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Algebra 1 FINAL Exam Review Name:-----''--"'----~'''--'''-___>."d:op;.___----=_.!'''T_--
DUE DATE: _ _ Period: _ Chapter 6 - Solving linear inequalities, graphing linear inequalities 2012-2013
• Number lines • Coordinate planes
Chapter 7 - Solving systems of equations (including word problems) and solving systems of linear inequalities
• Solve by o Substitution o Graphing o Elimination
Chapter 8 - Exponents and Scientific Notation
• Positive exponents
• Negative exponents
Chapter 9 - Polynomials
• Adding • Subtracting • Multiplying
o Distributing o Foil,
• Factoring
Chapter 10 - Graphing quadratic functions
• Parabolas
• Vertex • Axis of Symmetry
• Opening • Width in relation to the parent function y = x 2
Chapter 9 and Chapter 10 - Solving quadratic functions
4~S ~~c; ~ • Solve by
o Factoring Q~~~ o Graphing o Quadratic formula
L\~c;st~~ 'S~ tbChapter 11 (11.2) - Simplifying radicals
Date:
--
Chapter 12 (12.1) Inverse and direct variation
Polynomials Division (12.3)
• By monomials • By binomials
Chapter 3 (3.8) Solve literal equations
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You will be allowed to use your SOL formula sheet on the Final Exam!
Part 1: Solving inequalities - Directions: Solve each inequality and draw its graph.
1) 7(2 - v) ~ - (v - 8)V~.\ ~~~-t-.-+--+---. IL-\- U~-V Ol2.3
LU IU I
2) 4(x - 3) > 3(x + 4) - 9 X "7IS l\x - -:A /' ?J ---t. -\-YL-~
L\.x -\2... / 3 -X T-3x ,,'1- -:ox \':J.
\ L-&' 3) 2(2b - 1) - 3(b + 1) > 3b + 7 '0 "~=jIiii:~--+----I----+---.
L\'o-) -3b-3 7 6bt-1 '0 -5 73b +-7
-'0 =J -'0 -,
- ~ /aD -;;:~
-l97 D
\ L L\--'2 'X - 0<5) -2 < 2x - 1 :::. 3 \ \
- -\ 0 \ a - \ L~X:::Lt
to. ~ '
-~ LX I- ~ '2.. 6) 9 - 2x > 11 or 9 - 2x :::. -1
-~ -~ ~ -y_I-_-~\ ----..:.......:.---=...'tt":?~__r__r___r___r_........~
Part II: Graphing Linear Inequalities - Directions: Graph the linear inequalities.
7) Y
~ ~
o L --3>
t~
Solve the system of linear inequalities.
3 y ~ 4 x
9) 3x + y >-3
1 Y :::;
Part III:
11) Y '" -- 2x + 2 x-y=4
y
2x .::: - 3 f--t---+---+--+--+--+--t--J-+---+---+--+---.IIII*"-h-+...o.,J
~')( -3 f------I-+--+--+--+---t--+--+-+___+___+_~
Systems of Equations x+y=O
~~ =--..-I--+--+--+-I---1---+--+---1 X
12)
\Solve the systems of equation using th),graphing method. 3x + yy =-8 -!
'"'\
" ,
" ,\ ~
\)< \ '\
"' \ "'\ \ "" x
IS :'\ '\ "-\ r'\
" " r'\ 3"\ r"\ ,
--:J ~
1--t--+--+---+--+---+--+--I----H....l:-~+--+---l-t----1x
f---i-+--+-l--+--+- ---I--+-+----\-+-+-+-+-lF
y
3 !'olo:::-+--+--f---+--\+.T--4'-.:-jq-!:,-f.,-j.-""+''--''h-'"+'--\~+--f'''''''''
2 x + 2 Hr+~-':+-"~~
2 8) y> -"3x + 1
----
~ Solve the systems "Si:(e S,"bSti:)O" method.
x - Sy = 6 13) \
3x - 2y = 5 .
3)( -2~ --=-5 3(5 ~lo)-'2- -:- 5 \S~ ~ -'L~ :. 5
3 +- ~ ~5 -\~ -\R
~s)( -\l.\y-=-I.\; \.A 'I \~ -\b
3Cfx - ~ -~ ~
X-==--\ 35 -2-h~\S -q - 2-h -:;.- \~
q '1
- '-"" -:::- 2.J-\ ~~-\L-Solve the systems using any method.
