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 -4? 12
    
2.   Add:   6 and 3? 9
    
3.   Divide:   -9 and -3? 3
    
4.   Substract:   -15 and -3? -12
    
5.   Calculate: |16 · 17 + -15 · 20| 28
    
6.   Simplify the following expressions:
  • 3x + 20x + 1x 24x
        
  • 5x + 9x – -17x + 15y 31x+15y
        
  • -12x + -7y + 13x – 6z – -15x 16x-7y-6z
        
  • x-12 × y0 x-12 × y0
        
  • x-20
    x11
    x-31
        
  • (9x4)5 59049x20
        
7.   Which of the following expressions show the associative property?
  • -10 + -5 = -5 + -10
  • 2 × 1 = 2
  • ( m × n ) + 6 = 6 + ( m × n )
  • ( m + n ) + 8 = m + ( n + 8 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • 5 × 4 + y = y + 5 × 4
  • x + ( y + z ) = ( x + y ) + z
  • ( d × 1 ) × c = d × ( 1 × c )
  • Associative property of addition, Identity property of addition and Associative property of multiplication
  • Commutative property of multiplication, Associative property of multiplication and Identity property of multiplication
  • Commutative property of addition, Associative property of addition and Associative property of multiplication
  • Associative property of multiplication, Commutative property of addition and Identity property of multiplication
C
    
9.   Solve the following equations for x:
  • -x + 59 = 83 x = -24
        
  • -
    2
    7
    x = -
    30
    7
    x = 15
        
  • 16 = 44x – 28 x = 1
        
  • fx = b x = b/f
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -10x – 26 ≤ 14 x ≥ -4
        
  • x ≠ -93
  • -49 ≥ x < 95
  • 25
    5
    x > -40 x > -8
        
11.   Convert the following numbers into scientific notation:
  • 0.0000811 8.11 × 10-5
        
  • 50500000 5.05 × 107
        
12.   Add the following polynomials:
  • 6z6 + -11z4 + 10z2 + 11z1 + -9  and  12z10 + -9z4 + -13
    12z10 + 6z6 + -20z4 + 10z2 + 11z1 + -22
        
  • -11z20 + 4z18 + 1z12 + 13z5  and  15z20 + -15z18 + -11z13 + 9z10 4z20 + -11z18 + -11z13 + 1z12 + 9z10 + 13z5
        
13.   Multiply the following polynomials and simplify:
  • 5x4(3x4 + 5x3 + 7)
    15x8 + 25x7 + 35x4
        
  • (3x5 + 7x4 + 9x)(2x5 + x - 8)
    6x10 + 14x9 + 21x6 - 17x5 - 56x4 + 9x2 - 72x
        
14.   Divide:
  • 5x3 - 30x2 - 2x + 12 / x - 6
    5x2 - 2
        
15.   Find the greatest common factor of the following terms:
  • 42, 45
    3
        
  • 10x10y6, 90x10y8
    10x10y6
        
16.   Factor the following polynomials:
  • 48x4 - 28x3 - 48x2
    48x2(x -
    4
    3
    )(x +
    3
    4
    )
        
  • x2 + x - 90
    (x + 10)(x - 9)
        
  • x5 - 7x4 - 78x3
    x3(x + 6)(x - 13)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -10
    and
    9


        
  • x =
    0
    ,
    -6

    and
    13
        
18.   How many ways can 3 people wait in line?
  • 6
        
19.   Use the following data to construct a box and whiskers plot:
  • 38, 27, 9, 6, 36, 34, 10, 37
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 10
  • What is the probability of getting heads and 2?
    5.00%
        
  • What is the probability of getting tails and an odd number?
    25%
        
  • What is the probability of getting heads and a multiple of 3?
    15%
        
  • What is the probability of getting heads and a prime number?
    20%
        
  • What is the probability of not tails and not 6?
    45%
        
  • 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 tails?
    50%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 15
    x - y = -9
    A(3,12)
        
  • 8x - 10y = 19
    x + 2y = -11

    B(-2.77,-4.12)
        
22.   Write the following fractions in simplest form:
  • 50x9y3
    25xy5
    2x8
    y2
        
  • x8 + 11x7 + 18x6
    x4(x + 2)
    x2(x + 9)
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • x2 + 33 = 34x
    x1 = 33,   x2 = 1
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.98
    98
    99
        
25.   Solve the following equation:
  • 15
    x
    - 5 = 20
    x
    - 10
    x = 1
        
26.   Rationalize the denominator of each fraction below:
  • 6
    5 -
    21
    15 + 3
    21
    2
        
27.   Use a trigonometric ratio to find x:
x = 8.66 cm
    
28.   The sum of two consecutive even integers is 54. What are the integers? (Hint: use 2x as the first even integer)
a=26, b=28
    
