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:   16 and 8? 128
    
2.   Add:   4 and -18? -14
    
3.   Divide:   -5 and 1? -5
    
4.   Substract:   3 and -6? 9
    
5.   Calculate: |1 + 14 · 9| 127
    
6.   Simplify the following expressions:
  • 15x – -1 + -18x 1-3x
        
  • -2y + -9 + -18x + -19 -28-18x-2y
        
  • 5 + -4 – 5y + 17z – -5y 1+17z
        
  • x12 × y-4 × x14 × x-4 x22 × y-4
        
  • x19
    x17
    x2
        
  • (6x3)4 1296x12
        
7.   Which of the following expressions show the associative property?
  • ( x + y ) × 4 = 4 × ( y + x )
  • 5 × ( z + 6 + 4 ) = 5×z + 5×6 + 5×4
  • 6 + 7 = 7 + 6
  • ( m × n ) × 7 = m × ( n × 7 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • p + q + r + 0 = p + q + r
  • g + ( h + i ) = ( g + h ) + i
  • 1 × ( 13 + -7) = 1 × 13 + 1 × -7
  • Identity property of addition, Associative property of addition and Distributive property
  • Associative property of multiplication, Distributive property and Commutative property of addition
  • Commutative property of addition, Commutative property of multiplication and Identity property of multiplication
  • Associative property of multiplication, Associative property of addition and Distributive property
A
    
9.   Solve the following equations for x:
  • 65 · x = 65 x = 1
        
  • -
    15
    30
    =
    1
    10
    x x = -5
        
  • 29x + -92 = -63 x = 1
        
  • g = -ex + b x = (-g+b)/e
        
10.   Solve the following inequalities. Then graph a) on the number line
  • x + 25 ≤ 3 x ≤ -22
        
  • x ≠ 532
  • 98 > x < 4
  • 6
    2
    x < -
    36
    4
    x < -3
        
11.   Convert the following numbers into scientific notation:
  • 0.000997 9.97 × 10-4
        
  • 7180000000 7.18 × 109
        
12.   Add the following polynomials:
  • -3z10 + -13z9 + 5z8 + 2z6 + -2z3  and  -8z10 + 4z9 + -4z8 + 4z6 + 5z3
    -11z10 + -9z9 + 1z8 + 6z6 + 3z3
        
  • -3z17 + 8z13 + -13z4  and  -1z20 + -5z19 + 12z4 -1z20 + -5z19 + -3z17 + 8z13 + -1z4
        
13.   Multiply the following polynomials and simplify:
  • (4x4 + 3x)4x4
    16x8 + 12x5
        
  • (8x4 + x2)(5x4 + 7)
    40x8 + 5x6 + 56x4 + 7x2
        
14.   Divide:
  • 6x3 - 6x2 - 20x + 20 / 2x - 2
    3x2 - 10
        
15.   Find the greatest common factor of the following terms:
  • 100, 54
    2
        
  • 90x2y8, 12y5
    6y5
        
16.   Factor the following polynomials:
  • 30x5 - 56x4 + 24x3
    30x3(x -
    2
    3
    )(x -
    6
    5
    )
        
  • x2 - 5x - 24
    (x + 3)(x - 8)
        
  • x5 + 7x4 - 30x3
    x3(x - 3)(x + 10)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -3
    and
    8


        
  • x =
    0
    ,
    3

    and
    -10
        
18.   You can purchase your ice cream in a cup or a cone. Orders can be one or two scoops. Flavors can be chocolate or vanilla. How many choices do you have?
  • 8
        
19.   Use the following data to construct a box and whiskers plot:
  • 19, 23, 13, 29, 12, 10, 18, 40
        
20.   A bag contains 5 blue balls, 4 red balls, and 7 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    43.75%
        
  • A blue ball or red ball?
    56.25%
        
  • Two red balls?
    5.00%
        
  • A blue ball and a white ball?
    14.58%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 14
    x - y = -17
    A(-1.5,15.5)
        
  • 3x - 9y = -4
    3x + 9y = 9

    B(0.83,0.72)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 2)
    (x2 + 4x + 4)
    1
    x + 2
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -x2 = 15x + 54
    x1 = -6,   x2 = -9
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.767
    767
    999
        
25.   Solve the following equation:
  • -10
    x
    + 17 = 1
    x
    - 16
    x = 9
        
26.   Rationalize the denominator of each fraction below:
  • 14
    21
    - 7
    -
    21
    + 7
    2
        
27.   Use a trigonometric ratio to find x:
x = 18.38 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 12 blocks north and 16 blocks west. How far are you from your house?
  • I am
    20
    blocks from my house.
        
