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:   14 and 16? 224
    
2.   Add:   18 and 17? 35
    
3.   Divide:   18 and -2? -9
    
4.   Substract:   -18 and 3? -21
    
5.   Calculate: |6 · -15 + -5| 95
    
6.   Simplify the following expressions:
  • -4 – 7 – 1x -11-1x
        
  • 16x + -3y – -7y + -3y 16x+1y
        
  • 4x + -2y + 20y – 14x – 20 – 8y -20-10x+10y
        
  • x-9 × x12 × y-10 x3 × y-10
        
  • x-3
    x6
    x-9
        
  • (10x)7 10000000x7
        
7.   Which of the following expressions show the associative property?
  • 7( 9 + 8 ) = 7×9 + 7×8
  • ( m + n ) × 9 = 9 × ( m + n )
  • ( x × y ) × z = x × ( y × z )
  • ( x + y ) × 3 = 3 × ( y + x )
C
    
8.   Which properties are illustrated by the following three expressions?
  • o + ( p + 0 ) = ( o + p ) + 0
  • 1 × (l + 16) = l + 16
  • c × ( d × e ) = ( c × d ) × e
  • Identity property of addition, Associative property of multiplication and Associative property of addition
  • Associative property of multiplication, Commutative property of multiplication and Associative property of addition
  • Commutative property of addition, Associative property of addition and Associative property of multiplication
  • Associative property of addition, Identity property of multiplication and Associative property of multiplication
D
    
9.   Solve the following equations for x:
  • 2 + x = 25 x = 23
        
  • 7
    5
    =
    7
    5
    x x = 1
        
  • 25 = 2x + 13 x = 6
        
  • -b = gx + ax x = (-b)/(g+a)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 32x + -4 < 28 x < 1
        
  • x ≠ 39
  • -89 < x < 97
  • 27
    3
    x ≥ -
    36
    2
    x ≥ -2
        
11.   Convert the following numbers into scientific notation:
  • 0.00000326 3.26 × 10-6
        
  • 345000 3.45 × 105
        
12.   Add the following polynomials:
  • -7z10 + 11z9 + 10z3 + -12z1 + 14  and  3z9 + 2z6 + 12z3 + 9z2
    -7z10 + 14z9 + 2z6 + 22z3 + 9z2 + -12z1 + 14
        
  • -5z15 + 7z9 + 11z5  and  -11z15 + 6z9 + 1z5 -16z15 + 13z9 + 12z5
        
13.   Multiply the following polynomials and simplify:
  • -1(9x4 + 5x3)
    -9x4 - 5x3
        
  • (2x5 + 8x2 + 8)(8x - 5)
    16x6 - 10x5 + 64x3 - 40x2 + 64x - 40
        
14.   Divide:
  • 6x2 - 17x - 40 / 3x + 5
    (2x - 9) with a remainder of 5
        
15.   Find the greatest common factor of the following terms:
  • 98, 42, 90
    2
        
  • 27xy6, 45x9y5
    9xy5
        
16.   Factor the following polynomials:
  • 68x4 - 82x3 - 30x2
    68x2(x +
    5
    17
    )(x -
    3
    2
    )
        
  • x2 - 4x - 60
    (x + 6)(x - 10)
        
  • x5 - 9x4 - 52x3
    x3(x + 4)(x - 13)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -6
    and
    10


        
  • x =
    0
    ,
    -4

    and
    13
        
18.   How many ways can 5 people wait in line?
  • 120
        
19.   Use the following data to construct a box and whiskers plot:
  • 14, 35, 13, 5, 10, 12, 7, 16, 40, 36
        
20.   A bag contains 4 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?
    45.45%
        
  • A blue ball or red ball?
    54.55%
        
  • Two red balls?
    1.82%
        
  • A blue ball and a white ball?
    18.18%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -20
    x - y = 1
    A(-9.5,-10.5)
        
  • 7x - 9y = 3
    6x + 3y = -10

    B(-1.08,-1.17)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x - 7)3
    (x - 7)4
    1
    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 + 78 = 29x
    x1 = 3,   x2 = 26
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.383
    345
    900
        
25.   Solve the following equation:
  • 32
    x
    = 4
    x = 2
        
26.   Rationalize the denominator of each fraction below:
  • 2
    21
    5 +
    3
    5
    21
    - 3
    7
    11
        
27.   Use a trigonometric ratio to find x:
x = 48.00 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 12 blocks east and 9 blocks north. How far are you from your house?
  • I am
    15
    blocks from my house.
        
