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WorksheetsAlgebra
Total questions: 100
Worksheet time: 3hrs 16mins
Name
Class
Date
1.
Which of the following is NOT a linear equation?
a)
x2 + 7 = 62
b)
3x + 7 = 10
c)
y + 8 = 3
d)
3x - 8 = 2x + 12
2.
Identify the equation of the given statement:
Thrice the length of the hall is 120 m, if x is taken as the length of the hall
Thrice the length of the hall is 120 m, if x is taken as the length of the hall
a)
x⁄3 = 120
b)
3x = 120
c)
3x + 120 = 0
d)
None of the above
3.
Identify the equation of the following statement
'3 is taken away from the sum of x and y'
'3 is taken away from the sum of x and y'
a)
3 - (x + y)
b)
(x + y) - 3
c)
x - y - 3
d)
None of the above
4.
Determine if 3 is a root of the given equation:
3x + 3 = 11
3x + 3 = 11
a)
3 is a root
b)
3 is not a root
5.
Write the following in exponential form:
a × a × a______ 12 times
a × a × a______ 12 times
a)
a11
b)
a12
c)
a13
d)
None of the above
6.
Identify the expression for the following statement:
'y is multiplied by -5 and the result is added to 10'
'y is multiplied by -5 and the result is added to 10'
a)
10 - (-5y)
b)
10 + (-5y)
c)
5y - 10
d)
5y + 10
7.
The side of a square is given by 'a' units. The expression for the perimeter of the square is given by_______
a)
a + 4
b)
4a
c)
a4
d)
None of the above
8.
By taking Rahim's present age as y, what was his age 5 years back?
a)
y + 5
b)
y - 5
c)
y⁄5
d)
None of the above
9.
An expression containing four terms is called_____
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Quadrinomial
10.
The numerical value which satisfied a given equation is called its _________
a)
expression
b)
constant
c)
variable
d)
solution or root
11.
What is the degree classification of this polynomial?
x²+4x-8
x²+4x-8
a)
binomial
b)
trinomial
c)
quadratic
d)
cubic
12.
What is the term classification of the following polynomial?
x³-7x²+3
x³-7x²+3
a)
monomial
b)
binomial
c)
trinomial
d)
polynomial
13.
Which is an example of a linear polynomial?
a)
x²-5
b)
6x+4
c)
5x⁵
d)
2x³-9x²
14.
Which is an example of a cubic binomial?
a)
x³+5
b)
x²+3
c)
x²+5x-6
d)
5x³
15.
What is the leading coefficient of the following polynomial?
5x²-3x+6
5x²-3x+6
a)
2
b)
-3
c)
5
d)
6
16.
Which of these has a negative leading coefficient?
a)
x²+9x-4
b)
6x-9
c)
-8x+8
d)
9x
17.
Add the following polynomials:
(x³-2x²+3)+(2x³+3x²-1)
(x³-2x²+3)+(2x³+3x²-1)
a)
3x³-2x²+3x+2
b)
3x³+x²+2
c)
3x³-5x²-2
d)
3x³-x²+1
18.
Add the following polynomials
(x³-6x²+3)+(3x³+4x-1)
(x³-6x²+3)+(3x³+4x-1)
a)
4x³-2x²+2
b)
4x³-6x²+4x+2
c)
-2x³+2x+2
d)
4x³-2x²-2
19.
Subtract the following polynomials:
(3x²-3x+2)-(x²-2x+1)
(3x²-3x+2)-(x²-2x+1)
a)
2x²+x+1
b)
2x²-5x+3
c)
2x²-x+1
d)
4x²-5x+3
20.
Subtract the following polynomials:
(2x³+6x²+4x-2)-(x³+4x²-x)
(2x³+6x²+4x-2)-(x³+4x²-x)
a)
x³+2x²+5x-2
b)
x³+10x²+3x-2
c)
3x³+2x+4x-3
d)
3x³+10x²-3x-2
21.
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)
22.
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)
23.
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)
24.
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)
25.
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)
26.
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)
27.
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)
28.
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)
29.
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)
30.
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)
31.
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
32.
factor completely
81m2 - 1
81m2 - 1
a)
not factorable
b)
(m-9)(m+9)
c)
9m(9m-1)
d)
(9m-1)(9m+1)
33.
Factor Completely:
x2 - 36
x2 - 36
a)
(x + 9)(x - 4)
b)
(x - 6)(x - 6)
c)
(x - 9)(x + 4)
d)
(x + 6)(x - 6)
34.
Factor Completely:
2x2 - 2x - 6
2x2 - 2x - 6
a)
2(x + 3)(x - 1)
b)
2(x + 2)(x - 3)
c)
2(x2 - x - 3)
d)
2(x2 - 2x - 6)
35.
