--

./Algebra 1 Name: ----=--=..:~----------o

Your final SOL review! Use it also as a back-up final exam review! Date: Period:

This review is designed to give you at least one example of each Algebra 1 Standard of Learning.

Strand: Expressions and Operations

SOL A.1: The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables.

1) The formula h = 30 + 40t - St 2 h can be used to find the height, h, in meters, of.an object shot upward from the top of a 30 meter building at the initial speed of 40 meters per second after t seconds. Find the height above ground after 3 seconds.

D -=- 30-\-l.\t)C~) - 5(3)~ \S~-4S \DS ~. ~O \- \:A \) - 4S

2) Translate: One more than the square of a number is more than twice the same number less than 4.

SOL A.2: The student will perform operations on polynomials, including ­

a) applying laws of exponents to perform operations on expressions;

+y X 4 -L, \3~~ \\ ( _2x 2y-3

)

2

~implifY ­4-4 dX~~~~ xy

b) adding, subtracting, multiplying, and dividing polynomials;

x + bx-~

_L-\X

)(-3 - ~38) (2x2- 5x - 6) + (x - 1) x

--3x-~1o

~ -3>< ,3 '-/ ----~

c) factoring completely first- and second-degree binomials and trinomials in one or two variables.

Factor completely: ( JJ 29) 4x + 6 d ax +3 10) x + 6x + 8

11) ax' - lxy - 3y' z.. (:::,x j-jX~X ~:.1) -\Z -l ~ '('J.. _ otx~ 4-aX -.3 _ ' "2- ,

3 (;) x-31.\"'\ +-~C.;lx 3 ~')X. SOL ~j: STudents will express the square roots and cube roots of whole numbers and the

square root of a monomial algebraic expression in simplest radical form.

12) Simplify ~~X3y' J)(({ S(sJ- 13) Simplify ~54x'y6z' LJlo q to

14) Simplify ~ Simplify if48 d 'Jlo16) Simplify ~128 f\ f\ f}

~l~ 8 It> Co4a Strand: Equations and Inequalities

SOL A.4: The student will solve multi-step linear and quadratic equations in two variables, including ­

a) solving literal equations for a variable; kJ-7b Sh \..0 -7k.> ?\\f'17) Solve for a: w =5a + 7b Q- .5 - 5- iii- -C18) Solve for h: (surface area of a cylinder) SA =21t r(~ + r). b~ .;nrC

b) justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets;

19) Justify each step of solving the equation:

-6=-2x+3 G\\~ -6 + (-3) = -2x + 3 + (-3)-,-~-=~~~~~'·}'(}J~t\i~W,6.~lil,~w..::~'J.D:~e-.U.1~~~~-'" -9 = -2x + 0 \ . ~.

-9 = -2x -===>",~~.=o...::~_--l't.it.o=UJlio!--\,olo~..>..>ooo>.,,-"";------'--~----'--"\

:.~(~tiil-----,-----,~~~~~~~~ ,/ 9=x ~-~ ...",...r,;. 2 ---'_---=--c===--~{C.':.......r'\...,."t)~1D,o-....=1""-=."-, """,l..Aq-­

I . " ~\

c) solving quadratic equations algebraically and graphically;

220) Solve the equation by factoring: 5 - 3x = 2x Y-= ~, y...-=- \ -:;:( ')( '2 -1 X +-5 -=---CJ - \ d,Y.+-st.x- I}-=-D ~ "F)

I~

- \ (J.x L- +-'] Yo. -5:: ­ I

21) Solve the equation by graphing:-' ~ = _x 2 t xJ. --rd..X--2;,~ \-d-3~-~

'-I ­ ~~ -1- X=- \ 'X -=- -3 ~, I

22) Solve the equation using the quadratic formu

3x 2 +lOx = 4 'J --::., . 'X -:::;.. 3 "') +- \tlx -4- I

Round your answer ill th~ nearest hundre tho - \U ~ \00 - 4L-\d-.J -\0 i:- v 100 l'

(p ~ 'vd) solving multi-step linear equations algebraically and graphically;

23) 6x - 3(4 - 5x) =30. X-=- d. (verify your solution!)

