Algebra test generator



Name _____________________                                        Date:_____________________


Current difficulty level: Choose test difficulty:         Easy              Challenging
(current difficulty level: Easy)

                           

Solve the following problems:

Important instructions

(or click here to generate a new test)
1.   Multiply:   -13 and 1? -13
    
2.   Add:   -7 and -14? -21
    
3.   Divide:   3 and -3? -1
    
4.   Substract:   13 and -13? 26
    
5.   Calculate: |-14 + -16 · 20| 334
    
6.   Simplify the following expressions:
  • 4 + 20x – -3 7+20x
        
  • -1 + -5y – -13x – -15x -1+28x-5y
        
  • 2z + -2y – 1z – -19y – -13y – -4y 34y+1z
        
  • x-19 × y14 × x1 x-18 × y14
        
  • x2
    x3
    x-1
        
  • (5x3)4 625x12
        
7.   Which of the following expressions show the associative property?
  • ( m + n ) × 5 = 5 × ( m + n )
  • ( m × n ) × p = m × ( n × p )
  • c × ( d + 2 ) = cd + 2d
  • ( -8 + 6 ) × 5 = 5 × ( -8 + 6 )
B
    
8.   Which properties are illustrated by the following three expressions?
  • (-10 + x) × 3 = 3 × (-10 + x)
  • (i + j) × 1 = i + j
  • -18 × ( 18 × -10 ) = ( -18 × 18 ) × -10
  • Distributive property, Commutative property of addition and Associative property of addition
  • Identity property of addition, Associative property of multiplication and Commutative property of multiplication
  • Commutative property of multiplication, Associative property of addition and Identity property of addition
  • Commutative property of multiplication, Identity property of multiplication and Associative property of multiplication
D
    
9.   Solve the following equations for x:
  • 95 + -x = -50 x = 145
        
  • 28
    29
    = -
    4
    29
    x x = -7
        
  • -18x – -13 = -5 x = 1
        
  • dx = bx + g x = g/(d-b)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x – -14 ≥ 24 x ≤ -10
        
  • x ≠ 70
  • 83 ≥ x ≤ 23
  • -
    10
    5
    x <
    20
    10
    x > -1
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000000880 8.8 × 10-11
        
  • 294000 2.94 × 105
        
12.   Add the following polynomials:
  • 14z1 + 5  and  -9z10 + -10z8 + -14z6 + 12z1 + 7
    -9z10 + -10z8 + -14z6 + 26z1 + 12
        
  • -11z20 + 8z14 + -5z3 + 15  and  -6z17 + 11z14 + 10z6 + -15z3 + -6 -11z20 + -6z17 + 19z14 + 10z6 + -20z3 + 9
        
13.   Multiply the following polynomials and simplify:
  • (10x5 + 2x3)(4x5 + 9x3 + 6x2)
    40x10 + 98x8 + 60x7 + 18x6 + 12x5
        
  • (2x4 + 6x2)(3x4 + 6x)
    6x8 + 18x6 + 12x5 + 36x3
        
14.   Divide:
  • 20x2 - 74x + 60 / 4x - 10
    5x - 6
        
15.   Find the greatest common factor of the following terms:
  • 91, 90
    1
        
  • 30x3y6, 45x6y4, 66x3y5
    3x3y4
        
16.   Factor the following polynomials:
  • 56x5 - 80x4 - 6x3
    56x3(x -
    3
    2
    )(x +
    1
    14
    )
        
  • x2 - 3x + 2
    (x - 1)(x - 2)
        
  • x6 + 15x5 + 14x4
    x4(x + 1)(x + 14)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    1
    and
    2


        
  • x =
    0
    ,
    -1

    and
    -14
        
18.   You are seating 6 people on 6 chairs. How many different ways can those people sit?
  • 720
        
19.   Use the following data to construct a box and whiskers plot:
  • 37, 22, 36, 3, 8, 10, 6
        
20.   A bag contains 5 blue balls, 6 red balls, and 3 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    21.43%
        
  • A blue ball or red ball?
    78.57%
        
  • Two red balls?
    16.48%
        
  • A blue ball and a white ball?
    8.24%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 8
    x - y = 3
    A(5.5,2.5)
        
  • x - 8y = 4
    6x + 9y = 11

    B(2.18,-0.23)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • x5(x + 9)
    x4 + 5x3 - 36x2
    x3
    (x - 4)
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -18x + 77 = -x2
    x1 = 7,   x2 = 11
        
24.   Convert the following repeating decimal into a fraction:
  • x = 6.14
    553
    90
        
25.   Solve the following equation:
  • -
    9
    x
    = -2
    x =
    81
    4
        
26.   Rationalize the denominator of each fraction below:
  • 21
    9
    7
        
27.   Use a trigonometric ratio to find x:
x = 46.00 cm
    
28.   The sum of two consecutive even integers is 18. What are the integers? (Hint: use 2x as the first even integer)
a=8, b=10
    
29.   After you leave your house, you walk 4 blocks east and 3 blocks south. How far are you from your house?
  • I am
    5
    blocks from my house.
        
30.   The length of a rectangle is 10 less than 5 times the width. What are the dimensions of the rectangle if the area is 240m2?
  • width = 8,  length = 30
        


To print this algebra practice test, click here.



