unai m- heu · unai m- heu [p..35—,t chapter 2 review pg.1-4 pg. 5-8 chapter 3 review pg. 9-11...
TRANSCRIPT
unai
m- heu
[p..35—,T
Chapter 2 Review
Pg.1-4
Pg. 5-8
Chapter 3 Review Pg. 9-11
Chapter 5 Review Pg. 13-14
Chapter 6 Review^SB.Vi'SiN^sess
Pg.15-161
Chapter 7 Review Pg. 17-18
Chapter 7&8 Review Pg. 19-20
Chapter 8&9 Review Pg. 21-22
Chapter 1-9 Review Pg. 23-26
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Name Foundations Final Exam Review
ckQptemnRevieu
Define in your own words the following properties:
Additive Inverse 1^(- )^ \Aih<-r^ i^D.Jl mnC^l FX 4^rT^ bu, do^nq.-^rvf. C5ppo5<t^ ^adrl or ^jLbn-/irJ-) ^X\ 5-5 (yru-^+^
Multiplicative Inverse V\)hei^ L^)(A IDld+lpl^^C rltVl'dC tX^-H^.mJp^CCL\ -V-D cr&nc^\ ^^ 6-t o^-'-I.nT
Distributive "r^nNQ-^^ ^y^D i^o (jL ^nLL<-ri pl^ 4W. nutn<lh^'ou-h^de -vW. ^rir'ei^-^e^ To fV^e. r^TmS ^ side
Commutative_ Chcunaf. Ord-er ^ 2tl =.1-*-2
c3-2 =/Z-3
Name the properties for each step:/5T^_.3(,2x+'7)+9=4x-6
6x-t-21^-9)= 4x - 6 'TN)^^. pTT^p.6x+30 = 4x- 6- qy -^x2x+30= -6
-30 -3&2x = -36T ~Tx=-18
r.LTA-Tn
^L
A.Tn,M. Xn.
Solve the following equations:
1) 5(6+4)-6&=-24
\
g+zo@r-24- GLTr-lb.-Z(6^-2^
-^0 |~20-Jb.f-^i M.To.-1 ] -\Fbrt+tl
(\.Xn.
1
2) (2fc)- 6 fr 3&)
5to\^^+^+
iS>b
14
1^^
CLTMn {,
^°. MXn^
@
hh 51-8ch-7^(M-5c ^
18
--\'6 CLT
1-13 f^In
^ wnc^\
/TV.3) -2(0-3) =-8 ^-<'-2q^-^ u(i
-(^ ^-Dn,t±i-^Xn
-2
^ -!
/^.^..- --. ^..5) 2(^l)^3fe+5 "^{^t 0^-^7pZ\^W ^-^k |-2K
2^+-^ AXn-51 ^F^^l
What numbers are a part of the solution set? Circle all that apply. (There can be more than one)
6) -7c-\8 -11-?-^1
^t'-^0
--7
-I^(^^
a]
c) -4
x7) "1^23
4-1y
^}
^if3-5yi(1
,'a)) 3^4
X-3@>
"bD 9d) 10
2
•^ 0\^ r^o^\ nuunnV^jr^
Solve, graph, and describe each inequality:.<^\. >
8) 4(l-2t)^>
^-^-h
-•&t^-yE
/y\28 9) 4(w-2)-iv
28'-4•21-s
Nw)-X-^ -»o
3w -^i -10^
Z--5 ^Y^-<^<>-4 ^-2
All real nvjmfoerjIC^^CLH -^.
Solve, graph, and describe each compound inequality:
r
^
3v^f -^- ^^v^3 <-i—t
iW ^ -Z15
-( -2
3
4—>0
2
c
10) 7/ m+ 1 <
^1
11) 6y: -3y ^ 24-36
-^
fc-Xi; lt
^^12) 28 -I 9k
-I54qkl
c]
AU rto\ nitmbert\^S'S -^hojn c>^ ^(A-cbt -tt>"'^
u
-'5^mz-l
All na\ nu^toen qr^JfrVf\ajc\ or Q^^\ ^^Qd^5~>^0unu \. < -^'"o 1 >4-
0^—>
U^-?or4N>^ ^t- 4-(^VV^A^^—^>s
-G| -? ~'7 ^ -5
7,1 fc^^?,^^^ ^\\ r€(X\ nu^te(-5 yea-^-er-4^a^ ?>OLnd le^-^a^i^.