17) Sp+12q =13 t-\ 3... J 18) 3Y-6X=24~ . 0:0 ~ri ~ \\1.' .3 (3P + 4q = 3 ' Z- 8+2x=y -D~~
~(.lX+-~) -lox -:0-;)45 -\-\L~-=- \3> ~~ -=~ lox ~)l\ -lo X -=-~e C1 ~\lc\.. ~ - - 3 +-1-\ -:. 3- dl\ ~~4-- ~ -.~ 4~~
~;\ ~-~ 4
Part IV: Exponents
Simplify. Give answers in terms of positive exponents:
5 ~i% ~U (19) 1~·~ c,j 20)
;Y~ 3xy·
::,~~20 j
Oi ~~ CL 3a2 ~
23)22) -..;-24ab ~ 8b 2x 3
ic..L I -::: - ~b ~a..D ls>4 r:/. 'C?C)
<6~ 24) 14x-7 ><7 20) (Z-2 )-3
L..;-(L)32x
_ X le -
\dS 2J3
-~ 5
-1 J2 24) (~: J~ ~
~)~ LX'Y''' 23) (:~22) (;:J
Part v: Polynomials - Directions: Simplify.
25) (7x2-3XY+4y 2)+(2X2-xy_ y 2) Oi x?..- 4xj 'r3~L.-c2<>vL -\-~-L\
Ja.J.+-3~ \4- _;;.;:- ~:~ , L\ct"> + ud- - 1..\.<>-.
1.
27) (5x - 3)(2x + 1) \ bX - X-3 28) (3t - 2)(4t + 5) \d±£-~Ih- \D -\.R"X +- Sx ~~t \st
29) (x + 2)(x - 5) X 1,.. - 3x -\D 30) (x + 3)(x + 5) X"2-4-8 X + S
31) (c + 2)(c _ 5) ~.J. -~-\ D 32) (2a-1 )(2a2 + 3a - 4)
Part VI' Factoring - Directions: Facr completely.
33) x' - 11x + 28 L~--1'lx-4 34)
235) x + 3x - 54 ()(+~-y 36) x' - 10x - 24 (j. - \'d-J6s.+-~
&-~r3) 38) x'-3x-40 .L,,--ilx\-s) 39) Sy'-16y+3 (Sy¥~-3) 40) 9x
2
41) 3x' + 2x- sL3x.i?tY,- ~ 42) 3x2 + 19x + 6
44) 4x2- 49 (")..'6- Y-~X+--,)
+ 3x - 2 ~~-4---A--~3~+2) +~
Part VII: Graphing quadratic functions,
45) For the~(":O~ j~ 2x' + 1, find all olthe following
a) Vertex: \ b) Opening up or down: '\. !~ ~ \
c) Maximum or minimum: ---'-'-'1...Jl....'~c.=.~=:::.JL..li.........-..J
d) Axis of Symmetry: _~_-==--
e) x-intercepts (solutions}: _-.l~U-----!~~~~""'''''''''''JJ\
f) y-intercept: J b \ \)
g) Narrower, wider or the same as its parent function y = x 2
/,
I \ II
11.'
\,/ ., ..
