Download Math 0308 Departmental Final Exam-Review

Math 0308 Departmental Final Exam-Review
Solve the equation (Problems 1 -- 10).
1) 3x - 8x + 2 = -6x
Answer: - 2
1
Ah
3
for h
Answer: h =
3V
A
12) V =
2) 10r + 4 = 94
Answer: 9
13) A = P + PRT
3) -4(4x + 1) - 5 = -2(x + 3) + 3x
Answer: -
Answer: R =
3
17
14) F =
1
1
4) a - = -2
4
4
5
5) 2(2z - 4) = 3(z - 4)
Answer: -4
A-P
PT
C + 32
Answer: C =
Answer: -7
6)
9
for R
for C
5
(F - 32)
9
Solve the inequality. Graph the solution set and write it in
interval notation (15 -- 18).
15) 11x - 1 > 10x + 8
15
1 7
x+ = x
8
4 4
Answer: (9, )
Answer: -2
7) 6x + 5 - 8x - 5 = 6x - 8x - 3
Answer: no solution
16) -2(4x - 7) < -10x + 10
x
x
8) - 4 =
4
4
Answer: no solution
Answer: (- , -2)
9) 5(x + 3) = (5x + 15)
Answer: all real numbers
10) 2(x + 4) - (2x + 8) = 0
17) 7
2x + 3 17
Answer: all real numbers
Solve the formula for the specified variable (problems 11
-- 14).
11) I = Prt
for t
Answer: t =
I
Pr
Answer: [2, 7]
18) -17
-3x + 4
-5
Answer: [3, 7]
24) A certain vehicle has a weight limit for all
passengers and cargo of 1166 pounds. The four
passengers in the vehicle weigh an average of
160 pounds. Use an inequality to find the
maximum weight of the cargo that the vehicle
can handle.
Answer: at most 526 lb
19) Two angles are complementary if their sum is
90°. If the measure of the first angle is x°, and
the measure of the second angle is (3x - 2)°,
find the measure of each angle.
Answer: 1st angle = 23°; 2nd angle = 67°
20) A 6-ft. board is cut into 2 pieces so that one
piece is 2 feet longer than 3 times the shorter
piece. If the shorter piece is x feet long, find the
lengths of both pieces.
Answer: shorter piece: 1 ft; longer piece: 5 ft
21) The length of a rectangular room is 7 feet
longer than twice the width. If the room's
perimeter is 158 feet, what are the room's
dimensions?
25) A certain store has a fax machine available for
use by its customers. The store charges $1.75 to
send the first page and $0.40 for each
subsequent page. Use an inequality to find the
maximum number of pages that can be faxed
for $6.55
Answer: at most 13 pages
26) Plot the ordered pairs. State in which
quadrant or on which axis the point lies.
(a) (5, 2)
(b) (-3, -4)
(c) (0, 8)
(d) (6, -2)
Answer: quadrant I
Answer: Width = 24 ft; length = 55 ft
22) The owners of a candy store want to sell, for $6
per pound, a mixture of chocolate-covered
raisins, which usually sells for $3 per pound,
and chocolate-covered macadamia nuts,
which usually sells for $8 per pound. They
have a 60-pound barrel of the raisins. How
many pounds of the nuts should they mix with
the barrel of raisins so that they hit their target
value of $6 per pound for the mixture?
Answer: 90 lb
23) Claire has received scores of 85, 88, 87, and 80
on her algebra tests. What is the minimum
score she must receive on the fifth test to have
an overall test score average of at least 82?
(Hint: The average of a list of numbers is their
sum divided by the number of numbers in the
list.)
Answer: 70
0308Final Exam-Review
27) Find three ordered pair solutions by
completing the table. Then use the ordered
pairs to graph the equation.
y = 3x - 4
29) Graph the linear equation by finding and
plotting its intercepts.
-4x - 16y = 16
Answer:
x y
0
1
-1
Answer:
x
0
1
-1
y
-4
-1
-7
30) Graph the linear equation.
4y + 28x = -24
Answer:
28) Graph the linear equation by finding and
plotting its intercepts.
1
y+ x =3
3
Answer:
0308Final Exam-Review
31) Graph the linear equation.
y=5
Answer:
36) (4b)0
Answer: 1
37) (-5)0 + (-8)0
Answer: 2
Simplify the expression. Write the result using positive
exponents only (Problems 38 -- 43).
38) 3-2
Answer:
39)
y-9
y4
Answer:
32) Graph the linear equation.
x+2=0
40)
Answer:
1
9
1
y13
p9
p-6
Answer: p15
41)
(3x4) 3
x15
Answer:
27
x3
42) (z9 x9 )-3
Answer:
43)
33) Find the slope of the line.
y = 5x + 3
Answer: m = 5
34) Find the slope of the line.
