Download THT 3 MAT 1033 Summer 13

Take Home Test # 3 THT#3
DUE __________________________________
Name___________________________________MAT 1033
SHOW ALL WORK AND ATTACH
Decide whether the expression has been simplified correctly.
1) (ab)4 = a4 b4
A) No
2) (ab)9 = ab9
A) Yes
B) Yes
B) No
Evaluate the expression.
7 -3
3)
4 -4
A)
4)
2401
1024
256
343
C)
343
256
D)
1024
2401
1
-7 -3
A) -343
5)
B)
B) -49
C) 343
B) 81
C)
D) 49
1 -4
3
A) - 81
1
81
Evaluate the expression. Assume all variables represent nonzero numbers.
6) (-10)0 + (-12)0
A) 2
D) -
1
81
B) -22
C) 0
D) -2
7) -4 0 - x0
A) -2
B) 0
C) 2
D) 1
8) (11x)0
A) 11x
B) 1
C) 11
D) 0
Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if
necessary.
9) (-3)-2
A) - 9
10) (3p) -2
A)
1
6p-2
B)
B)
1
9
C) 9
1
C)
3p2
1
D) -
1
-6p2
D)
1
9
1
9p2
Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all
variables represent nonzero numbers.
x16
11)
x4
A) -x12
12)
C) x12
D) x20
B) x8
C) -x8
D)
C) x6
D)
x12
x8
x16
A)
13)
1
B)
1
x24
1
x8
x-12
x-6
A) -x18
B)
1
x6
1
x18
Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero
numbers.
(p-5 )3
14)
7p5
A)
15)
7
p130
B) 7p20
C)
p-10
75
D)
C)
y35
2x25
D)
1
7p20
2x3y-3 -5
x-2 y4
A)
y35
32x25
B)
y35
2x5
Identify the coefficient and degree of the term.
16) 9z
A) Coefficient: 0; Degree: 9
C) Coefficient: 9; Degree: 0
17) x
B) Coefficient: 1; Degree: 9
D) Coefficient: 9; Degree: 1
A) Coefficient: 0; Degree: 0
C) Coefficient: 1; Degree: 0
B) Coefficient: 1; Degree: 1
D) Coefficient: 0; Degree: 1
18) 14a 2b6
A) Coefficient: 1; Degree: 9
C) Coefficient: 14; Degree: 2
B) Coefficient: 14; Degree: 8
D) Coefficient: 1; Degree: 8
2
2x25
y35
Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
19) -5x2
A) Binomial, degree 0
B) Binomial, degree -5
C) Monomial, degree 2
D) Monomial, degree -5
20) 10y5 - 1
A) Binomial, degree 5
C) Monomial, degree 10
B) Binomial, degree 0
D) Binomial, degree 6
21) -11s6 + 3s - 7
A) Binomial, degree 7
C) Trinomial, degree 7
B) Trinomial, degree 8
D) Trinomial, degree 6
Combine terms.
22) y3 - 5y4 - 4y2 + y4 + 5y3
A) -4y8 + 4y6 - 4y2
B) -5y4 - y3 - 4y2
C) -4y4 + 6y3 - 4y2
Add or subtract as indicated.
23) (4 - 3x3 + 6x5 - 4x4 ) + (-7x4 + 9x3 + 2 + 7x5 )
A) 13x10 - 11x8 + 6x6 + 6
D) 4y4 - 4y3 + 4y2
B) -3x5 - 3x4 + 8x3 + 3
D) 13x5 - 11x 4 + 6x3 + 6
C) 8x24 + 6
For the given polynomial function, find the requested value.
24) f(x) = 8x + 6; find f(7)
A) 14
B) 62
C) 50
D) 112
B) -31
C) -59
D) -53
28) 2x(3x - 1)(6x + 8)
A) 32x3 + 38x 2 - 14x
B) 34x2 + 37x - 16
C) 36x3 + 36x 2 - 16x
D) 18x3 + 18x 2 - 8x
29) (x + 5)(x2 - x + 8)
A) x3 + 4x2 + 3x + 40
B) x3 + 6x2 + 13x + 40
C) x3 + 40
D) x3 + 4x2 + 40
30) (6p + 1)(6p - 1)
A) 36p2 - 1
B) 36p2 + 12p - 1
C) p2 - 1
D) 36p2 - 12p - 1
31) (12y + x)(12y - x)
A) 144y2 - 24xy - x2
B) 24y2 - x2
C) 144y2 - x2
D) 144y2 + 24xy - x2
25) f(x) = -9x2 - 4x - 5; find f(2)
A) -49
Find the product.
