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 -20? -60
    
2.   Add:   -9 and -2? -11
    
3.   Divide:   16 and 2? 8
    
4.   Substract:   -20 and -5? -15
    
5.   Calculate: |-10 + 19 · -4 + 5| 81
    
6.   Simplify the following expressions:
  • 5x – -10x + -1x 14x
        
  • 16x – 5 – 18y – 8y -5+16x-26y
        
  • -9 + -5y + 3x + 8 – -8 + -10x 7-7x-5y
        
  • y-19 × y-2 × y-11 y-32
        
  • x-4
    x-11
    x7
        
  • (5x3)2 25x6
        
7.   Which of the following expressions show the associative property?
  • 3 × ( x + 2 + 8 ) = 3×x + 3×2 + 3×8
  • 1 × 1 = 1
  • ( x + y ) + z = x + ( y + z )
  • 0 + -1x = -1x
C
    
8.   Which properties are illustrated by the following three expressions?
  • 0 + f + 17 = f + 17
  • g + h + 11 = 11 + g + h
  • 1 × (x + y) = x + y
  • Identity property of addition, Commutative property of addition and Identity property of multiplication
  • Commutative property of addition, Commutative property of multiplication and Associative property of multiplication
  • Commutative property of addition, Identity property of multiplication and Associative property of multiplication
  • Identity property of addition, Associative property of addition and Identity property of multiplication
A
    
9.   Solve the following equations for x:
  • -89 = x – -50 x = -139
        
  • 6
    14
    x = -
    12
    14
    x = -2
        
  • 56 + 2x = -82 x = -69
        
  • fx + e = -bx x = (-e)/(f+b)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -5x + 17 < 12 x > 1
        
  • x ≠ 726
  • -33 < x ≥ 60
  • -
    21
    3
    x ≥ -35 x ≤ 5
        
11.   Convert the following numbers into scientific notation:
  • 0.00000191 1.91 × 10-6
        
  • 217000000000 2.17 × 1011
        
12.   Add the following polynomials:
  • 8z10 + -13z8 + 5z1  and  -5z10 + 6z8 + -10z4 + 10z1
    3z10 + -7z8 + -10z4 + 15z1
        
  • -11z16 + 7z8 + -5z4 + -6z3  and  6z16 + -3z13 + -6z4 + -1z3 -5z16 + -3z13 + 7z8 + -11z4 + -7z3
        
13.   Multiply the following polynomials and simplify:
  • -2(1x3 + 6)
    -2x3 - 12
        
  • (6x4 + x3 - 8)(8x5 + 6x3)
    48x9 + 8x8 + 36x7 + 6x6 - 64x5 - 48x3
        
14.   Divide:
  • 3x2 - 4x + 1 / x - 1
    3x - 1
        
15.   Find the greatest common factor of the following terms:
  • 40, 78, 60
    2
        
  • 60x2y2, 90x5y
    30x2y
        
16.   Factor the following polynomials:
  • 4x5 + 19x4 - 5x3
    4x3(x -
    1
    4
    )(x + 5)
        
  • x2 + 16x + 64
    (x + 8)(x + 8)
        
  • x6 + 2x5 - 80x4
    x4(x + 10)(x - 8)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -8
    and
    -8


        
  • x =
    0
    ,
    -10

    and
    8
        
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:
  • 28, 40, 16, 8, 5, 3, 20
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 9
  • What is the probability of getting heads and 6?
    5.56%
        
  • What is the probability of getting tails and an even number?
    22.22%
        
  • What is the probability of getting tails and a multiple of 2?
    22.22%
        
  • What is the probability of getting tails and a prime number?
    22.22%
        
  • What is the probability of not heads and not 9?
    44.44%
        
  • 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 = -13
    x - y = -18
    A(-15.5,2.5)
        
  • 2x - 7y = 11
    5x + y = 16

    B(3.32,-0.62)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x - 1)
    (x2 - 2x + 1)
    1
    x - 1
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • x2 - 18x = -45
    x1 = 3,   x2 = 15
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.5800
    5795
    9990
        
25.   Solve the following equation:
  • -5
    x
    - 2 = -9
    x
    + 14
    x = 16
        
26.   Rationalize the denominator of each fraction below:
  • 7
    25 +
    7
    175 - 7
    7
    618
        
27.   Use a trigonometric ratio to find x:
x = 32.91 cm
    
28.   The sum of two consecutive odd integers is 16. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=7, b=9
    
29.   After you leave your house, you walk 5 blocks west and 12 blocks north. How far are you from your house?
  • I am
    13
    blocks from my house.
        
