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• When y is by itself, we can determine the 'Slop^>. _ and the \J — ^OV^PQ^3) Identify the slope and y-intercept of:
^\opel^ 3y-irtterc€p+: i°)~'Q^
4) Find the slope and y-intercept of:4^+ 2y |= 16^
^
M^[\^-^ ^opci3-^^2 I
^nteceph^ io.s)
5) Write the equation of the line that passes through the point (1, —4) and has a slope of 3.
\^^p^y^b.-4.5t ^^-b-4^^ +b
--1-- b
^^1\
5
6) Write the equation of the line that passes through the points (1,1) and (3, —9).
-I
m^^-v, ^-(Yz-^ 3-
\/ rfnx -^bI ---C)(Q ^-^I ^ -*5 ^b^ ^^L) ^ b
-10z
= -5
T35-x-^
7) Write the equation of the line^hat contains the points (-3, -4) and (-9,0).
m= Vi-Y, - o^^ - ^ _. zx^-x, -cl^s -^ 3
\^ ^ n^ x ^b0-.-l(-^).b
3
^-1,-.0-^^b-\o -I-b^b ,p^<x\ 50^
8) An exterminator charges $35 for a service call plus $50 per hour of service. Write an equation in slope-interceptform for the cost, C after h hoursof service. What will be the total cost for 7 hours of work? 10 hours of work?
C = 5^ + ^'5
~1 hour'sZT%oC-;^ ^ 3)5(c-^^1
J
O^OLLT^~C-^ 5600^^36l^^isi 6
Linear Inequalities:
Lines: 'U^'&It^U when < or >
c
Lines:
^^l^d when<or S
Shade: b^l 0\AJ when < orCltev-€. when > or >
: or
^\6,9) Match each inequality with its graph. Explain
your reasoning.
a. y < 2x- 6^ ^0\ ld^ \Q^| 0^'b. 2x-y-^6-ly.
da<sV^j beiow
-2X2-^ • - 2x ^
^.^- ZX-t^ to^low'
c. 2x<\-{0
2K-^
py+6
q>Zx-^
d. 2x-6^y
-^ (3)dasW.^ , ^atoo^~"ay>^vt
y r^^ ^ i -^^Q ^0-bovt dashed,
OK^VC
21
^SKSSK -10x x
y y^1
43
Dx
^01 tCi, bzlOA/
10) Graph 2x-8y^
-2x24
-ZX^-2X^-24
^
^ >. Tj X -3
Solid. 0<bo^&
y
s\\^^^ Kffi^ s^^ wffl^ N1\
M 1\1 1\M\1 ^^^ »
\s \
x
m
b
^
-1
Name a point in the solution: to 6)-)-
7
311) Graph y<^x-7
do^s'v^dj belckM3
m= ^
b: 1
Name a point in the solution: ^ '^
yr
^
^/T I IN
J\
^t
v
St'3—N I N n<
rrN N
KLN.
S4
x
^
^>
12) Graph x ^ 5
Solids above
m
b:
undffine.cl
Name a point in the solution: ^
y
^<;
x
Hi
13) Is the point (4, -9) on the line y = 2x- 4. Explain your answer. Use of the following grid is optional.
\l--lx-^^-2(^-^-^--<?-^-ci /4
Mo, t^,-^ is not »point on the \i^\/=Zx-4 becojiAS< -<?^':/ajnd i+ do^ nol- .^'e on ^ne
y ^
^
I
M
j^
x
^
(^4 11
dfe±
8
rName
(
curteK^RevreuFoundations Final Exam Review
.v^<»•'
1) a) Solve this system of equations graphically.
-(yy= a-4-10f4y+2y
1
-4
-IVK'^4-^x-4
Z 2-^-Z^-2
Solution (-4,^
b) Solve this system of equations using substitution:
(4x +2y=10y= x-13 V^'X-i'5
4x ^z(y-^^\oL^^ ^'2-y -2G? ^^o
L?>< -Z(fc ^(0+ ^ +2(^(^y = 3^L? ^y --^o
y^(o-t2>v^--i
Solution_ CQ>>--IN)
1^ A"^
ti^£G:
j4^ ^-l^-i-U J
-r-
\
-!-
t
^y^-lx-2
c) SolygJLhi^jystem of equations using e//mf'not/on;
Solution to, 2^)b) Solve this system of equations using substitution:
4x-y=20-^ ^ -^^^0l-2x-2y= 10 -^|X -4X
.2x-Z^^^-^+^-2x - ^ v. ^40 f^lO L^^ 4x -zo
-lox-^3j',°o |:w^°|
c) Solve this system of equations using elimination:
J^^x+3y=13)-9 ~l(^K—(^^ ~'Z(£?^l3x+2y=ll) ^ ^ ^ ^
^x
-»
[•^ ^ -8-10 0
X -5
Solution(5.-X\
^ -2^L^<"2~T -"7X=-1
3C-i^^pt+2Lt t \'
0 ^^
41z
^-~1^u^}Solution
10
c
3) Answer part a. Then use what you found to solve part b.
a. The school that Bronte goes to is selling tickets to a choral performance. On the 1st day of ticket sales theschool sold 3 adult tickets and 1 child ticket for a total of $38.The school took in $52 on the 2nd day byselling 3 adult tickets and 2 child tickets. Find thej.u.ice-aiamidtdUicket and the price of a child ticket.
