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WorksheetsAlgebra Practice Final Questions
Total questions: 90
Worksheet time: 7hrs 53mins
Name
Class
Date
1.
a)
(-1, -1)
b)
(-2, 1)
c)
(1, 1)
d)
NO SOLUTION
2.
a)
(1, 1)
b)
(1, 2)
c)
Infinitely many solutions
d)
No solution
3.
a)
(1, 1)
b)
(1, 2)
c)
Infinitely many solutions
d)
No solution
4.
a)
Infinitely man solutions.
b)
(-8, 1)
c)
(2, 4)
d)
(-1, -8)
5.
a)
(0, 3)
b)
(3, 0)
c)
(0, -3)
d)
(-3, -3)
6.
a)
Chickens have four legs this questions has no solution.
b)
160 chickens, 104 cows
c)
140 chickens, 124 cows
d)
214 chickens, 50 cows
7.
a)
36 dimes, 26 quarters
b)
26 dimes, 36 quarters
c)
I'm rich who cares.
d)
40 dimes, 12 quarters
8.
a)
1 adult, 203 children
b)
150 adults, 54 children
c)
84 adults, 120 children
d)
68 adults, 136 children
9.
Determine whether the ordered pair is a solution of the given system.
a)
Yes, it is a solution.
b)
No, it is not a solution.
10.
Determine whether the ordered pair is a solution of the given system.
a)
Yes, it is a solution.
b)
No, it is not a solution.
11.
What is the solution to the system of equations?
−4x − 2y = −12
4x + 8y = −24
−4x − 2y = −12
4x + 8y = −24
a)
(6, -6)
b)
(-6, 6)
c)
(-10, 2)
d)
(2, -10)
12.
What is the solution to the system of equations?
5x + y = 9
10x − 7y = −18
5x + y = 9
10x − 7y = −18
a)
(4, -11)
b)
(1, 4)
c)
(-1, 14)
d)
(-4, 29)
13.
What is the solution to the system of equations?
y = 3x - 8
y = 4 - x
y = 3x - 8
y = 4 - x
a)
(3,1)
b)
(1,3)
c)
(-3,1)
d)
(3,-1)
14.
Solve the system of equations.
x + 2y = -3
x - y = -12
x + 2y = -3
x - y = -12
a)
(-9, 3)
b)
(-7 ,5)
c)
(3, 15)
d)
(9, 6)
15.
Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Write a system to represent this situation assuming "a" represents # of adult tickets and "c" represents # of children's tickets.
a)
a + c = 21
6a + 4c = 104
6a + 4c = 104
b)
a + c = 104
6a + 4c = 21
6a + 4c = 21
c)
a + c = 21
6c + 4a = 104
6c + 4a = 104
d)
a + c = 104
6c + 4a = 21
6c + 4a = 21
16.
Enterprise charges to rent compact cars for a fixed amount per day plus a fixed amount for each mile driven. Batman rented a car for 6 days, drove it 550 miles and spent $337. Superman rented the same car for 3 days, drove for 350 miles and spent $185. Set up the system. Let "d" represent the fixed charge per day and "m" represent the cost per mile.
a)
6d + 550m = 337
3d + 350m = 185
3d + 350m = 185
b)
6d + 550m = 185
3d + 350m = 337
3d + 350m = 337
c)
6m + 550d = 337
3m + 350d = 185
3m + 350d = 185
d)
6m + 550d = 185
3m + 350d = 337
3m + 350d = 337
17.
David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?
a)
1.5x+0.5y=78.5
x+y=87
x+y=87
b)
1.5x+0.5y=78.5
1.5x+0.5y=87
1.5x+0.5y=87
c)
x+y=78.5
1.5x+0.5y=87
1.5x+0.5y=87
d)
x+y=78.5
x+y=87
x+y=87
18.
Solve for x and y
3x + 2y = 16
7x + y = 19
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
19.
