Math
h 104 Fina
al Exam R
Review
1. Use the graph off f(x) to answ
wer the questtions below..
a.
a Evaluatee f(1).
b.
b Determin
ne all valuess of x that pro
oduce f(x) = -1.
c.
c State thee domain of the
t function using intervval notation.
2. Writte in slope-in
ntercept form
m the equatio
on of the linne passing thrrough (6, -1)) to
perp
pendicular to
o 4x – 3y = -2
21.
x
ve the absolu
ute value inequality   3  2 . Wrrite your ansswer using innterval
3. Solv
2
notaation.
4. Two
o trains depaart simultaneously from a station, trav
aveling in oppposite directtions. One
averrages 8 km/h
hr more that the other, affter ½ an houur they are 100 km apartt. Determinee
the speed
s
of each train. (Use thhe addition methodd to solve the systeem of equations.)
plify the folllowing expreession. Writte your answ
wer in terms of positive eexponents.
5. Simp
Assu
ume that the variable x represents a positive
p
reall number.
 32 12 
 3x x 


5
9x
4
6. A co
oncrete walk
k of uniform width is to be
b built arouund a circulaar pool. The diameter off
the pool
p
is 24 meters
m
and en
nough concreete is availabble to cover 552π square m
meters. If alll
of th
he concrete is
i to be used, how wide should
s
the w
walk be?
1
7. Use the graph off the polynom
mial function, y = P(x) tto answer thee questions tthat follow.
a.
a List the x-intercepts
x
of the graph
h of y = P(x)..
b.
b Find two
o of the threee linear facto
ors of the pollynomial.
c.
c Solve P  x   0 . Giv
ve your answ
wer in intervval notation.
8. Solv
ve the equation 10 y 3  29 y 2  10 y by factoring.
9. Solv
ve by compleeting the squ
uare.
2 x 2  12 x  32  0
10. The height of a cannonball
c
is
i given by h(t )  9.8t 2  16t  15.2 , where h(t) represents
the height
h
of thee cannonball in meters an
nd t is the nuumber of secconds that haave elapsed
since the cannon
nball was fired. Determiine how manny seconds into the flighht the
max
ximum heigh
ht is reached and the high
hest point thhat the cannoonball reachees.
press the resuult in standarrd a + bi forrm.
11. Perfform the indiicated operattion and exp
85
7  6ii
on by rationalizing the ddenominatorr and then sim
mplifying.
12. Perfform the indiicated divisio
10
1 7
c longer th
han the side oof another sqquare. Theirr total area iss
13. The side of one square is 5 cm
2
mine the len
ngth of a sidee of each squuare.
193 cm . Determ
2
14. A bakery has 10 pounds of premium coffee that costs $7.50 per pound. A baker wants
to mix this with ordinary coffee which costs $3.50 per pound to make a mixture which
costs $6.00 per pound. How much ordinary coffee must be used? What will the weight
of the final mixture be?
15. Simplify the following expression. Write the result in lowest terms. Assume that the
variable w is restricted to values that prevent division by 0.
3w2  23w1  8
24  29 w1  4 w2
16. Simplify the following expression and write the result in standard a +bi form.
2 9  36
6
17. Solve the equation.
12
2 w  15
w3
 2

w  5 w  11w  30 w  6
18. Solve the equation below for b.
2A 
hb  B
1 b
19. Simplify the expression. Write the results in lowest terms. Assume x  0 .
13 x 2 2 x 3
 
6x 3
5
3
Math 104 Final Review Answers
1. (a) f(1) = 1
(b) x = -1, x = 0
(c) Domain: (-3, ∞)
3
7
2. y   x 
4
2
3. (2, 10)
4. r1 = 96 km/hr; r2 = 104 km/hr
5. 9x3
6. 2m
7. (a) (-3, 0), (3,0), (0,0)
(b) (x – 3), (x+3), x
(c) [-3, 3]
2
5
8. y  0, y  , y 
5
2
9. x = 2, x = -8
10. tmax= 1second; hmax = 25 meters
11. 7 + 6i
12. 

5 1 7

3
13. 7 cm, 12 cm
14. 6 lbs of the $3.50, 16 lbs of the final mixture
w  3
15.
3w  4
16. -1 + i
17. W = 12
B  2A
18. b 
2A  h
4
19.
3x
4