o^^^/vw^€>q ^ G? -i3
3
Solve each formula for the given variable
(Solve for re)13) A
2r 2
A2--^
r
15)^<3=|:•p
y-3k
(Solve for p)
-5
^-^-^ ^^^
5
14)V,D\
^ (Solve for m) 16)I
V-D - m
3+ (Solve for k)
K(^ls<iiiT^PL_^P
17) Find the three consecutive integers that have c(sum Ipf 81.\^-/
^- 3̂+F
^:^n+nt"n:^tF,j^^n^z=2^ 3n +'
2^,2^-28
I-5in ^"^'.^\ 5
n<F2<o18) Four consecutive |3ddjlntegers have afsumjsf 200. What are the integers?
l<>+^=n =^~7 pi+p+^+p+^+n+^F 2002'^A^n+2 r4tc?3rdfr=n^ =5tq^#:^n4-^> ^5^
j^4c),5i,6^
t4n + \1- --
Mn'ZT
200-12
(^4
n^-7 4
Name
rFoundations Final Exam Review
curteK^RevieuSlope Formula = i/y^ -. V ^
•X,-X. ^. v. ^i Vz1) Find the slope of the line that passes through the points (4,4) and (8,—1).
m--Vz-v, ^ -.I-4 ^Xz-x\ x-4
-(5^m
^
2) Sketch a linear equation with a pos'rtive, negative, zero and undefined slope.-po^^v^ ^e^a^nv^ -^erp
-
c
—
[±N:SE
-!-i-i-4-i-4.
11act
...i.-l
ia.
-T-
ffl"SB—I—
.U-i
m
Slope-lntercept Form:
--CH+) -4Xt! ::R:-ff. ±±fflqrr :t-i±tEE ...,J.4..U-
.i-1.-t-i -f
l±H±c &iffl4l±ti •m j
i.i-.ira ffFFRTI-t-t-1 -n-s7
XJ
L
M^:
H-l-ffl
1-.L
trfcfcld3xirt#
SEI:EI±i-••t-f-f-f-"r-i
ffl
-R--t-1
-
...i....[....L.l...i.JfSSBSR.
K-U-l.
:hl BE55BB3B:era
BB;±fcfcj
undefinedD: lk
^ H-l
ES5EF ,L..lu-t-T
BBEB F? —I-ffF •H-H-1-r
•h-1±rmf-l-t-
y -L4—1-J-m=ffl ..U..l-l—!—l- m-t-
±t:hy±i±arj±tfcl
L
f
• 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;
2^^=V20) 1^<- 1^- -40Tl6x 4- 7y = 30' ^ ^^^ -^ ^ ^ -^^
^ ~lo
-•5
?y^l£)C2^-io^X - 12 ^-20
-^12 -KZ
?^--1^.. ^,Y^-'l
Solution I - • )
^--T-
9
2) a) Solve this system of equations graphically.
3y+ 2x = 6•3y4l5y-2x= 10
+2/ ^ ^ ^-2
t
LX
^^-. -2.
-2X,
-2^3(
.^'^x^Z3'
<n--^ fl4b--2.
T "] ^z/-^'^k
-s^F>i
L
uo o..I-
0^2v^^1^ I
'H^-H4 •X
^ i—!—1'
2x^1dl»
^...--S 5£--
0-t-
.....J
+
r-i x .2
^='§x.2^1
m^z^
b^Z
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?
Le+ maW^e c.^ce =1^U-V ^ut|-(ahc ~- ^
m-^ZO
'5TTnore C3upe
multi p^cC^ace <
Lt<€3tt^
+ ^=20^ fi-ue/and 1-35
^aise esfio^9uv
^^151
5fc + \\m^ too
-sT^ -^rn ^> 2.0-)-?>nn = -bo
^ ^\\^ ^ 100 ^
gm=WT J[m^_5i
11
Name_ Foundations Final Exam Review.r
cur'teKnaRevieu
i\•^1
Arithmetic Sequence Formulas: Geometric Sequence Formulas:
t\ Gn^n-,+d^1
ao--o-n-i*<'
^ On --0->m
-- a, + dG^-^
c
ao=a,TA-I
Determine if the sequences are geometric, arithmetic, or neither. State the common difference or the common ratio.
