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:   65 and -97? -6305
    
2.   Add:   24 and -70? -46
    
3.   Divide:   29 and -1? -29
    
4.   Substract:   56 and 8? 48
    
5.   Calculate: |-59 · 72 + 71| 4177
    
6.   Simplify the following expressions:
  • -2x – 94x – 35x -131x
        
  • 20 + 61x + -44y + -93x 20-32x-44y
        
  • 83x – 94x – -94 – 31 + -79x + 15x 63-75x
        
  • y-29 × y-43 y-72
        
  • x-20
    x-17
    x-3
        
  • (6x4)3 216x12
        
7.   Which of the following expressions show the associative property?
  • d × ( e + 4 ) = de + 4e
  • -10 × ( z + 9 + 3 ) = -10×z + -10×9 + -10×3
  • ( m + n ) + p = m + ( n + p )
  • -3 × 1 = -3
C
    
8.   Which properties are illustrated by the following three expressions?
  • -99 + -67 = -99 + -67
  • ( m + n ) + l = m + ( n + l )
  • 0 + -44 = -44
  • Commutative property of addition, Associative property of addition and Identity property of addition
  • Distributive property, Associative property of multiplication and Identity property of multiplication
  • Associative property of addition, Commutative property of multiplication and Associative property of multiplication
  • Identity property of addition, Commutative property of multiplication and Commutative property of addition
A
    
9.   Solve the following equations for x:
  • 67 · -x = -67 x = 1
        
  • -
    2
    12
    x = -
    10
    12
    x = 5
        
  • 2 = -4x – 30 x = -8
        
  • a = bx x = a/b
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x – 16 < 4 x > -20
        
  • x ≠ -780
  • -83 ≤ x ≤ -78
  • 20
    5
    x < -
    32
    4
    x < -2
        
11.   Convert the following numbers into scientific notation:
  • 0.00000611 6.11 × 10-6
        
  • 603000 6.03 × 105
        
12.   Add the following polynomials:
  • -3z8 + 16z6 + -6z4  and  20z8 + 10z6 + -17z4
    17z8 + 26z6 + -23z4
        
  • 7z20 + 18z16 + -7z7 + 5z6 + 20z5  and  2z20 + 49z16 + 41z11 + -15z7 + 37z5 9z20 + 67z16 + 41z11 + -22z7 + 5z6 + 57z5
        
13.   Multiply the following polynomials and simplify:
  • (2x5 + 7x)(6x4 + x2 + 2)
    12x9 + 2x7 + 46x5 + 7x3 + 14x
        
  • (7x5 + 3x4 + 5x2)(5x3 + 5x)
    35x8 + 15x7 + 35x6 + 40x5 + 25x3
        
14.   Divide:
  • 3x3 + 12x2 - 3x - 12 / x + 4
    3x2 - 3
        
15.   Find the greatest common factor of the following terms:
  • 462, 450, 468
    6
        
  • 324x8y2, 180x9y8
    36x8y2
        
16.   Factor the following polynomials:
  • 8x4 - 40x3 + 38x2
    8x2(x -
    5 +
    6
    2
    )(x -
    5 -
    6
    2
    )
        
  • x2 + 10x + 16
    (x + 8)(x + 2)
        
  • x8 + 2x7 - 63x6
    x6(x + 9)(x - 7)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -8
    and
    -2


        
  • x =
    0
    ,
    -9

    and
    7
        
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 or vanilla. How many choices do you have?
  • 16
        
19.   Use the following data to construct a box and whiskers plot:
  • 3, 25, 30, 16, 36, 9, 38, 2, 10, 27
        
20.   A bag contains 2 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?
    38.46%
        
  • A blue ball or red ball?
    61.54%
        
  • Two red balls?
    19.23%
        
  • A blue ball and a white ball?
    6.41%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -6
    x - y = 15
    A(4.5,-10.5)
        
  • 8x - 5y = -2
    9x + 3y = 4

    B(0.2,0.72)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x2 + 8x + 16)
    (x + 4)
    x + 4
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -x2 = -9x + 20
    x1 = 4,   x2 = 5
        
24.   Convert the following repeating decimal into a fraction:
  • x = 4.131
    4127
    999
        
25.   Solve the following equation:
  • -19
    x
    + 17 = -20
    x
    + 19
    x = 4
        
26.   Rationalize the denominator of each fraction below:
  • 35
    8
    21
    21
    10
    42
    63
        
27.   Use a trigonometric ratio to find x:
x = 17.00 cm
    
28.   The sum of two consecutive odd integers is 40. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=19, b=21
    
29.   After you leave your house, you walk 8 blocks south and 6 blocks west. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   A rectangle has a width that is 10 ft less than its length. The area of the rectangle is 299ft2. What are the dimensions of the rectangle?
  • width = 13,  length = 23
        


