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:   -11 and 4? -44
    
2.   Add:   5 and 8? 13
    
3.   Divide:   -12 and 6? -2
    
4.   Substract:   8 and 16? -8
    
5.   Calculate: |1 + -8 · 7 + 9| 46
    
6.   Simplify the following expressions:
  • 6x – -8x – 8x 6x
        
  • 2 – -20 + 14y + 3y 22+17y
        
  • -7z – 18y – 5z + 16y + -3z -2y-15z
        
  • y5 × x4 × y-17 x4 × y-12
        
  • x4
    x-8
    x12
        
  • (10x)7 10000000x7
        
7.   Which of the following expressions show the associative property?
  • ( -9 + 8 ) × -8 = -8 × ( -9 + 8 )
  • ( x + y ) + z = x + ( y + z )
  • 0 + -5x = -5x
  • 4 + 9g + 5
B
    
8.   Which properties are illustrated by the following three expressions?
  • 1 × (c + 7) = c + 7
  • 11 + 10y = 10y + 11
  • (p + q) × -10 = -10 × (p + q)
  • Commutative property of multiplication, Distributive property and Associative property of multiplication
  • Commutative property of addition, Identity property of multiplication and Identity property of addition
  • Distributive property, Associative property of multiplication and Identity property of multiplication
  • Identity property of multiplication, Commutative property of addition and Commutative property of multiplication
D
    
9.   Solve the following equations for x:
  • 48 = 3 · x x = 16
        
  • 4
    29
    x = -
    16
    29
    x = -4
        
  • 51 = 43x + 94 x = -1
        
  • fx + e = ax x = (-e)/(f-a)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x + -22 ≤ -29 x ≥ 7
        
  • x ≠ -180
  • 66 > x ≥ -84
  • 22
    11
    x ≤ -18 x ≤ -9
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000218 2.18 × 10-8
        
  • 19400 1.94 × 104
        
12.   Add the following polynomials:
  • -2z8 + -5z6 + 11z2  and  9z8 + -11z4 + 13z3 + -13z2
    7z8 + -5z6 + -11z4 + 13z3 + -2z2
        
  • -12z20 + -12z18 + 14z10  and  -9z18 + -12z10 + 7z9 + -4 -12z20 + -21z18 + 2z10 + 7z9 + -4
        
13.   Multiply the following polynomials and simplify:
  • (10x5 + 10x)(5x + 8)
    50x6 + 80x5 + 50x2 + 80x
        
  • (9x2 + 4x - 8)(6x4 + 3x2)
    54x6 + 24x5 - 21x4 + 12x3 - 24x2
        
14.   Divide:
  • 20x2 + 45x + 10 / 4x + 1
    5x + 10
        
15.   Find the greatest common factor of the following terms:
  • 30, 54
    6
        
  • 52x10y4, 24x8y10
    4x8y4
        
16.   Factor the following polynomials:
  • 24x4 - 46x3 - 35x2
    24x2(x +
    7
    12
    )(x -
    5
    2
    )
        
  • x2 - 12x + 32
    (x - 4)(x - 8)
        
  • x7 + 7x6 - 44x5
    x5(x + 11)(x - 4)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    4
    and
    8


        
  • x =
    0
    ,
    -11

    and
    4
        
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:
  • 17, 20, 33, 37, 18, 19, 9
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 16
  • What is the probability of getting heads and 4?
    3.13%
        
  • What is the probability of getting heads and an even number?
    25%
        
  • What is the probability of getting tails and a multiple of 5?
    9.38%
        
  • What is the probability of getting tails and a prime number?
    18.75%
        
  • What is the probability of not tails and not 14?
    46.88%
        
  • What is the probability of getting not tails 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 = 5
    x - y = -10
    A(-2.5,7.5)
        
  • 6x - 5y = 4
    x + 5y = 11

    B(2.14,1.77)
        
22.   Write the following fractions in simplest form:
  • 36x6y3
    18x10y4
    2
    x4y
        
  • (x - 5)2
    (x - 5)4
    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 = 9x + 20
    x1 = -5,   x2 = -4
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.8
    8
    9
        
25.   Solve the following equation:
  • 12
    x
    + 12 = 10
    x
    + 14
    x = 1
        
26.   Rationalize the denominator of each fraction below:
  • 7
    2
    - 3
    -
    2
    - 3
        
27.   Use a trigonometric ratio to find x:
x = 18.48 cm
    
28.   The sum of two consecutive even integers is 58. What are the integers? (Hint: use 2x as the first even integer)
a=28, b=30
    
29.   After you leave your house, you walk 5 blocks east and 12 blocks south. How far are you from your house?
  • I am
    13
    blocks from my house.
        