... " ,
f\ CU\ .T II It
h) Graph:
6
I
\,
I'
J
\
\
\ \ 1 I
-I-H--+-t-+--+--+--+--++--If--++-I-+--+--+-+---1
'\ I
---. --- - ---t-Hl-+-t---f--il-t-++-t-+--+--t-+----j / --~-+--+--+--+--t-tt\-t-I-+-tt---/+---+--+---H--+-t-H
f----I - - -+-+-~~D--+--+--+-I--+--+-I-+-+---I
H---+--+-+--+--+--t-f--t-H---+--+-+--+---H-f-+--I/
I-+--+--+-+--+----H--+---+----I-·-+·-f-+--t-f-+--I-f-+--1
" 1--1 ·--!-+-I--+--+-I-+-I--I-+--+-+-+-+-II-I '
"
'S 'f;-\ :=::=::::-=:=-::--+----II-r--+--t--II---+--t-+---+--t----+-----1
..D \
\ f) y-intercept: ~lo)
f\. tf1 """ \-\r'!l
~WJ'\\.. 1 246) For the function y = - - x - 3, find all of the following:
a) Vertex: CD \-3L b) Opening up or down: •
c) Maximum or minimum: ri"'C'Q.ti}..X!\~
d) Axis of Symmetry: '/... --=-0
f) y-intercept:
g) Narrower, wider or the same as its parent function y = x 2
h) Graph: ~(>< +-3Yx-\) :;),,('1.L.- ~ '-~-3J
47) For the function y = 2X 2 + 4x - 6, find all of the following
a) Vertex: ( -\ \ - ~_ b) Opening up or down:J~ \ \
c) Maximum or minimum: rm\.X'\U'IT'\.~ J
d) Axis of Symmetry: 'A-:::.--\ e) x-intercepts (solutions): X-==-3 I '6:=- \
2g) Narrower, wider or the same as its parent function y = x
h) Graph:
~ ~ _\(,/l.- lJ,)<. -l--S) ~ - - l't 48) For the function y = - x 2 + 6x - 5 , find all of the following:
a) Vertex: l?) I 4,J-- b) Opening up or down: --===-_ \ \
c) Maximum or minimum: ~~\1~....;;,
d) Axis of Symmetry: >< -=-..3 e) x-intercepts (solutions): X7:- \) Y. -::- 5 f) y-intercept: L() I - s)
2g) Narrower, wider or the same as its parent function y = x S~
h) Graph:
7
Part VII: Solving quadratic equations.
Solve by factoring.
49) x2 -x-6 = 0 X ~ ~\ -"7.()<- ~i-L):="'O
52) x2 + 9 =10x ;("7-°1 1 \
t L_ \ X ct ':- D
Lx-or Cx-\ -=- D
50) 2x'-5x-3=0 x'=--~\ 3 51) x'+25=10x I< =-5 l~'X ~\'Y.f - '3') '=-D x1-- \D)(-\-dS =-D
(X -s"( )(- 5) =-D
Solve using the quadratic formula. Round answers to the nearest hundredth, if necessary.
Find the value of the discrimant. Then use it to decide how mamy different real-number roots the equation has.
59) x 2 -2x+3=0 -~ 60) 3x2 -8x+2=0 '-\D 61) 9x2 -12x+4=0 D \ t 2J'-- 4(~1 (-'6)'--'-\( :Xl.) (-Il-Y- liectY4 I
L\ - yL \0 - 'dL\- .L\L\- - L\L.\
Part VIII: Radicals - Directions: Simplify the radicals.
63) ~48 L\S3 64) J50 SJ7A \\p 3 :J'S" '2....
66) J99 3~ 1\ ~ t,
69) 213·13 2·3
74) __
J7f nl(" 77) if40 ~ ~ss- 78) if56
t'\.,. f\ lSS ~7
80) ~ 3 ~J3 81) ~:fif\ 13 5
71.3
fu ~ 1 ~
9
Part IX: Direct and Inverse Variation
Tell whether the equation represents direct variation, inverse variation, or neither
85) xy = -2 86) Y = x 87) Y = 3x-1 4
88) The variables x and y vary inversely, and y =-4 when x = 6. Write an inverse variation equation that relates x and y. Then find the value of y when x = 3. '/... -=- 0.
\, (-L\')-=-o-' _L'-\~o.-
89) The variables x and y vary inversely, and y =5 when x =-3. Write an inverse variation equation that relates x and y. Then find the value of y when x = 9.
x~ :::-loO 90) Tell whether the oredered pairs {(-20, -3), (-12, -5), (10, 6), (15, 4), (40, 1.5)} represent inverse variation. If so, write the inverse variation equation.
Part X: Polynomial Division - Directions: Simplify!
x-~ x-\ \ '/... l _
G )( 1-_ ')(
-~~ +3 -~x +.3 -
I I
-----
1Ox 2- 5x + 15 96) -3x
3- 6x
2 + 12X X1....+;]X - Lt 95) -5 -3x
Part XI: Literal Equations ~f\
1 £.: -::;:;... \,...97) Solve a + by =c for a. ~ -::. e.,.-'oj 98) Solve A = -b'll or h. _'----__-=1.J=__
2
'oj -~
1 . 99) What equation do you obtain when you solve the equation A = -(b1 + b2 )h for b1 ?
2
AC) b =--b D) b = 2A
1 2h 2 1 h-b
x X2
d f1""=- '0 \ +bL-. h
-
11
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