algerbra 1 quiz answers
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AlgerbraTRANSCRIPT
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Algebra and Functions Practice Quiz #1
Key : :Incorrect A nswer :Correct A nswer :Omitted Qu estion :Y ou r A nswer
Su m m a ry Det a ils
Percen t Correct : 9 0%
Nu m ber Correct : 1 8 ou t of 2 0 Nu m ber In correct : 2 Nu m ber Om it t ed: 0
If then
(A)
(B)
(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Com m u n ica t ion
Con t en t T opic: In teg er a n d Ra t ion a l Ex pon en ts
Expla n a t ion for Correct A n swer A :
Ch oice (A ) is cor r ect . Sin ce it follow s th a t
Expla n a t ion for In correct A n swer B :
Ch oice (B) is n ot cor r ect . If w er e equ a l to th en
w ou ld equ a l Bu t so
Expla n a t ion for In correct A n swer C :
Ch oice (C) is n ot cor r ect . If w er e equ a l to th en
w ou ld equ a l Bu t so
Expla n a t ion for In correct A n swer D :
Ch oice (D) is n ot cor r ect . Th e v a lu e of ca n n ot be
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beca u se th e squ a r e of a r ea l n u m ber ca n n ot be n eg a t iv e.
Expla n a t ion for In correct A n swer E :
Ch oice (E) is n ot cor r ect . Th e v a lu e of ca n n ot be
beca u se th e squ a r e of a r ea l n u m ber ca n n ot be n eg a t iv e.
If which of the following CANNOT be a v alue for
(A)
(B)
(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Rea son in g
Con t en t T opic: Solv in g Equ a tion s a n d In equ a lit ies
Expla n a t ion for Correct A n swer D :
Ch oice (D) is cor r ect . If th en ca n n ot be If w er e
th en w ou ld equ a l n ot
Expla n a t ion for In correct A n swer A :
Ch oice (A ) is n ot cor r ect . If th en ca n equ a l If
th en
Expla n a t ion for In correct A n swer B :
Ch oice (B) is n ot cor r ect . If th en ca n equ a l If
th en
Expla n a t ion for In correct A n swer C :
Ch oice (C) is n ot cor r ect . If th en ca n equ a l If
th en
Expla n a t ion for In correct A n swer E :
Ch oice (E) is n ot cor r ect . If th en ca n equ a l If
th en
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3Which of the following is equiv alent to
(A)
(B)
(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Repr esen ta t ion
Con t en t T opic: Oper a t ion s on A lg ebr a ic Ex pr ession s
Expla n a t ion for Correct A n swer E :
Ch oice (E) is cor r ect . Th e ex pr ession is equ iv a len t to
w h ich is equ iv a len t to
Expla n a t ion for In correct A n swer A :
Ch oice (A ) is n ot cor r ect . Th e ex pr ession is equ a l to
w h en is equ a l to Th e ex pr ession is equ a l to
w h en is equ a l to Sin ce th e tw o ex pr ession s a r e n ot equ a l
for a ll v a lu es of th ey ca n n ot be equ iv a len t .
Expla n a t ion for In correct A n swer B :
Ch oice (B) is n ot cor r ect . Th e ex pr ession is equ a l to
w h en is equ a l to Th e ex pr ession is equ a l to
w h en is equ a l to Sin ce th e tw o ex pr ession s a r e n ot equ a l
for a ll v a lu es of th ey ca n n ot be equ iv a len t .
Expla n a t ion for In correct A n swer C :
Ch oice (C) is n ot cor r ect . Th e ex pr ession is equ a l to w h en
is equ a l to Th e ex pr ession is equ a l to w h en
is equ a l to Sin ce th e tw o ex pr ession s a r e n ot equ a l for a ll
v a lu es of th ey ca n n ot be equ iv a len t .
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Expla n a t ion for In correct A n swer D :
Ch oice (D) is n ot cor r ect . Th e ex pr ession is equ a l to
w h en is equ a l to Th e ex pr ession is equ a l to
w h en is equ a l to Sin ce th e tw o ex pr ession s a r e n ot equ a l
for a ll v a lu es of th ey ca n n ot be equ iv a len t .
