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:   -8 and 10? -80
    
2.   Add:   15 and -1? 14
    
3.   Divide:   -6 and -2? 3
    
4.   Substract:   -17 and -7? -10
    
5.   Calculate: |20 · 20 + 10| 410
    
6.   Simplify the following expressions:
  • -1 – 9x – 1 -2-9x
        
  • 5x + 5y – 14 + -18 -32+5x+5y
        
  • -12x – -3 + 11x – 8z – 4 + 5z -1-1x-3z
        
  • y-19 × y6 × x12 x12 × y-13
        
  • x2
    x11
    x-9
        
  • (7x5)3 343x15
        
7.   Which of the following expressions show the associative property?
  • -6 × 2 = 2 × -6
  • ( 6 + 2 ) + 3 = 6 + ( 2 + 3 )
  • a + b = b + a
  • ( m × n ) + 3 = 3 + ( m × n )
B
    
8.   Which properties are illustrated by the following three expressions?
  • (y + 4) × (z + 8) = (z + 8) × (y + 4)
  • ( b × c ) × a = b × ( c × a )
  • (k + l) × 1 = k + l
  • Distributive property, Identity property of multiplication and Associative property of multiplication
  • Commutative property of multiplication, Associative property of multiplication and Identity property of multiplication
  • Identity property of addition, Commutative property of addition and Identity property of multiplication
  • Commutative property of multiplication, Associative property of multiplication and Identity property of addition
B
    
9.   Solve the following equations for x:
  • 5 · -x = -35 x = 7
        
  • -
    17
    25
    x = -
    17
    25
    x = 1
        
  • 59x – 31 = 87 x = 2
        
  • g = -cx x = -g/c
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -15x – -29 ≤ -1 x ≥ 2
        
  • x ≠ -635
  • -73 > x ≤ -43
  • 30
    15
    x ≤
    18
    9
    x ≤ 1
        
11.   Convert the following numbers into scientific notation:
  • 0.000000000118 1.18 × 10-10
        
  • 205000 2.05 × 105
        
12.   Add the following polynomials:
  • 3z10 + -12z6 + -4z4 + 10z3  and  10z10 + 15z6 + -6z4 + 14z3 + 7
    13z10 + 3z6 + -10z4 + 24z3 + 7
        
  • -11z20 + 9z16 + 15z8 + -1z4  and  -1z15 + 3z14 + -9z12 + 3z5 + 9 -11z20 + 9z16 + -1z15 + 3z14 + -9z12 + 15z8 + 3z5 + -1z4 + 9
        
13.   Multiply the following polynomials and simplify:
  • 9(8x4 + 6x2 + 7x)
    72x4 + 54x2 + 63x
        
  • (9x5 + 8)(8x5 + 9x3 + 3)
    72x10 + 81x8 + 91x5 + 72x3 + 24
        
14.   Divide:
  • 25x2 - 25 / 5x + 5
    5x - 5
        
15.   Find the greatest common factor of the following terms:
  • 60, 99, 9
    3
        
  • 15x10y10, 22x
    x
        
16.   Factor the following polynomials:
  • 39x5 + 33x4 + 6x3
    39x3(x -
    -11 +
    17
    26
    )(x -
    -11 -
    17
    26
    )
        
  • x2 - 3x - 18
    (x - 6)(x + 3)
        
  • x4 + x3 - 56x2
    x2(x - 7)(x + 8)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    6
    and
    -3


        
  • x =
    0
    ,
    7

    and
    -8
        
18.   You can purchase your ice cream in a cup or a cone. Orders can be one or two scoops. Flavors can be chocolate, vanilla, strawberry or peach. How many choices do you have?
  • 16
        
19.   Use the following data to construct a box and whiskers plot:
  • 32, 13, 7, 21, 37, 5, 22, 12, 25, 24
        
20.   A bag contains 3 blue balls, 2 red balls, and 4 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    44.44%
        
  • A blue ball or red ball?
    55.56%
        
  • Two red balls?
    4.94%
        
  • A blue ball and a white ball?
    14.81%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 9
    x - y = -18
    A(-4.5,13.5)
        
  • x - 5y = -18
    5x + 14y = -12

    B(-8,2)
        
22.   Write the following fractions in simplest form:
  • 18x8y9
    6x2y5
    3x6y4
        
  • (x2 + 20x + 100)
    (x + 10)
    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 + 2x = 8
    x1 = 2,   x2 = -4
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.992
    992
    999
        
25.   Solve the following equation:
  • 15
    x
    = 6
    x =
    225
    36
        
26.   Rationalize the denominator of each fraction below:
  • 14
    2
    - 35
    -
    14
    2
    + 490
    1223
        
27.   Use a trigonometric ratio to find x:
x = 24.25 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 6 blocks north and 8 blocks east. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   A rectangle has a width that is 7 ft less than its length. The area of the rectangle is 44ft2. What are the dimensions of the rectangle?
  • width = 4,  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:   10 and 14? 140
    
