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:   -3 and 2? -6
    
2.   Add:   14 and 20? 34
    
3.   Divide:   -1 and -1? 1
    
4.   Substract:   2 and 11? -9
    
5.   Calculate: |-20 + 18 · -8| 164
    
6.   Simplify the following expressions:
  • 18x – -3x + 20x 41x
        
  • -4 + 4y + 3x + -3x -4+4y
        
  • 9x + 2y – -4 – -3z + -15x 4-6x+2y+3z
        
  • y16 × y0 × y-9 × x1 x1 × y7
        
  • x-1
    x-8
    x7
        
  • (5x5)6 15625x30
        
7.   Which of the following expressions show the associative property?
  • 6( 7 + 6 ) = 6×7 + 6×6
  • ( -1 × 8 ) + -4 = -4 + ( -1 × 8 )
  • ( x × y ) × z = x × ( y × z )
  • 7 + 5h + 6
C
    
8.   Which properties are illustrated by the following three expressions?
  • c × (a + b) = (a + b) × c
  • 37 + 0 = 37
  • 1 × (v + w + x) = v + w + x
  • Associative property of addition, Associative property of multiplication and Commutative property of addition
  • Associative property of addition, Identity property of addition and Commutative property of addition
  • Commutative property of multiplication, Identity property of addition and Identity property of multiplication
  • Commutative property of addition, Associative property of multiplication and Identity property of multiplication
C
    
9.   Solve the following equations for x:
  • -x – 72 = -43 x = -29
        
  • 3
    11
    x =
    3
    11
    x = 1
        
  • 2 = -13 – 15x x = -1
        
  • bx = e x = e/b
        
10.   Solve the following inequalities. Then graph a) on the number line
  • x – -1 < -20 x < -21
        
  • x ≠ -105
  • -63 > x > -54
  • -
    34
    17
    x ≤ -22 x ≥ 11
        
11.   Convert the following numbers into scientific notation:
  • 0.000000000928 9.28 × 10-10
        
  • 267000000000 2.67 × 1011
        
12.   Add the following polynomials:
  • -8z5 + -5z3 + 10z2  and  -9z5 + 12z3 + 8z2 + -11
    -17z5 + 7z3 + 18z2 + -11
        
  • 7z17 + 9z7 + 10z5  and  -5z17 + 5z7 + -12z6 + -2z5 2z17 + 14z7 + -12z6 + 8z5
        
13.   Multiply the following polynomials and simplify:
  • (8x2 + 4x + 9)4x4
    32x6 + 16x5 + 36x4
        
  • (4x - 1)(9x3 + 9x2)
    36x4 + 27x3 - 9x2
        
14.   Divide:
  • 6x2 - 42x + 72 / 3x - 9
    2x - 8
        
15.   Find the greatest common factor of the following terms:
  • 55, 22, 75
    1
        
  • 90y8, 15x4y4
    15y4
        
16.   Factor the following polynomials:
  • 3x3 - 27x2 - 66x
    3x(x + 2)(x - 11)
        
  • x2 - 4x - 5
    (x + 1)(x - 5)
        
  • x8 - 12x7 - 45x6
    x6(x - 15)(x + 3)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -1
    and
    5


        
  • x =
    0
    ,
    15

    and
    -3
        
18.   How many ways can 3 people wait in line?
  • 6
        
19.   Use the following data to construct a box and whiskers plot:
  • 18, 33, 14, 2, 11, 22, 34
        
20.   A bag contains 6 blue balls, 5 red balls, and 6 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    35.29%
        
  • A blue ball or red ball?
    64.71%
        
  • Two red balls?
    8.65%
        
  • A blue ball and a white ball?
    12.46%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 14
    x - y = -10
    A(2,12)
        
  • 10x - 2y = -9
    6x + y = -17

    B(-1.95,-5.27)
        
22.   Write the following fractions in simplest form:
  • 16x7y7
    64x5y7
    x2
    4
        
  • x4 + 9x3 - 10x2
    x(x - 1)
    x(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.
  • 2x = x2 - 8
    x1 = 4,   x2 = -2
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.30
    30
    99
        
25.   Solve the following equation:
  • x - 9
    - 16 = -16
    x = 9
        
26.   Rationalize the denominator of each fraction below:
  • 5
    14 +
    7
    70 - 5
    7
    189
        
27.   Use a trigonometric ratio to find x:
x = 28.87 cm
    
28.   The sum of two consecutive odd integers is 52. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=25, b=27
    
29.   After you leave your house, you walk 6 blocks west and 8 blocks south. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   A rectangle has an area of 54ft2. Its width is 3 ft less than its length. What are the dimensions of the rectangle?
  • width = 6,  length = 9
        