8x - 3y = 24
Answer: m =
8
3
1
27
z x27
xy4 -2
x3y
Answer:
x4
y6
Write the number in scientific notation (Problems 44 &
45).
44) 0.00006427
Answer: 6.427 × 10-5
Simplify the expression (problems 35 -- 37).
35) -8y0
Answer: -8
0308Final Exam-Review
45) A light-year is a measure of length defined as
the distance that light travels in one year,
which is about 9,500,000,000,000 kilometers.
Write this number in scientific notation.
Answer: 9.5 × 1012
Write the number in standard notation (Problems 46 & 47).
46) 7.9353 × 105
Answer: 793,530
47) 5.14 × 10-4
Answer: 0.000514
56) (8y2 + 7) - (-6y4 - 4y2 + 7)
Answer: 6y4 + 12y2
57) (8x2 - xy - y2) + (x2 + 4xy + 8y2 )
Answer: 9x2 + 3xy + 7y2
58) Find the perimeter.
(x2 - 4x + 9)
units
(x2 + 3x + 13) units
(2x2 - x + 18) units
48) Evaluate the expression using exponential
rules. Write the result in standard notation.
24 × 104
4 × 108
Answer: 0.0006
Find the degree of the following polynomial and
determine whether it is a monomial, binomial, trinomial,
or none of these (Problems 49 -- 52).
49) -15a9
Answer: 9; monomial
50) -18y5 - 1
Answer: 5; binomial
51) 8
Answer: 1; monomial
52) 9y2 - 6y4 + 8
Answer: 4; trinomial
Perform the indicated operation (Problems 53 -- 70).
53) (-8y + 7) + (-2y2 + 3y - 3)
Answer: -2y2 - 5y + 4
54) (5y3 + 4y2 - 5) + (8y3 + 9y2 + 5)
Answer: 13y3 + 13y2
55) Subtract (26x + 4) from (-15x2 - 13x + 4).
Answer: (4x2 - 2x + 40) units
59) -4x(2x + 9)
Answer: -8x2 - 36x
60) -y(9x3 - 9y + 7x - 8y3 )
Answer: -9x3 y + 9y2 - 7xy + 8y4
61) (5z + 12)2
Answer: 25z 2 + 120z + 144
62) (9z + 11)2
Answer: 81z 2 + 198z + 121
63) (4x - 1)(x2 - 2x + 1)
Answer: 4x3 - 9x2 + 6x - 1
64) (8x - 1)(x2 - 5x + 1)
Answer: 8x3 - 41x2 + 13x - 1
65) (3x + 6)(x + 10)
Answer: 3x2 + 36x + 60
66) (x + 9)(x3 + 3x - 8)
Answer: x4 + 9x 3 + 3x2 + 19x - 72
67) (8x - 1)(x2 - 3x + 1)
Answer: 8x3 - 25x2 + 11x - 1
Answer: -15x2 - 39x
0308Final Exam-Review
68) (6y + x)(6y - x)
Answer: 36y2 - x2
69) (5p + 2)(5p - 2)
76) The area of the playing surface of the tennis
court shown is (49x2 + 49x - 18) square feet. If
its width is (7x - 2) feet, find its length.
Answer: 25p2 - 4
70) (3y + 7)(3y + 8)
(7x - 2) feet
Answer: 9y2 + 45y + 56
Perform the division (71 & 72).
-30x6 - 36x4 - 12x2
71)
-6x4
2
Answer: 5x2 + 6 +
x2
7x3y3 - 14xy - x2 y2
72)
7xy
xy
Answer: x2 y2 - 2 7
Find the quotient using long division (73, 74 & 75).
x2 + 15x + 56
73)
x+8
Answer: x + 7
74)
4x3 + 12x2 + 3x + 7
2x + 3
16
Answer: 2x2 + 3x - 3 +
2x + 3
75)
x3 - 8
x-2
Answer: x2 + 2x + 4
Answer: (7x + 9) ft
Factor out the GCF from the polynomial (Problems 77 -81).
