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:   45 and 75? 3375
    
2.   Add:   -83 and 71? -12
    
3.   Divide:   38 and -1? -38
    
4.   Substract:   41 and -96? 137
    
5.   Calculate: |96 · -74 + 25 · 64| 5504
    
6.   Simplify the following expressions:
  • 91x – -7x + 65x 163x
        
  • -28x – -86x + -80y – -90 90+58x-80y
        
  • 71z + 50x – 26x – -22x + -74y – 30z 46x-74y+41z
        
  • y92 × y32 × x-65 x-65 × y124
        
  • x-6
    x62
    x-68
        
  • (5x)5 3125x5
        
7.   Which of the following expressions show the associative property?
  • ( m + n ) + p = m + ( n + p )
  • ( x + y ) × 3 = 3 × ( y + x )
  • ( -5 × -9 ) + 8 = 8 + ( -5 × -9 )
  • 0 + 5x = 5x
A
    
8.   Which properties are illustrated by the following three expressions?
  • 1 × (s + t + u) = s + t + u
  • 15 + 4y = 4y + 15
  • 0 + 28 = 28
  • Associative property of multiplication, Identity property of addition and Associative property of addition
  • Identity property of addition, Distributive property and Associative property of multiplication
  • Associative property of addition, Identity property of multiplication and Commutative property of addition
  • Identity property of multiplication, Commutative property of addition and Identity property of addition
D
    
9.   Solve the following equations for x:
  • -96 = -6 – x x = 90
        
  • 2
    14
    =
    2
    14
    x x = 1
        
  • 71 = 48 + 23x x = 1
        
  • -c – bx = d x = (c+d)/(-b)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 2x – -4 ≥ 18 x ≥ 7
        
  • x ≠ -644
  • -80 > x ≥ 61
  • -2x ≤
    14
    7
    x ≥ -1
        
11.   Convert the following numbers into scientific notation:
  • 0.000000000452 4.52 × 10-10
        
  • 6600000 6.6 × 106
        
12.   Add the following polynomials:
  • 8z10 + -6z8 + 7z3 + 9z2 + 20z1  and  -12z10 + -3z8 + -3z3 + 19z1
    -4z10 + -9z8 + 4z3 + 9z2 + 39z1
        
  • -22z15 + -4z8 + -42z6 + 26z1  and  35z15 + 9z12 + 27z5 + 25z1 13z15 + 9z12 + -4z8 + -42z6 + 27z5 + 51z1
        
13.   Multiply the following polynomials and simplify:
  • (5x2 + 9x)(10x5 + 7x3)
    50x7 + 90x6 + 35x5 + 63x4
        
  • (3x5 + 4x4)(10x4 + 2x2 + 6)
    30x9 + 40x8 + 6x7 + 8x6 + 18x5 + 24x4
        
14.   Divide:
  • 5x3 + 45x2 - 3x - 27 / x + 9
    5x2 - 3
        
15.   Find the greatest common factor of the following terms:
  • 90, 260
    10
        
  • 160xy5, 60x6y8
    20xy5
        
16.   Factor the following polynomials:
  • 22x4 + 22x3 - 44x2
    22x2(x + 2)(x - 1)
        
  • x2 + 18x + 80
    (x + 8)(x + 10)
        
  • x9 + 20x8 + 84x7
    x7(x + 6)(x + 14)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -8
    and
    -10


        
  • x =
    0
    ,
    -6

    and
    -14
        
18.   You have 4 pants, 2 shirts, and 2 shoes. How many different ways can you dress?
  • 16
        
19.   Use the following data to construct a box and whiskers plot:
  • 1, 5, 21, 27, 2, 14, 20, 6, 36
        
20.   A bag contains 6 blue balls, 2 red balls, and 7 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    46.67%
        
  • A blue ball or red ball?
    53.33%
        
  • Two red balls?
    1.78%
        
  • A blue ball and a white ball?
    18.67%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 3
    x - y = 20
    A(11.5,-8.5)
        
  • 10x - 2y = 20
    12x + 3y = -3

    B(1,-5)
        
22.   Write the following fractions in simplest form:
  • 22x8y7
    88x8y6
    y
    4
        
  • (x - 3)6
    (x - 3)
    (x - 3)5
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -39 = x2 - 16x
    x1 = 13,   x2 = 3
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.7
    7
    9
        
25.   Solve the following equation:
  • -
    15
    x
    = -3
    x = 25
        
26.   Rationalize the denominator of each fraction below:
  • 9
    4
    9
    2
        
27.   Use a trigonometric ratio to find x:
x = 23.00 cm
    
28.   The sum of two consecutive even integers is 50. What are the integers? (Hint: use 2x as the first even integer)
a=24, b=26
    
29.   After you leave your house, you walk 9 blocks east and 12 blocks north. How far are you from your house?
  • I am
    15
    blocks from my house.
        
