Algebra test generator



Name _____________________                                        Date:_____________________


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

                           

Solve the following problems:

Important instructions

(or click here to generate a new test)
1.   Multiply:   -65 and 86? -5590
    
2.   Add:   53 and -81? -28
    
3.   Divide:   28 and -28? -1
    
4.   Substract:   45 and -38? 83
    
5.   Calculate: |57 · 22 + -49 · -60| 4194
    
6.   Simplify the following expressions:
  • 38x – -24x – -99 99+62x
        
  • -45y + -21 – -4x + 85 64+4x-45y
        
  • 8z + -96y – 71x – -71y – 53z + 61y -71x+36y-45z
        
  • y49 × y67 × y-32 × x56 x56 × y84
        
  • x-56
    x48
    x-104
        
  • (3x3)8 6561x24
        
7.   Which of the following expressions show the associative property?
  • ( x + y ) + z = x + ( y + z )
  • ( -8 × 3 ) + 1 = 1 + ( -8 × 3 )
  • 7 + 4n + 2
  • 6( 7 + 9 ) = 6×7 + 6×9
A
    
8.   Which properties are illustrated by the following three expressions?
  • 2 × -7 + x = x + 2 × -7
  • 1 × (g + h + i) = g + h + i
  • (x + 2) × (y + -8) = (y + -8) × (x + 2)
  • Commutative property of addition, Identity property of multiplication and Commutative property of multiplication
  • Distributive property, Associative property of addition and Identity property of addition
  • Associative property of multiplication, Distributive property and Identity property of multiplication
  • Associative property of addition, Identity property of multiplication and Associative property of multiplication
A
    
9.   Solve the following equations for x:
  • x · 29 = -29 x = -1
        
  • 1
    23
    x = -
    21
    23
    x = -21
        
  • -36x + -42 = 30 x = -2
        
  • g = fx x = g/f
        
10.   Solve the following inequalities. Then graph a) on the number line
  • x + -11 > -16 x > -5
        
  • x ≠ -976
  • -83 < x < -84
  • -
    33
    11
    x > -36 x < 12
        
11.   Convert the following numbers into scientific notation:
  • 0.000000907 9.07 × 10-7
        
  • 105000000 1.05 × 108
        
12.   Add the following polynomials:
  • 11z7 + -6z6 + 8z4  and  -9z7 + -1z6 + -16z3 + -1z1
    2z7 + -7z6 + 8z4 + -16z3 + -1z1
        
  • 16z16 + 14z13 + -42z3 + -36z1 + 38  and  26z17 + -17z3 + 41z1 + 23 26z17 + 16z16 + 14z13 + -59z3 + 5z1 + 61
        
13.   Multiply the following polynomials and simplify:
  • (6x3 + 5x2)(2x4 + 6x2 - 5)
    12x7 + 10x6 + 36x5 + 30x4 - 30x3 - 25x2
        
  • (7x5 + 4x)(3x3 + 2x2)
    21x8 + 14x7 + 12x4 + 8x3
        
14.   Divide:
  • 6x2 + 10x - 24 / 2x + 6
    3x - 4
        
15.   Find the greatest common factor of the following terms:
  • 108, 270, 468
    18
        
  • 300x6y, 450x6y8
    150x6y
        
16.   Factor the following polynomials:
  • 55x5 - 66x4 - 88x3
    55x3(x +
    4
    5
    )(x - 2)
        
  • x2 - x - 12
    (x - 4)(x + 3)
        
  • x5 + 30x4 + 225x3
    x3(x + 15)(x + 15)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    4
    and
    -3


        
  • x =
    0
    ,
    -15

    and
    -15
        
18.   You have 8 CDs. How many different ways can you listen to them?
  • 40320
        
19.   Use the following data to construct a box and whiskers plot:
  • 14, 39, 13, 30, 27, 31, 23, 34, 9
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 13
  • What is the probability of getting tails and 6?
    3.85%
        
  • What is the probability of getting tails and an even number?
    23.08%
        
  • What is the probability of getting heads and a multiple of 3?
    15.38%
        
  • What is the probability of getting tails and a prime number?
    23.08%
        
  • What is the probability of not tails and not 12?
    46.15%
        
  • What is the probability of getting not heads and not a whole number?
    0%
        
  • What is the probability of heads or tails and a whole number?
    100%
        
  • What is the probability of getting tails?
    50%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 19
    x - y = -2
    A(8.5,10.5)
        
  • 2x - 10y = 12
    2x + 4y = -16

    B(-4,-2)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • x7 + 4x6 - 32x5
    x6(x + 8)
    (x - 4)
    x
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • x2 + 5x = 14
    x1 = -7,   x2 = 2
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.287
    287
    999
        
25.   Solve the following equation:
  • 11 +
    4x + 1
    = 12
    x = 0
        
26.   Rationalize the denominator of each fraction below:
  • 10
    5
    - 7
    -
    5
    5
    + 35
    22
        
27.   Use a trigonometric ratio to find x:
x = 14.43 cm
    
28.   The sum of two consecutive odd integers is 48. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=23, b=25
    
29.   After you leave your house, you walk 6 blocks north and 8 blocks west. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   The sides of a square are increased by 4 m. The area of the newly created square is 169m2. What was the original length of one side of the square?
  • 9 m
        


To print this algebra practice test, click here.



