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 1? 19
    
2.   Add:   20 and -12? 8
    
3.   Divide:   5 and -1? -5
    
4.   Substract:   -12 and -13? 1
    
5.   Calculate: |-1 + -12 · 13| 157
    
6.   Simplify the following expressions:
  • 14x + 2x + 6x 22x
        
  • 8y – 1y + -14y – 14x -14x-7y
        
  • 14 – -13x – 15x – 3x + 8x + 5x 14+8x
        
  • y4 × y19 × y-4 × x12 x12 × y19
        
  • x-13
    x5
    x-18
        
  • (9x)2 81x2
        
7.   Which of the following expressions show the associative property?
  • ( 8 × 9 ) × 5 = 8 × ( 9 × 5 )
  • 6 × 3 = 3 × 6
  • c × ( d + 4 ) = cd + 4d
  • 8 × ( x + 7 + 6 ) = 8×x + 8×7 + 8×6
A
    
8.   Which properties are illustrated by the following three expressions?
  • ( 17 + 16 ) × x = 17 × x + 16 × x
  • 0 + 55 = 55
  • ( x × 1 ) × w = x × ( 1 × w )
  • Associative property of addition, Identity property of addition and Identity property of multiplication
  • Commutative property of multiplication, Associative property of multiplication and Identity property of addition
  • Commutative property of multiplication, Associative property of addition and Identity property of addition
  • Distributive property, Identity property of addition and Associative property of multiplication
D
    
9.   Solve the following equations for x:
  • 59 = -x – 57 x = -116
        
  • -
    13
    27
    = -
    1
    27
    x x = 13
        
  • -79 + -2x = -97 x = 9
        
  • -gx = d x = -d/g
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -3x + -32 > -29 x < -1
        
  • x ≠ -162
  • -3 < x ≥ -56
  • -
    30
    15
    x ≥
    8
    4
    x ≤ -1
        
11.   Convert the following numbers into scientific notation:
  • 0.000000520 5.2 × 10-7
        
  • 531000 5.31 × 105
        
12.   Add the following polynomials:
  • -1z9 + -4z8 + -2z2 + -11z1  and  6z9 + 11z5 + -4z1
    5z9 + -4z8 + 11z5 + -2z2 + -15z1
        
  • -2z16 + -4z15 + 6z12 + 9z10 + -8z5  and  -11z16 + -2z12 + 5z10 + -1z5 -13z16 + -4z15 + 4z12 + 14z10 + -9z5
        
13.   Multiply the following polynomials and simplify:
  • (9x5 + 6x4 + 3x)(1x5 - 7)
    9x10 + 6x9 + 3x6 - 63x5 - 42x4 - 21x
        
  • (7x3 + 2x2 - 1)(7x - 5)
    49x4 - 21x3 - 10x2 - 7x + 5
        
14.   Divide:
  • 5x3 - 25x2 + 9x - 45 / x - 5
    5x2 + 9
        
15.   Find the greatest common factor of the following terms:
  • 66, 52, 75
    1
        
  • 66y2, 78y10
    6y2
        
16.   Factor the following polynomials:
  • 12x5 - 45x4 - 12x3
    12x3(x +
    1
    4
    )(x - 4)
        
  • x2 - 4x + 3
    (x - 1)(x - 3)
        
  • x8 - 5x7 - 104x6
    x6(x + 8)(x - 13)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    1
    and
    3


        
  • x =
    0
    ,
    -8

    and
    13
        
18.   How many ways can 5 people wait in line?
  • 120
        
19.   Use the following data to construct a box and whiskers plot:
  • 17, 40, 35, 19, 31, 37, 26, 21
        
20.   A bag contains 7 blue balls, 7 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?
    22.22%
        
  • A blue ball or red ball?
    77.78%
        
  • Two red balls?
    15.12%
        
  • A blue ball and a white ball?
    8.64%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 12
    x - y = -11
    A(0.5,11.5)
        
  • 5x - y = -9
    4x + 7y = 6

    B(-1.46,1.69)
        
22.   Write the following fractions in simplest form:
  • 28x5y3
    14x5y3
    2
        
  • (x - 5)4
    (x - 5)2
    (x - 5)2
        
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 - 24
    x1 = -6,   x2 = 4
        
24.   Convert the following repeating decimal into a fraction:
  • x = 02
    1980
    90
        
25.   Solve the following equation:
  • 3
    x
    = 8
    x =
    9
    64
        
26.   Rationalize the denominator of each fraction below:
  • 15
    28
    15
    7
    14
        
27.   Use a trigonometric ratio to find x:
x = 13.86 cm
    
28.   The sum of two consecutive odd integers is 56. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=27, b=29
    
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.   Each side of a square is decreased by 3 ft. The area of the newly created square is 4ft2. What was the original length of one side of the square?
  • 5 ft
        


