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CHAPTER 3:
LESSONS 3.1-3.4
CHAPTER 4:
CHAPTER 5:
LESSONS 4.1 - 4.6, 4.8 o 4.9
LESSONS 5.2 - 5.8
CHAPTER 6:
LESSONS 6.1,6.3 - 6.6
CHAPTER 8:
LESSONS 8.2 - 8.6
Date
Standardized Tes
For use after Chapter 3
Multiple Choice
1. The graph of a linear system is shown.
How can you classify the ’system?
¯ 6. What is the solutionol~the system of
~quations be!qw?
x=7y+ 12
2x- 14y=ll
@ (12.5, 1)
® (5, -1)
(~) many ~olutions (~) no solution "
6. Which system of inequalities is represented
by the graph below?
@ consistent and independent
,(~) ~o~sistent and dependent
¯
(~) inconsistent
(~ inconsistent and independent
How many sointions does the system in
Exercise 1 have?
(g) none
® one
@ imSnitely many
3.
What is the solution of the system of
equations below?
3x + 4y= -6
x-2y=8
@ (-2, -3)
@ (2, -3)
4=
(~ (-2, 3)
@ ’(2, 3)
You haveS123.50 in quarters and dimes.
’There are 1202 coins altogethe;. Which
system of equations can yo~ use to find the
rmmber of each type of coin you have?
@ x + y = 1202
0.1x + 0.25Z = 123.5
(~) x + y = 123.5
0.1x + 0.25y,= !202
(~)x+y= 1202
0.1x + 0.25y = 12,350
(~)x+y= 1202
10x + 25y = 123.5
Chapter 3 Assessment,Book
@x+y<3
-4x + 2y>.1
(~) x + y > 3
-4x + 2y<_l
’ (~)x+y>_3
-4x + 2y> 1
(~ x + y<_3
-4x + 2y~l
7. What i~ the solution of thesystem o~
equations below?
-x + 3y -.2Z = 19
2x+y-z=5
=3x =-y + 2,z= -7
@ (-1, -4, -3) (~) (-1, -4, 3
@ (-1,.4, -3) @ (1, 4, 3)
A high school,s enro!lment i~ 950 students,
which includes sophomores, juniors, and
~eniors. Twlce the sQphomore enrollment is
three times the senior enrollment, and the
total number ofjuninrs and seniors enrolled
is 200 more than the number of sophomores
e~olied. How many se~ors are enrolled?
@ 250 geniots
(~) 375 seniors
¯
~
]Standardized Tes
condnued
~ "lForuse afterChapter3
What is the sum of the mat~ces?
Short Response
F7 31 + I--9 -41
~
L1-2J. L 1 llJ
Matrix M gives the number of minutes Amy
and Renee spent on three types of long
distance calls last month. Matrix C gives the
cost per minute for each type of call. Which
product is defined, MC pr’CM? Explflin.
¯Find this matrix and explain what itg
elements represent.
MatrixM
Amy ¯ Renee
What is the product?
-3 5
Local ’
State
International
’L 4 -6]
20 4
I0
Matrix C
L~cal State International
Costp~rnfin [0.05 0.1 1.2]
9
Extended Response
What is the determinant of the matrix?
~
5
¯ a. Write a system of linear equations with two
equations and t~o variables to represent the
si ,tFation. What do the variables represent?
Grldded Answer
You earned $141 last
week babysitting and
cleaning: You earned
$5 per hour babysitting
and $7 per ho&r cleaning.
You worked 9 more
hours babysitting than
cleaning. How many
hours did you work
last week?
The student cou#. cil is having a bake sale.
They spend $40 for the ingredients to make
brownies mad cookies. It costs $1.25 to make
a d0zen brownies and $1.50 to make a dozen
cookies. The brownies seI1 for $6 per dozen
and the cooldes sell for $7.50 per dozen~ The
¯ student council sells a total of $195in baked
goods.
NUse an ifiverse matrix to ’solve the system of
linear equations.
(i3
c. What profit did the student council make for
the brownies ’sold? for the cookies sold?
Algebra 2
Chapter 3 Assessment Book
’ ’~i.~!
"7~or ~se after Chapter 4
1. For the ftmcfiony = -x2 - 6x - 7, find the
v6rtex and axis of s.ymmetry.