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:   9 and 15? 135
    
2.   Add:   -2 and -6? -8
    
3.   Divide:   16 and -1? -16
    
4.   Substract:   -16 and -11? -5
    
5.   Calculate: |18 · -1 + -2 · 13| 44
    
6.   Simplify the following expressions:
  • 2 + -19 – -1x -17+1x
        
  • 17x + -12 – 18y + -12x -12+5x-18y
        
  • 2y – 1z + -9z + 13 – 6y + 8x 13+8x-4y-10z
        
  • y8 × x15 × x-4 x11 × y8
        
  • x-18
    x14
    x-32
        
  • (2x4)9 512x36
        
7.   Which of the following expressions show the associative property?
  • v × ( w + 2 ) = vw + 2w
  • ( 3 + 6 ) + 8 = 3 + ( 6 + 8 )
  • 6 + 2 = 2 + 6
  • 3 × 1 = 3
B
    
8.   Which properties are illustrated by the following three expressions?
  • x × ( y + 1 ) = x × y + x × 1
  • z × (x + y) = (x + y) × z
  • p + q + r + 0 = p + q + r
  • Commutative property of multiplication, Identity property of multiplication and Associative property of multiplication
  • Identity property of multiplication, Commutative property of addition and Associative property of multiplication
  • Distributive property, Associative property of multiplication and Commutative property of addition
  • Distributive property, Commutative property of multiplication and Identity property of addition
D
    
9.   Solve the following equations for x:
  • 69 = -x + -88 x = -157
        
  • 5
    10
    = -
    1
    2
    x x = -1
        
  • 2x – 1 = -33 x = -16
        
  • cx = -f – dx x = (-f)/(c+d)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 2x + 38 ≥ 34 x ≥ -2
        
  • x ≠ -711
  • 78 > x ≥ 10
  • -
    6
    3
    x ≤
    24
    3
    x ≥ -4
        
11.   Convert the following numbers into scientific notation:
  • 0.000000932 9.32 × 10-7
        
  • 430000000 4.3 × 108
        
12.   Add the following polynomials:
  • -3z10 + 8z8 + -1z7 + -11z4 + -8z3  and  -3z8 + 11z4 + -8z3
    -3z10 + 5z8 + -1z7 + -16z3
        
  • -2z20 + -14z14 + -1z5 + -4z1  and  -13z20 + 11z14 + -10z2 + 5z1 -15z20 + -3z14 + -1z5 + -10z2 + 1z1
        
13.   Multiply the following polynomials and simplify:
  • 4x(9x5 + 8x4 - 10)
    36x6 + 32x5 - 40x
        
  • (2x2 - 5)(2x2 + 6x - 3)
    4x4 + 12x3 - 16x2 - 30x + 15
        
14.   Divide:
  • 10x3 + 18x2 + 5x + 9 / 5x + 9
    2x2 + 1
        
15.   Find the greatest common factor of the following terms:
  • 66, 80
    2
        
  • 70x2y2, 72x7y5
    2x2y2
        
16.   Factor the following polynomials:
  • 28x5 + 35x4 - 63x3
    28x3(x +
    9
    4
    )(x - 1)
        
  • x2 - 14x + 40
    (x - 4)(x - 10)
        
  • x5 + 8x4 - 105x3
    x3(x - 7)(x + 15)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    4
    and
    10


        
  • x =
    0
    ,
    7

    and
    -15
        
18.   You have 4 books to read. How many different ways can you read your books?
  • 24
        
19.   Use the following data to construct a box and whiskers plot:
  • 17, 36, 23, 24, 34, 26, 35, 7, 14, 6
        
20.   A bag contains 5 blue balls, 4 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?
    35.71%
        
  • A blue ball or red ball?
    64.29%
        
  • Two red balls?
    8.16%
        
  • A blue ball and a white ball?
    12.76%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -7
    x - y = 9
    A(1,-8)
        
  • 14x - 6y = 18
    x + y = 17

    B(6,11)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x2 + 12x + 36)
    (x + 6)
    x + 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 - 66 = 31x
    x1 = 33,   x2 = -2
        
24.   Convert the following repeating decimal into a fraction:
  • x = 8.673
    7806
    900
        
25.   Solve the following equation:
  • -5
    x
    + 6 = -7
    x
    + 16
    x = 25
        
26.   Rationalize the denominator of each fraction below:
  • 10
    2
    + 14
    -
    5
    2
    - 70
    97
        
27.   Use a trigonometric ratio to find x:
x = 17.68 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 5 blocks west and 12 blocks south. How far are you from your house?
  • I am
    13
    blocks from my house.
        
30.   A rectangle has a length 10 ft greater than its width. The area of the rectangle is 264ft2. What are the length and width of the rectangle?
  • width = 12,  length = 22
        


To print this algebra practice test, click here.



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