If and what is the v alue of
(A)
(B)
(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Pr oblem Solv in g
Con t en t T opic: Solv in g Equ a tion s a n d In equ a lit ies
Expla n a t ion for Correct A n swer C :
Ch oice (C) is cor r ect . If a n d th en
su bst itu t in g for in th e fir st equ a t ion g iv es
Th is equ a t ion ca n be sim plified to
a n d fu r th er to
Expla n a t ion for In correct A n swer A :
Ch oice (A ) is n ot cor r ect . If a n d th en
ca n n ot be If w er e th en so
w ou ld equ a l Bu t is n ot a solu t ion for
beca u se
Expla n a t ion for In correct A n swer B :
Ch oice (B) is n ot cor r ect . If a n d th en
ca n n ot be If w er e th en so
w ou ld equ a l Bu t is n ot a solu t ion for
beca u se
Expla n a t ion for In correct A n swer D :
Ch oice (D) is n ot cor r ect . If a n d th en
ca n n ot be If w er e th en so w ou ld
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equ a l Bu t is n ot a solu t ion for beca u se
Expla n a t ion for In correct A n swer E :
Ch oice (E) is n ot cor r ect . If a n d th en
ca n n ot be If w er e th en so
w ou ld equ a l Bu t is n ot a solu t ion for
beca u se
Julie has cats, fish, and frogs for pets. The number of frogs she has is more
than the number of cats, and the number of fish is times the number of
frogs. Of the following, which could be the total number of these pets?
(A)
(B)
(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Repr esen ta t ion
Con t en t T opic: Wor d Pr oblem s, In clu din g A lg ebr a ic
Repr esen ta t ion s a n d Tr a n sla t ion
Expla n a t ion for Correct A n swer E :
Ch oice (E) is cor r ect . Let a n d r epr esen t th e n u m ber of
fr og s, ca ts, a n d fish , r espect iv ely . Th e n u m ber of fr og s is m or e
th a n th e n u m ber of ca ts, so Th e n u m ber of fish is
t im es th e n u m ber of fr og s, so It is n ow possible to
ex pr ess th e tota l n u m ber of pets, a s a sin g le v a r ia ble.
Su bst itu t in g for in th e equ a t ion g iv es
Th er efor e,
Th e tota l n u m ber
of pets cou ld be beca u se if th en Th a t is,
if th e n u m ber of ca ts is th en th e tota l n u m ber of pets w ill be
Expla n a t ion for In correct A n swer A :
Ch oice (A ) is n ot cor r ect . Fr om th e ex pla n a t ion for ch oice (E), it
is possible to r epr esen t th e tota l n u m ber of pets a s
w h er e is th e n u m ber of ca ts. Fr om th is, it ca n be seen th a t
th e tota l n u m ber of pets cou ld n ot be beca u se th er e is n o
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w h ole n u m ber solu t ion to th e equ a t ion
Expla n a t ion for In correct A n swer B :
Ch oice (B) is n ot cor r ect . Fr om th e ex pla n a t ion for ch oice (E), it
is possible to r epr esen t th e tota l n u m ber of pets a s
w h er e is th e n u m ber of ca ts. Fr om th is, it ca n be seen th a t
th e tota l n u m ber of pets cou ld n ot be beca u se th er e is n o
w h ole n u m ber solu t ion to th e equ a t ion
Expla n a t ion for In correct A n swer C :
Ch oice (C) is n ot cor r ect . Fr om th e ex pla n a t ion for ch oice (E), it
is possible to r epr esen t th e tota l n u m ber of pets a s
w h er e is th e n u m ber of ca ts. Fr om th is, it ca n be seen th a t
th e tota l n u m ber of pets cou ld n ot be beca u se th er e is n o
w h ole n u m ber solu t ion to th e equ a t ion
Expla n a t ion for In correct A n swer D :
Ch oice (D) is n ot cor r ect . Fr om th e ex pla n a t ion for ch oice (E), it
is possible to r epr esen t th e tota l n u m ber of pets a s
w h er e is th e n u m ber of ca ts. Fr om th is, it ca n be seen th a t
th e tota l n u m ber of pets cou ld n ot be beca u se th er e is n o
w h ole n u m ber solu t ion to th e equ a t ion
If what is the v alue of
(A)
(B)
(C)
(D)
(E) It cannot be determined from the information giv en.