77) 27x3 - 6x2 + 12x
Answer: 3x(9x2 - 2x + 4)
78) 12m 9 - 32m7 - 28m 5
Answer: 4m 5 (3m 4 - 8m 2 - 7)
79) 54x8y9 + 18x6 y6 + 24x3y4
Answer: 6x3 y4(9x5 y5 + 3x 3 y2 + 4)
80) 4a(a - b) + (a - b)
Answer: (a - b)(4a + 1)
81) 6(y + 15) - x(y + 15)
Answer: (y + 15)(6 - x)
Factor the binomial completely. (Problems: 82 - 87)
82) z2 - 4
Answer: (z + 2)(z - 2)
83) 49 - w2
Answer: (7 - w)(7 + w)
84) 9x2 - 4
Answer: (3x + 2)(3x - 2)
85) 49x2 + 25y2
Answer: (7x + 5y)(7x - 5y)
86) 81a 3 - 4a
Answer: a(9a + 2)(9a - 2)
0308Final Exam-Review
87) 49x2 - 36y2
Answer: (7x + 6y)(7x - 6y)
In problems 88 -- 97, factor the trinomial completely. If
the polynomial cannot be factored, write "prime."
88) x2 - x - 42
Answer: (x + 6)(x - 7)
89) x2 - 10x + 16
Answer: (x - 2)(x - 8)
90) 4x - 21 + x 2
Answer: (x + 7)(x - 3)
91) x2 + 13xy + 40y2
Answer: (x + 8y)(x + 5y)
92) x2 + 8xy + 16y2
Answer: (x + 4y)2
93) 81x2 - 36x + 4
Answer: (9x - 2)2
Solve the equation (Problems 101 -- 107).
101) x2 + 4x - 12 = 0
Answer: -6, 2
102) x2 - x = 30
Answer: -5, 6
103) x(3x + 16) = 12
Answer:
2
, -6
3
Solve the equation.
104) 13x2 - 3x = 0
Answer:
3
,0
13
105) 25x2 - 81 = 0
Answer:
9
9
,5
5
106) 3x2 + 15x + 18 = 0
Answer: - 3, - 2
107) (x + 3)(x + 1) = 35
94) 15z 2 + 4z - 4
Answer: (3z + 2)(5z - 2)
95) 7x2 - 16x - 15
Answer: (7x + 5)(x - 3)
96) 9x2 - 39x - 30
Answer: 3(3x + 2)(x - 5)
97) -16x3 + 52x2 - 30x
Answer: -2x(2x - 5)(4x - 3)
Factor the four-term polynomial by grouping (Problems
98 -- 100).
98) 5x + 35 + xy + 7y
Answer: (x + 7)(5 + y)
99) 15x2 + 18x - 25x - 30
Answer: (3x - 5)(5x + 6)
100) 5xy - 20x + 7y - 28
Answer: -8, 4
Solve the system of equations by graphing.
108) 2x + y = 2
3x + y = 1
Answer: (-1, 4)
In problems 109 & 110, decide without graphing:
(a) Are the graphs of the equations are identical lines,
parallel lines, or lines intersecting at a single point?
(b) How many solutions does the system have?
x = -y
109)
y + x = -4
Answer: parallel lines; no solution
x + 2y = 12
1
110)
y=- x+6
2
Answer: identical lines; infinite number of
solutions
Answer: (5x + 7)(y - 4)
0308Final Exam-Review
Solve the system of equations by the substitution method
(Problems 111 & 112).
y = 5x - 5
111)
2y + 8x = -28
Divide and simplify.
m2 - n2
m
÷
119)
m+n
m 2 - mn
Answer: (-1, -10)
112) -3x - 2y = -126
x = 4y
Answer: (36, 9)
Solve the system of equations by the addition method
(Problems 113).
113) x + 3y = 11
-6x + 2y = -6
Answer: (m - n)2
120)
z2 + 5z + 6
z2 + 3z
÷
z 2 + 10z + 16 z2 + 14z + 48
Answer:
z+6
z
Answer: (2, 3)
Solve the system of equations by the addition method
(Problems 115 & 116).
114) 2x - 3y = 2
3x - 5y = 2
Answer: (4, 2)
Solve.
115) Devon purchased tickets to an air show for 9
adults and 2 children. The total cost was $252.
The cost of a child's ticket was $6 less than the
cost of an adult's ticket. Find the price of an
adult's ticket and a child's ticket.
Answer: adult's ticket: $24; child's ticket: $18
116) Jamil always throws loose change into a pencil
holder on his desk and takes it out every two
weeks. This time it is all nickels and dimes.
There are 7 times as many dimes as nickels,
and the value of the dimes is $7.80 more than
the value of the nickels. How many nickels and
dimes does Jamil have?
Answer: 12 nickels and 84 dimes
Simplify the rational expression.
4x - 20
117)
5-x
Answer: -4
Mulitply and simplify.
8p - 8
8p2
·
118)
p
9p - 9
Answer:
64p
9
0308Final Exam-Review