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:   11 and 11? 121
    
2.   Add:   2 and 20? 22
    
3.   Divide:   -16 and -4? 4
    
4.   Substract:   6 and -16? 22
    
5.   Calculate: |-12 · 11 + -13| 145
    
6.   Simplify the following expressions:
  • -2 + -3x – 1 -3-3x
        
  • 14y + 20x – 10y – 20x 4y
        
  • -3 – 6y – 18z + 9x – 5x – -16 13+4x-6y-18z
        
  • x15 × y-9 × x1 x16 × y-9
        
  • x7
    x-9
    x16
        
  • (8x)8 16777216x8
        
7.   Which of the following expressions show the associative property?
  • ( m × n ) + 3 = 3 + ( m × n )
  • ( m × n ) × p = m × ( n × p )
  • 5 × ( y + 8 + 4 ) = 5×y + 5×8 + 5×4
  • 3( 9 + 6 ) = 3×9 + 3×6
B
    
8.   Which properties are illustrated by the following three expressions?
  • -20 × ( -4 × -5 ) = ( -20 × -4 ) × -5
  • -10 × 10 = -10 × 10
  • x × ( y + 0 ) = x × y + x × 0
  • Associative property of multiplication, Identity property of multiplication and Commutative property of multiplication
  • Associative property of multiplication, Associative property of addition and Distributive property
  • Distributive property, Associative property of addition and Commutative property of addition
  • Associative property of multiplication, Commutative property of multiplication and Distributive property
D
    
9.   Solve the following equations for x:
  • 92 = -77 + -x x = -169
        
  • 23
    19
    =
    23
    19
    x x = 1
        
  • -10x – -39 = 49 x = -1
        
  • b = -gx x = -b/g
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 26x + -29 ≤ -3 x ≤ 1
        
  • x ≠ 899
  • -52 ≥ x < 36
  • -
    18
    9
    x < -
    28
    2
    x > 7
        
11.   Convert the following numbers into scientific notation:
  • 0.00000000285 2.85 × 10-9
        
  • 46900 4.69 × 104
        
12.   Add the following polynomials:
  • 11z8 + -7z2  and  8z8 + 9z5
    19z8 + 9z5 + -7z2
        
  • 12z10 + -10z7 + 3z3 + 1z1 + 11z1  and  10z16 + 12z7 + 1z3 + 8z1 10z16 + 12z10 + 2z7 + 4z3 + 20z1
        
13.   Multiply the following polynomials and simplify:
  • (1x4 + 6x3 + 8x2)(3x4 + 7x3 + 5)
    3x8 + 25x7 + 66x6 + 56x5 + 5x4 + 30x3 + 40x2
        
  • (5x5 + x4)(5x5 + 6x2)
    25x10 + 5x9 + 30x7 + 6x6
        
14.   Divide:
  • 5x3 - 8x2 + 40x - 64 / 5x - 8
    x2 + 8
        
15.   Find the greatest common factor of the following terms:
  • 63, 36, 42
    3
        
  • 36x8y9, 45x7y8, 78x10y4
    3x7y4
        
16.   Factor the following polynomials:
  • 54x3 + 42x2 + 5x
    54x(x -
    -7 +
    19
    18
    )(x -
    -7 -
    19
    18
    )
        
  • x2 + 11x + 30
    (x + 6)(x + 5)
        
  • x9 - 22x8 + 105x7
    x7(x - 7)(x - 15)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -6
    and
    -5


        
  • x =
    0
    ,
    7

    and
    15
        
18.   You can purchase your ice cream in a cup or a cone. Orders can be one, two, three, or four scoops. Flavors can be chocolate, vanilla, strawberry, peach or kiwi. How many choices do you have?
  • 40
        
19.   Use the following data to construct a box and whiskers plot:
  • 19, 17, 8, 35, 9, 25, 10, 12, 38
        
20.   A bag contains 5 blue balls, 6 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?
    31.25%
        
  • A blue ball or red ball?
    68.75%
        
  • Two red balls?
    12.50%
        
  • A blue ball and a white ball?
    10.42%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 1
    x - y = 14
    A(7.5,-6.5)
        
  • 10x - 2y = 18
    2x + 6y = 8

    B(1.94,0.69)
        
22.   Write the following fractions in simplest form:
  • 22x5y8
    11x9y2
    2y6
    x4
        
  • x5(x + 8)
    x4 + 18x3 + 80x2
    x3
    (x + 10)
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • x2 + 35x = -66
    x1 = -33,   x2 = -2
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.3
    3
    9
        
25.   Solve the following equation:
  • 19
    x
    + 5 = 18
    x
    + 15
    x = 100
        
26.   Rationalize the denominator of each fraction below:
  • 5
    3
    5
    3
    3
        
27.   Use a trigonometric ratio to find x:
x = 32.33 cm
    
28.   The sum of two consecutive odd integers is 32. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=15, b=17
    
29.   After you leave your house, you walk 8 blocks south and 15 blocks west. How far are you from your house?
  • I am
    17
    blocks from my house.
        