ANSWERS AND EXPLANATIONS
Skill Grou p: Rea son in g
Con t en t T opic: Oper a t ion s on A lg ebr a ic Ex pr ession s
Expla n a t ion for Correct A n swer B :
Ch oice (B) is cor r ect . If th en Mu lt iply in g
both sides of th is equ a t ion by g iv es Fr om th is, it
follow s th a t
Expla n a t ion for In correct A n swer A :
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Ch oice (A ) is n ot cor r ect . Th e v a lu e of is n ot
Expla n a t ion for In correct A n swer C :
Ch oice (C) is n ot cor r ect . Th e v a lu e of is n ot
Expla n a t ion for In correct A n swer D :
Ch oice (D) is n ot cor r ect . Th e v a lu e of is n ot
Expla n a t ion for In correct A n swer E :
Ch oice (E) is n ot cor r ect . It is possible to deter m in e th a t th e
v a lu e of is fr om th e in for m a tion g iv en .
A student is awake hours each day and spends hours each day doing
homework. In terms of how many day s will it take the student to complete
homework assignments that require a total of hours?
(A)
(B)
(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Repr esen ta t ion
Con t en t T opic: Wor d Pr oblem s, In clu din g A lg ebr a ic
Repr esen ta t ion s a n d Tr a n sla t ion
Expla n a t ion for Correct A n swer D :
Ch oice (D) is cor r ect . If it ta kes da y s to do th e h ou r s of
h om ew or k, th en da y s t im es h ou r s per da y is equ a l to
Th is ca n be ex pr essed a s Fr om th is equ a t ion , it is
possible to ex pr ess in ter m s of Th a t is,
Expla n a t ion for In correct A n swer A :
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Ch oice (A ) is n ot cor r ect . If it w ou ld ta ke th e stu den t da y s
to com plete h ou r s of h om ew or k w or kin g h ou r s per da y ,
th en Th is m ea n s th a t
so Th is is im possible, beca u se th e stu den t ca n n ot be
a w a ke h ou r s per da y .
Expla n a t ion for In correct A n swer B :
Ch oice (B) is n ot cor r ect . If it w ou ld ta ke th e stu den t da y s to
com plete h ou r s of h om ew or k w or kin g h ou r s per da y ,
th en Th is m ea n s th a t so
Th is is im possible, beca u se th e stu den t ca n n ot be
a w a ke m or e th a n h ou r s per da y .
Expla n a t ion for In correct A n swer C :
Ch oice (C) is n ot cor r ect . If it w ou ld ta ke th e stu den t da y s to
com plete h ou r s of h om ew or k w or kin g h ou r s per da y ,
th en
Expla n a t ion for In correct A n swer E :
Ch oice (E) is n ot cor r ect . Ta kin g da y s to com plete
h ou r s of h om ew or k w or kin g h ou r s per da y is n ot r ea son a ble.
If th is w er e tr u e, th en th e m or e t im e spen t per da y w or kin g on
th e h om ew or k, th e g r ea ter th e n u m ber of da y s it w ou ld ta ke to
com plete th e w or k. Bu t th is does n ot m a ke sen se.
Each of the ordered pairs in the table abov e is on the graph of the function
in the plane. Which of the following could be true for all
(A)
(B)
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(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Con n ect ion s
Con t en t T opic: A lg ebr a ic Fu n ct ion s a n d Th eir Gr a ph s
Expla n a t ion for Correct A n swer E :
Ch oice (E) is cor r ect . If th en
w h ich is con sisten t w ith th e ta ble;
w h ich is con sisten t w ith th e ta ble; a n d
w h ich is con sisten t w ith th e ta ble.
Th er efor e, it is possible th a t for a ll
Expla n a t ion for In correct A n swer A :
Ch oice (A ) is n ot cor r ect . If th en
w h ich con tr a dicts th e ta ble.
Expla n a t ion for In correct A n swer B :
Ch oice (B) is n ot cor r ect . If th en
w h ich con tr a dicts th e ta ble.
Expla n a t ion for In correct A n swer C :
Ch oice (C) is n ot cor r ect . If th en
w h ich con tr a dicts th e ta ble.
