Algebra Semester 1 Exam Review Jan 2012 10-5-2011 Rev

7/27/2019 Algebra Semester 1 Exam Review Jan 2012 10-5-2011 Rev

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Algebra Semester 1 Review Name___________________________________

In order to earn full credit, ALL WORK must be sown on ALL !roblems"#e $uestions tat are circled are tose tat %ou sould not use a calculator to solve"

1.) To find the mileage, or how many miles per gallon a car can travel, you can use the expression

g

mwhere mis the distance in miles and gis the number of gallons of gas used. Find the mileage

for a car that travels 35 miles on 1! gallons of gas.

".) #valuate the expression ( )3"$3 +n , given n% 3.

3.) &implify ( ) ( )3"3"3

"335'5 +

!.) #valuate the expression 31216 xx+ , whenx% 3.

5.) &implify ( ) ( )3!3$'$ "" +

a.) "$ b.) "!3 c.) 1( d.) "'1

'.) &uppose one person can do a *ob inxminutes, and a different person can do the same *ob in yminutes.Thetime +in minutes) in which the *ob can be completed by both people woring together can be found using the

expressionyx

xy

+. -f it taes you ' minutes to sweep your itchen floor and it taes your brother ( minutes,

how long would it tae both you and your brother woring together

$.) -t is nown that a cyclist can travel !1.! miles in 3 hours. /t that rate, how far can the samecyclist travel in $ hours

a.) 5." milesb.) $.( miles c.) '.' miles d.) $.! miles

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Functionsy% "x0 3y% "x 3y% "x0 !y% 3x 3

-nput 2utput1 11 '! 5

(.) / shipping service charges .!3 for the first ounce and ." for each additional ounce of pacageweight.4rite an euation to represent the price Pof shipping a pacage that weighsxounces, for any whole numberof ounces greater than or eual to 1.

.) / store that sells gift basets is having a promotional sale. 6ustomers can mae their own fruit basetsto use

as gifts. 6ustomers pay 3. for a baset and add ." per pound for all types of fruit. The cost for abaset containingppounds of fruit is !.3. 4hich euation could be used to f indp, the number of pounds offruit in this baset

a.) 3. ."p% !.3 b.) +." !.3)p% 3.

c.) 3.+!.3 p) % 3. d.) ." 3.p% !.3

1.) 4rite an euation euivalent to the verbal statement7 8three times the sum of a number nand $ is 1'.8

11.) 9ae an input:output table for the function y% "x !. ;sex :values of 1, ", 3, !, and 5.

X

y

1".)


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15.) =ist a value ofxso that the relation is not a function. >+', "), +5, 3), +1, ), +x, !)?

1'.) #valuate the expression 12 .

1$.) ;se the concept of opposites to simplify @+0 +0+0+!)))).

1(.) Aeather is selling fruit as a fund raiser for the soccer team. &he has sold 5 pounds so far.The graph shows the profit related to the amount of fruit sold.

a.) 4rite a function rule for the graph. ;se the function rule to find theprofit if Aeather sells a total of 3 pounds of fruit.

b.) /nother student claims that Aeather must sell 5 pounds of fruit to maea profit of ". -s this true 4hy or why not

1.) Find the sum.

a.) 0! +013) b.) "(.!3 +013.1$) ".$.

".) 9elissa eeps trac of the profit made each month by her business. Aer profits for the threemonths of Bune, Buly, and /ugust were "',(5, 013,!, and 0!,!".

a.) 4hat was her total profit for the summer

b.) 9elissa adds the last two amounts in the list first, then adds that sum to the first amount.Aer business partner adds the first two amounts first, then adds that sum to the last amount.4ill they get the same sum 4hy or why not

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"1.) #valuate 0+0!) 0 +05) '

"".) Find the change in temperature from 013C6 to 15C6.

"3.) &implify the expression +0$) ' D0+" 0 3)E.

"!.) #valuate the expression ( ) 1028 x whenx% 015.