@ vertek (3, -2); axis of symmetry x = 3
(~) vertex (-3, 2); axis of symmetry x = 4
@ vertek (-3, 2); axis of symmetryx = -3
(~) vertex (3, -2); axis ofsymmeti-yx =-4
If the graph ofy = ax2 q2 bx + c opens
down, which of the following ’must be. true?
-@ a~O
@ c<O
® a>O
@ c>O
Which function does not have a maximum
value?
@y = -x2,- 5x- 6
(~) y = -x2 -2.- 6
@’y=3x2-15x+2
,#
@ y = 49 - X2
@ -3, 2-14
(~) 3,-I4
-3, 14
@ 3, 14
9. Factor the expr,,ession 8xz + ~8x + i2.
@ 2(x + 2)(4x + 3)
(g) 2(x + 3)(2x + 1)
@ 4(x + i)(2x ÷ 3)
@ 4(X + 3)(2x + 1)
Simplify the expression 2
2+ ~-’
@ 4 _ 2~/~-
@ (2, 4)
What are the x-intercept~ of
y = -2(x - 7)(x + 2)?
@ -7 and 2
~ + and -2
@ 14 and -4
@ 14 and -2
6. Factor the expression m2 -- 4m - 21.
@(m-7)(m-3) (~) (m -- 75(m + 3).
@(m+7)(m-3) (~) (m+7)(m÷3)
-5
’11. What are the solutions of the equation
W2 = -9w?
@ -9, 3
’ 4-- Wha{ is’tlie vertex ofy = -3(x - 2)2 - 4?
-~@ (-2, -4) ~ (~).(-2, 4)"
(2, -4)
8. What are the root~ of the equation
" Z2 q- 1 IZ -- 42 = O?
00,9
(~) O, -9
01,9’
What are the solutidns of
23=2(x-3)2+7?
@ -+3.
(~) 3~2J~
What are the s~lutions of -3 - y2 = 24?
@ -+3~f~
~ -+3i~/~
@ -+9~/~
@ -+9i~/~
14. What is the standard form of the
i9
. expressmn ~.
N Which
value of c makes the expression
x2 - 5x + c a perfect square trinomial?
5
5
i
2. 1
Algebra 2
Chapter 4 Assessment Book
Date
Name
For use after Chapter
What is the absolute value of 3 - 4i?
¯ Short¯ Response
~
-18. What is the vertex ofy 3x2 - 30x +. 77?
® {-5, -.2)
® (-5, 2)
(~ (5,-2)’
,(~) (5, 2)
"17. What is the value ofc ift~e discrimant of
-2x} - 3x + c is 41?
@ -4
.A bottle ro~et travels along ~ parabolic path
and reaches a maximum height of 2r feet
after traveling a horizontal distance of 7.feet.
a. Write a quadratic function of the form
y =: a(x - h)2 +/c that models the
bottle rocket’s path; assttming it leaves
the grmmd at the point (0, 0).
b. Describe how ~hanging the’values of
a, h, and/~ affect the flight path 0fthe
bottle rocket.
(~) 4
/\
18. Which’ineq~alityrepresents the graph
below?
Extended Response
2-1. A rectangular garden is 25 feet long by
10 feet wide. You have enough mulch to
cover 1000 square feet.
@2X2+X-- 15>-0
a. You would like to extend both the
length and the width of the .garden by
¯ x feet to use up all of the mulch. Write
an equation to represent the area of
the new garden.
I~. Solve the equatioh frompart (a).
c. Which solution do you have to reject?
Explain.
(~) --2X2 q-X- 15>_0
(~(2x+S)(x+3)~O’
(~) 2x2-x- 15>0
Grldded Answer
-19. 12Iow many real
number solutions
does the equation
7x2 - 5x + 1 =0
have?
Algebra2
~-’ "
Chapter 4 Assessment Book
(D
Date , .
Name
Standardized Test
For use after Chapter 5
at i~ the simplified form of 8a~be-19
Which polynomial represents the volume of
the cone show~?
12abac :
@2abac2
2a
V= ~rr h
(~ 3bac2
2x+ 5
212
3b2
,
~ What is (~.2 X 105)(I.4-X i0-2) written in
¯ ~ " scientific ttotation?
