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:   -5 and 14? -70
    
2.   Add:   2 and 18? 20
    
3.   Divide:   -9 and 1? -9
    
4.   Substract:   13 and -7? 20
    
5.   Calculate: |3 · -17 + 8| 43
    
6.   Simplify the following expressions:
  • 16x + -12x + -13x -9x
        
  • 11x + -5y – -6y – -11y 11x+12y
        
  • -12y + 10 + 4 – 5x – -9x + -13 1+4x-12y
        
  • x-14 × y-19 x-14 × y-19
        
  • x-4
    x-20
    x16
        
  • (4x)7 16384x7
        
7.   Which of the following expressions show the associative property?
  • ( 4 + 5 ) × -1 = -1 × ( 4 + 5 )
  • 9( 4 + 8 ) = 9×4 + 9×8
  • 2 × ( z + 1 + 9 ) = 2×z + 2×1 + 2×9
  • ( m × n ) × 5 = m × ( n × 5 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • 14 × (2 + z) = (2 + z) × 14
  • ( 10 × -12 ) × -15 = 10 × ( -12 × -15 )
  • 1 × (x + 18) = x + 18
  • Identity property of addition, Commutative property of addition and Commutative property of multiplication
  • Identity property of addition, Commutative property of addition and Associative property of addition
  • Associative property of multiplication, Associative property of addition and Distributive property
  • Commutative property of multiplication, Associative property of multiplication and Identity property of multiplication
D
    
9.   Solve the following equations for x:
  • x + 16 = 96 x = 80
        
  • -
    1
    2
    x =
    13
    26
    x = -1
        
  • 11 = 15x + -64 x = 5
        
  • d = -ex x = -d/e
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -8x – -40 < 24 x > 2
        
  • x ≠ 25
  • 44 < x > -26
  • -
    6
    3
    x < -32 x > 16
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000293 2.93 × 10-8
        
  • 76300 7.63 × 104
        
12.   Add the following polynomials:
  • -1z10 + 7z3  and  -5z10 + -5z8 + 6z7 + -1z3
    -6z10 + -5z8 + 6z7 + 6z3
        
  • 14z14 + -11z10 + 2z4 + 6z2  and  1z14 + 13z10 + 2z9 + 10z4 + 10z3 15z14 + 2z10 + 2z9 + 12z4 + 10z3 + 6z2
        
13.   Multiply the following polynomials and simplify:
  • 4x2(4x5 + 8)
    16x7 + 32x2
        
  • (4x4 + x)(2x4 + 10x - 5)
    8x8 + 42x5 - 20x4 + 10x2 - 5x
        
14.   Divide:
  • 2x2 + 17x - 9 / 2x - 1
    x + 9
        
15.   Find the greatest common factor of the following terms:
  • 60, 72
    12
        
  • 75x3y5, 54x8y
    3x3y
        
16.   Factor the following polynomials:
  • 6x3 - 17x2 + 5x
    6x(x -
    1
    3
    )(x -
    5
    2
    )
        
  • x2 - 8x + 12
    (x - 6)(x - 2)
        
  • x4 + 15x3 + 44x2
    x2(x + 11)(x + 4)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    6
    and
    2


        
  • x =
    0
    ,
    -11

    and
    -4
        
18.   You have 8 books to read. How many different ways can you read your books?
  • 40320
        
19.   Use the following data to construct a box and whiskers plot:
  • 31, 17, 21, 19, 29, 23, 4, 12
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 9
  • What is the probability of getting tails and 9?
    5.56%
        
  • What is the probability of getting heads and an odd number?
    22.22%
        
  • What is the probability of getting tails and a multiple of 4?
    11.11%
        
  • What is the probability of getting tails and a prime number?
    22.22%
        
  • What is the probability of not tails and not 7?
    44.44%
        
  • What is the probability of getting not heads and not a whole number?
    0%
        
  • What is the probability of heads or tails and a whole number?
    100%
        
  • What is the probability of getting heads?
    50%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 16
    x - y = 11
    A(13.5,2.5)
        
  • 7x - y = -9
    11x + 10y = 9

    B(-1,2)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 8)5
    (x + 8)6
    1
    x + 8
        
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 = -4
    x1 = 4,   x2 = 1
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.46
    46
    99
        
25.   Solve the following equation:
  • 3x + 1
    - 5 = -3
    x = 1
        
26.   Rationalize the denominator of each fraction below:
  • 14
    28
    7
        
27.   Use a trigonometric ratio to find x:
x = 28.00 cm
    
28.   The sum of two consecutive odd integers is 24. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=11, b=13
    
29.   After you leave your house, you walk 16 blocks east and 12 blocks south. How far are you from your house?
  • I am
    20
    blocks from my house.
        