Name _____________________                                        Date:_____________________


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

                           

Solve the following problems:

Important instructions

(or click here to generate a new test)
1.   Multiply:   -86 and 46? -3956
    
2.   Add:   85 and -48? 37
    
3.   Divide:   -13 and 1? -13
    
4.   Substract:   55 and -55? 110
    
5.   Calculate: |-93 · -59 + -15| 5472
    
6.   Simplify the following expressions:
  • 84 + -87x + -46x 84-133x
        
  • 5y – 73y + 63 – -3x 63+3x-68y
        
  • -40z + -59 + -25x – -83z + 42y -59-25x+42y+43z
        
  • x-78 × y-8 × y53 × x83 x5 × y45
        
  • x34
    x-10
    x44
        
  • (2x3)5 32x15
        
7.   Which of the following expressions show the associative property?
  • -3 × ( x + 4 + 7 ) = -3×x + -3×4 + -3×7
  • 0 + 5x = 5x
  • ( m × n ) × p = m × ( n × p )
  • 5 + 3 = 3 + 5
C
    
8.   Which properties are illustrated by the following three expressions?
  • (s + t) × u = u × (s + t)
  • -73 × 1 = -73
  • u × ( v + w ) = u × v + u × w
  • Identity property of multiplication, Associative property of addition and Identity property of addition
  • Commutative property of addition, Commutative property of multiplication and Distributive property
  • Commutative property of multiplication, Identity property of multiplication and Distributive property
  • Identity property of addition, Identity property of multiplication and Commutative property of addition
C
    
9.   Solve the following equations for x:
  • x + -36 = -49 x = -13
        
  • -
    6
    17
    x = -
    6
    17
    x = 1
        
  • 100 = -64 + 82x x = 2
        
  • a = -dx x = -a/d
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -51x – 16 > 35 x < -1
        
  • x ≠ 802
  • 21 ≤ x ≤ 51
  • -
    12
    3
    x ≤
    36
    9
    x ≥ -1
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000809 8.09 × 10-8
        
  • 107000000000 1.07 × 1011
        
12.   Add the following polynomials:
  • 12z9 + -4z3 + 6z1  and  -2z9 + 8z6 + 2z5 + -15z3 + -7z1
    10z9 + 8z6 + 2z5 + -19z3 + -1z1
        
  • 14z19 + 22z14 + 30z6 + -42z4 + -20z1  and  -9z19 + -14z15 + 18z14 + 35z1 5z19 + -14z15 + 40z14 + 30z6 + -42z4 + 15z1
        
13.   Multiply the following polynomials and simplify:
  • 10x2(3x5 + 6x4)
    30x7 + 60x6
        
  • (2x5 + 8x4 - 10)(3x3 + 3x2)
    6x8 + 30x7 + 24x6 - 30x3 - 30x2
        
14.   Divide:
  • 5x2 - 11x + 7 / x - 2
    (5x - 1) with a remainder of 5
        
15.   Find the greatest common factor of the following terms:
  • 154, 405, 462
    1
        
  • 90xy2, 312x4y4
    6xy2
        
16.   Factor the following polynomials:
  • 27x3 + 24x2 + 4x
    27x(x +
    2
    9
    )(x +
    2
    3
    )
        
  • x2 + 6x - 16
    (x + 8)(x - 2)
        
  • x9 - 4x8 - 5x7
    x7(x + 1)(x - 5)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -8
    and
    2


        
  • x =
    0
    ,
    -1

    and
    5
        
18.   You can purchase your ice cream in a cup or a cone. Orders can be one, two, or three scoops. Flavors can be chocolate, vanilla, strawberry or peach. How many choices do you have?
  • 24
        
19.   Use the following data to construct a box and whiskers plot:
  • 33, 15, 11, 1, 27, 18, 13, 14, 32, 29
        
20.   A bag contains 2 blue balls, 3 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?
    37.50%
        
  • A blue ball or red ball?
    62.50%
        
  • Two red balls?
    10.71%
        
  • A blue ball and a white ball?
    10.71%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -16
    x - y = 19
    A(1.5,-17.5)
        
  • x - 3y = -11
    9x + 8y = -19

    B(-4.14,2.29)
        
22.   Write the following fractions in simplest form:
  • 32x8y4
    8x2y
    4x6y3
        
  • (x - 5)4
    (x - 5)6
    1
    (x - 5)2
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • x2 - 22 = -9x
    x1 = -11,   x2 = 2
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.59
    59
    99
        
25.   Solve the following equation:
  • -6
    x
    - 20 = -7
    x
    - 3
    x = 289
        
26.   Rationalize the denominator of each fraction below:
  • 6
    14
    4 +
    7
    8
    14
    - 14
    2
    3
        
27.   Use a trigonometric ratio to find x:
x = 18.38 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 16 blocks south and 12 blocks east. How far are you from your house?
  • I am
    20
    blocks from my house.
        
30.   A rectangle has an area of 55ft2. Its width is 6 ft less than its length. What are the dimensions of the rectangle?
  • width = 5,  length = 11
        


To print this algebra practice test, click here.



Check out some of our top basic mathematics lessons.

Formula for percentage

Types of angles

Area of ​​irregular shapes

Math problem solver

Math skills assessment

Compatible numbers

Surface area of ​​a cube

Share this page:
Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.