Factor:
x2 - 49
x2 - 49
a)
(x + 7)(x - 7)
b)
(x + 7)2
c)
(x - 7)2
d)
(x+7)(x-1)
36.
(4x+1)(5x−2)
a)
20x2 + 3x − 2
b)
20x2 − 11x + 5
c)
20x2 − 18x + 2
d)
20x2 − 3x − 2
37.
(2x − 3)(2x + 3)
a)
4x2 − 12x + 9
b)
4x2 − 9
c)
4x2 + 9
d)
4x2 + 6x − 9
38.
Simplify the expression.
-3x2( 7x2 - x + 4)
-3x2( 7x2 - x + 4)
a)
-21x4 + 3x3 -12x2
b)
7x2 - x + 4 (-3x2)
c)
21x4 + 3x3 + 12x2
d)
-12x2 + 3x3 -21x4
39.
(5x+2)(x2-3x+6)
a)
5x3 - 17x2 +24x +12
b)
5x3 + 17x2 - 24x +12
c)
5x3 - 13x2 + 24x +12
d)
5x3 +13x2 - 24x - 12
40.
Simplify the expression.
-3x2( 7x2 - x + 4)
-3x2( 7x2 - x + 4)
a)
-21x4 + 3x3 -12x2
b)
7x2 - x + 4 (-3x2)
c)
21x4 + 3x3 + 12x2
d)
-12x2 + 3x3 -21x4
41.
Find the product.
(x + 7)2
(x + 7)2
a)
x2 + 7x + 7x + 49
b)
x2 + 7x + 7
c)
7x2 + x + 7
d)
x2 + 14x + 49
42.
(5x+2)(x2-3x+6)
a)
5x3 - 17x2 +24x +12
b)
5x3 + 17x2 - 24x +12
c)
5x3 - 13x2 + 24x +12
d)
5x3 +13x2 - 24x - 12
43.
Divide:
(24x + 4) / (6x+1)
(24x + 4) / (6x+1)
a)
4
b)
4 + 4/6x+1
c)
4x + 0
d)
4x
44.
Divide:
(9x2 + 6) / (3x)
(9x2 + 6) / (3x)
a)
3x + 6/3x
b)
3x + 2
c)
3 + 6/3x
d)
3x + 6
45.
True or False:
a)
True
b)
False
46.
Simplify the expression.
a)
76
b)
7-5
c)
1/75
d)
75
47.
Simplify the expression.
a)
1
b)
g10
c)
g25
d)
g
48.
Simplify the expression.
a)
122
b)
130
c)
622
d)
630
49.
Evaluate the expression using the quotient rule.
a)
34
b)
1/34
c)
3-12
d)
332
50.
Evaluate using the quotient rule:
a)
a8b13
b)
a2b7
c)
a15b30
51.
Quotient Rule states: keep the base the same and do this to the exponents.
a)
multiply
b)
add
c)
subtract
d)
divide
52.
Without a calculator, evaluate:
13,412 =
13,412 =
a)
3,412
b)
3,411
c)
0
d)
1
53.
True or False?
a)
True
b)
False
54.
True or False?
a)
True
b)
False
55.
Simplify using the product rule: x3y2x3=
a)
x6y2
b)
xy8
c)
x3y5
56.
Anything raised to a power of zero is always:
a)
0
b)
1
c)
itself
d)
negative
57.
How would you change this to a positive exponent:
1/x-3
1/x-3
a)
1/x3
b)
x3
c)
3x
d)
1/3x
58.
x⁻⁶
a)
1 ⁄ x⁶
b)
x⁶
c)
-x⁶
d)
-1 ⁄ x⁶
59.
(-2)³⋅(-2)⁶
a)
(-2)⁹
b)
(-2)¹⁸
c)
(-2)⁻³
d)
(-2)
60.
Simplify the following expression:
xy-7
xy-7
a)
xy7
b)
x/y7
c)
x7/y
d)
x7y
61.
(2x3y)6
a)
2x18y6
b)
64x18y6
c)
64x3y6
d)
2x3y6
62.
x3y/xy5
a)
x2y4
b)
x3y4
c)
x2/y4
d)
x2/y5
63.
(2x7)3
a)
6x21
b)
8x21
c)
6x10
d)
8x10
64.
(53x2y4)0
a)
5xy
b)
1
c)
0
d)
5
65.
3-3
a)
27
b)
-9
c)
-1/9
d)
1/27
66.
6x5y2 / 2x4y2
a)
3xy
b)
4x
c)
3x
d)
4xy
67.
a)
y3/8
b)
y3/24
c)
y/24
d)
y3/83
68.
-3xy3 . (4xy)2
a)
-12x3y5
b)
-48x2y4
c)
-48x3y5
d)
-12x2y6
69.
(-4r3s5)0 (3b4c2d)
a)
1
b)
-12b4c2d
c)
3b4c2d
d)
0
70.