Name _____________________                                        Date:_____________________


Current difficulty level: Choose test difficulty:         Easy              Challenging
(current difficulty level: Easy)

                           

Solve the following problems:

Important instructions

(or click here to generate a new test)
1.   Multiply:   -3 and 7? -21
    
2.   Add:   13 and -7? 6
    
3.   Divide:   20 and -1? -20
    
4.   Substract:   2 and 6? -4
    
5.   Calculate: |12 · 16 + -1 · -8| 200
    
6.   Simplify the following expressions:
  • 15x + 9x – 9x 15x
        
  • 3y + -4 – -3 + -20y -1-17y
        
  • -2y + 15z + 11 + 16 – -18z 27-2y+33z
        
  • x7 × x-3 × x17 × x10 x31
        
  • x-20
    x6
    x-26
        
  • (8x)10 1073741824x10
        
7.   Which of the following expressions show the associative property?
  • 6( 3 + 9 ) = 6×3 + 6×9
  • 7 + 10 = 10 + 7
  • ( 5 × 8 ) × 7 = 5 × ( 8 × 7 )
  • -5 × ( y + 7 + 8 ) = -5×y + -5×7 + -5×8
C
    
8.   Which properties are illustrated by the following three expressions?
  • -6 + ( -9 + 16 ) = ( -6 + -9 ) + 16
  • -14 × -19 + 9 = 9 + -14 × -19
  • 0 + o + 16 = o + 16
  • Associative property of addition, Commutative property of addition and Identity property of addition
  • Identity property of addition, Commutative property of multiplication and Commutative property of addition
  • Commutative property of multiplication, Associative property of addition and Commutative property of addition
  • Identity property of multiplication, Distributive property and Commutative property of multiplication
A
    
9.   Solve the following equations for x:
  • 25 – x = -1 x = 26
        
  • -
    5
    13
    x =
    10
    13
    x = -2
        
  • 87 + 5x = -3 x = -18
        
  • -d = ax x = -d/a
        
10.   Solve the following inequalities. Then graph a) on the number line
  • x – 33 ≥ 40 x ≥ 73
        
  • x ≠ 971
  • 57 ≥ x ≥ -37
  • -
    28
    14
    x < 16 x > -8
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000000494 4.94 × 10-11
        
  • 20900000000 2.09 × 1010
        
12.   Add the following polynomials:
  • 2z8 + 5z3  and  -3z8 + -9z7 + 9z6 + 12z3 + 3z1
    -1z8 + -9z7 + 9z6 + 17z3 + 3z1
        
  • 5z18 + -3z15 + -2z13  and  -12z15 + -4z13 + 1z5 5z18 + -15z15 + -6z13 + 1z5
        
13.   Multiply the following polynomials and simplify:
  • (6x5 + 4x3)(4x4 - 7)
    24x9 + 16x7 - 42x5 - 28x3
        
  • (2x3 + 8x)(5x5 - 1)
    10x8 + 40x6 - 2x3 - 8x
        
14.   Divide:
  • 10x2 + 19x + 30 / 2x + 1
    (5x + 7) with a remainder of 23
        
15.   Find the greatest common factor of the following terms:
  • 90, 9
    9
        
  • 84x7y7, 66y7, 50xy
    2y
        
16.   Factor the following polynomials:
  • 15x5 - 39x4 - 18x3
    15x3(x +
    2
    5
    )(x - 3)
        
  • x2 + 8x + 7
    (x + 7)(x + 1)
        
  • x9 + 11x8 - 60x7
    x7(x - 4)(x + 15)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -7
    and
    -1


        
  • x =
    0
    ,
    4

    and
    -15
        
18.   You are seating 5 people on 5 chairs. How many different ways can those people sit?
  • 120
        
19.   Use the following data to construct a box and whiskers plot:
  • 2, 3, 36, 22, 25, 5, 4, 38, 37
        
20.   A bag contains 4 blue balls, 5 red balls, and 3 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    25.00%
        
  • A blue ball or red ball?
    75.00%
        
  • Two red balls?
    15.15%
        
  • A blue ball and a white ball?
    9.09%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -10
    x - y = -20
    A(-15,5)
        
  • 7x - 5y = -12
    4x + 3y = -16

    B(-2.83,-1.56)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 8)2
    (x + 8)6
    1
    (x + 8)4
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -x2 = -20x - 21
    x1 = -1,   x2 = 21
        
24.   Convert the following repeating decimal into a fraction:
  • x = 6.38
    575
    90
        
25.   Solve the following equation:
  • -8
    x
    + 14 = -10
    x
    + 20
    x = 9
        
26.   Rationalize the denominator of each fraction below:
  • 15
    7
    - 9
    -
    15
    7
    + 135
    74
        
27.   Use a trigonometric ratio to find x:
x = 27.71 cm
    
28.   The sum of two consecutive odd integers is 16. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=7, b=9
    
29.   After you leave your house, you walk 8 blocks west and 15 blocks north. How far are you from your house?
  • I am
    17
    blocks from my house.
        
30.   The sides of a square are increased by 6 ft. The area of the newly created square is 121ft2. What was the original length of one side of the square?
  • 5 ft
        


To print this algebra practice test, click here.



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