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:   -13 and 6? -78
    
2.   Add:   -4 and -19? -23
    
3.   Divide:   6 and -1? -6
    
4.   Substract:   19 and 1? 18
    
5.   Calculate: |-4 + 18 · -8| 148
    
6.   Simplify the following expressions:
  • 5 + -15x + 9x 5-6x
        
  • 19y + 12x + 4x + 20x 36x+19y
        
  • -3z + -20z – 15 + -13y + -19z + -18y -15-31y-42z
        
  • x-2 × x-8 × y-13 x-10 × y-13
        
  • x16
    x-12
    x28
        
  • (8x4)3 512x12
        
7.   Which of the following expressions show the associative property?
  • ( m + n ) + p = m + ( n + p )
  • -10 × ( z + 3 + 6 ) = -10×z + -10×3 + -10×6
  • 9 + 5 = 5 + 9
  • 9x + -3 = -3 + 9x
A
    
8.   Which properties are illustrated by the following three expressions?
  • ( 16 + -8) × -17 = 16 × -17 + -8 × -17
  • e + 4 + 0 = e + 4
  • c + ( d + e ) = ( c + d ) + e
  • Distributive property, Identity property of addition and Associative property of addition
  • Commutative property of addition, Associative property of addition and Commutative property of multiplication
  • Identity property of addition, Commutative property of multiplication and Commutative property of addition
  • Identity property of addition, Commutative property of addition and Associative property of multiplication
A
    
9.   Solve the following equations for x:
  • -20 = -x · -10 x = -2
        
  • 17
    14
    = -
    17
    14
    x x = -1
        
  • 25 = -21x + 67 x = 2
        
  • a = -gx x = -a/g
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x + 10 ≤ 11 x ≥ -1
        
  • x ≠ 370
  • 15 < x < 31
  • -
    6
    3
    x <
    36
    6
    x > -3
        
11.   Convert the following numbers into scientific notation:
  • 0.000867 8.67 × 10-4
        
  • 549000 5.49 × 105
        
12.   Add the following polynomials:
  • 14z10 + 9z8 + -11z4 + 12z3  and  7z10 + -6z3
    21z10 + 9z8 + -11z4 + 6z3
        
  • 10z20 + 9z19 + 14z5 + -9z2 + 14z1  and  9z19 + 15z12 + -10z9 + 8z5 + 12z1 10z20 + 18z19 + 15z12 + -10z9 + 22z5 + -9z2 + 26z1
        
13.   Multiply the following polynomials and simplify:
  • (9x5 + 7x3)1x2
    9x7 + 7x5
        
  • (10x5 + 5x4 + 10x2)(6x4 + 8)
    60x9 + 30x8 + 60x6 + 80x5 + 40x4 + 80x2
        
14.   Divide:
  • 5x3 - 5x2 + x - 1 / x - 1
    5x2 + 1
        
15.   Find the greatest common factor of the following terms:
  • 54, 88, 44
    2
        
  • 60x9y7, 14x3y10, 91x7y8
    x3y7
        
16.   Factor the following polynomials:
  • 16x4 + 48x3 + 34x2
    16x2(x -
    -6 +
    2
    4
    )(x -
    -6 -
    2
    4
    )
        
  • x2 - 9x + 20
    (x - 5)(x - 4)
        
  • x6 - 8x5 - 105x4
    x4(x - 15)(x + 7)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    5
    and
    4


        
  • x =
    0
    ,
    15

    and
    -7
        
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:
  • 23, 20, 28, 33, 24, 37, 19, 35, 5, 8
        
20.   A bag contains 3 blue balls, 6 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?
    43.75%
        
  • A blue ball or red ball?
    56.25%
        
  • Two red balls?
    14.06%
        
  • A blue ball and a white ball?
    8.20%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -20
    x - y = 3
    A(-8.5,-11.5)
        
  • 2x - 5y = -11
    2x + 9y = -19

    B(-6.93,-0.57)
        
22.   Write the following fractions in simplest form:
  • 8x9y6
    32x5y3
    x4y3
    4
        
  • x8 - 3x7 + 2x6
    x4(x - 1)
    x2(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.
  • 60 = x2 + 11x
    x1 = -15,   x2 = 4
        
24.   Convert the following repeating decimal into a fraction:
  • x = 7.18
    711
    99
        
25.   Solve the following equation:
  • -6 -
    x - 10
    = -16
    x = 110
        
26.   Rationalize the denominator of each fraction below:
  • 9
    15
    + 6
    -
    3
    15
    - 18
    7
        
27.   Use a trigonometric ratio to find x:
x = 13.50 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 3 blocks west and 4 blocks south. How far are you from your house?
  • I am
    5
    blocks from my house.
        
