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:   19 and -8? -152
    
2.   Add:   -8 and -19? -27
    
3.   Divide:   -4 and -2? 2
    
4.   Substract:   -3 and -16? 13
    
5.   Calculate: |-9 + 2 · 6| 3
    
6.   Simplify the following expressions:
  • -1 – -18x – -2x -1+20x
        
  • -1x + 13x – -8x – -18 18+20x
        
  • 14y + -7x – 2z – -16y + -5y -7x+25y-2z
        
  • y8 × y-15 y-7
        
  • x-17
    x-9
    x-8
        
  • (6x)10 60466176x10
        
7.   Which of the following expressions show the associative property?
  • ( m × n ) + 8 = 8 + ( m × n )
  • ( 5 × -10 ) + -5 = -5 + ( 5 × -10 )
  • 5 × 8 = 8 × 5
  • ( m × n ) × p = m × ( n × p )
D
    
8.   Which properties are illustrated by the following three expressions?
  • x + y + z + 0 = x + y + z
  • ( y + z ) + x = y + ( z + x )
  • -4 + -5 × 7 = -5 × 7 + -4
  • Distributive property, Identity property of multiplication and Associative property of addition
  • Identity property of addition, Associative property of addition and Commutative property of addition
  • Distributive property, Identity property of addition and Identity property of multiplication
  • Distributive property, Identity property of addition and Commutative property of addition
B
    
9.   Solve the following equations for x:
  • x – 92 = 72 x = 164
        
  • -
    11
    28
    =
    11
    28
    x x = -1
        
  • -67 = -12x – 79 x = -1
        
  • dx = -e x = -e/d
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 6x – -35 < -1 x < -6
        
  • x ≠ 332
  • 20 > x < 17
  • 34
    17
    x > -12 x > -6
        
11.   Convert the following numbers into scientific notation:
  • 0.000000825 8.25 × 10-7
        
  • 21900000 2.19 × 107
        
12.   Add the following polynomials:
  • -12z4 + 11z3  and  7z9 + 12z6 + -2z4 + 3z3 + -8z2
    7z9 + 12z6 + -14z4 + 14z3 + -8z2
        
  • 2z19 + -9z15 + -9z5  and  5z19 + 7z15 + 10z5 7z19 + -2z15 + 1z5
        
13.   Multiply the following polynomials and simplify:
  • (1x4 + 5x3)1x3
    x7 + 5x6
        
  • (4x5 - 4)(5x5 + 5x)
    20x10 + 20x6 - 20x5 - 20x
        
14.   Divide:
  • 2x3 + 10x2 + 10x + 50 / 2x + 10
    x2 + 5
        
15.   Find the greatest common factor of the following terms:
  • 75, 15
    15
        
  • 50x3y3, 52xy9, 45x8y8
    xy3
        
16.   Factor the following polynomials:
  • 27x4 - 78x3 + 51x2
    27x2(x - 1)(x -
    17
    9
    )
        
  • x2 + 12x + 35
    (x + 7)(x + 5)
        
  • x7 + 16x6 + 15x5
    x5(x + 1)(x + 15)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -7
    and
    -5


        
  • x =
    0
    ,
    -1

    and
    -15
        
18.   You are seating 7 people on 7 chairs. How many different ways can those people sit?
  • 5040
        
19.   Use the following data to construct a box and whiskers plot:
  • 31, 7, 37, 20, 17, 29, 23
        
20.   A bag contains 4 blue balls, 6 red balls, and 5 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    33.33%
        
  • A blue ball or red ball?
    66.67%
        
  • Two red balls?
    16.00%
        
  • A blue ball and a white ball?
    8.89%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 12
    x - y = 14
    A(13,-1)
        
  • 3x - 9y = -20
    5x + 7y = -10

    B(-3.48,1.06)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • x6 - 2x5 - 80x4
    x6(x - 10)
    (x + 8)
    x2
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -x2 = -32x - 33
    x1 = -1,   x2 = 33
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.138
    137
    990
        
25.   Solve the following equation:
  • 2 +
    x + 10
    = 16
    x = 186
        
26.   Rationalize the denominator of each fraction below:
  • 3
    14 +
    35
    42 - 3
    35
    161
        
27.   Use a trigonometric ratio to find x:
x = 27.00 cm
    
28.   The sum of two consecutive odd integers is 44. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=21, b=23
    
29.   After you leave your house, you walk 3 blocks east and 4 blocks north. How far are you from your house?
  • I am
    5
    blocks from my house.
        
