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:   -6 and 5? -30
    
2.   Add:   14 and -16? -2
    
3.   Divide:   17 and 17? 1
    
4.   Substract:   1 and 9? -8
    
5.   Calculate: |4 · -11 + -10 · 17| 214
    
6.   Simplify the following expressions:
  • -5x + -2 – 8 -10-5x
        
  • 11y + 16y – 5y + -6y 16y
        
  • -5 – 6y – 13z – 14x + -12y -5-14x-18y-13z
        
  • y-2 × x15 × x7 × y-2 x22 × y-4
        
  • x-6
    x-10
    x4
        
  • (8x4)9 134217728x36
        
7.   Which of the following expressions show the associative property?
  • ( x + y ) × 4 = 4 × ( y + x )
  • ( x + y ) + z = x + ( y + z )
  • 0 + 6x = 6x
  • ( m × n ) + 7 = 7 + ( m × n )
B
    
8.   Which properties are illustrated by the following three expressions?
  • 9 + 3 = 9 + 3
  • ( e + 0 ) + d = e + ( 0 + d )
  • 13 × (6 + x) = (6 + x) × 13
  • Identity property of multiplication, Associative property of addition and Associative property of multiplication
  • Identity property of multiplication, Commutative property of multiplication and Associative property of addition
  • Associative property of addition, Associative property of multiplication and Commutative property of addition
  • Commutative property of addition, Associative property of addition and Commutative property of multiplication
D
    
9.   Solve the following equations for x:
  • -x + 77 = -32 x = 109
        
  • 17
    27
    x = -
    17
    27
    x = -1
        
  • -84 – 2x = -28 x = -28
        
  • bx = -f x = -f/b
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 3x + -5 ≥ -14 x ≥ -3
        
  • x ≠ -117
  • 66 ≥ x ≥ 38
  • -
    26
    13
    x ≤ -
    24
    6
    x ≥ 2
        
11.   Convert the following numbers into scientific notation:
  • 0.0000795 7.95 × 10-5
        
  • 95100000 9.51 × 107
        
12.   Add the following polynomials:
  • 1z8 + 13z4  and  1z8 + -4z4
    2z8 + 9z4
        
  • -7z16 + 9z13 + -4z2  and  8z16 + 6z13 + -9z3 + -3z2 1z16 + 15z13 + -9z3 + -7z2
        
13.   Multiply the following polynomials and simplify:
  • 8x3(9x3 + 5x)
    72x6 + 40x4
        
  • (4x5 - 5)(2x5 + x4 + 10x)
    8x10 + 4x9 + 40x6 - 10x5 - 5x4 - 50x
        
14.   Divide:
  • 8x2 + 4x - 12 / 2x - 2
    4x + 6
        
15.   Find the greatest common factor of the following terms:
  • 65, 66, 90
    1
        
  • 78x6y6, 72x6y4, 52x8y10
    2x6y4
        
16.   Factor the following polynomials:
  • 48x3 + 4x2 - 24x
    48x(x -
    2
    3
    )(x +
    3
    4
    )
        
  • x2 - 2x - 3
    (x + 1)(x - 3)
        
  • x8 - x7 - 156x6
    x6(x - 13)(x + 12)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -1
    and
    3


        
  • x =
    0
    ,
    13

    and
    -12
        
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:
  • 7, 26, 10, 3, 27, 14, 31, 36, 29, 8
        
20.   A bag contains 7 blue balls, 6 red balls, and 2 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    13.33%
        
  • A blue ball or red ball?
    86.67%
        
  • Two red balls?
    16.00%
        
  • A blue ball and a white ball?
    6.22%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -6
    x - y = -15
    A(-10.5,4.5)
        
  • 3x - 5y = 19
    4x + 9y = -11

    B(2.47,-2.32)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • x3(x + 10)
    x8 + 3x7 - 70x6
    1
    x3(x - 7)
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 10 = x2 - 9x
    x1 = 10,   x2 = -1
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.2281
    2259
    9900
        
25.   Solve the following equation:
  • 6
    x
    = 7
    x =
    36
    49
        
26.   Rationalize the denominator of each fraction below:
  • 9
    7 +
    14
    63 - 9
    14
    35
        
27.   Use a trigonometric ratio to find x:
x = 26.87 cm
    
28.   The sum of two consecutive odd integers is 36. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=17, b=19
    
29.   After you leave your house, you walk 8 blocks north and 15 blocks west. How far are you from your house?
  • I am
    17
    blocks from my house.
        