2.   Add:   -13 and -10? -23
    
3.   Divide:   7 and 1? 7
    
4.   Substract:   -10 and -10? 0
    
5.   Calculate: |12 + -20 · -20| 412
    
6.   Simplify the following expressions:
  • 20 – -19x – -8 28+19x
        
  • -13x + -16y + -6 + 19x -6+6x-16y
        
  • -19x – -17y + 15y – 13y – -13z -19x+19y+13z
        
  • y9 × x-2 x-2 × y9
        
  • x-6
    x-10
    x4
        
  • (7x4)5 16807x20
        
7.   Which of the following expressions show the associative property?
  • ( -4 × -8 ) + -7 = -7 + ( -4 × -8 )
  • ( x × y ) + 4 = 4 + ( y × x )
  • 0 + -4x = -4x
  • ( 9 + 2 ) + 8 = 9 + ( 2 + 8 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • -69 + 98 = -69 + 98
  • u × ( v × w ) = ( u × v ) × w
  • 0 + n + o = n + o
  • Distributive property, Associative property of addition and Associative property of multiplication
  • Commutative property of addition, Associative property of multiplication and Identity property of addition
  • Identity property of addition, Commutative property of addition and Identity property of multiplication
  • Commutative property of multiplication, Distributive property and Associative property of addition
B
    
9.   Solve the following equations for x:
  • -64 + x = -95 x = -31
        
  • -
    15
    7
    x =
    15
    7
    x = -1
        
  • -13x + -29 = -3 x = -2
        
  • gx = e x = e/g
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -9x – -13 ≤ -5 x ≥ 2
        
  • x ≠ 637
  • 70 > x < 57
  • -
    22
    11
    x < -
    36
    18
    x > 1
        
11.   Convert the following numbers into scientific notation:
  • 0.00000000737 7.37 × 10-9
        
  • 45600000 4.56 × 107
        
12.   Add the following polynomials:
  • 5z10 + 15z5  and  -9z10 + -3z6 + -7z5
    -4z10 + -3z6 + 8z5
        
  • -2z20 + -10z18 + 4z13 + 9z10  and  -13z20 + 9z16 + 5z2 -15z20 + -10z18 + 9z16 + 4z13 + 9z10 + 5z2
        
13.   Multiply the following polynomials and simplify:
  • (5x5 + 8x4 + 2x)(10x2 + 2)
    50x7 + 80x6 + 10x5 + 16x4 + 20x3 + 4x
        
  • (7x5 + 3x4 + 6x3)(5x5 + 4x3 + 7x2)
    35x10 + 15x9 + 58x8 + 61x7 + 45x6 + 42x5
        
14.   Divide:
  • 3x3 - 9x2 - 5x + 30 / x - 3
    (3x2 - 5) with a remainder of 15
        
15.   Find the greatest common factor of the following terms:
  • 28, 63, 90
    1
        
  • 52x3y5, 84x6y2, 18x3y2
    2x3y2
        
16.   Factor the following polynomials:
  • 16x3 + 16x2 + 3x
    16x(x +
    3
    4
    )(x +
    1
    4
    )
        
  • x2 - 3x - 54
    (x - 9)(x + 6)
        
  • x5 - 3x4 - 108x3
    x3(x - 12)(x + 9)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    9
    and
    -6


        
  • x =
    0
    ,
    12

    and
    -9
        
18.   You have 6 CDs. How many different ways can you listen to them?
  • 720
        
19.   Use the following data to construct a box and whiskers plot:
  • 10, 4, 20, 31, 3, 33, 24, 9, 18
        
20.   A bag contains 3 blue balls, 2 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?
    28.57%
        
  • A blue ball or red ball?
    71.43%
        
  • Two red balls?
    4.76%
        
  • A blue ball and a white ball?
    14.29%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -1
    x - y = -20
    A(-10.5,9.5)
        
  • x - 2y = 7
    4x + 5y = 16

    B(5.15,-0.92)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x2 - 20x + 100)
    (x - 10)
    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.
  • -9x + 20 = -x2
    x1 = 5,   x2 = 4
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.6780
    6713
    9900
        
25.   Solve the following equation:
  • 11
    x
    + 1 = 12
    x
    - 10
    x = 121
        
26.   Rationalize the denominator of each fraction below:
  • 5
    7
    - 15
    -
    5
    7
    + 75
    218
        
27.   Use a trigonometric ratio to find x:
x = 24.04 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 15 blocks north and 8 blocks west. How far are you from your house?
  • I am
    17
    blocks from my house.
        
30.   A rectangle has an area of 221ft2. Its width is 4 ft less than its length. What are the dimensions of the rectangle?
  • width = 13,  length = 17
        


To print this algebra practice test, click here.



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