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:   5 and -5? -25
    
2.   Add:   -9 and -14? -23
    
3.   Divide:   11 and -11? -1
    
4.   Substract:   1 and 6? -5
    
5.   Calculate: |13 + 6 · 8| 61
    
6.   Simplify the following expressions:
  • -2x – 13x – -16x 1x
        
  • -19y – 20y + -6y + 7x 7x-45y
        
  • 11y + 17z – 16 – 3z – -18z -16+11y+32z
        
  • x7 × y1 x7 × y1
        
  • x4
    x20
    x-16
        
  • (6x)5 7776x5
        
7.   Which of the following expressions show the associative property?
  • 1( 8 + 3 ) = 1×8 + 1×3
  • ( m + n ) + 3 = m + ( n + 3 )
  • 7 + 4j + 5
  • -1x + -8 = -8 + -1x
B
    
8.   Which properties are illustrated by the following three expressions?
  • 1 × (v + w + x) = v + w + x
  • 9 × -1 = 9 × -1
  • w × ( x × y ) = ( w × x ) × y
  • Identity property of multiplication, Commutative property of multiplication and Associative property of multiplication
  • Identity property of addition, Commutative property of multiplication and Associative property of addition
  • Commutative property of multiplication, Associative property of addition and Associative property of multiplication
  • Distributive property, Identity property of addition and Commutative property of multiplication
A
    
9.   Solve the following equations for x:
  • 47 · -x = -47 x = 1
        
  • 17
    26
    =
    1
    26
    x x = 17
        
  • 10 + -67x = -57 x = 1
        
  • -ax = c x = -c/a
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 9x + 38 ≤ 11 x ≤ -3
        
  • x ≠ 978
  • 89 < x ≤ -3
  • 26
    13
    x > -
    24
    2
    x > -6
        
11.   Convert the following numbers into scientific notation:
  • 0.00000000749 7.49 × 10-9
        
  • 916000000 9.16 × 108
        
12.   Add the following polynomials:
  • -6z10 + 11z7 + 9z6  and  -9z9 + -4z7 + -10z6 + -14z2
    -6z10 + -9z9 + 7z7 + -1z6 + -14z2
        
  • 6z15 + -10z14 + 10z12 + 3z7 + -5z6  and  -15z14 + -3z7 + -15z6 + 3z4 + -11z3 6z15 + -25z14 + 10z12 + -20z6 + 3z4 + -11z3
        
13.   Multiply the following polynomials and simplify:
  • (5x4 - 2)(8x3 + 3x)
    40x7 + 15x5 - 16x3 - 6x
        
  • (6x5 + 3x3)(9x5 + 3x)
    54x10 + 27x8 + 18x6 + 9x4
        
14.   Divide:
  • 4x3 + 20x2 - 10x - 46 / 2x + 10
    (2x2 - 5) with a remainder of 4
        
15.   Find the greatest common factor of the following terms:
  • 27, 72, 66
    3
        
  • 45y6, 33x4y6
    3y6
        
16.   Factor the following polynomials:
  • 16x5 - 9x4 - 7x3
    16x3(x +
    7
    16
    )(x - 1)
        
  • x2 - x - 56
    (x - 8)(x + 7)
        
  • x5 + 13x4 - 14x3
    x3(x - 1)(x + 14)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    8
    and
    -7


        
  • x =
    0
    ,
    1

    and
    -14
        
18.   You can purchase your ice cream in a cup or a cone. Orders can be one or two scoops. Flavors can be chocolate or vanilla. How many choices do you have?
  • 8
        
19.   Use the following data to construct a box and whiskers plot:
  • 20, 5, 28, 40, 12, 35, 29
        
20.   A bag contains 7 blue balls, 2 red balls, and 4 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    30.77%
        
  • A blue ball or red ball?
    69.23%
        
  • Two red balls?
    1.28%
        
  • A blue ball and a white ball?
    17.95%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 7
    x - y = 2
    A(4.5,2.5)
        
  • x - 3y = 19
    2x + 3y = 5

    B(8,-3.67)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x2 + 6x + 9)
    (x + 3)
    x + 3
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 16x + 28 = -x2
    x1 = -2,   x2 = -14
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.465
    465
    999
        
25.   Solve the following equation:
  • -
    6
    x
    = -3
    x = 4
        
26.   Rationalize the denominator of each fraction below:
  • 35
    20
    7
    5
    2
        
27.   Use a trigonometric ratio to find x:
x = 22.63 cm
    
28.   The sum of two consecutive even integers is 38. What are the integers? (Hint: use 2x as the first even integer)
a=18, b=20
    
29.   After you leave your house, you walk 9 blocks east and 12 blocks north. How far are you from your house?
  • I am
    15
    blocks from my house.
        