5³⋅5⁴
a)
5⁷
b)
5⁻¹
c)
5¹²
d)
5
20.
6⋅6⁷
a)
6⁸
b)
6⁶
c)
6⁷
d)
6
21.
(2⁸)²
a)
2¹⁶
b)
2¹⁰
c)
2⁶
d)
2⁴
22.
Anything raised to a power of zero is always:
a)
0
b)
1
c)
itself
d)
negative
23.
According to exponent rules, when we raise the power to a power we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
24.
According to exponent rules, when we multiply the expressions (with the same base) we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
25.
According to exponent rules, when we divide the expressions (with the same base) we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
26.
n²⋅n⁴⋅n⁵
a)
n¹¹
b)
n⁴⁰
c)
n¹³
d)
n²²
27.
8⁷ ⁄ 8²
a)
8⁵
b)
8⁹
c)
8¹⁴
d)
1⁵
28.
3⁻⁴
a)
1 ⁄ 34
b)
-34
c)
34
d)
1 ⁄ 12
29.
7⁰
a)
1
b)
7
c)
0
d)
-7
30.
(34x5y6z-7)0
a)
34x5y6 / z7
b)
34x5y6 / x-7
c)
0
d)
1
31.
(3y⁴)²
a)
9y⁸
b)
9y⁶
c)
6y⁸
d)
6y⁶
32.
3x⁻³
a)
1⁄3x³
b)
3⁄x³
c)
3x³
d)
-3x³
33.
Fill in the blank with the correct exponent to make the statement true.
316 = (38)(3_)
316 = (38)(3_)
a)
2
b)
8
c)
4
d)
1
34.
a)
a
b)
b
35.
a)
a
b)
b
36.
Can you leave a negative exponent in your answer?
a)
YES
b)
NO
37.
In 23 what is the base?
a)
2
b)
3
c)
23
38.
In 23 what is the exponent?
a)
2
b)
3
c)
23
39.
Which is equivalent to 5 x 5 x 5 x 5
a)
53
b)
54
c)
45
d)
55
40.
Which is equivalent to 34
a)
27
b)
9
c)
81
d)
12
41.
What is equivalent to 5 squared?
a)
25
b)
10
c)
55
d)
30
42.
a)
a
b)
b
43.
Simplify the exponential expression:
a)
10x-2
b)
2x2
c)
2x12
d)
10x12
44.
Simplify the exponential expression.
a)
2x6y12
b)
2x5y7
c)
8x6y12
d)
8x5y7
45.
2.) Simplify
(3x3y5)4
(3x3y5)4
a)
3x12y20
b)
81x12y20
c)
12x12y20
d)
81x7y9
46.
3.) Simplify
(45x6y2)/(5x4y9)
a)
(9x2)/y7
b)
40x2y7
c)
9x2y7
d)
9x10y11
47.
4.) Simplify
(16x4y-5)/(8a3b-8)
(16x4y-5)/(8a3b-8)
a)
(a3y5)/(2x4b8)
b)
(2x4b8)/(a3y5)
c)
(8x4b8)/(a3y5)
d)
2x4b8a3y5
48.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
49.
(7uv2)-5
a)
-35uv-10
b)
-5/7uv2
c)
1/75u5v10
d)
1/7uv10
50.
Simplify (-4r5)(2r8)
a)
-8r13
b)
-2r13
c)
-8r40
d)
-2y40
51.
Make this negative exponent positive.
9-3
9-3
a)
93
b)
1/9-3
c)
1/93
d)
729
52.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
53.
x3y/xy5
a)
x2y4
b)
x3y4
c)
x2/y4
d)
x2/y5
54.
Simplify each expression.
(6b3 + 6 - b4) - (8b3 - 6b4 + 2)
(6b3 + 6 - b4) - (8b3 - 6b4 + 2)
a)
4b4 - 2b3 + 7
b)
5b4 - 2b3 + 4
c)
b4 - 2b3 + 7
d)
5b4 - 2b3 + 7
55.