30.   Each side of a square is decreased by 7 ft. The area of the newly created square is 1ft2. What was the original length of one side of the square?
  • 6 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 -15? 285
    
2.   Add:   -14 and -17? -31
    
3.   Divide:   -20 and 5? -4
    
4.   Substract:   6 and -9? 15
    
5.   Calculate: |3 + 10 · -12| 117
    
6.   Simplify the following expressions:
  • 9x + 7x + -6x 10x
        
  • -3y – -13y – -15x + 12y 15x+22y
        
  • 16z + 8y – 2y + -5z + -8x -8x+6y+11z
        
  • x-6 × x2 × x13 × y17 x9 × y17
        
  • x3
    x-14
    x17
        
  • (10x3)6 1000000x18
        
7.   Which of the following expressions show the associative property?
  • 10x + -10 = -10 + 10x
  • 4 × -7 = -7 × 4
  • 0 + 5x = 5x
  • ( 4 + 8 ) + 7 = 4 + ( 8 + 7 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • -4z + 8 = 8 + -4z
  • -1 × ( 10 × 5 ) = ( -1 × 10 ) × 5
  • (d + e) × f = f × (d + e)
  • Identity property of addition, Commutative property of addition and Identity property of multiplication
  • Associative property of addition, Commutative property of addition and Commutative property of multiplication
  • Commutative property of addition, Associative property of multiplication and Commutative property of multiplication
  • Commutative property of addition, Associative property of addition and Identity property of multiplication
C
    
9.   Solve the following equations for x:
  • x – -20 = 6 x = -14
        
  • -
    13
    20
    =
    1
    20
    x x = -13
        
  • 17 + -2x = -41 x = 29
        
  • a = -bx x = -a/b
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -23x – 40 < -17 x > -1
        
  • x ≠ 825
  • 46 > x ≤ -49
  • 15
    5
    x ≤
    18
    3
    x ≤ 2
        
11.   Convert the following numbers into scientific notation:
  • 0.000261 2.61 × 10-4
        
  • 975000 9.75 × 105
        
12.   Add the following polynomials:
  • 7z5 + 10z4  and  -2z10 + 7z5 + 11z4
    -2z10 + 14z5 + 21z4
        
  • -13z19 + -13z17 + 13z12 + -6z11 + -9z10  and  6z19 + -11z17 + 2z12 + 4z11 + 12z10 -7z19 + -24z17 + 15z12 + -2z11 + 3z10
        
13.   Multiply the following polynomials and simplify:
  • 4x3(9x2 - 7)
    36x5 - 28x3
        
  • (2x2 + 8x - 7)(7x5 + 5x)
    14x7 + 56x6 - 49x5 + 10x3 + 40x2 - 35x
        
14.   Divide:
  • 5x2 + 8x + 33 / 5x + 3
    (x + 1) with a remainder of 30
        
15.   Find the greatest common factor of the following terms:
  • 99, 80
    1
        
  • 24x8, 65x8y2
    x8
        
16.   Factor the following polynomials:
  • 8x3 + 56x2 + 80x
    8x(x + 2)(x + 5)
        
  • x2 - 3x - 54
    (x - 9)(x + 6)
        
  • x9 + 6x8 - 72x7
    x7(x - 6)(x + 12)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    9
    and
    -6


        
  • x =
    0
    ,
    6

    and
    -12
        
18.   You have 4 pants, 3 shirts, and 2 shoes. How many different ways can you dress?
  • 24
        
19.   Use the following data to construct a box and whiskers plot:
  • 16, 35, 39, 21, 17, 26, 22, 27, 40
        
20.   A bag contains 5 blue balls, 6 red balls, and 3 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    21.43%
        
  • A blue ball or red ball?
    78.57%
        
  • Two red balls?
    16.48%
        
  • A blue ball and a white ball?
    8.24%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 16
    x - y = -1
    A(7.5,8.5)
        
  • 3x - 7y = 3
    5x + 3y = -17

    B(-2.5,-1.5)
        
22.   Write the following fractions in simplest form:
  • 21x4y7
    84x3y5
    xy2
    4
        
  • x6 - 13x5 + 30x4
    x3(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 - 54 = 3x
    x1 = 9,   x2 = -6
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.908
    908
    999
        
25.   Solve the following equation:
  • 32
    x
    = 2
    x = 8
        
26.   Rationalize the denominator of each fraction below:
  • 4
    15
    10
    28
    105
    35
        
27.   Use a trigonometric ratio to find x:
x = 32.53 cm
    
28.   The sum of two consecutive odd integers is 16. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=7, b=9
    
29.   After you leave your house, you walk 6 blocks west and 8 blocks north. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   A rectangle has an area of 368ft2. Its width is 7 ft less than its length. What are the dimensions of the rectangle?
  • width = 16,  length = 23
        


To print this algebra practice test, click here.



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