i
s
doesnotcont
ai
n
(
wher
e{
.
}r
epr
esent
sf
r
act
i
onal
par
tf
unct
i
on)
St
at
ement–2:
37. St
at
ement–1:
Let
beaf
unct
i
ondef
i
nedby
.Then
fi
smany–onef
unct
i
on.
St
at
ement–2:
I
fei
t
her
or
domai
noff
,
t
hen
f
unct
i
on.
38. Consi
dert
hef
ol
l
owi
ngst
at
ement
s:
St
at
ement–1:
i
saone–onef
unct
i
on.
St
at
ement–2:
Theper
i
odof
i
s and i
sani
r
r
at
i
onal
number
.
I
f
Sect
i
on–I
V:Compr
ehensi
onTy
pe
Compr
ehensi
onI
i
sabi
j
ect
i
v
ef
unct
i
ondef
i
nedby
wher
ea,
b,
car
enon
zer
or
eal
number
s,
t
hen
39. f(
2)i
sequal
t
o
(
A)2
(
C)0
(
B) wher
e
(
D)cannotbedet
er
mi
ned
40. Whi
choft
hef
ol
l
owi
ngi
soneoft
her
oot
s
(
A)
(
B)
(
C)
(
D)
i
s
41. Whi
choft
hef
ol
l
owi
ngi
snotav
al
ueofa?
(
A)
(
B)
(
C)
(
D)1
Compr
ehensi
onI
I
i
sone–one
Let
and
42.
i
snotdef
i
nedi
f
(
A)
(
B)
(
C)
(
D)
43. I
fdomai
nof
i
s[
–1,
2]
;
t
hen
(
A)
(
C)
(
B)
(
D)
44. I
fa=2andb=3t
henr
angeof
i
s
(
A)
(
B)
(
C)[
4,
8]
(
D)[
–1,
8]
Compr
ehensi
onI
I
I
Let
i
saf
unct
i
onsat
i
sf
y
i
ng
and
f
unct
i
onfanswert
hef
ol
l
owi
ng
45. I
f
t
henmi
ni
mum possi
bl
enumberofv
al
uesofxsat
i
sf
y
i
ng
i
s
(
A)21
(
C)11
46. Gr
aphofy=f(
x)i
s
(
A)sy
mmet
r
i
cal
aboutx=18
(
C)sy
mmet
r
i
cal
aboutx=8
47. I
f
t
hen
(
A)f
undament
al
per
i
odoff(
x)i
s1
(
C)per
i
odoff
(
x)can’
tbe1
(
B)sy
mmet
r
i
cal
aboutx=5
(
D)sy
mmet
r
i
cal
aboutx=20
(
B)f
undament
al
per
i
odoff
(
x)maybe1
(
D)f
undament
al
per
i
odoff
(
x)i
s8
sat
i
sf
y
t
hen
48. Val
ueofai
s
(
A)4
(
C)
(
B)2
(
D)1
49.
(
A)
(
C)
50. Numberofsol
ut
i
onsof
(
A)1
(
C)3
f
or
(
B)12
(
D)22
Compr
ehensi
onI
V
I
f
.Fort
hi
s
(
B)
(
D)0
i
s
(
B)2
(
D)4
,
Sect
i
onV
51. Mat
cht
hef
ol
l
owi
ng
Col
umnI
(
A) Thenumberofpossi
bl
ev
al
uesofki
ff
undament
al (
P)
per
i
odof
1
i
s ,
i
s
(
B) Number
s of el
ement
s i
n t
he domai
n of (
Q)
i
s
(
C)
(
R)
Per
i
odoft
hef
unct
i
on
i
s
2
(
D) I
ft
her
angeoft
hef
unct
i
on
4
and
t
hen
S)
i
s{
a,
b,
c} (
52. Mat
cht
hef
ol
l
owi
ng
(
B)
(
C)
(
D)
(
T)
Col
umnI
Funct
i
on
def
i
nedby
Funct
i
on
i
s
def
i
nedby
Funct
i
on
i
s
def
i
nedby
i
s
Funct
i
on
3
i
sequalt
o(
wher
e[
.