Expla n a t ion for In correct A n swer D :
Ch oice (D) is n ot cor r ect . If th en
w h ich con tr a dicts th e ta ble.
Luis earns dollars an hour for hours and then earns dollars an hour
for more hours. In terms of and how many dollars did he earn in
all?
(A)
(B)
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(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Repr esen ta t ion
Con t en t T opic: Wor d Pr oblem s, In clu din g A lg ebr a ic
Repr esen ta t ion s a n d Tr a n sla t ion
Expla n a t ion for Correct A n swer A :
Ch oice (A ) is cor r ect . Lu is ea r n s dolla r s a n h ou r for
h ou r s, so h e ea r n s dolla r s. He th en ea r n s
dolla r s a n h ou r for m or e h ou r s, or dolla r s. In tota l,
th er efor e, h e ea r n s dolla r s. Th is is equ iv a len t to
dolla r s.
Expla n a t ion for In correct A n swer B :
Ch oice (B) is n ot cor r ect . Th e ex pr ession w ou ld be
th e n u m ber of dolla r s Lu is ea r n s if h e ea r n ed dolla r s a n h ou r
for h ou r s a n d dolla r s a n h ou r for m or e h ou r s.
How ev er , h e ea r n s dolla r s a n h ou r for h ou r s a n d
dolla r s a n h ou r for m or e h ou r s.
Expla n a t ion for In correct A n swer C :
Ch oice (C) is n ot cor r ect . Th e ex pr ession w ou ld be
th e n u m ber of dolla r s Lu is ea r n s if h e ea r n ed dolla r s a n h ou r
for h ou r s a n d dolla r s a n h ou r for m or e h ou r s.
How ev er , h e ea r n s dolla r s a n h ou r for h ou r s a n d
dolla r s a n h ou r for m or e h ou r s.
Expla n a t ion for In correct A n swer D :
Ch oice (D) is n ot cor r ect . Th e ex pr ession w ou ld be
th e n u m ber of dolla r s Lu is ea r n s if h e ea r n ed dolla r s a n h ou r
for h ou r s a n d dolla r s a n h ou r for m or e h ou r s.
How ev er , h e ea r n s dolla r s a n h ou r for h ou r s a n d
dolla r s a n h ou r for m or e h ou r s.
Expla n a t ion for In correct A n swer E :
Ch oice (E) is n ot cor r ect . Th e ex pr ession w ou ld be
th e n u m ber of dolla r s Lu is ea r n s if h e ea r n ed dolla r s a n h ou r
for h ou r s a n d dolla r s a n h ou r for m or e h ou r s.
How ev er , h e ea r n s dolla r s a n h ou r for h ou r s a n d
dolla r s a n h ou r for m or e h ou r s.
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10If where then
(A)
(B)
(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Com m u n ica t ion
Con t en t T opic: Oper a t ion s on A lg ebr a ic Ex pr ession s
Expla n a t ion for Correct A n swer A :
Ch oice (A ) is cor r ect . Rew r it in g a s a n d a s
g iv es . Sin ce is n ot zer o, Solv in g
th e equ a t ion g iv es
Expla n a t ion for In correct A n swer B :
Ch oice (B) is n ot cor r ect . If th e ex pr ession h a d been
or th en w ou ld equ a l
Expla n a t ion for In correct A n swer C :
Ch oice (C) is n ot cor r ect . If th e ex pr ession h a d been
th en w ou ld equ a l
Expla n a t ion for In correct A n swer D :
Ch oice (D) is n ot cor r ect . If th e ex pr ession h a d been
th en w ou ld equ a l
Expla n a t ion for In correct A n swer E :
Ch oice (E) is n ot cor r ect . If th e ex pr ession h a d been
th en w ou ld equ a l
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11 If what is the v alue of
(A)
(B)
(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Pr oblem Solv in g
Con t en t T opic: In teg er a n d Ra t ion a l Ex pon en ts
Expla n a t ion for Correct A n swer B :
Ch oice (B) is cor r ect . By la w s of ex pon en ts,
so Sin ce it follow s th a t
(It is a lso possible to solv e th is pr oblem
by u sin g to fin d a n d th en su bst itu t in g th is
v a lu e of in )
Expla n a t ion for In correct A n swer A :
Ch oice (A ) is n ot cor r ect . If w er e th en w ou ld be
How ev er , it is g iv en th a t
Expla n a t ion for In correct A n swer C :
Ch oice (C) is n ot cor r ect . Th e v a lu e of is bu t th e v a lu e of
is
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Expla n a t ion for In correct A n swer D :
Ch oice (D) is n ot cor r ect . If w er e th en w ou ld be
How ev er , it is g iv en th a t
Expla n a t ion for In correct A n swer E :
Ch oice (E) is n ot cor r ect . If w er e th en w ou ld be
How ev er , it is g iv en th a t
Let for all integers and If and , what must
equal?