30.   A rectangle has an area of 96ft2. Its width is 10 ft less than its length. What are the dimensions of the rectangle?
  • width = 6,  length = 16
        


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:   4 and -2? -8
    
2.   Add:   12 and -4? 8
    
3.   Divide:   9 and 1? 9
    
4.   Substract:   19 and 7? 12
    
5.   Calculate: |14 · -8 + -4 · 12| 160
    
6.   Simplify the following expressions:
  • 20x + -9x + -7x 4x
        
  • 14x + 3y – 4y + 7x 21x-1y
        
  • 13x + 10z + -13z + -7y – -5y 13x-2y-3z
        
  • x18 × y17 × y7 × x18 x36 × y24
        
  • x12
    x-9
    x21
        
  • (5x2)4 625x8
        
7.   Which of the following expressions show the associative property?
  • a + b = b + a
  • 0 + 4x = 4x
  • ( m + n ) × 6 = 6 × ( m + n )
  • ( x + y ) + z = x + ( y + z )
D
    
8.   Which properties are illustrated by the following three expressions?
  • 15 + o + p = o + p + 15
  • (j + k + l) × 1 = j + k + l
  • n × ( o × 1 ) = ( n × o ) × 1
  • Associative property of multiplication, Commutative property of multiplication and Identity property of multiplication
  • Associative property of multiplication, Identity property of addition and Associative property of addition
  • Distributive property, Identity property of addition and Identity property of multiplication
  • Commutative property of addition, Identity property of multiplication and Associative property of multiplication
D
    
9.   Solve the following equations for x:
  • -55 + x = -1 x = 54
        
  • 28
    24
    = -
    2
    12
    x x = -7
        
  • -39x – 71 = -32 x = -1
        
  • -f = cx x = -f/c
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x + -24 ≤ -35 x ≥ 11
        
  • x ≠ -923
  • 67 > x > 97
  • -
    33
    11
    x >
    21
    7
    x < -1
        
11.   Convert the following numbers into scientific notation:
  • 0.00000911 9.11 × 10-6
        
  • 78500 7.85 × 104
        
12.   Add the following polynomials:
  • -4z7 + -10z2  and  -3z7 + 4z2
    -7z7 + -6z2
        
  • -3z6 + -15z5 + -12z1  and  -6z20 + -1z6 + 11z3 + 4z1 -6z20 + -4z6 + -15z5 + 11z3 + -8z1
        
13.   Multiply the following polynomials and simplify:
  • (10x5 + 8x2)6x2
    60x7 + 48x4
        
  • (9x4 + 6x2)(10x5 + 4x4 + 3x2)
    90x9 + 36x8 + 60x7 + 51x6 + 18x4
        
14.   Divide:
  • 12x2 - 15x + 3 / 3x - 3
    4x - 1
        
15.   Find the greatest common factor of the following terms:
  • 72, 60
    12
        
  • 75x4y6, 25xy
    25xy
        
16.   Factor the following polynomials:
  • 20x3 - 50x2 - 30x
    20x(x +
    1
    2
    )(x - 3)
        
  • x2 + 8x + 15
    (x + 5)(x + 3)
        
  • x6 + 5x5 - 150x4
    x4(x - 10)(x + 15)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -5
    and
    -3


        
  • x =
    0
    ,
    10

    and
    -15
        
18.   You have 3 CDs. How many different ways can you listen to them?
  • 6
        
19.   Use the following data to construct a box and whiskers plot:
  • 15, 16, 11, 3, 28, 23, 20, 30
        
20.   A bag contains 3 blue balls, 2 red balls, and 7 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    58.33%
        
  • A blue ball or red ball?
    41.67%
        
  • Two red balls?
    2.78%
        
  • A blue ball and a white ball?
    14.58%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 7
    x - y = -12
    A(-2.5,9.5)
        
  • 10x - 9y = 18
    9x + 9y = -6

    B(0.63,-1.3)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 6)4
    (x + 6)
    (x + 6)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 + 39 = -x2
    x1 = -3,   x2 = -13
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.1
    1
    9
        
25.   Solve the following equation:
  • 14
    x
    - 16 = 8
    x
    - 10
    x = 1
        
26.   Rationalize the denominator of each fraction below:
  • 6
    5
    14
    2
    3
    10
    14
        
27.   Use a trigonometric ratio to find x:
x = 34.00 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 8 blocks south and 6 blocks east. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   Each side of a square is lengthened by 2 ft. This makes the area of the square 169ft2. What is the original length of a side of the square?
  • 11 ft
        


To print this algebra practice test, click here.



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