"5.) &implify +0$)+5)+')

"'.) &implify the expression )"+1 c

"$.) &implify7 5+x0 5y)

"(.) ill wants to simplify the following expression7 5+3x0 "y) "+x "y) 0 3+3x0 "y)

4hich of the following expressions is euivalent to the expression above

a.) (x b.) (x0 1"y c.) (xy d.) (x0 (y

".) &implify7 0!+x 3)

3.) &implify the expression 0"+"x (+03 x))

31.) Gat wrote this mathematical sentence7 '33 1"3) xxx =+ . #xplain her mistae and how to correct it.

3".) Find the uotient.

)

!1"

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33.) 4hat is the multiplicative inverse of1

a.) 1 b.) c.)

1d.)

1

1

3!.) Find the uotient3

""(

a.) 3 b.)31"1 c.) 3

" d.)'!3

35.) 4hich of the following is an irrational number

a.) 1! b.)'

5c.) ...5$5$5$. d.) )

3'.) Find all suare roots of the number .'!.

3$.) &olve the following euations7

a.) "'1" =+x b.) 155

=x c.) 3

3

"=x

3(.) / college student has set aside "! for the rest of the school year to use the coin:operated laundry facility inhis dormitory. #ach time he uses the machines, it costs $.5. 6hoose the euation that represents theamount remaining in his fund, f, after he has done laundryxtimes. Find the amount remaining in the fundafter 1" trips to the laundry facility.

a.) f% "! 0 $.5xH . b.) f% "! 0 $.5xH 15.

c.) f% $.5 0 "!xH 15. d.) f% $.5 0 "!xH .

3.) The temperature wasxC F. -t rose 15C F and is now 3C F.4rite and solve an euation to find the original temperature.

!.) IaryJs cellular phone bill averages 5'.35 per month, based on a fixed fee of ".5 and ."" per minute ofusage. The phone company has decided to reduce the per:minute charge to .1(. Aow much does thischange save Iary in an average month

!1.) Kou are going to varnish a floor that is "$ ft. by '3 ft. 2ne pint of varnish covers "3 yd"of space.Aow many pints of varnish do you need

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!".) Bohn wors as a salesman for a cellular telephone service. Ae is paid "5 per wee plus 15 for eachcontract a customer signs. Ae needs to earn at least !5 per wee in order to meet his living expenses.4hat is the fewest number of contracts he needs to sell each wee to meet his living expenses

!3.) 9ichelle wants to earn selling "" nit scarves. &he wants to sell each scarf for ! less than hercompetitor. -fxis the price charged by her competitor, which euation models the situation

a.) "+"") "x % b.) ""x% c.) ""+x0 !) % d.) "" !x%

!!.) / rental car agency charges 1! per day plus .1! per mile to rent a certain car. /nother agency charges1( per day plus .$ per mile to rent the same type of car. Aow many miles per day will have to be drivenfor the cost of a car from the first agency to eual the cost of a car from the second agency

!5.) &olve the euation.

a.) "(1

!=+y b.) 5

!"=+

xxc.) 55"3$ =++ nn

d.)1"$

5

"5=

x

x

e.) ( ) $3!1

=+y f.) ( )

11""5 = nn

g.) zz (5!3 += h.) !33 += xx i.) ( )"!"1!5 +=+ xxx

*.)w

5

!

(= .)

xx

5

!

3=

!'.) Two machines can complete 5 tass every ! days. =et trepresent the number of tass these machines can

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complete in a 31:day month. 4hich proportion can you use to find the value of t

a.)!11

31 t= b.)

531

! t= c.)31!

5 t= d.)

315

! t=

!$.) / cyclist can travel ".' miles in " hours. /t this rate, how far can the same cyclist travel in !5 minutes

!(.) 9adison solved the following euation7 ( ) '5"5

"=x .

/s a first step, she rewrote the euation as 1552 =x .

a.) y what number did 9adison multiply both sides of the euation 4hy did she choose this number

b.) 4hat is the solution of the euation

!.) Laul uses '.$ pounds of ground beef to mae a casserole that serves 1$ people. Aow many pounds wouldhe need to mae the casserole for 13 people

5.) / classroom contains 1( girls and "! boys. 4rite the ratio of girls to boys in the classroom as a fraction inlowest terms.