Lev adu\-v -^c^s> '-^^G,V><YA-^C^^-=C
(\^\-v CO^TV^c^e-te-HcV-e^^dTenOr>d t\\\
1^^
cost
Find theju.iceeaf-en-adtdULcket and
-^^c.7^)'^-(-ZC-52-^-tc-^
C = i^l3LOk.N>+U'^\?>S ^.^-5a 4-l-^yl
b. How much will it cost for a family of 2 adults and 2 children to attend the concert?
2ti
^0.
^ d -- tos^ ^ 2ft^ ZC^d'indcA^ 2CS^2(iM)=ci
L)^zd
CO ^++^6v/^axYd-C-1-t^4 +t>fomi ^ C^ncerha-^d •^e
4) Colonel Dickinson is giving a test with 20 total questions consisting of multiple choice and true/falsequestions. The true/false questions are worth 3 points each and multiple choice questions are worth 11 pointseach. If the test is worth 100 points, how many of each type of question are on the test?
3. When factored completely the expression3j(2 - 9x +6 is &quivalent to
(1) (3x-3)(x-2) (2) (3x+3)^-2)
(3) 3(< + l)(x - 2) ^(4)5 30c - 1)(» - 2)
§X2 -c\ X +^^ 3
3(X2-2>X+^3[X-lUY-2N)
2.
a.c=i-2--2• -32
3t .2>
-3-2)
(4x-5y)(4x+5y)
(2) (4x-Sy)(4x-5y)
(3) (8x-Sy)(&«-+5y)
(4) (&r-5y)(8x-5y)
JU?.
X7'.26'.
t
4'x-Al
f^\ft/XT
1^
^5
^(Mx+5^y4x-5^
4. Factor completely: 3xt+15x- 42
^^15x -^2,5 3
3«^5.-^ a;^^.^jq|4-5
iT7-z^ ^ +^ ^^
18
5. Factor completely: x3 + 5jE2 + fee
)(34-5x2+^^Y "7
a.c-.i-^X(xz+5x-t-^ ''.Jl+5
.ynir><j\<»
Z Express 4j^J-25^as the product of twobmoiiMals.''
Y^T:..
^Cx^^ ^itj)
•r\
4-. 22 . Yy^
^
^5/f25;
^^(^-5))6. Rictor coinpletdy; 2x3+2sz-l'lx
^ +^x2 -_11^ ^p( 2)
2x(x2+x -^a-c ^ l --^
Y-Z^+^
+1-(^
cb-I ^)
\^,^
8, Factw contpletely; 3ri + 5rz - 12f
;^^5t2-l_2^ &.C.3.-U•^ € ~k .^j^
^(3^+51 - 12^ -iT^~/\ -Z,CS(
^^ -^-l2) ^•3F-3T -^ -¥
35t^
^?-
^(%^+3)-4(*^TT&t-^^+s^
9. Find the vertex and axis of symmetry of the equation y = 2xz - 16x + 3
V^2^)t-1^4)^ -^. a':2,,2& ^ b"'^
^-"zt? Y---(-\^ C=3.20^(wtex-.t^,-^)) ^-
10. Find the vertex and axiS 6T symmetry of the equation y = -x2 + 4x + 3
t.-n.}^%i)^ ^^^y^= 1 ^-i^x
WV<x^] x"%19
v^
Name
1, What arc the roots of the equation J(2-10.r+21 =0?