(-4r3s5)0 (3b4c2d)
a)
1
b)
-12b4c2d
c)
3b4c2d
d)
0
71.
w15 . 1/w5
a)
w10
b)
w20
c)
w3
d)
1/w75
72.
Find the area of the triangle given:
B = 3b2
H = 12p7b19
B = 3b2
H = 12p7b19
a)
18b21p7
b)
18b7p21
c)
36b21p7
d)
36b38p7
73.
a)
2a2b6
b)
1/2a2b6
c)
b6/2a2
d)
2b6/a2
74.
(x-4)3
a)
x12
b)
x-1
c)
1/x-1
d)
1/x12
75.
Explain the error in the simplification below:
(x3y)(x-4z-2) = x-1yz-2
(x3y)(x-4z-2) = x-1yz-2
a)
Should have multiplied the x exponents.
b)
Should have subtracted the x exponents.
c)
Should have moved the negative exponents to the bottom of a fraction.
d)
There is no error.
76.
(3x4y5)2⋅(-2x2y-1)3
a)
-72x14y7
b)
72x14y13
c)
-72x2y13
d)
-6x14y7
77.
( b2 / b7 )3
a)
b-5
b)
b15
c)
1/b5
d)
1/b15
78.
Evaluate 1001/2
a)
50
b)
10
c)
1000
d)
200
79.
Evaluate 45/2
a)
32
b)
16
c)
8
d)
2
80.
What value of x satisfies this equation?
16x = 2
16x = 2
a)
4
b)
1/4
c)
1/8
d)
3/4
81.
What value of x satisfies this equation?
8x = 16
8x = 16
a)
2
b)
4/3
c)
3/4
d)
1/2
82.
Simplify the following expression:
a)
5
b)
25
c)
125
d)
625
83.
Simplify:
a)
2
b)
8
c)
16
d)
32
84.
Express the following in Interval Notation
{ x | -8 ≤ x < 8 }
{ x | -8 ≤ x < 8 }
a)
[-8, 8]
b)
[-8,8)
c)
(-8, 8]
d)
(-8, 8)
85.
Express the following interval in Set notation:
[3, 5]
[3, 5]
a)
{ x | 3 ≤ x ≤ 5 }
b)
{ x | 3 < x < 5 }
c)
{ x | 3 ≤ x ≥ 5 }
d)
{ x | 3 < x > 5 }
86.
Write the following in interval notation
x ≥ 100
x ≥ 100
a)
(0, 100]
b)
(∞, 100]
c)
[100, ∞)
d)
(∞, 100)
87.
What interval notation does the number line graph represent?
a)
[∞, -5)
b)
(∞, -5)
c)
[-5, ∞)
d)
(-5, ∞)
88.
Write the inequality in interval notation
x > -1
x > -1
a)
(-∞, -1)
b)
(-1, ∞]
c)
(-∞, -1]
d)
(-1, ∞)
89.
Write the inequality in interval notation
-3≤ x < 4.
-3≤ x < 4.
a)
(-3, 4]
b)
[-3, 4)
c)
(4, -3]
d)
(-3, 4)
90.
Write the inequality in interval notation.
a)
(-2,5)
b)
(-∞,-2) ⋃ (5,∞)
c)
[-2,5]
d)
(-∞,-2] ∪ [5,∞)
91.
Write the inequality in interval notation.
a)
[-4, -1)
b)
(-4, -1)
c)
(-4, -1]
d)
[-4, -1]
92.
Write an inequality for Graph 4.
a)
-2 < x < 5
b)
x < -2 or x > 5
c)
x ≥ -2 or x < 5
d)
-2 ≤ x ≤ 5
93.
-15 - 3
a)
12
b)
-12
c)
-18
d)
18
94.
3 + -7
a)
10
b)
4
c)
-10
d)
-4
95.
-9 + (-5)
a)
-14
b)
14
c)
-4
96.
The temperature changed from 3 degrees below zero at midnight to 7 degrees below zero at 2 a.m. How much did the temperature decrease?
a)
5 degrees
b)
4 degrees
c)
10 degrees
d)
it stayed the same
97.
Which expression is evaluated first?
(18 - 14)2 - 6 x 10
(18 - 14)2 - 6 x 10
a)
18 - 14
b)
42
c)
6 x 10
d)
16 - 6
98.
Evaluate:
36 ÷ 32 + 5 ⋅ 6
36 ÷ 32 + 5 ⋅ 6
a)
35
b)
60
c)
34
d)
54
99.
Evaluate:
100 - 25 x 4 + 17
100 - 25 x 4 + 17
a)
317
b)
117
c)
0
d)
17
100.
Evaluate:
(72 + 51) ÷ (4 x 25)
(72 + 51) ÷ (4 x 25)
a)
1
b)
0
c)
100
d)
2
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