51.) 2f every 5 hot dogs 9artha sold, 3 had sauerraut. 4hat percent of the hot dogs sold had sauerraut

a.) M' b.) M5

3c.) M' d.) M'.

5".) &hown below is a picture and its enlargement. The width and length of the smaller picture are and 1"inches respectively. The length of the larger picture is "( inches. 4hat is the width of the larger picture

53.) / survey was taen to determine the favorite sub*ects of (th graders. The results are shown in the graph./bout what percent of students chose &ocial &tudies as their favorite sub*ect

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5!.) &olve y%(

5 b 1 for b.

55.) Iraph the euation x% 05. 5'.) 4hat is the range of the function in the graph

5$.) &etch the graphs ofx % 0" and y% 0!.Find the point at which the two graphs intersect.

5(.) &tate thex : and y :intercepts of the linewith the euation y% 0"x !.

5.) &etch the line given by, 3x !y =01".=abel thex : and y :intercepts.

'.) Find the slope of the line that contains +0(, ") and +$, 0!).

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'1.) Find the slope of the line passing through the pointsA +(, 1) and B +03, 0').

'".) #xplain the difference between positive slope and negative slope.

'3.) Lewrite the euations in slope:intercept form and graph the line.

a.) 5x0 "y% $ b.) 3x0 y0 " %

'!.) Find the slope and y:intercept of the line ''

1+= xy . -s the line parallel to '' += xy

'5.) The depth of the water in BeanneJs hot tub varies directly with the number of minutes that the faucet isturned on. /t (715 /.9. Beanne started filling her circular hot tub with water. /t (75 /.9. there was a foot of

water in the tub. 4hen will the hot tub have!

3" feet of water in it

a.) 11715 /.9. b.) 175 /.9. c.) 1715 /.9. d.) 171' /.9.

''.) / monthly phone bill, b(m), consists of a "( service fee plus .13 perminute, m, of long distance calls, given by the function b(m)% "( .13m.


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'$.) Iraph the function x!

3)x+g = .

'(.) Find the value of x so thatf+x) % 13. f+x) % x 0 1

'.) 6hoose an euation, in slope:intercept form, of a line with a slope $ and a y:intercept of 0.

a.) y% $x0 b.) y% $x c.) x% $y0 d.) $

1= xy

$.) 4hen /idan had his picture taen, the photographer chargeda 1 sitting fee and ' for each sheet of pictures purchased.

a.) 4rite the function for the situation, wherexis thenumber of sheets purchased.

b.) Iraph this function.

$1.) 4rite an euation in slope:intercept form of the graph.

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$".) The cost of a school banuet is 5 plus 15 for each person attending. 4rite an euation that gives totalcost as a function of the number of people attending. 4hat is the cost for $$ people

a.) y% 1'x0 5 H 1' b.) y% 5x 15 H $33

c.) y% 15x 5 H 1"5 d.) y% 5x 15 H $3

$3.) 4rite an euation of the line with slope 3

1

andy:intercept 0!.

$!.) 4rite an euation of the line shown.

$5.) 4rite an euation for the function in the form, f +x) % mx + b.

f +0!) % 033, f +) % 05

$'.) 4rite an euation of the line passing through the point +0$, 0') with slope m% !.

$$.) The graph for a stable that charges a " flat fee plus 1 per hour forhorsebac riding is shown. Aow will the graph change if the stable changesits charges to a flat fee of 3 plus 15 per hour

$(.) 4rite the euation in slope:intercept form of the line that passes through the points +$, 01) and +", ).

$.) 4rite an euation, in point:slope form, of the line that passes through the point +', 05) and has the slope2

1

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(.) 4rite an euation in point:slope form of the line that passes through the points +05, 0!) and +', 3).

a.) )5+11

$! +=+ xy b.) )5+

$

11! +=+ xy

c.) )!+11

$5 +=+ xy d.) )!+

$

115 +=+ xy

(1.) 4rite an euation in point:slope form of the line that passes through +0$,1) and has slope m%2

1.

(".) 4rite an euation in point:slope form of the line that passes through the points +0", 05) and +0', !).

(3.) 4rite the euation of the horiOontal line passing through the point +$, !).

