~ ','
~
ame~~")[l~tlrV-{)--+-'11-,,--,0,--=-'l_ _
Date_ _ _ _ _ _ _ _ _ _ __
Math 4 Pre-Calculus
Spring 20 II Laddon
N
Exam 1
Read all of the directions to the problems carefully! You may use a scientific calculator on this exam. Show all of your work. Ifno
work is shown, you will not receive full credit. If you do work on another sheet of paper, make a note on the exam that you have
done so. Number all problems done on separate paper in order. Show only one solution for each problem. Give exact simplified
answers; do 110t give decimal approximations. Box or circle your final answer.
~/"-~~========~----------------_/'
Factor completely.
~ ({'rl)('t'-I) = (~-t~Y~ .,.-::f.'(I-+'-t){l(j-,)('t~+~-H)
l+7/-8
1.
Simplify the expression.
4
(x+h)2
2.
/
--Y
L\- X -v_ i-f ex: +-k)
h x lx 1- h.') ~
4
x
2
h
l,JPOINTS
:::;
.tt)( ~~')L
/ '
~
"2-_' (
-
4: h ~
~ )(~ LX. t-~y2--
"2-
- L\ (2.. >,- +-~
-)( ~()(+~Y"
SimplifY the Expression
3.
2X2
+ 7x + 6
3
4X4
+ 6x + 9x
2
.....
-
5 POINTS
(9-x- ~d-,x: t-~J>C (.ii ')( v t" k,'t ~l\)
"­
Z'd-)(+ 3~6u-:f)
"f-. J.. ( r ~ '3_ d- 1-)
7..
~.
(~~.-(C~q,>
1­
~l>(+-?j fl~(ti'A '--
~d-)
.,­
t-~
Solve the formula for the specified variable.
4.
A=P+Prl
solveforP
5 POINTS
A- ::; 'f Ct -r Ii) l:rt
~F
(2, -1) and C(5, -4) are 3 points, fmd:
a)
139­
The distance AB
b)
c)
10 POINTS
1'\PrF> .=:;
-­
~~
_( +1-
---~ ~
(p
jV\
~-l
.J
1­
--c ~-~ \
Page 1 of6
-::..
-110
Simplify the expressions. Your final answer should not contain fractional coefficients or neg~.~a~tiv~e~e~x~~=:::==:::::::~
5
_ _5_
10 ~ ..... \. S - i O X - lDVI-lf;
- lO
2x + 2h + 3
2x + 3 (
.~
6.
5 POINTS
----h--h (1--)<..-t'-z.V. .t"".3) Z-- X -t'O)
( 2- x t- 2-h 1"' 3 )(Z.X -r3)
4(X2+1)3(2x)(4x+3)~ _(x 2 +If (~}4X+3f~ (4)
5 POINTS
7. ((4X+3)XJ _ 'I:
.
()L ~+i)'"(1-\ tra)~ [ ;i.)«J.fXt3) -
~ ex~+ I)J
(f-{y-t-O)
"
-z.. r \ 'J- -
X. .,-
\"l
J... ('" \ _1\6 [Lt )l. (Lty -t- o)- (X "2--+- l)J
To receive fitll credit, you must define any variables
answer the question.
8. tha"lJ:Q
ou!:!..1fus~e~w.e..JJJ1..e£j"IJiJJ..J[{ll1,....s.I:lQl1L~~'t*-ffHj'fJit!ry'J'W'.ljequation,
and
A rectangular piece of cardboard whose length is twice its width is used to construct an open box. Cutting a 1 inch by 1 inch
square off of each corner and folding up the edges will yield an open box (assuming these edges are taped together) , If the
desired volume is 84 cubic inches, what are the dimensions (length and width) of the original piece of cardboard? The figure is
not drawn
/0
8 POINTS
scale.
(y.. - i) (~X - :J-)(I) ::: 'r't
~ )L 7-___ {p X' ~Ii -:;. ~tf
-T-~\n-l
- v·~-~rlUJ- . ­
d-x.1--,.. {p y>-«O ?-D
Y-- ~ -- 3y ~tfo ~ '?;;- :;:; tJ
1.Ja,4.-
~ \11\ ~O
\\
IlR ,~ .
\
()C -1){X+; )"' D_ _ - (ca'" -j-Iw<f~
'f.~~
d
X -- ')
Page 2 of6
Solve. Solutions may be real or imaginary. Check/or extraneous solutions.
9.