1) 12, 4, -4, -12, .-^ \^ v^-^ -s' -^
2) 2, -12, 72, -432,\/\/\^a -Ip »-(^ ••—(^
d---^ar^in^+TC
Given the following sequences write the recursive equation:
r---^»et
3) 3, 6, 12, 18, 36,,vv^^,
.2 .-2@-2ncf\h€A"-
257) 225, 75, 25. ^, ...v\'v
•± 'J- .43^3
8)-75, -61, -47, -33,.\^ \^ \^-
4l<4 ^\^ Jr\^
»> i. ^. !-A--Y^VL^ti"^ --4
an=Q.^^ a<,-<^.,+\^\
O.n=0.r>-,-" 4For questions 11-15, given the following sequences, write the explicit equation and find the 10th term
12) 3, 6, 12, 18, 36,...10) 12, 4, -4, -12,
-^^11) 2, -12, 72, -432,,
* -(<? —L? —L? nef-Ww
an--i2-^n-iN) O.^Z'I.-^T
12
2513) 225, 75, 25, ^. .\^\^^•vy^
14) -75, -61, -47, -33,,^ \^ ^
^|L( ^\^ +^
15) 480, -240, 120, -60..
WY,-i-'14
an-225.(^-* &.-^+'^n-^ a,-^-G-iVExponential Growth/Decay Formula:
GTD^V\- Deccu^:
y^ad-r-Tu><
\f^0<i\^}16) The population in Buffalo was 550,000 in 1985. The population declines at a rate of 1.4% each year. Find the
population in 2010 to the nearest person. "2.01 ^
V.Q(l-r')< -Jl!^y= 550(0oo(l --Qi4TVT 5^2 2 people)
17) The value of a diamond ring appreciates at a rate of 12% each year. Find the value of the ring after 7 years if the
ring was originally $7,000. ^^^
Y^ad^r^'y=--1,00^(1 +-.i2yV^i^,L<^.T'
18)A new car that costed $40,000 depreciates at a rate of 15% per year.a. Write a rule that models the value of the car.
-X
x
^v I
y^ati-ry^ ^Op0o( I - • i
b. Find the value of the car after 5 years.
'y^4QOOo(^-j5^fy=<ln,l4?.2)| 13
Name Foundations Final Exam Review
H8 (o BHMBDetermine whether the given graphs, tables, and sets of ordered pairs are functions. Write yes or no.
1. x y
'^% ^'^y
-2
^
-1
-1
-2
2.
<-
3. ^
^i2L -> ^
^4. 4
/ \j
^
/\1
^e5
-^ <
/
No
5. ^/v\ /r\
$ ^
^ M/
v
VesNo7^0
6. {(-1/2)- ,(-3,4), (-4^ '(-5,5)} 7. {(1,4),(2^), (9,10),((2)B)} S. {(1, 3),(2,3),(3,3), (4,3)}
Yes No Ye&9. Sketch a picture of any linear equation 10. Sketch a picture of any exponential equation
/T\
c/I\
\J
> ^
M/
11. Give the inequalities in interval notation:
-2 <x^ 10
(-2,101S<x<7
(->,-''>13 ^x< 22
[l5,Z2) t
12. Give the domain and range for each function:
{(1,4), (2,7), (9,10). (12,8)} /(x) =3x+14 g(x-) = 2(50)x
v '^i, 2,ct. i2? r^. ^ fea^ nwbw^. ft\\ r^ nuw1~1>)'<~^ u'(-CO)CO) u -OOZL^^<
d'. ^ ,~1^, }0[ ^:f\\\fw.\f\w^ers^: o^i^/-oo
nu^berj00
^-co,oo)
14
13. Let f(x) = -3x + 6 let g(x) = 6x - 8 and let h(x) = ^.Evaluate each function.
a./(-2)=.-3(-Z^+<^ b.5(S)^ L»^')-y c.^-3) s <^^^(-2^ ^+tp ^(^ ~- 3o -S' hC-^) ^ ^iR-2^= (Z ^'5Y-^ 22
d./©=^}«^
-3(i) ^
^ - ( +-<p
--S
B./(-2)+/g)
=(24-5
=n
f.5(6)+/g)=U(^)-^ ^ 5
-3^-^ -^5
-- S3
14. Given the function /(x) = 2x - 4,a. If the domain is {3, 5,7} what is the range?
+(5^^2(?,s>-^ --ZfW-ZC^-t^^^t-i) =2H)^^0
2^^0J
b. If the domain is (2,8], what is the range?