30.   Each side of a square is decreased by 5 ft. The area of the newly created square is 225ft2. What was the original length of one side of the square?
  • 20 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:   -19 and -1? 19
    
2.   Add:   1 and 4? 5
    
3.   Divide:   -12 and -4? 3
    
4.   Substract:   14 and -13? 27
    
5.   Calculate: |3 + -6 · -4 + 3| 30
    
6.   Simplify the following expressions:
  • -6x – -13 – -20x 13+14x
        
  • -4 + -4x – -6y + 20 16-4x+6y
        
  • 10x – -9 + 1z – 14x + 10z – 17 -8-4x+11z
        
  • x6 × x-18 × x-4 × x-8 x-24
        
  • x-19
    x15
    x-34
        
  • (9x2)4 6561x8
        
7.   Which of the following expressions show the associative property?
  • a + b = b + a
  • ( m + n ) + 6 = m + ( n + 6 )
  • ( x + y ) × 5 = 5 × ( y + x )
  • 9 + 7m + 10
B
    
8.   Which properties are illustrated by the following three expressions?
  • ( z + 1 ) × y = z × y + 1 × y
  • -63 + 0 = -63
  • (h + 14) × 1 = h + 14
  • Commutative property of multiplication, Identity property of addition and Associative property of multiplication
  • Distributive property, Identity property of addition and Identity property of multiplication
  • Distributive property, Associative property of multiplication and Associative property of addition
  • Associative property of addition, Associative property of multiplication and Commutative property of addition
B
    
9.   Solve the following equations for x:
  • -6 = -x + -17 x = -11
        
  • -
    5
    23
    x =
    15
    23
    x = -3
        
  • -97 = -17x – -39 x = 8
        
  • -gx = e – a x = (-e+a)/g
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 3x – 26 ≤ -5 x ≤ 7
        
  • x ≠ -457
  • 50 < x < 51
  • 38
    19
    x > -
    34
    17
    x > -1
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000000615 6.15 × 10-11
        
  • 83300 8.33 × 104
        
12.   Add the following polynomials:
  • -3z9 + -6z7 + 15z4  and  4z7 + -3z3 + -6z1 + 3
    -3z9 + -2z7 + 15z4 + -3z3 + -6z1 + 3
        
  • -15z9 + -5z5 + -13z2  and  9z9 + 14z5 + -10z2 -6z9 + 9z5 + -23z2
        
13.   Multiply the following polynomials and simplify:
  • (8x4 + x)(4x5 + 6x)
    32x9 + 4x6 + 48x5 + 6x2
        
  • (4x4 + 9x3)(3x5 + 5x3 + 2x2)
    12x9 + 27x8 + 20x7 + 53x6 + 18x5
        
14.   Divide:
  • 3x3 + 3x2 - 3x - 3 / 3x + 3
    x2 - 1
        
15.   Find the greatest common factor of the following terms:
  • 33, 90, 60
    3
        
  • 10x8y10, 40x7y4, 45x7y3
    5x7y3
        
16.   Factor the following polynomials:
  • 3x4 + 12x3 + 12x2
    3x2(x + 2)(x + 2)
        
  • x2 + x - 2
    (x - 1)(x + 2)
        
  • x8 - 13x7 + 12x6
    x6(x - 12)(x - 1)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    1
    and
    -2


        
  • x =
    0
    ,
    12

    and
    1
        
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 or strawberry. How many choices do you have?
  • 18
        
19.   Use the following data to construct a box and whiskers plot:
  • 38, 7, 39, 15, 9, 27, 20
        
20.   A bag contains 7 blue balls, 7 red balls, and 2 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    12.50%
        
  • A blue ball or red ball?
    87.50%
        
  • Two red balls?
    17.50%
        
  • A blue ball and a white ball?
    5.83%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -9
    x - y = -13
    A(-11,2)
        
  • 2x - 7y = 6
    3x + 3y = 3

    B(1.44,-0.44)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x - 4)
    (x2 - 8x + 16)
    1
    x - 4
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 45 = x2 - 12x
    x1 = 15,   x2 = -3
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.71
    71
    99
        
25.   Solve the following equation:
  • 9
    x
    = 7
    x =
    81
    49
        
26.   Rationalize the denominator of each fraction below:
  • 15
    3
    21
    28
    5
    21
    98
        
27.   Use a trigonometric ratio to find x:
x = 20.78 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 5 blocks west and 12 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 ft. This makes the area of the square 100ft2. What is the original length of a side of the square?
  • 5 ft
        


To print this algebra practice test, click here.



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