30.   Each side of a square is decreased by 10 ft. The area of the newly created square is 16ft2. What was the original length of one side of the square?
  • 14 ft
        


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:   61 and 57? 3477
    
2.   Add:   -80 and -11? -91
    
3.   Divide:   88 and -44? -2
    
4.   Substract:   79 and -39? 118
    
5.   Calculate: |2 – -38 – 85| 45
    
6.   Simplify the following expressions:
  • -27x + -9x + -45 -45-36x
        
  • 48y + 20x – -34y + -17y 20x+65y
        
  • -5x – -55x – -36 – 76y + 46 – -13z 82+50x-76y+13z
        
  • x83 × x11 × y61 × y-63 x94 × y-2
        
  • x-27
    x-40
    x13
        
  • (4x2)3 64x6
        
7.   Which of the following expressions show the associative property?
  • 0 + -4x = -4x
  • ( 2 × 8 ) × 3 = 2 × ( 8 × 3 )
  • -8 × ( y + 9 + 5 ) = -8×y + -8×9 + -8×5
  • -4 + 9 = 9 + -4
B
    
8.   Which properties are illustrated by the following three expressions?
  • x × ( -1 + 8 ) = x × -1 + x × 8
  • -2 + 11 × 18 = 11 × 18 + -2
  • ( c + 0 ) + b = c + ( 0 + b )
  • Commutative property of multiplication, Identity property of addition and Associative property of multiplication
  • Distributive property, Commutative property of addition and Associative property of addition
  • Associative property of addition, Identity property of addition and Identity property of multiplication
  • Identity property of multiplication, Commutative property of multiplication and Identity property of addition
B
    
9.   Solve the following equations for x:
  • -x – 76 = -45 x = -31
        
  • -
    1
    9
    x = -
    7
    9
    x = 7
        
  • -40 = -2x + 54 x = 47
        
  • -dx – c = -f x = (-c+f)/d
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -2x + 38 ≥ -4 x ≤ 21
        
  • x ≠ -283
  • -30 ≤ x ≤ -73
  • 20
    10
    x ≤
    20
    5
    x ≤ 2
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000687 6.87 × 10-8
        
  • 6340000 6.34 × 106
        
12.   Add the following polynomials:
  • -7z6 + 17z1  and  -4z10 + -13z7 + 13z6 + -4z4 + 13z1
    -4z10 + -13z7 + 6z6 + -4z4 + 30z1
        
  • -3z19 + 7z8 + 43z6 + -36z5  and  15z19 + -13z11 + -34z8 + 3z6 + 23z5 12z19 + -13z11 + -27z8 + 46z6 + -13z5
        
13.   Multiply the following polynomials and simplify:
  • 6(8x3 - 5)
    48x3 - 30
        
  • (2x4 - 5)(3x4 + 5x2 + 4x)
    6x8 + 10x6 + 8x5 - 15x4 - 25x2 - 20x
        
14.   Divide:
  • 20x3 - 25x2 + 8x + 13 / 4x - 5
    (5x2 + 2) with a remainder of 23
        
15.   Find the greatest common factor of the following terms:
  • 132, 168
    12
        
  • 45x8y6, 490x9y8, 288x6y8
    x6y6
        
16.   Factor the following polynomials:
  • 7x3 + 49x2 + 56x
    7x(x -
    -7 +
    17
    2
    )(x -
    -7 -
    17
    2
    )
        
  • x2 + 2x - 35
    (x + 7)(x - 5)
        
  • x7 - 5x6 - 104x5
    x5(x + 8)(x - 13)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -7
    and
    5


        
  • x =
    0
    ,
    -8

    and
    13
        
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:
  • 30, 22, 13, 21, 9, 18, 17, 2, 23
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 8
  • What is the probability of getting heads and 6?
    6.25%
        
  • What is the probability of getting tails and an even number?
    25%
        
  • What is the probability of getting heads and a multiple of 4?
    12.5%
        
  • What is the probability of getting heads and a prime number?
    25%
        
  • What is the probability of not heads and not 3?
    43.75%
        
  • What is the probability of getting not heads 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 = 3
    x - y = -8
    A(-2.5,5.5)
        
  • 6x - 8y = -19
    8x + 7y = -17

    B(-2.54,0.47)
        
22.   Write the following fractions in simplest form:
  • 17x3y7
    68x7y2
    y5
    4x4
        
  • x6(x + 4)
    x4 - 6x3 - 40x2
    x4
    (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.
  • 90 = x2 + x
    x1 = 9,   x2 = -10
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.18
    17
    90
        
25.   Solve the following equation:
  • 2x - 6
    + 1 = 5
    x = 11
        
26.   Rationalize the denominator of each fraction below:
  • 3
    2 +
    5
    -(6 - 3
    5
    )
        
27.   Use a trigonometric ratio to find x:
x = 28.00 cm
    
28.   The sum of two consecutive even integers is 18. What are the integers? (Hint: use 2x as the first even integer)
a=8, b=10
    
29.   After you leave your house, you walk 8 blocks north and 6 blocks west. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   Each side of a square is lengthened by 10 ft. This makes the area of the square 361ft2. What is the original length of a side of the square?
  • 9 ft
        


To print this algebra practice test, click here.



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