30.   The length of a rectangle is 6 more than thrice its width. The area of the rectangle is 360m2. What is the length and width of the rectangle?
  • width = 10,  length = 36
        


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:   14 and -12? -168
    
2.   Add:   13 and 1? 14
    
3.   Divide:   -20 and 5? -4
    
4.   Substract:   -1 and 8? -9
    
5.   Calculate: |-3 + -11 · 7| 80
    
6.   Simplify the following expressions:
  • -19x – 12x + 5x -26x
        
  • 1x – -10 – -13x + -12x 10+2x
        
  • 9z + -11y – 6 + -18x + 19z -6-18x-11y+28z
        
  • y-1 × x5 × x13 × y9 x18 × y8
        
  • x10
    x-1
    x11
        
  • (9x2)3 729x6
        
7.   Which of the following expressions show the associative property?
  • -4 + -5 = -5 + -4
  • ( x × y ) + 5 = 5 + ( y × x )
  • 5( 4 + 4 ) = 5×4 + 5×4
  • ( x × y ) × z = x × ( y × z )
D
    
8.   Which properties are illustrated by the following three expressions?
  • o + p + q + 0 = o + p + q
  • t × (r + s) = (r + s) × t
  • ( 4 + 19 ) + 5 = 4 + ( 19 + 5 )
  • Identity property of multiplication, Distributive property and Associative property of addition
  • Identity property of addition, Commutative property of multiplication and Associative property of addition
  • Identity property of addition, Associative property of multiplication and Associative property of addition
  • Distributive property, Identity property of multiplication and Commutative property of addition
B
    
9.   Solve the following equations for x:
  • -36 – x = -4 x = -32
        
  • 1
    2
    x = -
    1
    2
    x = -1
        
  • 23x + 2 = 71 x = 3
        
  • -ex + cx = -f x = f/(e-c)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -5x – 35 > 40 x < -15
        
  • x ≠ 292
  • -27 ≤ x ≥ 13
  • 40
    10
    x ≥
    40
    2
    x ≥ 5
        
11.   Convert the following numbers into scientific notation:
  • 0.00000311 3.11 × 10-6
        
  • 6840000 6.84 × 106
        
12.   Add the following polynomials:
  • -8z10 + 7z9 + 8z4 + 5z3 + -6z1  and  2z7 + 8z4 + 7z2
    -8z10 + 7z9 + 2z7 + 16z4 + 5z3 + 7z2 + -6z1
        
  • -13z18 + 7z16 + 4z5 + 5z3 + -8z1  and  10z16 + 6z15 + 1z5 + -3z3 + 11z1 -13z18 + 17z16 + 6z15 + 5z5 + 2z3 + 3z1
        
13.   Multiply the following polynomials and simplify:
  • (9x4 + x3 + 8x)(9x5 + 5x4 + 3x2)
    81x9 + 54x8 + 5x7 + 99x6 + 43x5 + 24x3
        
  • (3x3 + 9x - 7)(9x2 + 9x)
    27x5 + 27x4 + 81x3 + 18x2 - 63x
        
14.   Divide:
  • 4x3 + 3x2 + 32x + 28 / 4x + 3
    (x2 + 8) with a remainder of 4
        
15.   Find the greatest common factor of the following terms:
  • 78, 72
    6
        
  • 56x4y3, 36x3y6
    4x3y3
        
16.   Factor the following polynomials:
  • 36x5 + 9x4 - 27x3
    36x3(x + 1)(x -
    3
    4
    )
        
  • x2 + 9x - 10
    (x - 1)(x + 10)
        
  • x7 + 6x6 - 91x5
    x5(x + 13)(x - 7)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    1
    and
    -10


        
  • x =
    0
    ,
    -13

    and
    7
        
18.   How many ways can 5 people wait in line?
  • 120
        
19.   Use the following data to construct a box and whiskers plot:
  • 18, 26, 2, 39, 6, 29, 24
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 4
  • What is the probability of getting tails and 1?
    12.50%
        
  • What is the probability of getting tails and an even number?
    25%
        
  • What is the probability of getting tails and a multiple of 2?
    25%
        
  • What is the probability of getting tails and a prime number?
    25%
        
  • What is the probability of not tails and not 2?
    37.5%
        
  • 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 = 7
    x - y = 12
    A(9.5,-2.5)
        
  • 2x - y = -2
    x + 9y = 18

    B(0,2)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 8)
    (x2 + 16x + 64)
    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.
  • 19x + 70 = -x2
    x1 = -14,   x2 = -5
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.319
    319
    999
        
25.   Solve the following equation:
  • -15
    x
    - 17 = -16
    x
    + 19
    x = 1296
        
26.   Rationalize the denominator of each fraction below:
  • 3
    4 -
    6
    12 + 3
    6
    10
        
27.   Use a trigonometric ratio to find x:
x = 20.78 cm
    
28.   The sum of two consecutive even integers is 30. What are the integers? (Hint: use 2x as the first even integer)
a=14, b=16
    
29.   After you leave your house, you walk 12 blocks west and 5 blocks north. How far are you from your house?
  • I am
    13
    blocks from my house.
        
30.   Each side of a square is decreased by 3 ft. The area of the newly created square is 361ft2. What was the original length of one side of the square?
  • 22 ft
        


To print this algebra practice test, click here.



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