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:   15 and 4? 60
    
2.   Add:   -3 and -13? -16
    
3.   Divide:   16 and 4? 4
    
4.   Substract:   -16 and -13? -3
    
5.   Calculate: |-15 – -9 – -19| 13
    
6.   Simplify the following expressions:
  • -14 – 3 – 18x -17-18x
        
  • -3x + 15 – -12x – 7 8+9x
        
  • 6 + 3 + 3z – 6x – -5x + 1 10-1x+3z
        
  • x-7 × y-16 × y14 x-7 × y-2
        
  • x-3
    x4
    x-7
        
  • (3x4)10 59049x40
        
7.   Which of the following expressions show the associative property?
  • 0 + -9x = -9x
  • ( m × n ) × 2 = m × ( n × 2 )
  • -2 × ( z + 9 + 2 ) = -2×z + -2×9 + -2×2
  • ( 2 × 5 ) + -6 = -6 + ( 2 × 5 )
B
    
8.   Which properties are illustrated by the following three expressions?
  • -8 + -4 × 20 = -4 × 20 + -8
  • x × ( y + 0 ) = x × y + x × 0
  • (x + -1) × (y + -4) = (y + -4) × (x + -1)
  • Associative property of addition, Commutative property of addition and Identity property of multiplication
  • Identity property of addition, Identity property of multiplication and Distributive property
  • Commutative property of addition, Distributive property and Commutative property of multiplication
  • Commutative property of multiplication, Commutative property of addition and Identity property of multiplication
C
    
9.   Solve the following equations for x:
  • -73 = -x – -67 x = 140
        
  • 19
    29
    = -
    1
    29
    x x = -19
        
  • -4x + 67 = 31 x = 9
        
  • -ax = e x = -e/a
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -13x + -8 ≤ -34 x ≥ 2
        
  • x ≠ 400
  • 55 ≤ x > -96
  • 22
    11
    x ≤ -
    16
    8
    x ≤ -1
        
11.   Convert the following numbers into scientific notation:
  • 0.000337 3.37 × 10-4
        
  • 2470000 2.47 × 106
        
12.   Add the following polynomials:
  • 14z7 + 8z6 + 9z3 + 15z2 + 8z1  and  -6z6 + -2z3 + -8z2
    14z7 + 2z6 + 7z3 + 7z2 + 8z1
        
  • 5z19 + -6z9 + -2z5  and  12z19 + -13z13 + 7z9 + 14z6 + 6z1 17z19 + -13z13 + 1z9 + 14z6 + -2z5 + 6z1
        
13.   Multiply the following polynomials and simplify:
  • (9x5 + 5x2 + 4x)(10x2 + 6x - 8)
    90x7 + 54x6 - 72x5 + 50x4 + 70x3 - 16x2 - 32x
        
  • (5x5 + 2x2 + 5)(9x3 + x + 5)
    45x8 + 5x6 + 43x5 + 47x3 + 10x2 + 5x + 25
        
14.   Divide:
  • 15x2 - 40 / 3x - 6
    (5x + 10) with a remainder of 20
        
15.   Find the greatest common factor of the following terms:
  • 60, 30
    30
        
  • 66x8, 44y8
    22
        
16.   Factor the following polynomials:
  • 12x3 - 62x2 - 34x
    12x(x +
    1
    2
    )(x -
    17
    3
    )
        
  • x2 + x - 56
    (x - 7)(x + 8)
        
  • x8 - 9x7 - 70x6
    x6(x - 14)(x + 5)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    7
    and
    -8


        
  • x =
    0
    ,
    14

    and
    -5
        
18.   You have 6 books to read. How many different ways can you read your books?
  • 720
        
19.   Use the following data to construct a box and whiskers plot:
  • 18, 38, 24, 30, 17, 31, 7, 6
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 15
  • What is the probability of getting heads and 15?
    3.33%
        
  • What is the probability of getting heads and an odd number?
    23.33%
        
  • What is the probability of getting heads and a multiple of 7?
    6.67%
        
  • What is the probability of getting tails and a prime number?
    20%
        
  • What is the probability of not tails and not 10?
    46.67%
        
  • 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 = 19
    x - y = -14
    A(2.5,16.5)
        
  • 8x - 4y = 19
    9x + 9y = 14

    B(2.1,-0.55)
        
22.   Write the following fractions in simplest form:
  • 16x7y5
    4x3y
    4x4y4
        
  • (x + 6)
    (x2 + 12x + 36)
    1
    x + 6
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -x = x2 - 30
    x1 = 5,   x2 = -6
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.3586
    3583
    9990
        
25.   Solve the following equation:
  • 12
    x
    + 1 = 19
    x
    - 20
    x = 9
        
26.   Rationalize the denominator of each fraction below:
  • 4
    7 -
    6
    28 + 4
    6
    43
        
27.   Use a trigonometric ratio to find x:
x = 32.33 cm
    
28.   The sum of two consecutive odd integers is 32. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=15, b=17
    
29.   After you leave your house, you walk 8 blocks west and 6 blocks north. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   A rectangle has an area of 105m2. Its width is 8 m less than its length. What are the dimensions of the rectangle?
  • width = 7,  length = 15
        