(~) 4.4~ × 107
,@ 4.48 x iO3
(~) 44:8 X 103
x-2
(~ 44.8 X 107
3. Which equation is the graph of the
polynomial function shown?"
~
(~) x2-}"
3
,rrx
107r
3
7. What is the complete factorization of
3x4 -- 3x2?
¯ @ 3~(x~- 1)
@ f(x) = -Z~3 + x2 -- 2
(!~ 3x~(x -- 1)(x + 1)
@. 3x(x 7 ~)(x + 1)
@ ~(x~ - ~)
8.’ Ifx + 3 is d factor ofx3 - x2 - 17x - 15,
whist is another factor?
4. What’is the degree of the polyaomial
h(t).= -St2 + 5 - 3t37
@1.-®2 @3
5. Wl~at is the greatest common monomiaI
factor ofgx3y2 + 15x2y - 6xya?
@ 3x2
(i~ 3y=
(g) x+ 1
9. Ifx - 2 is a facior.ofapolynomialf(x),
whicl~ of the following statements does
not have to be true?
@ f(2)= .0
""
. (~ f(-2) = 0
(~) 2 is a root off(x).
(~ 2 is a zero off(x).
~
~ Fo~use~qfterChapter5
"
’10. Which is not a possiNe ration!! sohition of
f(x) = 3x3 - 1 lx2 + 5X -- 6?
(~) _+2
(!~ _+6
Ba~e~ upon D;scartes’ l~uIe of Signs,’
which of the following is the only possible
¯classification df the rogts of the function
u(k) = -3k3 ÷ 5k~- k + 4?
~
@
(~
3 positives, 0 negatives, 0 i~:aaginar~,
0 positives, 3 negatives, 0 imaginary
1 positiye, 1 negative, i imaginary
(~) 2 positives’.1 negativ4, 0 imaginary
A package has a length 10 inches greater
than its width and a height 12 inches less
than its width.
.
a. Determine the polynomial funStio~
that will calcqlate’the volurne of a
package with width w.
b. To carry this package onto an
airplane, it cannot be larger ’than
4800 cubic inches. What should its
dimensions be if you "$vant to havethe
maximum allowable volume?
(~
"12. What is (are) the local’minimum value(s)
for v(x) = 2x3 - x2 ÷ 1?
(~) There are none.
students who use a.college
lab is tracked for several academic
yem-s. The results are summarized in the
table below.
St~d~I 1287 I i365 11402 11693
-1994 1995 1996 1997
GHdded Answer
13; How many solutions does
j(m) = -7m3 - m4 + 1 have?
@
~=
"/
a. Let 1990 correspond to year x = 0,
1991 to year x = 1, and so on. Enter
the data into your graphing
calculator arid make a scatterplot.
Which polynomial fimction does
it seem to model? Use polynomial
regression to obtain a model. Romad
to tw6 decimal places What is the
regresgion equation you obtained?
b. Graph the model mad predict what the
nmnber of students wili be i~-20~,6.
~. Graphy =. 500 in the same’
viewing window. F~nd the
intersection point(s). Explain the,
’ °~
~ ¯ ~ignificance~o~:ou_r res~Jts
¯
Algebra 2
’Chapter 5 Assessment BoOk
71
Name
¯
’
Date
Standardized Test
Fofi~se_qfter Chapte~ 6
Mu~lLiple Choice
1. What is the valne of (-243)3/5?
@ -27
(~) -3
(~3
(~ 27
2. What is the solution to 3x5. + 350 = -379?
729
¯
729
~
Which expression is the simplest form of
4~ ([~) 3"~-
8. Given u(x) = ~ - 1 and v(x) = x - 5r
what is the domain of u(v(x))?
@ All real numbers (~ x 2 0
@x>¼
4
9. Which function represents the inverse of the
graph shown?
([~) 6~
x
~what i{ the simplified expression of the
~’." length of the triangle’s hypotenuse? ,
/t
3X112
(~)y= -5x + 3,
2x3/2
@ ~ 3x1/2
(~ ~ + 9x
1
®y=gx-3
@y=~x+3 .(~) y= 5X+3
(~) 2x3/2 + 3x1/2
@ 4x3 -t- 9x2
Assuming gll variables are positive, what is
the simplified form of
10. What is the inverse of the power function
¯ g(t) = .2-~qTt37 "
(~ h(t) = 2 3
=
’-z2@ + 3~?