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 10 m. The area of the newly created square is 196m2. What was the original length of one side of the square?
  • 24 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:   -6 and 3? -18
    
2.   Add:   19 and -17? 2
    
3.   Divide:   9 and 1? 9
    
4.   Substract:   12 and 8? 4
    
5.   Calculate: |-9 · 13 + -7 · 5| 152
    
6.   Simplify the following expressions:
  • -5x – -14x – -9x 18x
        
  • 5y – -6y – -8y + 7x 7x+19y
        
  • -12z + 11y + 6 – -3 – 14x 9-14x+11y-12z
        
  • y8 × x-3 x-3 × y8
        
  • x2
    x-3
    x5
        
  • (3x)5 243x5
        
7.   Which of the following expressions show the associative property?
  • ( 4 + 2 ) + 6 = 4 + ( 2 + 6 )
  • 3 × -2 = -2 × 3
  • 6 × 1 = 6
  • ( -1 + -5 ) × 10 = 10 × ( -1 + -5 )
A
    
8.   Which properties are illustrated by the following three expressions?
  • 1 × (s + t) = s + t
  • x × ( -2 + 5 ) = x × -2 + x × 5
  • 11 × (4 + y) = (4 + y) × 11
  • Identity property of addition, Identity property of multiplication and Associative property of multiplication
  • Identity property of multiplication, Distributive property and Commutative property of multiplication
  • Distributive property, Associative property of multiplication and Identity property of multiplication
  • Commutative property of multiplication, Distributive property and Commutative property of addition
B
    
9.   Solve the following equations for x:
  • -62 = 31 · x x = -2
        
  • 30
    23
    x =
    30
    23
    x = 1
        
  • -45 = -56x + 67 x = 2
        
  • bx = ex + d x = d/(b-e)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -14x + 16 ≥ 30 x ≤ -1
        
  • x ≠ 218
  • -22 < x ≥ -83
  • -
    40
    20
    x > -20 x < 10
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000000155 1.55 × 10-11
        
  • 996000 9.96 × 105
        
12.   Add the following polynomials:
  • 3z8 + -12z3 + 9z1  and  -15z9 + -3z6 + -3z5 + 2z3 + -2
    -15z9 + 3z8 + -3z6 + -3z5 + -10z3 + 9z1 + -2
        
  • 15z7 + -11z2 + 3z1  and  13z7 + 6z2 + 7z1 28z7 + -5z2 + 10z1
        
13.   Multiply the following polynomials and simplify:
  • 1x5(5x5 + 5x + 9)
    5x10 + 5x6 + 9x5
        
  • (7x5 + 6x2 + 6x)(6x5 + 10x2 + 1)
    42x10 + 106x7 + 36x6 + 7x5 + 60x4 + 60x3 + 6x2 + 6x
        
14.   Divide:
  • 8x2 - 16x - 10 / 4x + 2
    2x - 5
        
15.   Find the greatest common factor of the following terms:
  • 36, 72
    36
        
  • 45x7y3, 84x6y5
    3x6y3
        
16.   Factor the following polynomials:
  • 28x3 + 99x2 + 81x
    28x(x +
    9
    7
    )(x +
    9
    4
    )
        
  • x2 + 4x - 45
    (x - 5)(x + 9)
        
  • x4 - 2x3 - 48x2
    x2(x + 6)(x - 8)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    5
    and
    -9


        
  • x =
    0
    ,
    -6

    and
    8
        
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:
  • 23, 27, 12, 18, 6, 14, 3
        
20.   A bag contains 3 blue balls, 4 red balls, and 3 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    30.00%
        
  • A blue ball or red ball?
    70.00%
        
  • Two red balls?
    16.00%
        
  • A blue ball and a white ball?
    9.00%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -7
    x - y = 7
    A(0,-7)
        
  • 3x - 6y = 8
    5x + 5y = -15

    B(-1.11,-1.89)
        
22.   Write the following fractions in simplest form:
  • 40x5y4
    20xy2
    2x4y2
        
  • (x2 + 14x + 49)
    (x + 7)
    x + 7
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • x2 - 90 = -9x
    x1 = -15,   x2 = 6
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.428
    386
    900
        
25.   Solve the following equation:
  • -13 +
    3x - 3
    = -4
    x = 28
        
26.   Rationalize the denominator of each fraction below:
  • 10
    2
    - 35
    -
    10
    2
    + 350
    1223
        
27.   Use a trigonometric ratio to find x:
x = 24.25 cm
    
28.   The sum of two consecutive odd integers is 36. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=17, b=19
    
29.   After you leave your house, you walk 6 blocks south and 8 blocks east. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   The length of a rectangle is 6 more than thrice its width. The area of the rectangle is 45m2. What is the length and width of the rectangle?
  • width = 3,  length = 15
        


To print this algebra practice test, click here.



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