Simplify each expression.
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
a)
-8n2 - 8n + 3
b)
-7n2 - 8n + 3
c)
-6n2 - 8n + 3
d)
-7n2 - 4n + 3
56.
Simplify each expression.
(6x + 4x4 - 3x2) + (7x4 + 5x2 + 8x)
(6x + 4x4 - 3x2) + (7x4 + 5x2 + 8x)
a)
11x4 + 2x2 + 14x
b)
16x4 + x2 + 14x
c)
11x4 + x2 + 14x
d)
11x4 + 2x2 + 10x
57.
Simplify the expression.
(4a3 - 8a - 4a2) + (7a3 - 7 - 6a)
(4a3 - 8a - 4a2) + (7a3 - 7 - 6a)
a)
11a3 - 4a2 - 14a - 7
b)
5a3 - 4a2 - 14a - 7
c)
5a3 - 4a2 - 20a - 7
d)
5a3 - 9a2 - 20a - 7
58.
Factor by GCF:
4b5 + 4b3 + 16b2
4b5 + 4b3 + 16b2
a)
4b3(b4+b2+4b)
b)
4b3(b4+4b+5)
c)
4(b5+b3+4b2)
d)
4b2(b3+b+4)
59.
What is the GCF of the trinomial?
3x2 - 9x -120
3x2 - 9x -120
a)
3
b)
2
c)
6
d)
9
60.
Factor by GCF:
10x2 + 15x - 5
10x2 + 15x - 5
a)
25(10x3+45x-15)
b)
5(2x3 + 3x2-x)
c)
x(10x3+15x-5)
d)
5(2x2+3x-1)
61.
8x(2x2 + 6x + 10)
a)
10x3 + 14x2 + 18x
b)
16x3 + 48x2 + 80x
c)
16x2 + 48x + 80
d)
10x2 + 14x + 80
62.
(7r+6)(7r+6)
a)
49r2+36
b)
49r2-36
c)
49r2+84r+36
d)
49r2+42r+36
63.
(x+4)2
a)
x2+16
b)
x2-16
c)
x2+8x+16
d)
x2+8x-16
64.
What does FOIL stand for?
a)
Failing Only in Latin
b)
Farming Only in Lakewood
c)
First Outside Inside Last
d)
Fresh Only in Lakes
65.
Find the product:
(x + 5)(x - 4)
(x + 5)(x - 4)
a)
x2 + 9x + 20
b)
x2 + 9x - 20
c)
x2 + 1x - 20
d)
x2 - 1x - 20
66.
Factor
k2+7x+10
k2+7x+10
a)
(k+2)(k+5)
b)
(k-2)(k-5)
c)
(k+10)(k+4)
d)
(k+2)(k-5)
67.
Factor
n2 + 16n + 63
n2 + 16n + 63
a)
(n-7)(n+4)
b)
(n+7)(n-9)
c)
(n-3)(n-10)
d)
(n+7)(n+9)
68.
Factor
k2 -2k - 24
k2 -2k - 24
a)
(k+4)(k-6)
b)
(k+4)(k+6)
c)
(k+6)(k-1)
d)
(k-4)(k+6)
69.
Factor
3v2 - 4v - 7
3v2 - 4v - 7
a)
(3v-7)(v+1)
b)
3(v-7)(v-1)
c)
(3v+1)(v-9)
d)
(3v+1)(v-10)
70.
Factor
n2-13n+40
n2-13n+40
a)
(n-5)(n-8)
b)
(n+5)(n-8)
c)
(n-5)(n+8)
d)
(n+6)(n+1)
71.
Factor
3a2 + 4a + 1
3a2 + 4a + 1
a)
(7a-10)(a-8)
b)
Not factorable
c)
(3a+1)(a+1)
d)
(3a-1)(a-1)
72.
