Intermediate Algebra
Final Exam Review
Name
1. Express the set in roster fonn.
-4
6
{x \ e I and — < x < —}
^ '
3
3^
2. Consider the following set of numbers. • ^f64, 5 | , -6, 0, 0.7, TT, V8^4.9, 12
a. List the rational n u m b e r s ^ " ^ ^ ^ S ^ ^
^
^ '^^^ i
\
b. List the irrational numbers
3. Arrange the numbers from smallesf to biggest.
4.
Simplify:
-(-9)'+9(-3^)
-(-0.187),
5.
11
1.18, 116
-0.2
Simplify:
6. Simplify:
2-^49-2(2'-5-2')
^-^z
5-3(|2-7|%5)
H-2C
7.
Simplify:^
[(4r(3-5))-7f
^
„ I
T
3
6'"^]^
8.
Simplify:
4
11
5^62
9. Evaluate for x = 25 and >' = 36 :
10. Simplify.
ll.Multipl
12, Simplify.
3
6 ^ 4 ^
lO^lS'
(-2Vj^^(^xVz)
4L„-5
V
S a c "
C
u p
h
14. Simplify.
13. Convert the following to standard form.
7.698x10'
(1.5xlQ')(2.4xlO')
T
(6x10-')
GxlO
Zl
on
16. Simplify.
15. Simplify.
4jc-7(9>^-3) + 2(>' + 3x)-4>'
7
x+ —x + - - •1f -
17. Solve for .
iX-dX-Z
- 3(6 - 4x) = 4 - {5x - [6x -(4x - (3x + 2))]}
.
18. Solve for .X .
5,
L
7
2
X=2
19. Solve for > r ^
±
-
20 Solve ;i = - / ^ ( a + /?)for or.
7-(^>' + 4) = 3(-^>^ + 2)
^ 12...
21. A yield sign on a particular road has an area of 150 in^ What is the length of the base if the
height is 12 inches?
i / ^ (o
Remember: A^^^bh
150
6
I
- —
22. You are choosing between two long-distance telephone plans. One plan has a monthly fee of $25 with a
charge of 25<^ per minute. The other plan has a monthly fee of $ 10 with a charge of 30<^ per minute. For
how many minutes of long-distance calls will the costs for the two^lans be the same?
J3.
23. If French roast coffee sells for $8.50 per pound and vanilla hazelnut coffee sells for $12.50 per pound,
how many pounds of vanilla hazelnut should you mix with 9 pounds of French roast to get a blend
that is sold for $11 per pound? T a S c K ^
6 . 5 t i ^ f Z . ' ^ O / , - \U)CVV)
^ 1
" ^ ^ ^ ^ v c ^ ^ s .
,5 - W ^
-J
r-
24. Say you were running 6 miles an hour, and your friend was running 4 miles an hour. How long did it
take to get 1 mile ahead of your friend?
Rate
Time
Distance
You
A
friend
('•X
K
J
t M J I
J l i t . ivij
6)C
25. Solve the inequahty, express your answer in interval notation, and graph the solution.
.
•6 - C p
- 3
26. Solve the inequality, express your answer in interval notation, and graph the solution.
3
—
•<
S53
"yO
-75
— -3
27. Solve and express your answer in interval notation.
28. Solve the folloWinf:
2>^-6| = | l 0 - ^ j ;
4
i\
29. Determine if the following graphs represent a function. It does represent a function, then state the domain
y
a)
y
b)
c)
A
31. Write the equation of the line.
32. Wrile an equation of the hne that goes tlu-ougli the point (4, -1) and perpendicular to the line
33. The population of the United States, in millions, in 1980 was 226.5 million, and in 1990 was 250
milUon. This infoimation is shown in the following graph.
(20.228.5)
r(\ 2.35
0
10
20
30
JO
50
Y««r>aft>r 1960
a. Determine a Imear function that can be used to estimate the population of the United
States, P, in millions, in terms of t years after 1960.
b. Use the function determined in part a) to determine the population of the United States in
2013 t = ^ 3 'fe 20Vi
c.
Use the function determined in part a) to estimate the year at which the population of the
United States will be 500 miUion.