26) (5m 3 )(5m 3 )
27) 10x5(2x + 10)
3
32) (a - 1)(a + 1)
A) a2 + 2a - 1
B) a2 - 2
C) a2 - 1
D) a2 - 2a - 1
B) x2 + 4x - 8
C) x2 - 4x - 8
4
D) x2 64
34) (n + 16)2
A) n 2 + 32n + 256
B) n 2 + 256
C) n + 256
D) 256n 2 + 32n + 256
35) (4a - 3)2
A) 16a 2 - 24a + 9
B) 4a 2 + 9
C) 16a 2 + 9
D) 4a 2 - 24a + 9
33) x +
2
2
x8
8
A) x2 - 4
36) [(2x - y) + 3z][(2x - y) - 3z]
A) 4x2 - 4xy + y2 - 9z2
C) 4x2 + y2 - 9z2
B) 4x2 + y2 + 12xz + 6yz - 9z 2
D) 4x2 - 4xy + y2 + 12xz + 6yz - 9z 2
Express the area of the figure as a polynomial in descending powers of the variable x.
4x - 3
37)
x+3
A) 4x2 + 9x - 9
B) -4x2 + 8x + 9
C) 4x2 + 15x - 6
D) 3x2 - 15x + 9
38)
x2 + 8x - 1
4x + 2
A) 2x3 - 17x2 + 6x + 1
B) 2x3 + 17x2 + 6x - 1
D) 2x3 - 15x2 - 10x - 1
C) 2x3 + 15x2 + 10x - 1
Divide.
39)
5x7 + 9x6 + x2
x
A) 14
40)
B) 5x7 + 9x6 + x
C) 5x6 + 9x5 + x
D) 5x6 + 9x6 + x2
B) -16x8 + 7x2
C) 4x4 + 7x2
D) 11x10
-16x8 - 28x6
-4x4
A) 4x4 - 28x6
4
41)
16st4 - 5t6 + 64st3
4st3
A) 4t - st3 + 16
B) 4t -
t3
+ 16
s
C) 4t -
Find the greatest common factor of the terms.
42) 10m 5, 40m 7
A) 400m2
B) 10m 2
5t3
+ 16
4s
D) 4st -
C) 10m 5
D) 40m 5
5t3
+ 16
4s
43) 64a 8b4, 40a5 b8
A) 320a8 b8
B) 4a 3 b4
C) 8a 5 b4
D) 8a 8 b8
44) 21m 3, 189m 7 , 441m4
A) 21m 4
B) 21m 3
C) 3969m 4
D) 189m3
B) (9x - 2)2
C) (9x + 2)(9x - 2)
D) (81x + 1)(x - 4)
Factor out the greatest common factor.
45) 5x3 + 15x
46) 15wx - 20wy - 25wz
47) 2x(5x - 2) + 3(5x - 2)
48) (x - 9)(x + 9) + (x - 9)(x + 3)
Factor by grouping.
49) sx + tx + sa + ta
50) 3xa + 3xb - 5a - 5b
Factor the trinomial completely.
51) z2 + 7z + 12
52) -x2 - 8x + 20
53) z2 - 2zw + 63w2
54) 16x2 + 24x + 9
55) 9z 2 + 6z - 8
Factor the polynomial completely.