30.   A rectangle has a width that is 9 ft less than its length. The area of the rectangle is 22ft2. What are the dimensions of the rectangle?
  • width = 2,  length = 11
        


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:   13 and -7? -91
    
2.   Add:   14 and 7? 21
    
3.   Divide:   1 and 1? 1
    
4.   Substract:   5 and -10? 15
    
5.   Calculate: |3 · -18 + 6| 48
    
6.   Simplify the following expressions:
  • 6x + 13x – 19x
        
  • 19y – -18 + 17x – -4 22+17x+19y
        
  • -10x + 3y – -13z + -5z – -12x – -2z 2x+3y+10z
        
  • x-9 × x12 x3
        
  • x5
    x-15
    x20
        
  • (7x5)10 282475249x50
        
7.   Which of the following expressions show the associative property?
  • ( x + y ) × 4 = 4 × ( y + x )
  • ( x × y ) × z = x × ( y × z )
  • -10 × 1 = -10
  • -3x + 7 = 7 + -3x
B
    
8.   Which properties are illustrated by the following three expressions?
  • 0 + -11 = -11
  • -3 × 9 + x = x + -3 × 9
  • ( z + 1 ) × y = z × y + 1 × y
  • Commutative property of addition, Associative property of addition and Identity property of multiplication
  • Identity property of addition, Commutative property of addition and Distributive property
  • Identity property of addition, Identity property of multiplication and Associative property of multiplication
  • Distributive property, Associative property of addition and Identity property of multiplication
B
    
9.   Solve the following equations for x:
  • 82 = 80 – x x = -2
        
  • 7
    29
    =
    1
    29
    x x = 7
        
  • -9 = -53 + -11x x = -4
        
  • d = -ex x = -d/e
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -13x + -26 < -13 x > -1
        
  • x ≠ -440
  • 90 > x ≤ 97
  • -
    30
    15
    x <
    32
    8
    x > -2
        
11.   Convert the following numbers into scientific notation:
  • 0.000000000251 2.51 × 10-10
        
  • 47400000000 4.74 × 1010
        
12.   Add the following polynomials:
  • -5z1 + 7  and  1z9 + -8
    1z9 + -5z1 + -1
        
  • 12z18 + -12z9 + 3z7 + 4z5 + 1z4  and  8z18 + 7z7 + -6z5 20z18 + -12z9 + 10z7 + -2z5 + 1z4
        
13.   Multiply the following polynomials and simplify:
  • (7x3 + 3x2 + 6)-6
    -42x3 - 18x2 - 36
        
  • (9x3 + 9x)(5x5 + 8x3)
    45x8 + 117x6 + 72x4
        
14.   Divide:
  • 20x3 - 24x2 + 35x - 35 / 5x - 6
    (4x2 + 7) with a remainder of 7
        
15.   Find the greatest common factor of the following terms:
  • 12, 90
    6
        
  • 33xy9, 10x6y6
    xy6
        
16.   Factor the following polynomials:
  • 24x4 - 99x3 + 12x2
    24x2(x - 4)(x -
    1
    8
    )
        
  • x2 - 14x + 40
    (x - 4)(x - 10)
        
  • x4 + 25x3 + 156x2
    x2(x + 13)(x + 12)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    4
    and
    10


        
  • x =
    0
    ,
    -13

    and
    -12
        
18.   You have 5 books to read. How many different ways can you read your books?
  • 120
        
19.   Use the following data to construct a box and whiskers plot:
  • 21, 30, 4, 19, 33, 11, 32, 38
        
20.   A bag contains 3 blue balls, 4 red balls, and 5 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    41.67%
        
  • A blue ball or red ball?
    58.33%
        
  • Two red balls?
    9.09%
        
  • A blue ball and a white ball?
    11.36%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -9
    x - y = -4
    A(-6.5,-2.5)
        
  • 5x - 5y = 12
    2x + 4y = 17

    B(4.43,2.03)
        
22.   Write the following fractions in simplest form:
  • 51x10y
    17x10y7
    3
    y6
        
  • (x2 - 2x + 1)
    (x - 1)
    x - 1
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • x2 + 11x = 26
    x1 = 2,   x2 = -13
        
24.   Convert the following repeating decimal into a fraction:
  • x = 5.5
    50
    9
        
25.   Solve the following equation:
  • 24
    x
    = 2
    x = 6
        
26.   Rationalize the denominator of each fraction below:
  • 49
    6
    49
    6
    6
        
27.   Use a trigonometric ratio to find x:
x = 22.52 cm
    
28.   The sum of two consecutive odd integers is 56. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=27, b=29
    
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.   A rectangle has a length 2 m greater than its width. The area of the rectangle is 399m2. What are the length and width of the rectangle?
  • width = 19,  length = 21
        


To print this algebra practice test, click here.



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