@-z3~zz
~ 14z3~zz
(~ ]4z4~zz
(~) 92z3~zz
Ifh(O = t2/3 9 andj(t) = 3t + 5t2/3,
what is h(O -j(t)?
1 I. Which of the following paJ~s of functions are
not thverses of one another?
(g) u(x) = x - 2; v(x) = x + 2
@ --4t~/3 -- 3t - 9 (~) .4t2/3 + 3t + 9
® u(x) = 5x - 1; v(x) = ~x + ~
@ 3t + 6t4/3 "
® u(x) = x3 + 1; v(x) = ~xx - i
(~) -7t713 - 9
Algebra 2
Chapter 6 Assessment Book
85
Date
Name
CSAPTE" ]Standardized Test.
continued
12. The graph ofy = ~ is shined 2 ~its up
~d 3 ~its to &e leA. ~ch is the equation
of the tr~slated Nnction?
Short Response
You are digging a garden in your bacl~ard.
You would like the length to be 5 feet grea~er
than th~ width. Determine the fomction
A(x) to calculate the area of the g~rden.
What should the dimensions of the garden
be if you’would like your garden to cover
104 square feet of gro}~,nd?
@y = ~3 +’2
13. What are the domahl and range of the
functiony = 5~xx - 22
@ Domain: all real numbers;
range: all real numbers
~=x~e~ded Response
"17. The XYZ Widget Company determines that
it costs them $4 to produce each widget plus "
an initial fixed cost of $2250.
a, Determine the cost ftmcf!on C(x) for
producing x number.of widgets.
Un~’ortunately, the sharp increase in
fuel prices.have led the company’s
pricing analysts to believe that.
costs vail increase overall by 10%.
Determine the functionf(x) which
represents a 10% increase.
Which composition of functions
makes sense to calculate the total cost
with the 10% increase, C(f(x)) or
f(C(x))? Why?
Hay< much will .it cost the company to
produc~ I 0q,000 widgets before and
aftei the increase?
(~) DOmain: x .-> 2; range: all real numbers
@ Domain: all real numbers; range: y > 0 "
@ Do~aain: X -> 2; range: y > 0
14. What is (are) the solution(s) to
x-2=~x=l?
@x=l
(~) x= 5
@ x = ! and 5
(~ No solution
What is the solution of
(x - 5)~/3 - 2. = 2?
86
Algebra 2 _- - .... ......
Chapter 6 Assessr~ent Book .....
- <-~
~
~’
Name
Date
Standardized Test
For use after Chapter 8
’
Multiple Choice
¯ " ~. Which equation represents inverse variation?
5
@~-=x
,(!~ y=x+ 5
(~) y ~ 5x
~Ifx v~es directly Wi~y andy = -12 when
~ ~ x = 4, what is the value ofy whenx = -3?
6. Whicfi function has the domain of all real
numbers except -2?
x-2
@Y~x+2
.(~ Y = x
,
x-2
(~)y x+2
x-2
y=x~2
7. What ar~ the asymptotes of the ftmction
4x2 + 3x + 19
Y = x2- 1 .
@x=0, y=0
1
~
Let r v~y ~rectly with s and inversely
wi~ t. ~ich equation represents t~s
relationship?
at
a
(~)
st
Which function represents the graph shown?
(~) x = 0,~c= 1,y=4
(~)x=-,1,x= 1,y=~
What ~s the simplified form of 2x - 9x+109
x2+xs-6
Z-c - 5.
2x-5’
@
x-3
(~) x+3
2)+5
@ 2x+5
9. Which expressionis theproduct of
24a?b ¯ 39a~c37
13abc’ 8b2c~"
7
"@ Y- x2- 9’
@Y=x2_9
7x
(~y=
..
@y
9
7x3
¯ 2
-9
_ x~
What is (are) the vertical asYmptote(s) of the
function in Exercise 4? "
(~) x=3
@x=_+3
118
Algebra 2, - ....
Chapter 8 Asses~-r~nt Book
There are none,
~ b~ "
(~ 9aab2
2
.(~)
13bll7aab~
117a3ba
@ 7 i~
1.O. The least common multiple of .which pair of
expressi6ns is 3x(x + 2)(x+ 1)?