5= 2 . "^Ot ^
34 Let fix) ^ x' - - x + 3and
= 2.-5
Si2i5-^^
5^> OXX^ 2CR6
c.
Fmd
'ind
i^f) = 2t^)-Q «\ ^ " z D \
aph
35. Grap
~—
4JC-2V<2
2,
36. Find the inequality that describes the shaded region.
1
3
X
Solve the following linear system by graphing.
37.
x+y = \
3/y
= -5
Solve the following linear systems by the method of ypur choice.
^
38.
J
7.
3x + J + r = 8
2x + 2 y - z = 10
j c - 3 j ; + 2z = -4
39. You invested $10,000 in two funds paying 3% and 5% annual interest. At the end of the year, the interest from
the 5% investment exceeded the interest from the 3% investment by $20. How much money was invested at
each rate?
Equations
40. Jesse, Maria and Charles went to the local craft store to purchase supplies for making decorations for
the upcoming dance at the high school. Jesse purchased tlnee sheets of craft paper, four boxes of
markers and five glue sticks. His bill, before taxes was $24.40. Maria spent $30.40 when she bought
six sheets of craft paper, five boxes of markers and two glue sticks. Charles, purchases totaled $13.40
when he bought three sheets of craft paper, two boxes of markers and one glue stick. Detennine the
unit cost of each item?
Let X =
CX<^ p l p r x l ^ ^ i ' ^ - y
LetU =
Let V. ^
/
(JM
(KM
oluf V>ti(K(^.^
E q u a t i o n . ^ ' ^->X V
H
U
.
.
^
i
Solve the following system of linear inequalities by graphing.
41.
^-2|<3 _Jz£ii=_-X+|:£3
-(j>:X+z
42. Indicate whether monomial, binomial, or trinomial, and
state the degree:
Type of polynomial
43. Subtrtet:
5o|ahon
(6x' - 4 ± 8 ) + (-t-9jc' + ^ ^ + ^)
^V\COfe\
Degree of polynomial
44. Multipjy
45. Divide:
- 36;c>'z -
1 6 J C > ' + 4JC>''Z'
1 iJtCt:)^^
46. Divide using long division:
(4^:" + 6x' + 3x + 2) - (2x' +1)
47. Divide using synthetic division:
; \
5;C^+3;C'-12.X^-A: + 2
2
A:
|\
-
5
^ 2- 2- -
zM
-Z
5 5 -IQ - 5 o
•
i
48. Factor.
a'-Z>'+46-4
50. Factor.
51. Factor.
8l/(;t_f5)-(;c+_5)
l-27:tV
(x+^l^Jc^+\Y5X vC^3X-\
""i + sxy+^^t^^]^
52. Solve for r.
5r^-Ur
=
- 7)^ + ^'^ = (jt + 2)^^
- 3 - e
54. Find the area of the shaded region in factored
form:
55. Find the difference of the volumes of the two cubes
in factored form:
^3 A ^ y ^ i ^ S ^ ^ *
56. Find the missmg lengths by usffiigtEe Pythagorean Theorem,
x+7
=
, and thSm -fectoriflg:
\
\
57. Fmd an equation whose graph will have the x-intercepts
— ,0 and (-4,0).
2X-5=0
58. A rectangular garden measures 16 feet by 12 feet. A path of uniform width is to be added so as to
surround the entire garden. The landscape artist doing the work wants the garden and path to cover an
area of 60 square feet. How wide should the path be?
59. You throw a ball straight up from a rooftop 160 feet high with an initial speed of 48 feet per second.
The function h(() = -I6t^ + 48/ + 160 describes the ball's height above the ground, h(t), in feet, t
seconds after you threw it.
a.
Find the time it takes ftr Ae ball to hit the ground.
Ti"
^ •'f-
b. Find the time it takes the ball to be at a height of 192 feet.
t-\t+-2LV0
60. A 15-ft ladder is leaning against a building. The ladder reaches up the wall 3 feet more than the distance of the
ground between the base of the ladder to the building. Find the length the ladder reaches up the wall and the
distance of the ground between the base of the ladder to the building.
2^
15 feel
6^
,1. .f.v.^ ^ 7S