56) 81x2 - 4
A) (9x + 2)2
5
57) 144k2 - 25m 2
A) (144k + m)(k - 25m)
B) (12k + 5m)2
D) (12k - 5m)2
C) (12k + 5m)(12k - 5m)
58) x2 - 20x + 100
B) (x - 10)2
C) (x + 10)2
D) Prime
59) m 2 + 6m + 9
A) (m - 3)2
B) (m + 3)(m - 3)
C) (m + 3)2
D) Prime
60) 25x2 + 30xy + 9y2
A) (25x + 1)(x + 9)
B) (5x + 3y)2
C) (5x + 3y)(5x - 3y)
D) (5x - 3y)2
A) (x + 10)(x - 10)
61) z3 - 27p3
A) (z - 3p)(z 2 + 3zp + 9p2)
C) (z - 3p)(z 2 + 9p2)
B) (z + 27p)(z + p)(z - p)
D) (z + 3p)(z 2 - 3zp + 9p2)
Find all numbers not in the domain of the function.
3
62) f(x) =
x-4
A) 0
63) f(x) =
C) 4
D) None
B) -8
C) 0
D) 8
B) 0
C) -6
D) 6
3
x+8
A) None
64) f(x) =
B) -4
x-6
8
A) None
Express the rational expression in lowest terms.
40m 2 p2
65)
8m 8 p
A) 5m 6 p2
66)
B) 5mp
C)
5m 6
p
D)
y-2
y+4
C)
2y + 8
8y - 8
D) -
5p
m6
y2 + 2y - 8
y2 + 8y + 16
A)
2y - 8
8y + 16
B)
6
y2 + 2y - 8
y2 + 8y + 16
67)
z3 + 8
z 3 - 2z 2 + 4z
A)
68)
z+4
z
B)
z+2
z
C)
z-2
2
D)
z-2
z
B)
3x - 5y
2x - 7y
C)
3x + 5y
2x - 7y
D)
3x + 5y
3x - 5y
9x2 - 25y2
6x2 - 31xy + 35y2
A)
3x + 5y
2x + 7y
Simplify the expression. Use the order of operations.
69) -2( 25) - (-2)(-2)
A) -14
B) -6
70) -11[13 + (-15)]
A) 22
B) -30
Evaluate the expression if a = -5, b = 16, and c = 7.
71) abc + b2
A) -304
B) -114
C) 4
D) -10
C) 360
D) -39
C) 114
D) -108
Complete the statement so that the indicated property is illustrated. Simplify the answer, if possible.
72) -5m - 3n =
(commutative property)
A) (-5 + 3)mn = -2mn
73) -5 + (15 + 9) =
B) -3n - 5m
C) (-5 - 3)mn = -8mn
D) -3n - 5m = -8nm
(associative property)
A) (15 + 9) - 5 = 19
C) 9 + (15 - 5) = 19
B) (-5 + 15) + (-5 + 9) = 14
D) (-5 + 15) + 9 = 19
Solve the problem.
74) A room has an area of 352 ft2 . One dimension is 6 ft more than the other. Find the dimensions of the room.
A) 10 ft, 16 ft
B) 16 ft, 22 ft
C) 18 ft, 24 ft
D) 22 ft, 28 ft
75) A rectangular garden is 12 ft by 5 ft. A gravel path of equal width is to be built around the garden. How wide
can the path be if there is enough gravel for 138 ft2?
A) 4 ft
Solve.
B) 10 ft
C) 5 ft
D) 3 ft
76) An airplane travels 800 miles against the wind in 5 hours, and makes the return trip with the same wind in
2 hours. Find the rate of the wind.
A) 120 mph
B) 280 mph
C) 400 mph
D) 160 mph
7
Solve the problem.
77) A sum of money amounting to $6.10 consists of dimes and quarters. If there are 31 coins in all, how many are
quarters?
A) 11 quarters
B) 25 quarters
C) 20 quarters
D) 13 quarters
Solve.
78) 4x - 6 = 3
3 9
,
A)
4 4
79) |8 - 4p|= 40
A) - 8, 12
B) -
7
1
,6
6
C) -
B) 12
9
3
,4
4
C) -12, 8
Solve the inequality, giving its solution set in both interval and graph forms.
80) 28a + 4 > 4(6a - 6)
81) 5 < -3b + 5 17
Solve the equation for the specified variable.
3y - x
for y
82) w =
y
Solve the system by substitution.
83) 3x - 13 = -y
2x + 9y = -8
Solve the system by graphing.
84) 4x + 4y = 28
4x + 2y = 20
8
D)
1 7
,
6 6
D) -12, - 8