@ x~ +3x + 2;x ~ 2
(~) x~ +3x + 2; 3x + 6
@ x2 +3x + 2; 3X2÷ 6x
@ x2 +3?c + 2; ’3x3 + 6x~
@
IFor~’~eoiterChepter8
The legs of a right triangle have lengths
) and x~. What is ~e sin~plified ratio of
the area of the triangle to the hypotenuse?
x,/g
X
Sh~rt Response
You join a health club which charges you a
$175 regisb’ation fee plus a $25 per month
charge.
a." Determine the equation which
calculates the total amount y you have
paid in fees for your membership
through month x.
. b. Determine the equation which
calculates the average montl’fly
payment y you hav~ made through
month x. Which is the firs{ month you
average less than $40 per month for
membership?
Ex~ended Response.
12. "fiNch expression represents the simplified
form of 3x
.?
1 - 25"
@x
.
3x - 2
~-2
~ 2{~x -T)
(3x - 2)(x - 2) ¯
x(3x - 2)(x .2 2)
’{~) 3x - 5 (~
2(3x - 5)
Gridded Answer
What is the solution
of x--]
2=
.Q
A pack}ging engineer for the Bubble
Beverage Company is given the task of
designing a new can. The company would
like to minimize the surface area of the can
in order to min’tmize overall packaging cost..
a. What is the surface area ofa cari with
radios r and height h? What is the
volume of a can with radius rand
height h?
la, If the can must h~ld 35~ mL,
determine the formula for the surface
area 0fthe can in terms of radius r.
(Hint: Use the fact that the volume is
355 mL and delve for h in terms ofr.)
,, For what value of’r is the surface area.
a minimum? Rotmd to one decimal
place. (Hint: 1 cm3 = 1 mL)
d. If aluminum costs the company $.001
per square centimeter, how much will
it cost the company to supply the
aluminum for the can?
Algebra 2
Chapter 8 Assessment Book
StandardizedTest
1.A 2. B 3. C 4.A 5.D 6:B’
8. A’9. D !0. C 11.D’:12.25 13. CMis
defined. I~ is possible to multiply a 1 × 3 matrix
by a 3 × 2 matrix, but not the other way around.
CM ~epresents the dollar amount spent byAmy
and Kenee on all long distance calls.
¯ 14. a. 1.25x + 1.5y = ~0; 6x + 7.5~ ~ 195; , .,
x represents the. dozens of brownies¯ ~old,
y represent~ the dozens of cookies so!d,
b. x = 20 dozen; y = 10 dozen c. $95 pro~t for
the brownies; $60 profit for the cookies.
Standardized -Test
"14. a. V = w3 - 2w~ - 120w b. ~vidth: 20 in.,
length: 30.in., height: 8 ih.
¯
’15. ~dratic;y = -2p.17x~ + 262.56x +
t 144.~1_b. 182 c. There ar~ two, intersection
points atx U" -2 andx ~15. This means that
the num)er of students was 500 in about¯ 1988 "
and 2005.
Standardized Test
I.A 2. C 3. B 4. C 5. C 6. A2.7. D.8. B
9. A’10, C ~I;B 12. D’~3.3
14. a-y = "175 + 25x b.y = 1~ + 25; month 12
15. a: s~face area =.2~r: + 2~rh, " ’
vol~e ~ ~r:h b, s~face ~da ,=2vr: -t-710
c. 3.8 cm d. abou~ $.28/~ _ _
Standardized Tes~
’I.C 2. A 3. C 4. C 5. B 6.~ 7. C 8. B
9. D 10. C 11.B 12. B 13. B 14, D
15]C 16. D ~7. B ~8~A 19.0
3
20. a.y = -~(x -- 7)2 +21 b. ~swers will
v~. 2t a. 100’0 = (10 +’x)(25 +x)
b.~ = 15 orx = =50 c.x = -50 becanse you
c~ot have a negative len~.
Standard~zed Test
¯ .
’1.A 2. B 3. B 4. C 5. B 6. A 7. B
8. D 9. C 10. C 1~.C ’12. D 13. D
I~.B 15. 13 16.A(x)=x(x-5)i13ftby8ft
17. a. C(x) = 4x + 2250 b.f(x) = 1.10x
¢.f(C(x)~ because the I0% increase will not
’affect the $2250 otherwise, d. before: $402,250;
after: $442,475
.