Algebra test generator



Name _____________________                                        Date:_____________________


Current difficulty level: Choose test difficulty:         Easy              Challenging
(current difficulty level: Challenging)

                           

Solve the following problems:

Important instructions

(or click here to generate a new test)
1.   Multiply:   45 and 89? 4005
    
2.   Add:   82 and -21? 61
    
3.   Divide:   49 and 1? 49
    
4.   Substract:   -88 and -49? -39
    
5.   Calculate: |-57 + 38 · -82 + -89| 3262
    
6.   Simplify the following expressions:
  • -82 + -27x – -19 -63-27x
        
  • -23x – -70y + -44x – -88y -67x+158y
        
  • 4z – 7z – 10y + -66x + 61x -5x-10y-3z
        
  • x-41 × y12 × x91 × y70 x50 × y82
        
  • x49
    x-13
    x62
        
  • (7x5)4 2401x20
        
7.   Which of the following expressions show the associative property?
  • ( x × y ) + 9 = 9 + ( y × x )
  • ( x + y ) + z = x + ( y + z )
  • ( -5 × -1 ) + 7 = 7 + ( -5 × -1 )
  • -3 + -5 = -5 + -3
B
    
8.   Which properties are illustrated by the following three expressions?
  • ( 2 × -20 ) × -13 = 2 × ( -20 × -13 )
  • p + ( q + r ) = ( p + q ) + r
  • o + 5 + 0 = o + 5
  • Identity property of addition, Commutative property of addition and Identity property of multiplication
  • Commutative property of addition, Associative property of addition and Identity property of multiplication
  • Identity property of addition, Distributive property and Associative property of multiplication
  • Associative property of multiplication, Associative property of addition and Identity property of addition
D
    
9.   Solve the following equations for x:
  • -27 = -x + 96 x = 123
        
  • 13
    15
    x = -
    26
    15
    x = -2
        
  • 6x – -80 = -94 x = -29
        
  • c – bx = -fx x = c/(b-f)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 7x – 1 ≤ -29 x ≤ -4
        
  • x ≠ 795
  • 31 ≤ x ≥ -15
  • 12
    6
    x ≥ -
    36
    6
    x ≥ -3
        
11.   Convert the following numbers into scientific notation:
  • 0.0000774 7.74 × 10-5
        
  • 358000000 3.58 × 108
        
12.   Add the following polynomials:
  • -15z10 + -16z8 + -1z6 + -12z3 + 19  and  -8z10 + -11z7 + 1
    -23z10 + -16z8 + -11z7 + -1z6 + -12z3 + 20
        
  • 38z16 + 45z9 + 20z6 + 36z2  and  -25z16 + -45z12 + -8z10 + -17z6 13z16 + -45z12 + -8z10 + 45z9 + 3z6 + 36z2
        
13.   Multiply the following polynomials and simplify:
  • (5x4 + 9x2 - 4)(1x5 + 7x4 + 3x)
    5x9 + 35x8 + 9x7 + 63x6 + 11x5 - 28x4 + 27x3 - 12x
        
  • (6x5 + 10x4 + 4)(7x3 - 5)
    42x8 + 70x7 - 30x5 - 50x4 + 28x3 - 20
        
14.   Divide:
  • 16x2 - 8x - 3 / 4x - 3
    4x + 1
        
15.   Find the greatest common factor of the following terms:
  • 200, 270
    10
        
  • 378x3y7, 432x6y10
    54x3y7
        
16.   Factor the following polynomials:
  • 30x4 - 30x3 + 6x2
    30x2(x -
    5 +
    5
    10
    )(x -
    5 -
    5
    10
    )
        
  • x2 - 10x + 21
    (x - 7)(x - 3)
        
  • x8 - 6x7 + 5x6
    x6(x - 5)(x - 1)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    7
    and
    3


        
  • x =
    0
    ,
    5

    and
    1
        
18.   You have 4 pants, 4 shirts, and 2 shoes. How many different ways can you dress?
  • 32
        
19.   Use the following data to construct a box and whiskers plot:
  • 23, 20, 30, 33, 19, 29, 17, 14, 27
        
20.   A bag contains 6 blue balls, 4 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?
    16.67%
        
  • A blue ball or red ball?
    83.33%
        
  • Two red balls?
    9.09%
        
  • A blue ball and a white ball?
    9.09%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 9
    x - y = -6
    A(1.5,7.5)
        
  • 4x - 4y = 16
    2x + 8y = 4

    B(3.6,-0.4)
        
22.   Write the following fractions in simplest form:
  • 19xy6
    38x8y
    y5
    2x7
        
  • (x - 7)
    (x2 - 14x + 49)
    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 = -11x - 26
    x1 = 13,   x2 = -2
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.170
    1690
    9900
        
25.   Solve the following equation:
  • 17
    x
    + 16 = 18
    x
    - 9
    x = 625
        
26.   Rationalize the denominator of each fraction below:
  • 2
    6
    21 +
    21
    7
    6
    -
    14
    70
        
27.   Use a trigonometric ratio to find x:
x = 15.00 cm
    
28.   The sum of two consecutive odd integers is 60. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=29, b=31
    
29.   After you leave your house, you walk 5 blocks east and 12 blocks south. How far are you from your house?
  • I am
    13
    blocks from my house.
        
