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:   16 and 3? 48
    
2.   Add:   -9 and -17? -26
    
3.   Divide:   -13 and 13? -1
    
4.   Substract:   -8 and -3? -5
    
5.   Calculate: |8 · 10| 80
    
6.   Simplify the following expressions:
  • -12x + 16x – -12x 16x
        
  • 6x – 16 + 3x – 8 -24+9x
        
  • -2y – -14y + -5 – -17 + 5y + 8 20+17y
        
  • x-9 × x19 × x2 x12
        
  • x20
    x3
    x17
        
  • (7x3)5 16807x15
        
7.   Which of the following expressions show the associative property?
  • ( x + y ) + z = x + ( y + z )
  • -7 × ( z + 8 + 7 ) = -7×z + -7×8 + -7×7
  • ( m × n ) + 2 = 2 + ( m × n )
  • 0 + -2x = -2x
A
    
8.   Which properties are illustrated by the following three expressions?
  • (1 + z) × 6 = 6 × (1 + z)
  • i + j + k + 0 = i + j + k
  • q × ( r × s ) = ( q × r ) × s
  • Associative property of multiplication, Distributive property and Identity property of multiplication
  • Associative property of addition, Associative property of multiplication and Identity property of multiplication
  • Distributive property, Identity property of multiplication and Identity property of addition
  • Commutative property of multiplication, Identity property of addition and Associative property of multiplication
D
    
9.   Solve the following equations for x:
  • -72 = x · -18 x = 4
        
  • 1
    25
    x = -
    9
    25
    x = -9
        
  • 56 = -5x + 26 x = -6
        
  • cx = -d x = -d/c
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 2x + -1 ≥ -5 x ≥ -2
        
  • x ≠ -884
  • 54 ≥ x ≤ 94
  • -
    16
    2
    x ≥ -16 x ≤ 2
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000662 6.62 × 10-8
        
  • 40900000 4.09 × 107
        
12.   Add the following polynomials:
  • -5z7 + 11z6  and  -9z9 + 15z7 + 1z4 + 15z2 + -4z1
    -9z9 + 10z7 + 11z6 + 1z4 + 15z2 + -4z1
        
  • -14z14 + -5z5 + -1z4 + -4z2  and  -11z14 + 3z5 + -4z4 + 15z2 + 7z1 -25z14 + -2z5 + -5z4 + 11z2 + 7z1
        
13.   Multiply the following polynomials and simplify:
  • (7x2 + 7x)2
    14x2 + 14x
        
  • (6x3 + 6x - 7)(5x5 + 7x4)
    30x8 + 42x7 + 30x6 + 7x5 - 49x4
        
14.   Divide:
  • 6x2 + 24x + 51 / 2x + 4
    (3x + 6) with a remainder of 27
        
15.   Find the greatest common factor of the following terms:
  • 100, 50
    50
        
  • 13x5y8, 84x7y10
    x5y8
        
16.   Factor the following polynomials:
  • 66x5 - 19x4 - 5x3
    66x3(x +
    1
    6
    )(x -
    5
    11
    )
        
  • x2 + 11x + 18
    (x + 2)(x + 9)
        
  • x5 + 3x4 - 18x3
    x3(x - 3)(x + 6)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -2
    and
    -9


        
  • x =
    0
    ,
    3

    and
    -6
        
18.   You have 7 books to read. How many different ways can you read your books?
  • 5040
        
19.   Use the following data to construct a box and whiskers plot:
  • 5, 12, 14, 22, 1, 18, 4, 38, 33, 17
        
20.   A bag contains 7 blue balls, 4 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?
    26.67%
        
  • A blue ball or red ball?
    73.33%
        
  • Two red balls?
    5.71%
        
  • A blue ball and a white ball?
    13.33%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -4
    x - y = -19
    A(-11.5,7.5)
        
  • 4x - 3y = -18
    8x + 4y = 17

    B(-0.53,5.3)
        
22.   Write the following fractions in simplest form:
  • 22x6y
    66x9y7
    1
    3x3y6
        
  • (x + 2)4
    (x + 2)3
    x + 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 - 42 = -x
    x1 = -7,   x2 = 6
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.3849
    3811
    9900
        
25.   Solve the following equation:
  • 40
    x
    = 2
    x = 10
        
26.   Rationalize the denominator of each fraction below:
  • 15
    15
    21 +
    7
    315
    15
    - 15
    105
    434
        
27.   Use a trigonometric ratio to find x:
x = 16.17 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 12 blocks east and 5 blocks north. How far are you from your house?
  • I am
    13
    blocks from my house.
        