30.   Each side of a square is lengthened by 4 ft. This makes the area of the square 81ft2. What is the original length of a side of the square?
  • 5 ft
        


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:   5 and -19? -95
    
2.   Add:   20 and -9? 11
    
3.   Divide:   -14 and -2? 7
    
4.   Substract:   -13 and -7? -6
    
5.   Calculate: |18 + -13 · -1 + -14| 17
    
6.   Simplify the following expressions:
  • 5x + 3x – 18x -10x
        
  • 3x + 7 – 16y – 11y 7+3x-27y
        
  • 13z + 1x – 1 – 12 – -2 + -14y -11+1x-14y+13z
        
  • y19 × y5 × y0 y24
        
  • x-15
    x13
    x-28
        
  • (7x4)10 282475249x40
        
7.   Which of the following expressions show the associative property?
  • ( x × y ) + 9 = 9 + ( y × x )
  • a + b = b + a
  • ( m × n ) × 7 = m × ( n × 7 )
  • 2 + 5h + 10
C
    
8.   Which properties are illustrated by the following three expressions?
  • 1 × (l + m + n) = l + m + n
  • 17 × -15 + -6 = -6 + 17 × -15
  • b × ( c × 1 ) = ( b × c ) × 1
  • Associative property of addition, Commutative property of addition and Identity property of addition
  • Identity property of multiplication, Commutative property of addition and Associative property of multiplication
  • Commutative property of multiplication, Commutative property of addition and Associative property of multiplication
  • Identity property of multiplication, Associative property of multiplication and Associative property of addition
B
    
9.   Solve the following equations for x:
  • -54 = 27 · x x = -2
        
  • -
    2
    3
    x = -
    6
    9
    x = 1
        
  • -39x – -6 = -33 x = 1
        
  • d = -gx x = -d/g
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 5x + 32 > -3 x > -7
        
  • x ≠ 422
  • -98 < x ≤ 8
  • 26
    13
    x >
    40
    5
    x > 4
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000891 8.91 × 10-8
        
  • 3470000000 3.47 × 109
        
12.   Add the following polynomials:
  • 13z10 + -11z5 + 10z4  and  -2z10 + 14z5
    11z10 + 3z5 + 10z4
        
  • 5z20 + 14z19 + 2z18 + -13z17 + 4z5  and  13z18 + -5z10 + 7z5 + -1 5z20 + 14z19 + 15z18 + -13z17 + -5z10 + 11z5 + -1
        
13.   Multiply the following polynomials and simplify:
  • (3x4 + 8x3 + 9x2)(1x3 + 8x - 6)
    3x7 + 8x6 + 33x5 + 46x4 + 24x3 - 54x2
        
  • (9x5 + 3x2)(1x4 + 8x2)
    9x9 + 72x7 + 3x6 + 24x4
        
14.   Divide:
  • 12x2 - 50x + 50 / 4x - 10
    3x - 5
        
15.   Find the greatest common factor of the following terms:
  • 35, 32, 30
    1
        
  • 42x7y5, 50x5y8
    2x5y5
        
16.   Factor the following polynomials:
  • 56x3 - 98x2 + 42x
    56x(x -
    3
    4
    )(x - 1)
        
  • x2 - 2x - 80
    (x - 10)(x + 8)
        
  • x5 - 20x4 + 91x3
    x3(x - 13)(x - 7)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    10
    and
    -8


        
  • x =
    0
    ,
    13

    and
    7
        
18.   You have 7 CDs. How many different ways can you listen to them?
  • 5040
        
19.   Use the following data to construct a box and whiskers plot:
  • 13, 12, 28, 11, 22, 3, 9
        
20.   A bag contains 2 blue balls, 3 red balls, and 6 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    54.55%
        
  • A blue ball or red ball?
    45.45%
        
  • Two red balls?
    5.45%
        
  • A blue ball and a white ball?
    10.91%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -13
    x - y = -19
    A(-16,3)
        
  • 3x - 7y = 10
    8x + 4y = 7

    B(1.31,-0.87)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x - 5)3
    (x - 5)2
    x - 5
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -25 = x2 + 10x
    x1 = -5,   x2 = -5
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.32
    29
    90
        
25.   Solve the following equation:
  • -
    x + 3
    + 13 = -8
    x = 438
        
26.   Rationalize the denominator of each fraction below:
  • 49
    21 -
    15
    1029 + 49
    15
    426
        
27.   Use a trigonometric ratio to find x:
x = 34.00 cm
    
28.   The sum of two consecutive even integers is 46. What are the integers? (Hint: use 2x as the first even integer)
a=22, b=24
    
29.   After you leave your house, you walk 8 blocks east and 6 blocks north. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   The length of a rectangle is 3 more than thrice its width. The area of the rectangle is 396ft2. What is the length and width of the rectangle?
  • width = 11,  length = 36
        


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.