(A)
(B)
(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Rea son in g
Con t en t T opic: A lg ebr a ic Fu n ct ion s a n d Th eir Gr a ph s
Expla n a t ion for Correct A n swer B :
Ch oice (B) is cor r ect . If th en by th e defin it ion of
it m u st be tr u e th a t Sin ce it
follow s th a t Th is m ea n s th a t a t lea st on e of
a n d m u st be equ a l to Sin ce it m u st be tr u e th a t
a n d .
Expla n a t ion for In correct A n swer A :
Ch oice (A ) is n ot cor r ect . If th en by th e defin it ion of
it m u st be tr u e th a t If w er e equ a l to
th en w ou ld be equ a l to How ev er , th is ca n n ot
be tr u e, beca u se
Expla n a t ion for In correct A n swer C :
Ch oice (C) is n ot cor r ect . If th en by th e defin it ion of
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it m u st be tr u e th a t If w er e equ a l to
th en w ou ld be equ a l to How ev er , th is ca n n ot be
tr u e, beca u se
Expla n a t ion for In correct A n swer D :
Ch oice (D) is n ot cor r ect . If th en by th e defin it ion of
it m u st be tr u e th a t If w er e equ a l to th en
w ou ld be equ a l to How ev er , th is ca n n ot be tr u e,
beca u se
Expla n a t ion for In correct A n swer E :
Ch oice (E) is n ot cor r ect . If th en by th e defin it ion of
it m u st be tr u e th a t If w er e equ a l to
th en w ou ld be equ a l to How ev er , th is ca n n ot be
tr u e, beca u se
Line in the -coordinate sy stem abov e is the graph of the equation
Which of the following must be true?
(A)
(B)
(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Con n ect ion s
Con t en t T opic: A lg ebr a ic Fu n ct ion s a n d Th eir Gr a ph s
Expla n a t ion for Correct A n swer C :
Ch oice (C) is cor r ect . Th e slope a n d -in ter cept of th e g r a ph of
a r e a n d r espect iv ely . Fr om th e g r a ph , it
ca n be seen th a t lin e h a s a n eg a t iv e slope a n d a posit iv e -
in ter cept . Th er efor e, a n d so
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Expla n a t ion for In correct A n swer A :
Ch oice (A ) is n ot cor r ect . If w er e equ a l to th en a t lea st
on e of a n d w ou ld be equ a l to Beca u se lin e is n ot
pa r a llel to th e -a x is, it does n ot h a v e a slope of so is n ot
Beca u se lin e does n ot g o th r ou g h th e or ig in , is n ot
Th er efor e, ca n n ot be equ a l to
Expla n a t ion for In correct A n swer B :
Ch oice (B) is n ot cor r ect . Fr om th e g r a ph of lin e it ca n be seen
th a t a n d It follow s th a t Th er efor e,
ca n n ot be equ a l to
Expla n a t ion for In correct A n swer D :
Ch oice (D) is n ot cor r ect . Fr om th e g r a ph of lin e it ca n be seen
th a t a n d Th er efor e, it ca n n ot be tr u e th a t
Expla n a t ion for In correct A n swer E :
Ch oice (E) is n ot cor r ect . It is tr u e th a t a n d h a v e opposite
sig n s. How ev er , fr om th e g r a ph of lin e it a ppea r s th a t is
a ppr ox im a tely a n d th a t is a ppr ox im a tely Th u s, it is
n ot ev en pla u sible th a t w ou ld h old. Fu r th er m or e,
th er e is n oth in g in th e fig u r e th a t w ou ld im ply th a t it m u st
h old.
