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:   1 and 16? 16
    
2.   Add:   -9 and 18? 9
    
3.   Divide:   -4 and -2? 2
    
4.   Substract:   -18 and -4? -14
    
5.   Calculate: |-13 · 15 + 1 · -7| 202
    
6.   Simplify the following expressions:
  • -10x + 15x – 8 -8+5x
        
  • 14x – -14x – 11x + -4x 13x
        
  • -4y – -6y + -7y + 11y – 20z 6y-20z
        
  • x-12 × y16 × y-19 × y-13 x-12 × y-16
        
  • x13
    x-18
    x31
        
  • (2x5)2 4x10
        
7.   Which of the following expressions show the associative property?
  • ( -6 + 10 ) × -2 = -2 × ( -6 + 10 )
  • ( 3 + 9 ) + 6 = 3 + ( 9 + 6 )
  • r × ( s + 5 ) = rs + 5s
  • 6( 4 + 4 ) = 6×4 + 6×4
B
    
8.   Which properties are illustrated by the following three expressions?
  • (2 + z) × 8 = 8 × (2 + z)
  • 1 × (u + v) = u + v
  • 16 + 15 × -5 = 15 × -5 + 16
  • Identity property of addition, Identity property of multiplication and Associative property of multiplication
  • Associative property of multiplication, Identity property of multiplication and Associative property of addition
  • Commutative property of multiplication, Identity property of multiplication and Commutative property of addition
  • Distributive property, Associative property of addition and Identity property of multiplication
C
    
9.   Solve the following equations for x:
  • -52 = -6 + -x x = 46
        
  • 16
    7
    = -
    8
    7
    x x = -2
        
  • -75 = 74 + 149x x = -1
        
  • fx = -cx – g x = (-g)/(f+c)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 11x – -20 > 31 x > 1
        
  • x ≠ 277
  • 16 ≤ x < 85
  • 33
    11
    x ≤
    30
    10
    x ≤ 1
        
11.   Convert the following numbers into scientific notation:
  • 0.000845 8.45 × 10-4
        
  • 48600 4.86 × 104
        
12.   Add the following polynomials:
  • 15z7 + -6z6 + -9z2 + -8z2 + 10  and  -2z10 + -11z7 + -12z4 + 12z2 + 7z1
    -2z10 + 4z7 + -6z6 + -12z4 + -5z2 + 7z1 + 10
        
  • -15z20 + -14z18 + 7z11 + -13  and  11z11 + 10z8 + 6z6 + 11 -15z20 + -14z18 + 18z11 + 10z8 + 6z6 + -2
        
13.   Multiply the following polynomials and simplify:
  • (4x + 10)(1x3 + 9)
    4x4 + 10x3 + 36x + 90
        
  • (6x2 + 4x - 6)(7x4 - 9)
    42x6 + 28x5 - 42x4 - 54x2 - 36x + 54
        
14.   Divide:
  • 2x3 - 3x2 - 10x + 15 / 2x - 3
    x2 - 5
        
15.   Find the greatest common factor of the following terms:
  • 42, 90
    6
        
  • 18x5y9, 54x6y10
    18x5y9
        
16.   Factor the following polynomials:
  • x4 + 27x3 + 72x2
    x2(x + 3)(x + 24)
        
  • x2 + 18x + 80
    (x + 10)(x + 8)
        
  • x7 - 21x6 + 98x5
    x5(x - 14)(x - 7)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -10
    and
    -8


        
  • x =
    0
    ,
    14

    and
    7
        
18.   How many ways can 6 people wait in line?
  • 720
        
19.   Use the following data to construct a box and whiskers plot:
  • 1, 25, 38, 35, 18, 39, 13, 11
        
20.   A bag contains 7 blue balls, 3 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?
    41.18%
        
  • A blue ball or red ball?
    58.82%
        
  • Two red balls?
    3.11%
        
  • A blue ball and a white ball?
    16.96%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 1
    x - y = -18
    A(-8.5,9.5)
        
  • 2x - 8y = 18
    6x + 10y = 10

    B(3.82,-1.29)
        
22.   Write the following fractions in simplest form:
  • 20x4y4
    60x7y4
    1
    3x3
        
  • x8 + 7x7 - 30x6
    x5(x + 10)
    x(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.
  • x2 - 37x = 78
    x1 = 39,   x2 = -2
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.2759
    2732
    9900
        
25.   Solve the following equation:
  • 14
    x
    = 5
    x =
    196
    25
        
26.   Rationalize the denominator of each fraction below:
  • 4
    28
    15
    12
    4
    21
    45
        
27.   Use a trigonometric ratio to find x:
x = 35.36 cm
    
28.   The sum of two consecutive even integers is 14. What are the integers? (Hint: use 2x as the first even integer)
a=6, b=8
    
29.   After you leave your house, you walk 8 blocks east and 15 blocks south. How far are you from your house?
  • I am
    17
    blocks from my house.
        