30.   A rectangle has a width that is 8 m less than its length. The area of the rectangle is 308m2. What are the dimensions of the rectangle?
  • width = 14,  length = 22
        


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:   10 and -2? -20
    
2.   Add:   -1 and -6? -7
    
3.   Divide:   11 and -1? -11
    
4.   Substract:   10 and -10? 20
    
5.   Calculate: |-20 + 14 · 18| 232
    
6.   Simplify the following expressions:
  • 3x + -5 – 14 -19+3x
        
  • 5x + -3y – -9y + 15x 20x+6y
        
  • -11x – 4 – 2y – 4z – -3z -4-11x-2y-1z
        
  • x-6 × y-20 × y-5 x-6 × y-25
        
  • x8
    x-2
    x10
        
  • (7x5)4 2401x20
        
7.   Which of the following expressions show the associative property?
  • -8 × 1 = -8
  • ( x + y ) + z = x + ( y + z )
  • 8 + 4s + 7
  • 3 × ( z + 1 + 5 ) = 3×z + 3×1 + 3×5
B
    
8.   Which properties are illustrated by the following three expressions?
  • ( s × t ) × r = s × ( t × r )
  • x × ( y + 0 ) = x × y + x × 0
  • ( p + q ) + o = p + ( q + o )
  • Commutative property of multiplication, Identity property of multiplication and Identity property of addition
  • Identity property of addition, Associative property of multiplication and Identity property of multiplication
  • Associative property of addition, Identity property of multiplication and Identity property of addition
  • Associative property of multiplication, Distributive property and Associative property of addition
D
    
9.   Solve the following equations for x:
  • 5 · x = 50 x = 10
        
  • 26
    28
    = -
    1
    14
    x x = -13
        
  • 3x – 37 = 32 x = 23
        
  • dx = g x = g/d
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -7x + -18 ≤ -11 x ≥ -1
        
  • x ≠ -595
  • -70 ≥ x > 38
  • -
    4
    2
    x < -40 x > 20
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000577 5.77 × 10-8
        
  • 5130000000 5.13 × 109
        
12.   Add the following polynomials:
  • -13z10 + -15z9 + -5z4 + -7z1 + 7  and  -14z10 + -10z9 + -15z4 + 2z1 + -3
    -27z10 + -25z9 + -20z4 + -5z1 + 4
        
  • -10z14 + 11z6 + -14z5  and  -3z19 + -14z14 + -9z6 + 4z5 -3z19 + -24z14 + 2z6 + -10z5
        
13.   Multiply the following polynomials and simplify:
  • (9x5 + 7x3 + 3x2)(10x4 + 4x)
    90x9 + 70x7 + 66x6 + 28x4 + 12x3
        
  • (3x5 + 6x + 8)(5x3 + 1)
    15x8 + 3x5 + 30x4 + 40x3 + 6x + 8
        
14.   Divide:
  • 10x2 - 46x - 20 / 5x + 2
    2x - 10
        
15.   Find the greatest common factor of the following terms:
  • 90, 60, 14
    2
        
  • 54x5y5, 12x8y7, 80x7y7
    2x5y5
        
16.   Factor the following polynomials:
  • 32x5 - 88x4 + 36x3
    32x3(x -
    9
    4
    )(x -
    1
    2
    )
        
  • x2 - 6x + 9
    (x - 3)(x - 3)
        
  • x6 + 9x5 + 20x4
    x4(x + 5)(x + 4)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    3
    and
    3


        
  • x =
    0
    ,
    -5

    and
    -4
        
18.   You are seating 5 people on 5 chairs. How many different ways can those people sit?
  • 120
        
19.   Use the following data to construct a box and whiskers plot:
  • 19, 36, 35, 39, 9, 5, 32, 40, 38, 24
        
20.   A bag contains 3 blue balls, 5 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?
    20.00%
        
  • A blue ball or red ball?
    80.00%
        
  • Two red balls?
    25.00%
        
  • A blue ball and a white ball?
    6.00%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -8
    x - y = 1
    A(-3.5,-4.5)
        
  • 10x - 4y = 2
    4x + 8y = -19

    B(-0.63,-2.06)
        
22.   Write the following fractions in simplest form:
  • 7x7y3
    28x2y6
    x5
    4y3
        
  • (x + 9)
    (x2 + 18x + 81)
    1
    x + 9
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 6x = x2 - 40
    x1 = -4,   x2 = 10
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.4436
    4392
    9900
        
25.   Solve the following equation:
  • -9 -
    x - 6
    = -11
    x = 10
        
26.   Rationalize the denominator of each fraction below:
  • 2
    3
    - 15
    -
    3
    + 15
    111
        
27.   Use a trigonometric ratio to find x:
x = 12.12 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 9 blocks south and 12 blocks west. How far are you from your house?
  • I am
    15
    blocks from my house.
        
30.   The length of a rectangle is 4 less than 2 times the width. What are the dimensions of the rectangle if the area is 160ft2?
  • width = 10,  length = 16
        


To print this algebra practice test, click here.



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