If and are positiv e odd integers, which of the following is greatest?
(A)
(B)
(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Pr oblem Solv in g
Con t en t T opic: In teg er a n d Ra t ion a l Ex pon en ts
Expla n a t ion for Correct A n swer D :
Ch oice (D) is cor r ect . Sin ce a n d a r e posit iv e odd in teg er s,
a n d a n eg a t iv e in teg er r a ised to a posit iv e odd in teg er pow er is
n eg a t iv e, tw o of th e ex pr ession s a r e n eg a t iv e a n d th r ee a r e
posit iv e. Th e g r ea test of th e fiv e ch oices m u st be on e of th e th r ee
posit iv e ex pr ession s, w h ich a r e a n d We
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h a v e a n d Sin ce
it follow s by su bst itu t ion th a t
Th u s, th e g r ea test of th e fiv e
ex pr ession s is
Expla n a t ion for In correct A n swer A :
Ch oice (A ) is n ot cor r ect . Th e ex pr ession is less th a n
a n d so ca n n ot be th e g r ea test of th e fiv e
ex pr ession s.
Expla n a t ion for In correct A n swer B :
Ch oice (B) is n ot cor r ect . Sin ce a n d a r e posit iv e odd
in teg er s, is a n eg a t iv e in teg er r a ised to a posit iv e odd
in teg er pow er , w h ich is n eg a t iv e. Sin ce th r ee of th e fiv e
ex pr ession s a r e posit iv e, ca n n ot be th e g r ea test of th e
fiv e ex pr ession s.
Expla n a t ion for In correct A n swer C :
Ch oice (C) is n ot cor r ect . Th e ex pr ession is less th a n
so ca n n ot be th e g r ea test of th e fiv e
ex pr ession s.
Expla n a t ion for In correct A n swer E :
Ch oice (E) is n ot cor r ect . Sin ce a n d a r e posit iv e odd
in teg er s, is a n eg a t iv e in teg er r a ised to a posit iv e odd
in teg er pow er , w h ich is n eg a t iv e. Sin ce th r ee of th e fiv e
ex pr ession s a r e posit iv e, ca n n ot be th e g r ea test of th e
fiv e ex pr ession s.
The graph of the function in the -plane is shown abov e. If is another
function defined for and if then could be which of
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the following?
(A)
(B)
(C)
(D)
(E)
ANSWERS AND EXPLANATIONS
Skill Grou p: Con n ect ion s
Con t en t T opic: A lg ebr a ic Fu n ct ion s a n d Th eir Gr a ph s
Expla n a t ion for Correct A n swer C :
Ch oice (C) is cor r ect . Th e poin t is on th e g r a ph of
Th er efor e, Sin ce it cou ld be possible th a t
beca u se
(Th e fa ct th a t th e tw o fu n ct ion s a g r ee a t on e v a lu e of is n ot
en ou g h to con clu de th a t th ey a r e th e sa m e fu n ct ion , bu t if th is
is a ll th a t is kn ow n a bou t th e r ela t ion sh ip betw een th e tw o
fu n ct ion s, it is en ou g h to con clu de th a t th ey cou ld be th e sa m e.)
Expla n a t ion for In correct A n swer A :
Ch oice (A ) is n ot cor r ect . It ca n n ot be possible th a t is equ a l to
beca u se
Th e fa ct th a t th e tw o fu n ct ion s h a v e differ en t v a lu es a t
is en ou g h to con clu de th a t a n d ca n n ot be th e sa m e
fu n ct ion .
Expla n a t ion for In correct A n swer B :
Ch oice (B) is n ot cor r ect . It ca n n ot be possible th a t is equ a l to
beca u se
Th e fa ct th a t th e tw o fu n ct ion s h a v e differ en t v a lu es a t
is en ou g h to con clu de th a t a n d ca n n ot be th e sa m e
fu n ct ion .
Expla n a t ion for In correct A n swer D :
Ch oice (D) is n ot cor r ect . It ca n n ot be possible th a t is equ a l to
beca u se
Th e fa ct th a t th e tw o fu n ct ion s h a v e differ en t v a lu es a t
is en ou g h to con clu de th a t a n d ca n n ot be th e sa m e
fu n ct ion .