A. 1 and 21
Ci 3 and 7
B. -5 and ~5
D. -3 add-7
(x-3)(.y-i) =oX-3=c>+3 +3Y=3
\-~i^a+~1 v~1Y=~l
3, What is (he solution set of (he cqiiation^^x-QsQf
Foundations Final Exam Review
2. The roote Of the equation 2x? ~ 8x= 0 are
A. ~2 and 2
C. 0, -2, and 2
B. 0 and -4
LE^ 0 and 4
^2^ ^o^ 2i
2xCx-4^o2x^^ k-^^o
^4-4x^
Z 2|x=o|
4. What is. the solnttoo set of the equdtioitjt2-3jc-4=0?
(^ (3.-2) B. {-3,-2}
C {-$,1} D, (3,2}
CX-31^+2.^0X-3^q
+3+3X=3
X+Z^O-2 -2y=-2
5. What is the solution set of^2-jr-20 a O?
a-4}c. [-wai
B. {-5,4}
D, {10,-2}
(x-5yy+Lt^=oy-s^o
^6 +5y^5
y^<4 -'0-^ -+x^-4
A. (-3,1)
C. (-4.11
B; {4,-l}
D. (3.-1}
(x-^Cx+t^ ^oX-^ro+^^y--^
X -»-( ^0-I Hx---\
6. What is the solution set of the equations(r-aX.r+A)=0?
^ (a,-A}
C. {-a.-fc]
B. {-fl.A}
D. 0
Cx-oi')C^<+'o'>^^x-a^o
+o^ -vc<
y^(X
y ^-^^o-b -b
x^-to
20
8, Which type of function is graphed below?y
^»-x
A. linear B. quadi-atic
C.) expOrteatiaI D. absolute 'ralue
9. Which oidercd pair is a solution of the system ofcqiiatioos shown ia dMs graph bctcw?
y
\
)A4SJ
^^
(
-I'Mpr^I ^
r<
^
*-x
A. (-3,1)
C. (0.-1)
(-3.5)
D, (p,-4)
10. Solve the following system of equations graphically:
y=x2-4x+3 —^ )(y=x-l
rvi--iI
b---'
-I0
2
45
?50
0
5s'
^^^
^^
-^-lN(^
^^
z
frX
^^
^
\i\)0} Oa-id 14)^
21
Name Foundations Final Exam Review^
CUPtCR IBI Revieu1) Which graph does WOT represent the graph of a function? 2) Which interval notation represents
5< x < 7 ?
D y
^
\v
2) ! 4)
1N̂
y
M
\
4
^I/
/
D [5,7]2) (5,7)3) [5,7)PS (5, 7]
\/
2) The value of a diamond ring appreciates at a rate of 12% each year. Findthe value of the ring after 7 years if the ring
was originally $7,000. ^^ ^.^ ^( ( ^ ^0"
c y^^oooCl+'.i^'^al5^'74.-l'l
3) When 5x2 - 6x + 10 is subtracted.from 6x2 + 12x - 8, the result is"(W^S
(oy^+izx-y-^y?-^^os)?\
Wl^/-ttX 2 5x +L3X/-1
p~+l^x-l^I4) What is the product of 2r2-5 and 3r?
^~~>3r^2r2-^
1^~\^<-\22
I
5) (3C+4)2
(x-1-^^6) (3x-6)(2x+5)
x2 4 x Mx +1 CD
Yl^x +1(^
7) What is the product of 3x4y and -10x2y5
3x^'(-loy2^^ Q»2o x '4 J
3v -L,
2xz-\ly^y
i5y ^-30&
G,x2 +^K-30
8) Factor Completely:
a. x2 - lOx - 24
](x^)Cx-iz^C2,-i2
-2^1-ffOb. x2-64 T>C3?<S!
25/o
X2:,
^i> ^-^A^
x x¥ V -
Cxt-^Cx-^
c. ^3+24x2+36^
^X 3x 3<<
3x^2+Xx+ll) 'Jl}4-—^}^(x^}^^)
»»^G^
9) Find the roots of the equations:
a. y=j:'-10x-24 •-2ill—t0
0^-vi-lDx -2^ _^TO^C<+2)(A-IZ) -2,111
X+2-^-2'Z
X-(2^0 2'~12-M2 +/1
23(0
-<0
y^izx-z
b. y=x2-64
o^x2-^2X':
0=(^«)(x-^^-1
^\/.y
ss
y^^-s-s
y -?roH ^
"x^T^^23
10) Find the vertex and axis of symmetry of the equation y =—2x2 + 12x —8^
V---ZC^2+»2t$HXC^V=l° Y-OZ^
a—zb=120^-^
fverV-w -- (3,' o)|._^•- ^^t' ^x^
11) Solve for x in eadi equation or inequality, and justify each step.<1^.^. •"'""•'" "~r ^\ /-
a. 15x-3(3x+4)
l5x—qx-12^
+12.
c(p
6
CP^ ^. prc/pCLT
b. 2(x-4)^f(5-3x)2x-^ ^^ -^,
-?
(px -12 -:f(^_ p,^^. ^x1
+12. A-
(j>x 4 II ^.^r\.5x-^-^l2
(p ^
+ x
tx-r-2j x
2
^
Zl>-y^fv7 2: 5
12) What is an equation of the line that passes through the points (5,1) and (—5,7)?
m=^-V, - -'-' . ^ _ -a^^->, -5-5 -10
^^Vn^-^b1^-1^^
5
&
y^ ~i x +4^
i^ -3 J>-^ b=t4r3 T3
13) What is the slope of the line whose equation is: 3x — 7y-3x
9
|-3x^ -3x +^ct
--7 -~?
DiS^-. pn^>.
A.Xn..
A.x^.
M.IK
=2x-^^^ -=j
m^ s_-1
24
14) Kevin went to the movies and bought two jumbo popcorns and two drinks for $17.00. Robert went to themovie and bought one jumbo popcorn and three drinks for $15.50. How much does each item cost?
f> ^•'^
same
L^-pcyco'fn = "PL<adnn^& '- d
^£_,_2d^l "1.00-2'ZTp+^>d=>15'50^
popcorn co^ $5.oolOnd dnn^ costjrs^i,c'->'s,.
^\J
2^^id=n.^o-y? -Gp^-3i-^
~-qd=-14~?^-^rId ^5^0
(p-3C3.9C>)=|5.56\p ^- io^o ^i5^
^/^66 -^_06fp^s&00^
15) On the set of axes below, solve the following system of inequalities graphically. State a point in the solution.