^(^-2(^.y^ ^oR8y--2(^-1/ =/2
(OJZ]
x15. A local gym charges $25 per month plus a $99 enrollment fee tosign up. Findthedomain and range
over a one year period. I
)er month plus a
=Z5x+^?(o').Z6(o-)+qcK-F(o^crci?(^---250z)+^^\z} -- y)^
bcmain: o^x^iz[0/'^1
^ounc^: °[ci^L.W[w.^l
("Name Foundations Final Exam Review
^\1) Simpli^: -3xf^ - 41 - 2x(x
cupteK—Revieu
23x
+ 2) Find
^-izx^zxfB^-t-
26x
of3x2 +4x-2ar\dx2-5x+3v^
l'^^£2^^y1Fs^^
5v^ ^x ^-\X H
c
3) ?>Qt -4^+2 subtracted from Ig7- +5^-1 4)4x2 + 7x- 5 is subtracted from 9a:2 - 2x + 3<^TC>O+-^ (-^nhV^
~1^2 .5^-1 41^1^+2) ^2-2x ^3 •^^5}^t^\G^-7n}\ (^xl^A^ ^\%5^(3Q^\^^~7
4£^ _^5xz-qx^
^ST'^^"^.5) d-lOx2 +x - 3) -(4^2 +4x +'4)
~^^>./2 24lOx +-X x
6) Simplify: (3^20(®c{2]
llx3^?~I^K2-^Y--l1
7) The product of —3x2y and CSxvL+ xy) is
-3X2^5X^ r'X'^')
J ^i^-^xy./
16
8) What is the product of (3x + 2) and (^ - 7)?
(^x.2^V>)(®i-l4y(- 2.1 x
3yT^nx-iLH
_^=:^>'_10) Find the product: (5x - 2)(7x - 5)
3c?y2C2c)~x)(^<4x)+10
35x2-^>ctx+lb
9) (x-6)2
(K-^)C^~^
y -(o
^T^
i-k> '3^
x
-^
X2-|2y+?>^
11) (2x+10)(3x2+6x-2)
2x' +10
(
z^^^./
12 X2<£;
^x/| -20
^xz
-t-lfl^
-2
\ ^X" ^2x2+5(r>K-20
17
Name. Foundations Final Exam Review
^
1. What we the factors of J^ - Wx- 24?
(1) (^-4)(x+6) (2) (x-4Xx:-6)
3)J^-12X.»;+2) (4) (x+12)(x-2)
^ /^Factored, the expression l&t2 - 25y1 is
cquiv"e°tl° Xps^-P.^.^
A.C:l-z'+
(Y^y-\i}-2M 4.^0
-t,2M
-z,l^-T,^-4^
2^>/o
5z
c (T^zl-io)
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.
y
y>
/ j^/ivt MI^- i^/ii^/vviii^ ^y«»^^.i 11 v/i iii^-\^wuiih*'^«/^iu|>/< ii^-uii y •
<2x+i dx^ed, be\ow^ ^^2 ^b^ \^g3gg|^@^-jx+4^id,otoove, m^,b^4'^^^fl
((Oi2N)
16) Graph the following system of equations and identify all solutions:
71̂7to
..\v
..a"b-^f
*£
TON#f.^" w
.V.L--1.
^ _u-\ ^m^ KJYJ
^ -4N-
ib
^
y = -2x2 - 4x + 6
y=-X+6
rn-^-\
\
b^b
x
t0>^Ojndt-l.5,Z6')
-4
-2-I
0
Iz
^0^1^Ip
0[-10
^
I..L....,..L
Bd&
^
^̂^'/
iL^