(PX - \~ \ \Sx -::-3D \:i. -~ (4- -\b\ ~1) 'A\ 'X - \~ ~ \ cl \ ~ + -:;..3D\d.. \),

~\'1. - ~) ~

y., - ~ e) solving systems of two linear equations in two variables algebraically a~graphically;

24) 'Solve using the elimination method~3X + 7y = 2 C3> t -\ ) ~-I:?~7-3 l 2x + 3Y = 3 lJ) -.;;; ­

(p X '4 ~ -=: l+ J X -- ~ - 3 01.Px ~qj -Ci ax ~lP

S~ - -s x-;.-.] u- ­ 1\-\~ ~\-

25) Solve using the substitution method: x.= Y ~ -- .3 1 \ 2x-5y=-1

'Y -=--~ -,\ ~ (j -\) -S~~--\

d~-d - 5 =- ~-=--5 - ~\.\ - L- -::- ­

.~ _ l X?- ---l \ -~j - \ 3

1\ \ I

~3 I II

(_\ \-'-\1' \ \ /

.~~ \ I ...

la: " . r\ " \ 1/

'-...j(

-'-T~

.

V

y ~ ~ I \ I ~ II \ . .

I \ ' I

1\ I

\

X \

I I r-.. I II ' \

:\ J I '\

\

2x + Y = 426) Solve using the graphing method:

[d..ID\ 5X~~ I\·SJ\-y\l)

L\ -\- ~l\ V

\0 -~ 0 \\J~

~y "\

f) solving real-world problems involving equations and systems of equations.

27) John's weekly salary is $10 less than twice his brother's. The sum of their salaries is $160,

Which equation can determine'the brother's salary? eX:: .j~,,\5

@A) x - (2x - 10) =160 B) x + (2x + 10) =160 . 'l) . ....l.-~ \.S

'6\~ :r h, - .. .DJ'Q\ C) ) x + (2x -10) =160 D) C. W­

e=> 'T l\O-~X ~1\J) ~ 0 28) A car agency charges $150 a week plus $0.25 per mile for each mile over 100 miles. Bob budgeted a total of $300 to rent a car for a week. How many miles can he drive? :JU) m",\e..S

X ~ -W I\'\'I~ D~ \tDf\n~

jOD - \SO -\- '2£x 6DD \- \CD \C;O ~ ~S X ­i

'X ~lDOD 29) ~ane would like a 90 average on the five math tests this semester. Her average for the first four tests so far is an 88. What grade must she earn on the fifth test to achieve the~ verage?9

\} ~ -\- ~~. +- %~ \-&~ I T X --:::.-QD Q'--'-- S - == -II x~qg 0

3 ~+-~ ~ ~';b 30) Jose bought 9 movie tickets for a total of $54. Adult tickets cost $8 each and child tickets

cost $3.50 ea~h.How ~any adult tickets did he buy? X -=-QC.\.u.St ,~"x-.st:.. ~ .~ ~( X~~ C1) ~ ( - --- ,~ ~ ~t\ ~ t ~P -:: o.L~ -\-i .

( i; '

'iZXt-3P~D.:1:::SL+ 1/( J.\\_--:-,,\,~.\-.\I I

~OL A.4: The student will solve multi-step linear inequalities, including - 4- c...'n~~<\. -1-\ ~\;) ) \ I a) solving multi-step linear inequalities al~ebraically and graphicall "

'0 . '6)( t ~ j ~J L 4 ..~ - \~ X+-Lt=:: o )( -t 3'~J "'-S j.=-tt )( =

31) Solve -2x - 27 ~ -5x - 6. Then graph the solution. S~ 02.7 'SX d7

-7 -5 -3 -1 3 5 7

32) Which ineq'uality below solves 2x - 6 < x < 5x + 127 ~ aX-lr>-<-X Xi-Sx+-\'2­