30.   A rectangle has a length 4 m greater than its width. The area of the rectangle is 252m2. What are the length and width of the rectangle?
  • width = 14,  length = 18
        


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:   1 and 2? 2
    
2.   Add:   -12 and -20? -32
    
3.   Divide:   9 and -3? -3
    
4.   Substract:   -10 and 4? -14
    
5.   Calculate: |14 – 13 + 16 – 1| 16
    
6.   Simplify the following expressions:
  • 1x + -5x – -6x 2x
        
  • 14x – 2y – 13 – -11x -13+25x-2y
        
  • -3 – -20x + 15 – -12z + 2x – 20x 12+2x+12z
        
  • x-20 × y-14 × x17 × x-16 x-19 × y-14
        
  • x3
    x6
    x-3
        
  • (10x3)3 1000x9
        
7.   Which of the following expressions show the associative property?
  • 2( 7 + 9 ) = 2×7 + 2×9
  • ( m + n ) + 2 = m + ( n + 2 )
  • a + b = b + a
  • -8 × ( y + 2 + 7 ) = -8×y + -8×2 + -8×7
B
    
8.   Which properties are illustrated by the following three expressions?
  • 6 + -46 = 6 + -46
  • x × ( y + 1 ) = x × y + x × 1
  • ( 20 × -5 ) × 1 = 20 × ( -5 × 1 )
  • Associative property of addition, Commutative property of multiplication and Identity property of addition
  • Commutative property of multiplication, Associative property of addition and Identity property of multiplication
  • Distributive property, Identity property of addition and Associative property of multiplication
  • Commutative property of addition, Distributive property and Associative property of multiplication
D
    
9.   Solve the following equations for x:
  • -27 = -x · -27 x = -1
        
  • 10
    3
    = -
    10
    3
    x x = -1
        
  • 39 = 62 – -23x x = -1
        
  • -c = -fx – g x = (c-g)/f
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 3x – -34 ≤ -32 x ≤ -22
        
  • x ≠ -763
  • -68 ≤ x ≤ 81
  • -7x ≤
    28
    2
    x ≥ -2
        
11.   Convert the following numbers into scientific notation:
  • 0.00000000848 8.48 × 10-9
        
  • 5130000000 5.13 × 109
        
12.   Add the following polynomials:
  • -9z9 + 10z6 + 7z3 + 15z1  and  -1z9 + -12z6 + -3z3 + -13z1 + -1
    -10z9 + -2z6 + 4z3 + 2z1 + -1
        
  • 8z15 + 2z12 + -2z5  and  -2z16 + 8z15 + 6z12 + -3z1 -2z16 + 16z15 + 8z12 + -2z5 + -3z1
        
13.   Multiply the following polynomials and simplify:
  • (2x5 + 9x4 + 1)2x5
    4x10 + 18x9 + 2x5
        
  • (7x5 + 10x3)(9x2 + 6x)
    63x7 + 42x6 + 90x5 + 60x4
        
14.   Divide:
  • 4x2 - 26x - 14 / x - 7
    4x + 2
        
15.   Find the greatest common factor of the following terms:
  • 36, 45
    9
        
  • 60x9y5, 45x10y5
    15x9y5
        
16.   Factor the following polynomials:
  • 42x4 - 9x3 - 33x2
    42x2(x +
    11
    14
    )(x - 1)
        
  • x2 - 12x + 27
    (x - 3)(x - 9)
        
  • x4 + 15x3 + 56x2
    x2(x + 7)(x + 8)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    3
    and
    9


        
  • x =
    0
    ,
    -7

    and
    -8
        
18.   You are seating 8 people on 8 chairs. How many different ways can those people sit?
  • 40320
        
19.   Use the following data to construct a box and whiskers plot:
  • 16, 4, 39, 31, 20, 3, 22, 34, 36
        
20.   A bag contains 3 blue balls, 2 red balls, and 2 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    28.57%
        
  • A blue ball or red ball?
    71.43%
        
  • Two red balls?
    8.16%
        
  • A blue ball and a white ball?
    12.24%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -18
    x - y = -9
    A(-13.5,-4.5)
        
  • 15x - 3y = 15
    x + y = 7

    B(2,5)
        
22.   Write the following fractions in simplest form:
  • 32x5y4
    8x5y
    4y3
        
  • (x - 3)5
    (x - 3)4
    x - 3
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 24 = x2 + 2x
    x1 = -6,   x2 = 4
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.473
    469
    990
        
25.   Solve the following equation:
  • 18
    x
    = 3
    x = 2
        
26.   Rationalize the denominator of each fraction below:
  • 9
    9
    10
    14
    27
    14
    140
        
27.   Use a trigonometric ratio to find x:
x = 23.33 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 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 an area of 66ft2. Its width is 5 ft less than its length. What are the dimensions of the rectangle?
  • width = 6,  length = 11
        


To print this algebra practice test, click here.



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