(!.) 4rite the euation of the vertical line passing through the point +05, ").

(5.) 4rite an euation of the line with undefined slope that passes through the point +(, 01).

('.) The clearing house has resistors that sell for 3.5 each and circuit boards that sell for "."5 each.4rite an ineuality that represents how many of each type of electronic euipment can be bought with atleast $.

($.) 4rite an euation in standard form of the line that passes through the two given points. +03, ") and +1, 0 !).

((.) 4rite an euation of the line that passes through +01(, 0!) and is parallel to the line 33

1+= xy .

(.) 4hich of the following lines is P2T parallel to the line shown in the graph

a.) 33 =+yx b.) 3 = xy

c.) !1" =+ yx d.) 33 = yx

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.) 4rite an euation of the line that passes through +!, ) and is perpendicular to the line 15

1 += xy .

1.) Tell whetherxand yshow apositive correlation, negative correlation,or relatively no correlation.

".) ianca is maing home:made cards to send to friends

and family and to sell at the local craft fair. This scatter

plot shows the total number of cards she had made after

each hour she wored on the tas. ;sing this information,

predict the number of cards that ianca can mae in 1" hours.

3.) / biology student recorded data for a science pro*ect and graphedthem on a scatter plot.

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33x +

represent your dogJs healthy weight win ilograms.

(.) &olve and graph the ineuality7 0( S !x " S (

.) &olve and graph the ineuality7 x 3 S ! and 0"xQ 1

1.) &olve7 3"! =+x

101.)&olve and graph the ineuality7 !x0 "Q 3

1".) &olve and graph the ineuality

13.) Iraph the ineualities.

a.) xS 0$ b.) yQ$

3x@ "

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1!.) &olve the system

+=

=+

x"

13y

yx

by graphing.

15.) ;se the addition method to solve the system of euations.

=

=+

y"!x

3"y"x5

1'.) 9r. Franel bought $ ticets to a puppet show and spent !3. Ae bought a combination of child ticets for! each and adult ticets for each. 4hich system of euations below will determine the number of adultticets aU and the number of child ticets cU he bought

a.)

=+=

!3c!a))ca b.)

=+=+$ca

!3c!a) c.)

=+=+31ca$ca d.)

=+

=+

$ca

5c!a!

1$.) &olve the system for the value ofx.

==+

)yx"yx

1(.) &olve the linear system by any method.

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a.)

=+

=

3yx

1yxb.)

=

+=

3xy

"x3

"y

1.) The length of a rectangle is ( cm more than four times the width. -f the perimeterof the rectangle is !' cm, what are the dimensions

11.) ;se the substitution method to solve the system of euations.

=

=+

$yx"

1y!x

111.) / rental car agency charges 15 per day plus 11 cents per mile to rent a certain car. /nother agency charges 1( per day plus ( cents per mile to rent the same car. Aow many miles will have to be driven for the cost of

a car from the first agency to eual the cost of a car from the second agency #xpress the problem as asystem of linear euations and solve using the method of your choice.

11".) The sum of the ages of Getra and her mother is 53. Aer mother is 11 years more than twice as old as Getra.

Aow old are Getra and her mother

113.) &olve the system of euations using the elimination method7

=

=+

11y'x

)y'x3

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11!.) 4hich system of euations has no solution

a.)

=

=+

1!y"$x"1

5y)x$b.)

=+

=+

1!y$x!

5y)x$ c.)

=

=

!y3'x$

1y)x$d.)

=

=

1y1)x1!

5y)x$

115.) 4hich of the following describes the solution+s) of the system.

=+

=+

"y1"x(

1y!x'

a.) Po &olution b.) +0$, 13) c.) +5, 05) d.) +01, !)

11'.) 4hich choice best describes the solution+s) of the system of euations

=+

=+

15y5x15

"!y(x"!

a.) -nfinitely 9any &olutions b.) +01, ) is the only solution

c.) +1, !() is the only solution d.) Po &olution

Solve te s%stem of linear ine$ualities b% gra!ing"

11$.)

3y

1x"y

11(.)

(x"y

!xy

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Algebra Semester 1 Exam Review Jan 2012 10-5-2011 Rev