A) -3::: x < 6 B) -6::: x < 3 C) -6::: x < 12 Eq~ X :7-3

b) Justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets;

32) Justify each step of solving the inequality:

c) salvin real-world problems involving inequalities: C,Frank works at a convenience store. Which graph best represents this situation? _.-:;:;::;;.--­

33) e He earns $7.50 per hour when he frank's Weekly Earnings frank's Weekly Earnings

works during the day. v yl!!.... 50 l!!" 50 :>~ o .21 40 S ~ 40• He earns $12.50 per hour when :I:Z :I:Z

he works at night. 'E 'l;; 30 (~~ 30 () A 1ii -g 20 q~ 20

$300 per week. • He wants to earn at least ..o~

~ 0 10~ ~ 10 i3: .~,­o

I !I

I

~

''-.....10 20 30 40 50 V- 0

I'...

~

'''-..."10 20 30 40 set V

Number of Hours Worked Number of Hours Worked During the Day During the Day'1-=

Fran!'l's W~eldy Earnings Frank's We~ldy Earnings , y y~:::--W en.... 50 ~ .. 50

... .1: :J..cS.21 40 o.~ 40

:I:Z '0 'l;; 30 '0 ~ 30

U B 1ii -g 20 o D 1ii al 20(.r:;olT-\~.9)j? 3CD :I:Z

,c-", ,cE -"" ... 10§ ~ 10 :l 0z3:

z3:

1\ \

\ , f\

" o

I1\ I

I\ I

\ I 10 20 30 40 50' Xo 10 20 30 40 50'(\"~_ 0 0 ~3C)O Number of Hours Worked Number of Hours Worked

During the Day During the Day

"jU<\ ~ =- dL+ -t~

--2x + 5::;: y

-1\' < -x + 2 ~ - 2

d) solving systems of inequalities.

SOL A.6: The student will graph linear equations and linear inequalities in two variables, including ­

a) determining the slope of a line when given the equation of the line, the graph of the line, or

two points on the linej

Determine the slope:

y

\ 36) x = 4 ND~7) y =-2~'J 38) 2x - 3y =8

340) --2- 41 ) 2/\ 42)

y , ,

, x

I\.

X

y

/

1/ x

/

y

x

Using the inequalities shown/ create a system of two inequalities that could be represented by this graph.

y

34) III

'''r-,. ........ fr-.... ..., I I......

- ..... ......II ..... ..... c.- '4 'i' , ;...... ..:. ~.

I 2 __ II

~-I- ­ '.1--r­ -, ." i-,'.,... ,

~ W -~)(\-L-35) Solve th~tem of linear inequalities.

-1 y,­ -x +2

2

-1 ,. < -x f- 2 2x + 5 < Y-' 2

.. S_y

56)

lj;:Ls-\ ~

44) (1, 1) and (5,4) '+ 45) (5,2) and (4,7) -\ 46) (-3, -4) and (5, -4) ~t:> '-'h :~ ('\ {\ \ () U

47) (4, -4) and (4,6) ,J\j:DdJJ~- ~

b) writing the equation of the line when given the graph of the line, two points on the line, or~

the slope and a point on the line.

Write the equation of the line graphed:

51 ) X-:::- ~lo y

x x

, 1\

x

\

y 17

1­/

x

48) ~ ~ ~;( +-4 49) 1:)"'" :1<-3

52) Write the equation of the line that passes through (5, 2) and (4, 7) in both stqndard form and slope-intercept form.

fY\~~ j ~ 5x-\- 7 . 5 6T ~=d.1 ~ - -5(5) +-'0 d- -=:- -dS~b

53) Write the equation of the line that passes through (-8, 1) with a slope of ~ in both standard 4

l fOi~~tP;~tercePt form j ~ l XJr-7 t~-~ '0 n-I

Strand: Functions

SOL A.7: The student will investigate and analyze functions (linear and quadratic) families and their characteristics both algebraically and graphically, including ­

a) determine whether a relation is a function;

54) Is the relation {(-:1, 3), (2, -8), (0, -5), (4, -8)} a function?