30.   Each side of a square is decreased by 4 m. The area of the newly created square is 361m2. What was the original length of one side of the square?
  • 23 m
        


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 16? 160
    
2.   Add:   3 and -9? -6
    
3.   Divide:   -5 and 5? -1
    
4.   Substract:   -14 and 12? -26
    
5.   Calculate: |9 · -5 + -12 · 10| 165
    
6.   Simplify the following expressions:
  • 9x – 13x – -3x -1x
        
  • -9y – -14x – -8x – 9 -9+22x-9y
        
  • 10 – -11y + 10x + 12z – -5y – 3x 10+7x+16y+12z
        
  • x-14 × x-9 × y4 x-23 × y4
        
  • x-5
    x12
    x-17
        
  • (5x5)10 9765625x50
        
7.   Which of the following expressions show the associative property?
  • 6 × -2 = -2 × 6
  • ( 2 + -10 ) × 9 = 9 × ( 2 + -10 )
  • ( x + y ) × 6 = 6 × ( y + x )
  • ( 4 + 3 ) + 7 = 4 + ( 3 + 7 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • k + ( l + 0 ) = ( k + l ) + 0
  • y × ( 16 + -3 ) = y × 16 + y × -3
  • 17 × 2 + -19 = -19 + 17 × 2
  • Associative property of multiplication, Associative property of addition and Distributive property
  • Identity property of addition, Associative property of multiplication and Distributive property
  • Distributive property, Commutative property of multiplication and Identity property of addition
  • Associative property of addition, Distributive property and Commutative property of addition
D
    
9.   Solve the following equations for x:
  • 55 = x + -79 x = 134
        
  • 5
    8
    x = -
    20
    16
    x = -2
        
  • 19x – -24 = 62 x = 2
        
  • g = -ax x = -g/a
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x + -9 ≤ 30 x ≥ -39
        
  • x ≠ -262
  • -21 ≤ x > -70
  • 28
    14
    x <
    32
    16
    x < 1
        
11.   Convert the following numbers into scientific notation:
  • 0.000000000548 5.48 × 10-10
        
  • 9790000 9.79 × 106
        
12.   Add the following polynomials:
  • -1z9 + -10z5 + -13z3  and  -10z10 + 5z9 + 12z3 + 7
    -10z10 + 4z9 + -10z5 + -1z3 + 7
        
  • 2z20 + 15z16 + -10z15 + 11z8  and  7z16 + -12z16 + -14z15 + 3z8 2z20 + 10z16 + -24z15 + 14z8
        
13.   Multiply the following polynomials and simplify:
  • (3x3 + 10x + 3)(2x5 + x - 4)
    6x8 + 20x6 + 6x5 + 3x4 - 12x3 + 10x2 - 37x - 12
        
  • (10x5 + x2)(9x2 + 9x)
    90x7 + 90x6 + 9x4 + 9x3
        
14.   Divide:
  • 3x2 + 17x - 56 / x + 8
    3x - 7
        
15.   Find the greatest common factor of the following terms:
  • 90, 30, 52
    2
        
  • 60x2y3, 48x4y5, 36y2
    12y2
        
16.   Factor the following polynomials:
  • 60x3 - 100x2 + 10x
    60x(x -
    5 +
    19
    6
    )(x -
    5 -
    19
    6
    )
        
  • x2 - x - 2
    (x - 2)(x + 1)
        
  • x6 - 12x5 + 36x4
    x4(x - 6)(x - 6)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    2
    and
    -1


        
  • x =
    0
    ,
    6

    and
    6
        
18.   You are seating 4 people on 4 chairs. How many different ways can those people sit?
  • 24
        
19.   Use the following data to construct a box and whiskers plot:
  • 6, 21, 30, 3, 33, 37, 24, 7, 9
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 6
  • What is the probability of getting heads and 1?
    8.33%
        
  • What is the probability of getting tails and an odd number?
    25%
        
  • What is the probability of getting heads and a multiple of 2?
    25%
        
  • What is the probability of getting heads and a prime number?
    25%
        
  • What is the probability of not heads and not 2?
    41.67%
        
  • 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 = -19
    x - y = -4
    A(-11.5,-7.5)
        
  • 8x - 6y = -4
    6x + 4y = 6

    B(0.29,1.06)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x - 7)7
    (x - 7)5
    (x - 7)2
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 4x + 4 = -x2
    x1 = -2,   x2 = -2
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.319
    288
    900
        
25.   Solve the following equation:
  • x - 10
    + 6 = 20
    x = 206
        
26.   Rationalize the denominator of each fraction below:
  • 25
    3
    - 35
    -
    25
    3
    + 875
    1222
        
27.   Use a trigonometric ratio to find x:
x = 21.21 cm
    
28.   The sum of two consecutive even integers is 26. What are the integers? (Hint: use 2x as the first even integer)
a=12, b=14
    
29.   After you leave your house, you walk 15 blocks east and 8 blocks north. How far are you from your house?
  • I am
    17
    blocks from my house.
        
30.   Each side of a square is decreased by 3 ft. The area of the newly created square is 361ft2. What was the original length of one side of the square?
  • 22 ft
        


To print this algebra practice test, click here.



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