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:   83 and 79? 6557
    
2.   Add:   -79 and -4? -83
    
3.   Divide:   -68 and -2? 34
    
4.   Substract:   90 and 78? 12
    
5.   Calculate: |19 · 36 + 94| 778
    
6.   Simplify the following expressions:
  • -58 – 45x + -91 -149-45x
        
  • -18x – 82x + 66y + -65 -65-100x+66y
        
  • 21 – -4x – -38x – -41 – 19y 62+42x-19y
        
  • x36 × y-77 x36 × y-77
        
  • x91
    x-32
    x123
        
  • (9x2)5 59049x10
        
7.   Which of the following expressions show the associative property?
  • 0 + -7x = -7x
  • 3( 6 + 9 ) = 3×6 + 3×9
  • 1 × ( y + 3 + 8 ) = 1×y + 1×3 + 1×8
  • ( 4 × 7 ) × 6 = 4 × ( 7 × 6 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • i + ( j + 0 ) = ( i + j ) + 0
  • b × ( c + d ) = b × c + b × d
  • 0 + v + w = v + w
  • Associative property of addition, Distributive property and Identity property of addition
  • Identity property of multiplication, Associative property of multiplication and Identity property of addition
  • Identity property of multiplication, Commutative property of addition and Associative property of addition
  • Identity property of addition, Associative property of addition and Associative property of multiplication
A
    
9.   Solve the following equations for x:
  • -44 = 18 – x x = 62
        
  • 26
    3
    x =
    26
    3
    x = 1
        
  • -16 = 64 + 8x x = -10
        
  • -fx = a x = -a/f
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -23x – -39 ≤ -7 x ≥ 2
        
  • x ≠ 3
  • 16 < x > 77
  • -
    9
    3
    x ≥ -12 x ≤ 4
        
11.   Convert the following numbers into scientific notation:
  • 0.00000517 5.17 × 10-6
        
  • 3770000 3.77 × 106
        
12.   Add the following polynomials:
  • -16z7 + 5z5  and  19z10 + -1z8 + 20z7 + 6z6 + -18z5
    19z10 + -1z8 + 4z7 + 6z6 + -13z5
        
  • -38z14 + 20z10 + 38z9 + 2z5 + -22  and  -17z14 + 41z10 + 7z9 + -41z2 -55z14 + 61z10 + 45z9 + 2z5 + -41z2 + -22
        
13.   Multiply the following polynomials and simplify:
  • (1x4 + x2 + 3x)(4x5 + 2x3 - 1)
    4x9 + 6x7 + 12x6 + 2x5 + 5x4 - x2 - 3x
        
  • (6x5 + 5x4)(7x3 + 2x2)
    42x8 + 47x7 + 10x6
        
14.   Divide:
  • 15x2 - 44x + 6 / 5x + 2
    (3x - 10) with a remainder of 26
        
15.   Find the greatest common factor of the following terms:
  • 252, 231
    21
        
  • 450x5y9, 330y3
    30y3
        
16.   Factor the following polynomials:
  • 5x5 + 70x4 - 75x3
    5x3(x - 1)(x + 15)
        
  • x2 - x - 90
    (x + 9)(x - 10)
        
  • x4 + 3x3 - 28x2
    x2(x + 7)(x - 4)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -9
    and
    10


        
  • x =
    0
    ,
    -7

    and
    4
        
18.   How many ways can 5 people wait in line?
  • 120
        
19.   Use the following data to construct a box and whiskers plot:
  • 2, 30, 32, 3, 29, 27, 23, 16, 1, 6
        
20.   A bag contains 5 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?
    16.67%
        
  • A blue ball or red ball?
    83.33%
        
  • Two red balls?
    17.36%
        
  • A blue ball and a white ball?
    6.94%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 4
    x - y = 19
    A(11.5,-7.5)
        
  • 5x - 9y = 8
    2x + 3y = -6

    B(-0.91,-1.39)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x - 8)7
    (x - 8)
    (x - 8)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 = -20x + 75
    x1 = 5,   x2 = 15
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.154
    153
    990
        
25.   Solve the following equation:
  • -12
    x
    + 17 = -11
    x
    - 11
    x = 784
        
26.   Rationalize the denominator of each fraction below:
  • 25
    35
    + 10
    -
    5
    35
    - 50
    13
        
27.   Use a trigonometric ratio to find x:
x = 27.00 cm
    
28.   The sum of two consecutive even integers is 46. What are the integers? (Hint: use 2x as the first even integer)
a=22, b=24
    
29.   After you leave your house, you walk 9 blocks east and 12 blocks south. How far are you from your house?
  • I am
    15
    blocks from my house.
        
30.   A rectangle has a length 10 ft greater than its width. The area of the rectangle is 375ft2. What are the length and width of the rectangle?
  • width = 15,  length = 25
        


To print this algebra practice test, click here.



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