]
denot
esgr
eat
esti
nt
eger
)
(
A)
def
i
nedby
i
s
0
Col
umnI
I
(
P) onet
oonef
unct
i
on
(
Q) many –
f
unct
i
on
(
R) i
nt
of
unct
i
on
Col
umnI
(
A) I
fsmal
l
estposi
t
i
v
ei
nt
egr
alv
al
ueofxf
orwhi
ch (
P)
i
s ,
t
hen
i
sequal
t
o
(
B) Numberofsol
Q)
ut
i
on(
s)of
i
s(
wher
e[
.
](
(
D)
{
.
}ar
egr
eat
esti
nt
egerandl
easti
nt
egerf
unct
i
ons
r
espect
i
v
el
y
)
I
f
andmaxi
mum v
al
ueof
i
s
t
hen i
sequal
t
o
f
oral
l
t
henper
i
odof
one
(
S) ont
of
unct
i
on
53. Mat
cht
hef
ol
l
owi
ng
(
C)
Col
umnI
I
4
Col
umnI
I
1
(
R)
2
(
S)
0
(
T)
3
i
s
54. Mat
cht
hef
ol
l
owi
ng
Col
umnI
(
A) I
ff
unct
i
onf
(
x)i
sdef
i
nedi
n[
–2,2]
,t
hendomai
nof (
P)
i
s
(
B)
(
Q)
Rangeoft
hef
unct
i
on
i
s
(
C) Rangeoft
hef
unct
i
on
i
s
(
R)
Col
umnI
I
[
–1,
1]
(
D) Rangeof
(
S)
i
s
(
T)
55. Mat
cht
hef
ol
l
owi
ng
(
A)
(
B)
Col
umnI
Domai
nof
i
s
Rangeof
Col
umnI
I
(
P)
(
Q)
i
s
(
C) Setofal
lv
al
ues ofp f
orwhi
ch t
he f
unct
i
on (
R)
i
sbi
j
ect
i
v
ei
s
(
D) I
S)
f
i
sdef
i
nedby
t
hen (
setAf
orwhi
chf
(
x)becomesi
nv
er
t
i
bl
e,
i
s
(
T)
56. Mat
cht
her
angeoff
unct
i
onsgi
v
eni
nCol
umn–Iwi
t
hcol
umn–I
I
Col
umnI
(
A)
(
P)
(
B)
(
Q)
(
C)
(
R)
(
D)
(
S)
Col
umnI
I
Sect
i
on–VI
I
nt
egerAnswerTy
pe
57. Fi
ndt
henumberofsol
ut
i
onsoft
heequat
i
on
(
wher
e[
x]and{
x}denot
esi
nt
egr
al
andf
r
act
i
onal
par
tofx)
58. I
f
f
unct
i
onwi
t
h
f
oral
l
r
eal
v
al
uesofxandyandf(
x)i
sapol
y
nomi
al
,
t
henf
i
ndt
hev
al
ueof
59. Thef
unct
i
onal
r
el
at
i
on
wher
e
.
i
ssat
i
sf
y
i
ngbyt
hef
unct
i
on
t
henf
i
ndv
al
ueof
60. Fi
ndnumberofi
nt
egr
al
sol
ut
i
onsoft
heequat
i
on
.Her
e[
.
]denot
esgr
eat
est
i
nt
egerf
unct
i
on.
61. I
fdomai
nof
i
s
,
t
henf
i
ndt
hev
al
ueof
.
ANSWERS(
FUNCTI
ON)
1.
5.
9.
13.
17.
21.
25.
29.
33.
37.
41.
45.
49.
51.
52.
53.
54.
55.
56.
57.
61.
D
C
A
B
D
ABC
ABCD
A
C
C
D
A
C
AQ
APR
AP
AQ
AR
AR
2
5
2.
C
6.
B
10. C
14. B
18. A
22. AB
26. ABC
30. D
34. B
38. A
42. A
46. A
50. C
BQ
BPS
BT
B T
BS
BQ
58. 9
3.
7.
11.
15.
19.
23.
27.
31.
35.
39.
43.
47.
B
A
D
D
C
AB
D
C
A
C
A
C
CQ
CQSDQS
CT
CR
CQ
CS
59. 1
4.
8.
12.
16.
20.
24.
28.
32.
36.
40.
44.
48.
A
D
B
B
ABCD
AD
D
A
A
A
C
A
DR
D T
DS
D P
D R
60. 2