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:   -18 and -17? 306
    
2.   Add:   -10 and 8? -2
    
3.   Divide:   18 and 2? 9
    
4.   Substract:   11 and -10? 21
    
5.   Calculate: |12 · -6 + -6 · 13| 150
    
6.   Simplify the following expressions:
  • -11x + 20x + -13x -4x
        
  • -15y – -2x + 9x – 18y 11x-33y
        
  • 2 + -9x + -18x + -15y – 11x 2-38x-15y
        
  • y6 × y17 × x-11 × y-7 x-11 × y16
        
  • x1
    x13
    x-12
        
  • (9x5)5 59049x25
        
7.   Which of the following expressions show the associative property?
  • -1 × ( z + 2 + 9 ) = -1×z + -1×2 + -1×9
  • -8x + -8 = -8 + -8x
  • 9( 8 + 1 ) = 9×8 + 9×1
  • ( 4 × 5 ) × 3 = 4 × ( 5 × 3 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • 43 + 47 = 43 + 47
  • 0 + t + 10 = t + 10
  • 14 × (-7 + y) = (-7 + y) × 14
  • Commutative property of addition, Identity property of addition and Commutative property of multiplication
  • Associative property of multiplication, Commutative property of multiplication and Associative property of addition
  • Identity property of multiplication, Commutative property of addition and Commutative property of multiplication
  • Commutative property of addition, Associative property of addition and Commutative property of multiplication
A
    
9.   Solve the following equations for x:
  • x · -69 = 69 x = -1
        
  • 23
    3
    = -
    1
    3
    x x = -23
        
  • 43x + 57 = -29 x = -2
        
  • a = -fx x = -a/f
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 4x + -33 ≥ -13 x ≥ 5
        
  • x ≠ -974
  • -16 ≥ x < 87
  • -4x > 16 x < -4
        
11.   Convert the following numbers into scientific notation:
  • 0.000000000327 3.27 × 10-10
        
  • 12900000 1.29 × 107
        
12.   Add the following polynomials:
  • -5z10 + -2z6 + 1z5 + -3z4 + -2z2  and  14z10 + -12z9 + -8z6 + -14z5 + -5z2
    9z10 + -12z9 + -10z6 + -13z5 + -3z4 + -7z2
        
  • 4z14 + -1z10 + 5z5  and  7z14 + -12z10 + 2z8 + 9z5 + -8z1 11z14 + -13z10 + 2z8 + 14z5 + -8z1
        
13.   Multiply the following polynomials and simplify:
  • (8x + 1)(2x5 + 9x2 - 3)
    16x6 + 2x5 + 72x3 + 9x2 - 24x - 3
        
  • (5x5 + 8x3 - 10)(1x5 + 6x3)
    5x10 + 38x8 + 48x6 - 10x5 - 60x3
        
14.   Divide:
  • 12x3 + 36x2 - 6x - 18 / 3x + 9
    4x2 - 2
        
15.   Find the greatest common factor of the following terms:
  • 100, 33, 15
    1
        
  • 18x9y3, 84x9y8, 81x6y7
    3x6y3
        
16.   Factor the following polynomials:
  • 8x5 - 29x4 + 15x3
    8x3(x - 3)(x -
    5
    8
    )
        
  • x2 + 6x - 27
    (x - 3)(x + 9)
        
  • x8 + 6x7 - 112x6
    x6(x + 14)(x - 8)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    3
    and
    -9


        
  • x =
    0
    ,
    -14

    and
    8
        
18.   You have 8 CDs. How many different ways can you listen to them?
  • 40320
        
19.   Use the following data to construct a box and whiskers plot:
  • 27, 39, 7, 33, 8, 12, 28, 20, 4, 23
        
20.   A bag contains 2 blue balls, 5 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?
    50.00%
        
  • A blue ball or red ball?
    50.00%
        
  • Two red balls?
    12.76%
        
  • A blue ball and a white ball?
    7.14%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 17
    x - y = -12
    A(2.5,14.5)
        
  • 3x - 4y = 7
    10x + 7y = -19

    B(-0.44,-2.08)
        
22.   Write the following fractions in simplest form:
  • 21x7y5
    84x6y7
    x
    4y2
        
  • (x + 4)
    (x2 + 8x + 16)
    1
    x + 4
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -5x = x2 + 6
    x1 = -2,   x2 = -3
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.510
    505
    990
        
25.   Solve the following equation:
  • -
    2x + 6
    - 4 = -20
    x = 125
        
26.   Rationalize the denominator of each fraction below:
  • 21
    15 +
    2
    315 - 21
    2
    223
        
27.   Use a trigonometric ratio to find x:
x = 29.44 cm
    
28.   The sum of two consecutive odd integers is 40. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=19, b=21
    
29.   After you leave your house, you walk 8 blocks south and 15 blocks east. How far are you from your house?
  • I am
    17
    blocks from my house.
        
30.   A rectangle has an area of 63ft2. Its width is 2 ft less than its length. What are the dimensions of the rectangle?
  • width = 7,  length = 9
        


To print this algebra practice test, click here.



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