30.   Each side of a square is decreased by 9 m. The area of the newly created square is 121m2. What was the original length of one side of the square?
  • 20 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:   8 and 12? 96
    
2.   Add:   -8 and 15? 7
    
3.   Divide:   19 and -19? -1
    
4.   Substract:   -11 and -18? 7
    
5.   Calculate: |9 + -11 · -1| 20
    
6.   Simplify the following expressions:
  • -9x + -15x + -18x -42x
        
  • 11x + 15x – -3y – 15 -15+26x+3y
        
  • -12y – 13 – -7y – -14y – -2 + -18 -29+9y
        
  • x2 × y10 x2 × y10
        
  • x11
    x-15
    x26
        
  • (2x5)5 32x25
        
7.   Which of the following expressions show the associative property?
  • 0 + -6x = -6x
  • a + b = b + a
  • ( 7 + 2 ) + 8 = 7 + ( 2 + 8 )
  • p × ( q + 4 ) = pq + 4q
C
    
8.   Which properties are illustrated by the following three expressions?
  • 9 × -11 = 9 × -11
  • k + ( l + 0 ) = ( k + l ) + 0
  • ( 6 + 11 ) × x = 6 × x + 11 × x
  • Distributive property, Identity property of multiplication and Commutative property of addition
  • Commutative property of multiplication, Associative property of addition and Distributive property
  • Identity property of addition, Distributive property and Associative property of multiplication
  • Associative property of addition, Commutative property of multiplication and Identity property of multiplication
B
    
9.   Solve the following equations for x:
  • -x · -2 = -32 x = -16
        
  • -
    16
    6
    = -
    4
    6
    x x = 4
        
  • 57 – 92x = -35 x = 1
        
  • ax + d = gx x = (-d)/(a-g)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -2x + 22 ≥ -26 x ≤ 24
        
  • x ≠ 88
  • -7 ≥ x ≥ 16
  • -
    40
    2
    x ≥ 20 x ≤ -1
        
11.   Convert the following numbers into scientific notation:
  • 0.000984 9.84 × 10-4
        
  • 981000000000 9.81 × 1011
        
12.   Add the following polynomials:
  • -10z9 + -10z1  and  -2z9 + 8z3 + 11z2 + 10z1
    -12z9 + 8z3 + 11z2
        
  • -15z17 + -1z15 + -5z12 + -9z7 + 7z4  and  6z19 + 12z17 + -1z12 + -15z7 + 7z4 6z19 + -3z17 + -1z15 + -6z12 + -24z7 + 14z4
        
13.   Multiply the following polynomials and simplify:
  • (10x5 + 4x2 + 10x)(7x4 + 7x - 3)
    70x9 + 98x6 + 40x5 + 28x3 + 58x2 - 30x
        
  • (9x4 + 5x3 + 10)(5x3 + 7)
    45x7 + 25x6 + 63x4 + 85x3 + 70
        
14.   Divide:
  • 9x2 + 18x - 16 / 3x - 2
    3x + 8
        
15.   Find the greatest common factor of the following terms:
  • 60, 90, 11
    1
        
  • 96x5y5, 36xy9, 65x6y8
    xy5
        
16.   Factor the following polynomials:
  • 56x4 + 0x3 - 14x2
    56x2(x +
    1
    2
    )(x -
    1
    2
    )
        
  • x2 - 14x + 40
    (x - 10)(x - 4)
        
  • x8 + 18x7 + 45x6
    x6(x + 15)(x + 3)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    10
    and
    4


        
  • x =
    0
    ,
    -15

    and
    -3
        
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:
  • 8, 26, 15, 24, 2, 29, 11, 7, 5, 23
        
20.   A bag contains 5 blue balls, 2 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?
    1.52%
        
  • A blue ball and a white ball?
    18.94%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 7
    x - y = -10
    A(-1.5,8.5)
        
  • 3x - 8y = -1
    4x + 3y = -20

    B(-3.98,-1.37)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x2 + 14x + 49)
    (x + 7)
    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.
  • x2 + x = 12
    x1 = 3,   x2 = -4
        
24.   Convert the following repeating decimal into a fraction:
  • x = 9.131
    9040
    990
        
25.   Solve the following equation:
  • -16 +
    5x - 6
    = 1
    x = 59
        
26.   Rationalize the denominator of each fraction below:
  • 7
    21 -
    6
    147 + 7
    6
    435
        
27.   Use a trigonometric ratio to find x:
x = 21.00 cm
    
28.   The sum of two consecutive even integers is 62. What are the integers? (Hint: use 2x as the first even integer)
a=30, b=32
    
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 an area of 20m2. Its width is 8 m less than its length. What are the dimensions of the rectangle?
  • width = 2,  length = 10
        


To print this algebra practice test, click here.



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