Does each table below represent a function?

55) .k - u)\-,~

59) What is the domain of the relation: t--.....:~=---+-~"'-f-'~r---'""'-Y-=-t __

~

..

x

Decide whether each graph is a function or a relationl\ I (\ \\ , 57) M ~~~~!\' y 11' 58) D&.:-IW.L.....,...--

y\ I \ I \ II

\ I \ if

r-..... J x

i

i ,/

b) domain and range; y

l.,.oooi ~ ...."­, " I

II II x \ 'I

1/i'. i."""

~. ;r

Use the graph at the right to answer 59-61 :

60) What is the range of the relation: \---l-4--"'O,---+-\",-+-~>--------\

61) At the point where x: -3, what is the value oly?

62) Which describes the domain of the function shown: ~

y

r--:", b..

I\. r\.

" I ....... I ~ '\,

x ~ I

\ II ~ '/

\

Ii.

H-+----ftc-l-t-t-+--t-l\-t--+-+--t-t---H x

~? B) -6:: y :: 5 G,~I,./ C) 5~X~4 D) ~~y~4

Which describes the ~of the function shown:

~

c) zeros of a function;

63)

64) The graph of f(x) =x 2 + 4x ­ 5 is shown.

Identilyeach solution to I~l

X-=-\ \ X-::: -s

d) x- and y-intercepts;

67) Identify each function that has an x-intercept of 3.

~?(X)~-4tY ~ g(X)~3~~X' X (:i""~ h(X)~~~X-5 X i)\<t- S) .., ~

vlLD j(X)~(:+3)(X-5) X l~\('t -..:>,5 1_ )\_ 3) ~D C-7k(X)~3X' -1lx+6 ~ l? X-; 'i(~j ~

\. ­

~ e) Finding the values of a function for elements in its domain;

- \ - \ t-\ 68) f(x) = _x2

- 4x + 8. Find f(-3). __\-'---"\'-- _ -91-\~ +-~ ;)D -C) -9 -f)t-l j ~_

69) What is the range of f (x) = _x2 - X + 1 if the domain is {-3, 1, 2}? L-5 )~\ \f

f) making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.

SOL A.8: The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.

Determine if Y varies directly or inversely as x. If so, write the variation equation, \\' - --.L ')\1 --" - YD N '

70) \,/\J'\.9.L\ \ ~ ~01\ 71) ~ ,';6 ~, X 72) -----=--~.g,,;~~~=='""

~ ~-10 ~ ~L---,-4_

~~ Xj~~b

.CD

73) Which graph represents a direct variation?ky yy l'

A) r+++-'H--++-H-t-+-H-t-H B) c) D)

x x

y

x

74) Y varies directly as x, and y is -48 when x is -8. Find y when x =7. U -=-~~). tJ ::::- 4cl '!J -:;.~ -~C( -- - ~O- 0... ~ lD .::J "3 'j -=- ls, t> 7

75) Y varies dir~ctly as x)and Y is 2; when x is 18. Find y when x =6'J~"iX j j::=" ~-:::.OJ( ;},'"I - \k CA... -:r \~If J " _ 76) Y varies inversely as x, and y is 23 when x is 8. Find y when x = 4. ~ ~ T ~-==--::tWJ j~~ ;<3 -:::;- Q-=-\'(4- \6'iJ4 -l~ 77) Y varies inversely as x, and y is -g when x is 16. Find y "jhen x =-3. j:=- -Xj 2:J =4% j-:W-~ -OJ-;.."\ ~~-\Y4 -t4L\,-3 78) The volume of a ga't varies inversely as the pressure. If the volume is 80 m3 under 4 kg ofVpressure, find the volume under 10 kg of pressure. \} 3>:t 0 '2') '3

