Algerbra 1 Quiz Answers

7/17/2014 The Official SAT Online Course

https://satonlinecourse.collegeboard.org/SR/viewanswersexplanations.do?qnum=18#18 1/20

1

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



2

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)


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


Ch oice (B) is n ot cor r ect . If th en ca n equ a l If

th en


Ch oice (C) is n ot cor r ect . If th en ca n equ a l If

th en


Ch oice (E) is n ot cor r ect . If th en ca n equ a l If

th en



3Which of the following is equiv alent to

(A)

(B)

(C)

(D)

(E)


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


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 .


Ch oice (B) is n ot cor r ect . Th e ex pr ession is equ a l to





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 .



4


Ch oice (D) is n ot cor r ect . Th e ex pr ession is equ a l to




If and what is the v alue of

(A)

(B)

(C)

(D)

(E)


Skill Grou p: Pr oblem Solv in g


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


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


Ch oice (B) is n ot cor r ect . If a n d th en



beca u se


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



5

equ a l Bu t is n ot a solu t ion for beca u se


Ch oice (E) is n ot cor r ect . If a n d th en



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)



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


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


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



6

w h ole n u m ber solu t ion to th e equ a t ion


Ch oice (B) is n ot cor r ect . Fr om th e ex pla n a t ion for ch oice (E), it






Ch oice (C) is n ot cor r ect . Fr om th e ex pla n a t ion for ch oice (E), it






Ch oice (D) is n ot cor r ect . Fr om th e ex pla n a t ion for ch oice (E), it





If what is the v alue of

(A)

(B)

(C)

(D)

(E) It cannot be determined from the information giv en.




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




7

Ch oice (A ) is n ot cor r ect . Th e v a lu e of is n ot


Ch oice (C) is n ot cor r ect . Th e v a lu e of is n ot


Ch oice (D) is n ot cor r ect . Th e v a lu e of is n ot


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)






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,




8

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 .


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 .


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


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)



9

(C)

(D)

(E)


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


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


Ch oice (A ) is n ot cor r ect . If th en

w h ich con tr a dicts th e ta ble.


Ch oice (B) is n ot cor r ect . If th en



Ch oice (C) is n ot cor r ect . If th en



Ch oice (D) is n ot cor r ect . If th en


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)



(C)

(D)

(E)






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.


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.


Ch oice (C) is n ot cor r ect . Th e ex pr ession w ou ld be






Ch oice (D) is n ot cor r ect . Th e ex pr ession w ou ld be






Ch oice (E) is n ot cor r ect . Th e ex pr ession w ou ld be







10If where then

(A)

(B)

(C)

(D)

(E)


Skill Grou p: Com m u n ica t ion



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


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


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


Ch oice (D) is n ot cor r ect . If th e ex pr ession h a d been



Ch oice (E) is n ot cor r ect . If th e ex pr ession h a d been




11 If what is the v alue of

(A)

(B)

(C)

(D)

(E)





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 )


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


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



12


Ch oice (D) is n ot cor r ect . If w er e th en w ou ld be



Ch oice (E) is n ot cor r ect . If w er e th en w ou ld be


Let for all integers and If and , what must

equal?

(A)

(B)

(C)

(D)

(E)





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 .


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


Ch oice (C) is n ot cor r ect . If th en by th e defin it ion of



13


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


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


Ch oice (E) is n ot cor r ect . If th en by th e defin it ion of


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)





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



14


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


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


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


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)





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



15

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


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.


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.


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.


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



the following?

(A)

(B)

(C)

(D)

(E)





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.)


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 .


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



fu n ct ion .


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



fu n ct ion .


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




16

17


fu n ct ion .

If and what is the v alue of



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


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,



18

19

Let be defined as the sum of all integers between and For example,

What is the v alue of



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



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 .



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?




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

Date post:	08-Nov-2015
Category:	Documents
Upload:	sam
View:	24 times
Download:	4 times

Algerbra 1 Quiz Answers

Documents