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:   13 and 12? 156
    
2.   Add:   -15 and -12? -27
    
3.   Divide:   -12 and -6? 2
    
4.   Substract:   -10 and -12? 2
    
5.   Calculate: |-9 · 7 + -20| 83
    
6.   Simplify the following expressions:
  • -7x – 12 – -6x -12-1x
        
  • -7y – -9 + 2x – -20 29+2x-7y
        
  • -13 – -4x – -2 – -11 – 5z – -11x 15x-5z
        
  • y-13 × y3 × y-16 × y-16 y-42
        
  • x-11
    x-7
    x-4
        
  • (7x2)3 343x6
        
7.   Which of the following expressions show the associative property?
  • 0 + -3x = -3x
  • ( x × y ) × z = x × ( y × z )
  • ( x × y ) + 3 = 3 + ( y × x )
  • a + b = b + a
B
    
8.   Which properties are illustrated by the following three expressions?
  • ( p × q ) × o = p × ( q × o )
  • 1 × (l + 14) = l + 14
  • 0 + n + o + p = n + o + p
  • Associative property of multiplication, Commutative property of multiplication and Distributive property
  • Associative property of multiplication, Identity property of multiplication and Identity property of addition
  • Identity property of addition, Associative property of addition and Commutative property of multiplication
  • Distributive property, Identity property of addition and Associative property of addition
B
    
9.   Solve the following equations for x:
  • 68 = -68 · -x x = 1
        
  • 2
    7
    x = -
    2
    7
    x = -1
        
  • 40 = -129x + -89 x = -1
        
  • -ex – a = gx x = (-a)/(e+g)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • x + 5 > 14 x > 9
        
  • x ≠ 14
  • -11 ≥ x > 70
  • -
    32
    4
    x > 24 x < -3
        
11.   Convert the following numbers into scientific notation:
  • 0.00000147 1.47 × 10-6
        
  • 509000000 5.09 × 108
        
12.   Add the following polynomials:
  • 6z6 + 13z5 + 12z4  and  2z8 + -3z7 + -12z5 + 12z4 + 11
    2z8 + -3z7 + 6z6 + 1z5 + 24z4 + 11
        
  • -3z10 + -14z8 + -1z2  and  -10z16 + -15z10 + 7z7 + -6z6 + 2z2 -10z16 + -18z10 + -14z8 + 7z7 + -6z6 + 1z2
        
13.   Multiply the following polynomials and simplify:
  • 5x5(9x3 + 7x + 6)
    45x8 + 35x6 + 30x5
        
  • (7x4 + 5x3)(8x3 + 4)
    56x7 + 40x6 + 28x4 + 20x3
        
14.   Divide:
  • 5x3 - 40x2 - 9x + 72 / x - 8
    5x2 - 9
        
15.   Find the greatest common factor of the following terms:
  • 88, 56
    8
        
  • 12x2y3, 81x7y3
    3x2y3
        
16.   Factor the following polynomials:
  • 36x5 + 96x4 + 45x3
    36x3(x -
    -8 +
    19
    6
    )(x -
    -8 -
    19
    6
    )
        
  • x2 - 12x + 35
    (x - 5)(x - 7)
        
  • x4 + 0x3 - 4x2
    x2(x - 2)(x + 2)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    5
    and
    7


        
  • x =
    0
    ,
    2

    and
    -2
        
18.   You have 2 pants, 5 shirts, and 5 shoes. How many different ways can you dress?
  • 50
        
19.   Use the following data to construct a box and whiskers plot:
  • 35, 2, 31, 39, 25, 26, 30
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 5
  • What is the probability of getting tails and 1?
    10.00%
        
  • What is the probability of getting tails and an odd number?
    20%
        
  • What is the probability of getting tails 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 1?
    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 heads?
    50%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -4
    x - y = -19
    A(-11.5,7.5)
        
  • 6x - y = 12
    4x + y = -17

    B(-0.5,-15)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 2)3
    (x + 2)7
    1
    (x + 2)4
        
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 - 63
    x1 = 9,   x2 = -7
        
24.   Convert the following repeating decimal into a fraction:
  • x = 5.16
    465
    90
        
25.   Solve the following equation:
  • 17
    x
    + 7 = 20
    x
    - 20
    x = 81
        
26.   Rationalize the denominator of each fraction below:
  • 5
    9 -
    5
    45 + 5
    5
    76
        
27.   Use a trigonometric ratio to find x:
x = 25.00 cm
    
28.   The sum of two consecutive even integers is 22. What are the integers? (Hint: use 2x as the first even integer)
a=10, b=12
    
29.   After you leave your house, you walk 4 blocks west and 3 blocks south. 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 189m2. What is the length and width of the rectangle?
  • width = 7,  length = 27
        


To print this algebra practice test, click here.



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