30.   Each side of a square is lengthened by 5 m. This makes the area of the square 81m2. What is the original length of a side of the square?
  • 4 m
        


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:   10 and 10? 100
    
2.   Add:   -16 and 14? -2
    
3.   Divide:   -11 and 11? -1
    
4.   Substract:   -20 and 16? -36
    
5.   Calculate: |-5 · -13 + 1 · -13| 52
    
6.   Simplify the following expressions:
  • 4x + 19 + -19 4x
        
  • 3 – -13y + -15x – 13y 3-15x
        
  • 9y + -19z + 19x + -17x + 20y + -16y 2x+13y-19z
        
  • y12 × y9 × y10 × x-7 x-7 × y31
        
  • x-5
    x-19
    x14
        
  • (8x2)5 32768x10
        
7.   Which of the following expressions show the associative property?
  • 6( 2 + 4 ) = 6×2 + 6×4
  • -4x + 2 = 2 + -4x
  • 2 + 4d + 10
  • ( m × n ) × 9 = m × ( n × 9 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • ( 19 + 20) × -11 = 19 × -11 + 20 × -11
  • r + ( s + t ) = ( r + s ) + t
  • r + s + 0 = r + s
  • Identity property of addition, Identity property of multiplication and Associative property of multiplication
  • Commutative property of multiplication, Associative property of multiplication and Distributive property
  • Distributive property, Associative property of addition and Identity property of addition
  • Associative property of addition, Commutative property of multiplication and Distributive property
C
    
9.   Solve the following equations for x:
  • 93 – x = 51 x = 42
        
  • -
    1
    19
    x = -
    5
    19
    x = 5
        
  • 76 – 2x = -100 x = 88
        
  • -fx = d x = -d/f
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x – 6 < 37 x > -43
        
  • x ≠ 473
  • 33 < x ≤ 40
  • -
    16
    4
    x > -
    32
    4
    x < 2
        
11.   Convert the following numbers into scientific notation:
  • 0.00000000772 7.72 × 10-9
        
  • 6060000 6.06 × 106
        
12.   Add the following polynomials:
  • -5z10 + -2z7 + 12z6 + -8z5  and  2z10 + -14z7 + 3z6 + -4z5 + -12
    -3z10 + -16z7 + 15z6 + -12z5 + -12
        
  • 11z16 + 5z11 + -14z3  and  13z15 + 13z11 + -1z7 + 2z4 + -15 11z16 + 13z15 + 18z11 + -1z7 + 2z4 + -14z3 + -15
        
13.   Multiply the following polynomials and simplify:
  • (8x2 + 7x)4x3
    32x5 + 28x4
        
  • (10x4 - 3)(10x2 + 5)
    100x6 + 50x4 - 30x2 - 15
        
14.   Divide:
  • 20x2 + 21x + 4 / 5x + 4
    4x + 1
        
15.   Find the greatest common factor of the following terms:
  • 75, 33
    3
        
  • 72x6y7, 60y3
    12y3
        
16.   Factor the following polynomials:
  • 38x4 + 57x3 + 19x2
    38x2(x +
    1
    2
    )(x + 1)
        
  • x2 + 11x + 24
    (x + 8)(x + 3)
        
  • x4 + 23x3 + 126x2
    x2(x + 14)(x + 9)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -8
    and
    -3


        
  • x =
    0
    ,
    -14

    and
    -9
        
18.   You are seating 3 people on 3 chairs. How many different ways can those people sit?
  • 6
        
19.   Use the following data to construct a box and whiskers plot:
  • 39, 14, 15, 1, 17, 23, 34
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 17
  • What is the probability of getting heads and 6?
    2.94%
        
  • What is the probability of getting tails and an odd number?
    23.53%
        
  • What is the probability of getting tails and a multiple of 3?
    14.71%
        
  • What is the probability of getting tails and a prime number?
    20.59%
        
  • What is the probability of not tails and not 10?
    47.06%
        
  • 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 = 7
    x - y = -20
    A(-6.5,13.5)
        
  • 6x - 8y = -20
    3x + 2y = -10

    B(-3.33,0)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • x6 - 17x5 + 70x4
    x6(x - 10)
    (x - 7)
    x2
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -x2 = -23x - 78
    x1 = -3,   x2 = 26
        
24.   Convert the following repeating decimal into a fraction:
  • x = 8.37
    829
    99
        
25.   Solve the following equation:
  • 4
    x
    - 20 = 3
    x
    - 2
    x = 324
        
26.   Rationalize the denominator of each fraction below:
  • 15
    14
    15
    14
    14
        
27.   Use a trigonometric ratio to find x:
x = 16.26 cm
    
28.   The sum of two consecutive even integers is 54. What are the integers? (Hint: use 2x as the first even integer)
a=26, b=28
    
29.   After you leave your house, you walk 16 blocks east and 12 blocks north. How far are you from your house?
  • I am
    20
    blocks from my house.
        
30.   A rectangle has a width that is 2 ft less than its length. The area of the rectangle is 120ft2. What are the dimensions of the rectangle?
  • width = 10,  length = 12
        


To print this algebra practice test, click here.



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