CL. CA.- V-- D _-~

V =- ~ '60=- ~=3dO ~) v- ~ 79) The weight of an object on the moon varies directly as its weight on earth. On earth"~n object's weight is 90 kg. But on the moon, its weight is 14.4 kg. What would be the weight of an

Obj~the moon ~ ea~-:~h~SoJ~~) ~o.lloE' \~4J d 'A~ \~ )

~ 0.\\0 \2D')Strand: Statistics

SOL A.9: The student, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standar9.sle~tion,~

y -::. ::JiP..Q -;:...<6D Using the data set {80, .90, 75, 100, 80, 60, 75}, find the.: 7

--

d) x- and y-intercepts;

67) Identify each function that has an x-intercept of 3.

'f:7t(X)~ -4V ~

9(X)=3-!X2 X (;j2

5h(x) =--x-5 X 6Jl

3 Xvitj) j(x)=(x+3)(x-5)

C-=,k(X) = 3x2 -llx + 6 ~

l)\ \(\\"

e) Finding the values of a function for elements in its domain;

-I-I+-\ 68) f (x) = _x2

- 4x + 8. Find f (-3). __\-"-'\'-- _ -9-\-\~-t--~ ~D-~ -9-&1-1 f ~

69) What is the range of f (x) = _x2 - X + 1 if the domain is {-3, 1, 2}? L-:S J~\ \ f

f) making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.

SOL A.8: The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.

Determine if Y varies directly or inversely as x. If so, write the variation equation. \"\ - ~ ')v '---7 YD N ....l-\

70) \J V\QL\ \ b~cN\. 71) ~c-i--_.X· 72) ..Q....\ ~--'-----'-......0.....-..,---",---....;..-\

.~

~ ~-1°1[iJIEuJQ]~JIJ ~_-4_

Xj==- ~b

ol-..l.---I:lJ-.:lJ-~="'-±:f:=Jt:=~::JI---l_-l

41------+.-::i<h1l"-i

21--~oh'

81---------it---7~----__I

61--------dt --m

82) Using the table, which of the 4 students raised the greatest number of dollars?

Mean for class Standard deviation for class Student's z-score Jill /9 ~ ~ellQ &- ,.~

60 58

11 12

1.8 2.1

Monroe --,~.J. 55 13 1.4 Tim ~ l­ 57 10 2.5

~ '" -~~~'l- ""aI\\J\~ X 13" 2- ~~ . ili1L- lJ:2 ;;(, \ ~ 1< -s~ \. Lt==-~ ~ x-S7 lo~-::- ~=1C1.~ \'1.- t2-> \083i The data on the annual rainfall for 32 cities is summarized in this histogram.

>(-=81.­• The mean amount of rainfall for these cities is 32.5 inches•

• The standard deviation of the data is 4 inches.

On the histograml identify each interval tha~vedata points within 1.S standard deviations

22 26 2 30 32 34 3 3

84) A data set has a mean of 68.42 and a standard deviation of 7.91, An element in this set is 57. What !:'...the z-score for 571 Round the answer to the nearest hundredth. \ I

Z =- i ~Y L - S1- ~~~ L. '--;; -\" 4~ D 7~ct)

SOL A.1 0: The student will compare and contrast multiple univariate date sets, using box-and­whisker plots. .

85) Draw a box:-and.-~ker plot for ~~n data b~Sl;.it 3~' \~ isr~~~'~" ~'~~~i7~lt~" ,3~·"tJ'

"'0 31 'I ~ . ~

18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38

\

•

of the mean.

10

13 '.i:J

~ o ... ~ E :::l z

C/- \ ~+ 1)

Annual Rainfall of Cities ~d ..s- -:;..~8 IIS 3~/S +-4- -:::. ~ ..S

\ & S S-\­~ %.S -, d - .:)to.S

co­~lo~S d ~ ,,~

Annual Rainfall (in.)