30.   Each side of a square is lengthened by 2 ft. This makes the area of the square 49ft2. What is the original length of a side of the square?
  • 5 ft
        


To print this algebra practice test, click here.



Name _____________________                                        Date:_____________________


Current difficulty level: Choose test difficulty:         Easy              Challenging
(current difficulty level: Challenging)

                           

Solve the following problems:

Important instructions

(or click here to generate a new test)
1.   Multiply:   96 and -89? -8544
    
2.   Add:   40 and 67? 107
    
3.   Divide:   -41 and -41? 1
    
4.   Substract:   31 and -76? 107
    
5.   Calculate: |37 + -52 · 54 + 17| 2754
    
6.   Simplify the following expressions:
  • -62x + -69x – -44x -87x
        
  • -100x + 19x + -93x – -80x -94x
        
  • -13 + -17y – 60y – 46y + -6 + 6 -13-123y
        
  • y-4 × x-10 × y54 x-10 × y50
        
  • x47
    x21
    x26
        
  • (3x3)6 729x18
        
7.   Which of the following expressions show the associative property?
  • ( m × n ) × 6 = m × ( n × 6 )
  • 9 + 3a + 2
  • ( x × y ) + 7 = 7 + ( y × x )
  • m × ( n + 2 ) = mn + 2n
A
    
8.   Which properties are illustrated by the following three expressions?
  • -7 × ( 3 × -18 ) = ( -7 × 3 ) × -18
  • e + ( f + 0 ) = ( e + f ) + 0
  • ( -6 + -10) × -19 = -6 × -19 + -10 × -19
  • Associative property of addition, Distributive property and Commutative property of addition
  • Identity property of addition, Distributive property and Commutative property of addition
  • Commutative property of addition, Commutative property of multiplication and Distributive property
  • Associative property of multiplication, Associative property of addition and Distributive property
D
    
9.   Solve the following equations for x:
  • 42 = 14 · x x = 3
        
  • -
    22
    7
    =
    1
    7
    x x = -22
        
  • 85 + -14x = 71 x = 1
        
  • bx = g x = g/b
        
10.   Solve the following inequalities. Then graph a) on the number line
  • x – -7 < 38 x < 31
        
  • x ≠ -135
  • 22 ≥ x > -40
  • 4
    2
    x ≤ -
    30
    15
    x ≤ -1
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000000161 1.61 × 10-11
        
  • 120000000000 1.2 × 1011
        
12.   Add the following polynomials:
  • 14z8 + 6z7 + 9z2  and  -11z8 + 3z7 + 15z5 + -7z2 + -15z1
    3z8 + 9z7 + 15z5 + 2z2 + -15z1
        
  • -31z17 + 21z5 + 20z1  and  -29z19 + 1z10 + -46z5 + -31z1 + 19 -29z19 + -31z17 + 1z10 + -25z5 + -11z1 + 19
        
13.   Multiply the following polynomials and simplify:
  • (7x3 + 6)5x5
    35x8 + 30x5
        
  • (6x4 + 3x)(5x5 + x3 + 2x2)
    30x9 + 6x7 + 27x6 + 3x4 + 6x3
        
14.   Divide:
  • 10x3 - 12x2 - 25x + 33 / 5x - 6
    (2x2 - 5) with a remainder of 3
        
15.   Find the greatest common factor of the following terms:
  • 396, 300
    12
        
  • 99x5y9, 120x4y9
    3x4y9
        
16.   Factor the following polynomials:
  • 6x3 - 75x2 - 39x
    6x(x +
    1
    2
    )(x - 13)
        
  • x2 + 3x - 70
    (x + 10)(x - 7)
        
  • x4 + 7x3 + 12x2
    x2(x + 4)(x + 3)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -10
    and
    7


        
  • x =
    0
    ,
    -4

    and
    -3
        
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:
  • 28, 40, 13, 22, 17, 31, 33, 29, 25, 37
        
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 = -6
    x - y = 5
    A(-0.5,-5.5)
        
  • 10x - 8y = -19
    3x + 5y = 15

    B(0.34,2.8)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x - 6)
    (x2 - 12x + 36)
    1
    x - 6
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -x2 = -5x - 6
    x1 = -1,   x2 = 6
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.6
    6
    9
        
25.   Solve the following equation:
  • 7
    x
    - 17 = 10
    x
    - 20
    x = 1
        
26.   Rationalize the denominator of each fraction below:
  • 1
    14
    + 35
    -
    14
    - 35
    1211
        
27.   Use a trigonometric ratio to find x:
x = 26.87 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 8 blocks north and 6 blocks east. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   The sides of a square are increased by 4 ft. The area of the newly created square is 289ft2. What was the original length of one side of the square?
  • 13 ft
        


To print this algebra practice test, click here.



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