30.   A rectangle has a width that is 2 ft less than its length. The area of the rectangle is 99ft2. What are the dimensions of the rectangle?
  • width = 9,  length = 11
        


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:   -5 and 10? -50
    
2.   Add:   8 and -20? -12
    
3.   Divide:   19 and 1? 19
    
4.   Substract:   20 and -2? 22
    
5.   Calculate: |20 + -11 – -9 – -14| 32
    
6.   Simplify the following expressions:
  • 4x + -20 + -2 -22+4x
        
  • -14y + 8x + -11x + -18x -21x-14y
        
  • -2 + -1y – 14x + 19z + -14 + 4 -12-14x-1y+19z
        
  • y11 × y-18 × y-4 y-11
        
  • x18
    x6
    x12
        
  • (10x3)10 10000000000x30
        
7.   Which of the following expressions show the associative property?
  • ( 6 × 8 ) × 5 = 6 × ( 8 × 5 )
  • 0 + 6x = 6x
  • ( m × n ) + 2 = 2 + ( m × n )
  • ( x × y ) + 4 = 4 + ( y × x )
A
    
8.   Which properties are illustrated by the following three expressions?
  • ( v + w ) × u = v × u + w × u
  • 0 + j + k + l = j + k + l
  • (a + b + c) × 1 = a + b + c
  • Identity property of addition, Associative property of multiplication and Associative property of addition
  • Distributive property, Identity property of addition and Identity property of multiplication
  • Identity property of addition, Distributive property and Commutative property of multiplication
  • Commutative property of multiplication, Associative property of multiplication and Associative property of addition
B
    
9.   Solve the following equations for x:
  • -56 – x = -49 x = -7
        
  • -
    16
    23
    = -
    16
    23
    x x = 1
        
  • 56 = 86 – 10x x = 3
        
  • d – gx = ax x = d/(g+a)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • x + -12 ≥ -8 x ≥ 4
        
  • x ≠ 96
  • 99 ≤ x > 33
  • -
    18
    9
    x > -20 x < 10
        
11.   Convert the following numbers into scientific notation:
  • 0.000000000896 8.96 × 10-10
        
  • 315000 3.15 × 105
        
12.   Add the following polynomials:
  • -1z10 + 12z5 + 10z4  and  -7z10 + -13z5
    -8z10 + -1z5 + 10z4
        
  • 15z14 + -13z11 + 14z8 + 1z3  and  -10z14 + 4z3 + -5 5z14 + -13z11 + 14z8 + 5z3 + -5
        
13.   Multiply the following polynomials and simplify:
  • 9x5(3x5 + 3x - 8)
    27x10 + 27x6 - 72x5
        
  • (10x3 + 2x2 - 6)(4x3 + 8x)
    40x6 + 8x5 + 80x4 - 8x3 - 48x
        
14.   Divide:
  • 2x2 + 15x - 27 / 2x - 3
    x + 9
        
15.   Find the greatest common factor of the following terms:
  • 72, 90, 84
    6
        
  • 18y5, 35xy10, 70x3y7
    y5
        
16.   Factor the following polynomials:
  • 36x5 + 54x4 + 19x3
    36x3(x -
    -9 +
    5
    12
    )(x -
    -9 -
    5
    12
    )
        
  • x2 - x - 6
    (x + 2)(x - 3)
        
  • x9 + 3x8 - 10x7
    x7(x + 5)(x - 2)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -2
    and
    3


        
  • x =
    0
    ,
    -5

    and
    2
        
18.   You have 3 pants, 4 shirts, and 5 shoes. How many different ways can you dress?
  • 60
        
19.   Use the following data to construct a box and whiskers plot:
  • 37, 34, 3, 20, 2, 10, 4, 30
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 5
  • What is the probability of getting heads and 4?
    10.00%
        
  • What is the probability of getting tails and an even number?
    20%
        
  • What is the probability of getting heads and a multiple of 2?
    20%
        
  • What is the probability of getting tails and a prime number?
    30%
        
  • What is the probability of not heads and not 3?
    40%
        
  • What is the probability of getting not tails 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 tails?
    50%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 4
    x - y = 3
    A(3.5,0.5)
        
  • x - 5y = 3
    4x + y = -9

    B(-2,-1)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x - 4)
    (x - 4)3
    1
    (x - 4)2
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -x2 = 15x + 50
    x1 = -5,   x2 = -10
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.737
    664
    900
        
25.   Solve the following equation:
  • 6
    x
    = 9
    x =
    36
    81
        
26.   Rationalize the denominator of each fraction below:
  • 14
    6
    5 +
    7
    35
    6
    - 7
    42
    9
        
27.   Use a trigonometric ratio to find x:
x = 20.00 cm
    
28.   The sum of two consecutive odd integers is 28. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=13, b=15
    
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 5 ft. This makes the area of the square 169ft2. What is the original length of a side of the square?
  • 8 ft
        


To print this algebra practice test, click here.



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