Expla n a t ion for In correct A n swer E :
Ch oice (E) is n ot cor r ect . It ca n n ot be possible th a t is equ a l to
beca u se
Th e fa ct th a t th e tw o fu n ct ion s h a v e differ en t v a lu es a t
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is en ou g h to con clu de th a t a n d ca n n ot be th e sa m e
fu n ct ion .
If and what is the v alue of
Skill Grou p: Repr esen ta t ion
Con t en t T opic: Solv in g Equ a tion s a n d In equ a lit ies
You r Respon se: .2
Correct Respon se(s): 1 /5 , .2
Expla n a t ion :
Th e cor r ect a n sw er is or . If th en
Fr om th is, it follow s th a t Sin ce
th e v a lu e of m u st be Th e decim a l for m m a y a lso be
g r idded a s th e a n sw er .
For what v alue of is
Skill Grou p: Pr oblem Solv in g
Con t en t T opic: Qu a dr a t ics
You r Respon se: 0
Correct Respon se(s): 0
Expla n a t ion :
Th e cor r ect a n sw er is . Ex pa n din g both sides of
g iv es
Su btr a ct in g a n d fr om ea ch side of th is equ a t ion g iv es
a n d th en a ddin g to ea ch side g iv es
Th er efor e,
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Let be defined as the sum of all integers between and For example,
What is the v alue of
Skill Grou p: Rea son in g
Con t en t T opic: A lg ebr a ic Fu n ct ion s a n d Th eir Gr a ph s
You r Respon se: 1
Correct Respon se(s): 1 9 0
Expla n a t ion :
Th e cor r ect a n sw er is . Wh en th e tw o ex pr ession s a r e
ex pa n ded a ccor din g to th e defin it ion of w e h a v e
Wh en th e su btr a ct ion is per for m ed,
th e com m on in teg er s a r e elim in a ted. On ly a n d r em a in
fr om th e fir st su m , beca u se th ey a r e th e on ly tw o in teg er s n ot
con ta in ed in th e secon d su m . Th er efor e, th e ex pr ession
is equ a l to
If where is an integer, what is one possible v alue of
Skill Grou p: Repr esen ta t ion
Con t en t T opic: Solv in g Equ a tion s a n d In equ a lit ies
You r Respon se: 1 4
Correct Respon se(s): 1 3 or 1 4
Expla n a t ion :
Th e possible cor r ect a n sw er s a r e or . Th e in equ a lit ies
a r e equ iv a len t to beca u se
m u lt iply in g ev er y ter m by th e posit iv e n u m ber keeps th e
in equ a lit ies in th e sa m e dir ect ion . Th e on ly in teg er s th a t
sa t isfy a r e a n d Eith er or is a
cor r ect a n sw er .
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20 The cells of a certain ty pe of bacteria increase in number by each splitting
into two cells ev ery minutes. At this rate, if a colony of this ty pe of
bacteria starts with a single cell, how many hours elapse before the colony
contains cells?
Skill Grou p: Pr oblem Solv in g
Con t en t T opic: Wor d Pr oblem s, In clu din g A lg ebr a ic
Repr esen ta t ion s a n d Tr a n sla t ion
You r Respon se: 5 .5
Correct Respon se(s): 1 1 /2 , 5 .5
Expla n a t ion :
Th e cor r ect a n sw er is or . Sin ce ea ch cell in th e colon y
splits in to tw o cells ev er y m in u tes, th e n u m ber of cells is
m u lt iplied by ev er y m in u tes. Th er efor e, a fter of th ese
-m in u te per iods, th e colon y w ill con ta in cells; a fter
of th ese per iods, th e colon y w ill con ta in cells; a n d so on ,
u n til a fter of th ese -m in u te per iods, th e colon y w ill
con ta in cells. Ea ch -m in u te per iod is equ iv a len t to
h ou r , so of th ese per iods a r e equ iv a len t to h ou r s. Eith er
or ca n be g r idded a s th e a n sw er . (Do n ot g r id
w h ich w ou ld be r ea d a s )
Pr in t Close