Factor
2x2 - 13x - 70
2x2 - 13x - 70
a)
(2x-7)(x+10)
b)
(7x+5)(x+2)
c)
(2x+7)(x-10)
d)
2(x+7)(x+10)
73.
Factor
5x2-28x+32
5x2-28x+32
a)
(3x-10)(x+6)
b)
(x-8)(5x-4)
c)
(5x-8)(x-4)
d)
(5x-8)(x+7)
74.
Factor
4n2-17n-15
4n2-17n-15
a)
(n-10)(6n+1)
b)
(4n-5)(n-3)
c)
(n-5)(4n-3)
d)
(n-5)(4n+3)
75.
Factor
9x2-6x-8
9x2-6x-8
a)
(3x+2)(3x-4)
b)
(3x+2)(3x+4)
c)
(3x-2)(3x-4)
d)
(x-1)(9x+8)
76.
Factor
9x2+9x-10
9x2+9x-10
a)
(3x-5)(3x+2)
b)
(3x+5)(3x-2)
c)
(3x+5)(3x+2)
d)
Not Factorable
77.
Factor
4x2-25x+25
4x2-25x+25
a)
4(x-5)(x+5)
b)
(x+5)(4x+5)
c)
(x-5)(4x-5)
d)
(x+2)(9x+1)
78.
Factor
3v2 - 4v - 7
3v2 - 4v - 7
a)
(3v-7)(v+1)
b)
3(v-7)(v-1)
c)
(3v+1)(v-9)
d)
(3v+1)(v-10)
79.
Factor
3a2 + 4a + 1
3a2 + 4a + 1
a)
(7a-10)(a-8)
b)
Not factorable
c)
(3a+1)(a+1)
d)
(3a-1)(a-1)
80.
Factor:
5n² - 6n - 27
5n² - 6n - 27
a)
(5n + 3)(n-9)
b)
(5n - 3)(n + 9)
c)
(5n + 9)(n - 3)
d)
(5n - 9)(n + 3)
81.
Factor:
3x² + 5x - 12
3x² + 5x - 12
a)
(3x + 4)(x-3)
b)
(3x - 4)(x + 3)
c)
(3x + 3)(x -4)
d)
(3x - 3)(x + 4)
82.
Factor:
2x² - 3x - 2
2x² - 3x - 2
a)
(2x - 2)(x + 1)
b)
(2x + 1)(x - 2)
c)
(2x - 1)(x - 2)
d)
(2x - 1) (x - 1)
83.
factor:x2 - 25
a)
( x + 5 ) ( x - 5 )
b)
( x - 5 ) ( x - 5 )
c)
( x + 5 ) ( x + 5 )
d)
Prime
84.
Factor
81m2 - 1
81m2 - 1
a)
not factorable
b)
(m-9)(m+9)
c)
9m(9m-1)
d)
(9m-1)(9m+1)
85.
Factor
v2 - 6v + 9
v2 - 6v + 9
a)
(v-3)2
b)
(v-6)2
c)
(v-9)(v+6)
d)
not factorable
86.
12x + 9
a)
3(4x + 3)
b)
x(12+9)
c)
3(4x - 3)
d)
not factorable
87.
6m2 + 16m
a)
2(3m2 + 8m)
b)
2m(3m + 8)
c)
2m(3m - 8m)
d)
not factorable
88.
Factor
v2 - 6v + 9
v2 - 6v + 9
a)
(v-3)2
b)
(v-6)2
c)
(v-9)(v+6)
d)
not factorable
89.
Factor completely
k2+7x+10
k2+7x+10
a)
(k+2)(k+5)
b)
(k-2)(k-5)
c)
(k+10)(k+4)
d)
(k+2)(k-5)
90.
Factor completely
81m2 - 1
81m2 - 1
a)
not factorable
b)
(m-9)(m+9)
c)
9m(9m-1)
d)
(9m-1)(9m+1)
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