4x4 - 11x 2 = 3
bo.c~
iu "-- //u - 3 0
5 POINTS
'6 'f."
="
(.2{u + ')(Gl-3J~D
1- 2-- :;. - '1'1
.ifu.-,.. /:=- O« u. - 3 ~D
1- : : , - /4 ::- !
Ifu. ~ -I
tA- ~ Solve. Express the solution in
10.
12x+ll-s < 14
It-f
LA..
C/<'
~
·
J.I '"I
-:;.3
)
w IA -:: 3
terms~--;)
~v
5 POINTS
1;}~~ II L 19
-- l q L :1-t.-+ I L- f 1 ". ~o L ;f-'¥- Lit
11
EO
L '1L'1 (
II.
13x-21 ~ 7
:J-
5 POINTS
'3 )(.. - d- ':'it
CCUJ..e;a-
'?xI/7/9
1(~3
~-
111
(x - 3)(x 2 - 8x - 9) <
(1--i'){,. -q')(-x.-t-l)LO 1 m.d Jt
C\
-
~ ~~
oP­
~ (-ol) - ~
12.
?J -y:. - ;}- L
oP--
fit Ql" C k CV1.j--~
[;00)1
;/
- :J.
-5
~~ - 56
5 POINTS
-\­ + -t
+ +T
-\-+ +
Page 3 of6
For problem 13, use the graph below o/the/unction, /, to answer parts a) throughf) .
13 .
\
\
\.
\
:
a)
Domain of /
b)
Range of /
c)
(J /)(1)
- 4 ~ x~5
- 2f:it~
o-<
~ .-\ C
t CJ\) ~~ (- d-J-=-
0
d)
All x-values for which /
e)
Graph
/
d-
or
y=-/(x)+!
[- '1J
Sl
2 POINTS
[-~J ~1
2 POINTS
2 POINTS
0
(x) 2: 0 -tt~)( =-~
d
[-tt, d.-J
2 POINTS
3 POIN TS
/
,/
:
f)
Graph y
= /(
Ixl )
3 PorN TS
Page 4 of 6
Use the following two functions to answer parts a through d,
f (x)
= _2_1- and
g (x)
x - 4
14.
a)
= .J;+l.
Find the domain of f.
2 POINTS
\ (--w) -J..}u (;..? 1:7-) V ('J.)'JOJ 1,
b)
c)
2 POINTS
Find
(f g) (x)
0
2 POINTS
. State restrictions on xl
~~)L\) ~~(~) ::: (~r:
)c.*~ - L\
d)
Find (f g )(8) .
I POINTS
0
~('tf(~)\
- \
(VI):O-\ ('3') "'
15. Match each graph with an equation. Write the correct function for each graph in the corresponding blank. For all
graphs, one square is one unit.
2 POINTS EACH
a)
f (x)
b)
g
I
=
2x
(x) = (x - 1)2
h (x)
d)
k(x)=I~1
e)
l(x)=ffi
t)
m(x)
=
~x
2
4
I
g)
n(x) = ­
h)
p(x)
x-2
=
f--
Ix 31
c)
=
l"-
_x 3
e. .
(J... .
l&)~fIxf
I
I
II
I
\
I
I
II
e.. .
~lj-)~ \)(; I
_ f_
{ /)_-;-=-",±"X
1\
'-..
V
,.­ -- ---- -~I- -_...
i/
_- 1-1­
Page 5 of6
For problem 16, to receive full credit, you must define any variables that you use, write functions as asked, show steps in which
you use your jitnct ion (s) to find the answers the questions.
16. An open rectangular storage shelter, consisting of two 4-foot-wide vertical sides and a flat roof, is to be attached to an
existing structure, as illustrated. The flat roof is made of tin and costs $5 per square foot, and the two sides are made of
plywood that costs $2 per square foot.
h
Not to scale I
4ft
a) If$400 is available for the plywood and tin, express the width, w, as a function of height, h. In other words, write
a "cost equation" for the total area that includes wand h, then solve for w. Remember square feet measure area
and that the "length" is 4 feet'
-:::::
4 POfNTS
Jt 00 ::: ~(L\ h. (~) + S- 'tW') ~ ifOO ~ /1Ph +C1Ow j b)
c)
I
6
d)
:;;I- f) What is the maximum volume of storage shelter? 1vlo..K v
oluMe.-
V wkl
V\.
2 POrNTS
l'S
tA -=- \?-"~
W-:::
'tDO --~'J-'1....)
;J-O
Page 6 of6