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 2? -6
    
2.   Add:   1 and 9? 10
    
3.   Divide:   -2 and 2? -1
    
4.   Substract:   -8 and -18? 10
    
5.   Calculate: |-11 + -10 · 4| 51
    
6.   Simplify the following expressions:
  • -9x – 18x + 19x -8x
        
  • -15x – -1 + 17 + -6x 18-21x
        
  • -16z + -3z + 6x – 5y – -18x – 5z 24x-5y-24z
        
  • x-13 × x0 × x-9 x-22
        
  • x15
    x-6
    x21
        
  • (2x2)6 64x12
        
7.   Which of the following expressions show the associative property?
  • ( x × y ) + 3 = 3 + ( y × x )
  • ( 3 + 5 ) + 4 = 3 + ( 5 + 4 )
  • 8 × -9 = -9 × 8
  • ( m × n ) + 6 = 6 + ( m × n )
B
    
8.   Which properties are illustrated by the following three expressions?
  • ( t + u ) + s = t + ( u + s )
  • h × ( i × 1 ) = ( h × i ) × 1
  • 0 + g + 1 = g + 1
  • Commutative property of multiplication, Associative property of multiplication and Associative property of addition
  • Associative property of multiplication, Identity property of multiplication and Associative property of addition
  • Commutative property of addition, Identity property of addition and Associative property of addition
  • Associative property of addition, Associative property of multiplication and Identity property of addition
D
    
9.   Solve the following equations for x:
  • -47 = 34 – x x = 81
        
  • -
    1
    23
    x = -
    19
    23
    x = 19
        
  • 96 = -39 + 45x x = 3
        
  • g – ax = -bx x = g/(a-b)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 12x + -39 < 21 x < 5
        
  • x ≠ -145
  • 94 ≤ x < -61
  • -
    18
    9
    x ≥ 30 x ≤ -15
        
11.   Convert the following numbers into scientific notation:
  • 0.000000000733 7.33 × 10-10
        
  • 784000000 7.84 × 108
        
12.   Add the following polynomials:
  • 15z6 + -3z4 + -12  and  -7z8 + -14
    -7z8 + 15z6 + -3z4 + -26
        
  • -7z16 + 15z13 + -1z6 + -1z3  and  -1z16 + -4z15 + 9z13 + -5z6 -8z16 + -4z15 + 24z13 + -6z6 + -1z3
        
13.   Multiply the following polynomials and simplify:
  • (3x5 + 3x)(6x5 + 4x4 + 2x2)
    18x10 + 12x9 + 6x7 + 18x6 + 12x5 + 6x3
        
  • (1x5 + 7x3 + 9)(2x5 + 3x + 3)
    2x10 + 14x8 + 3x6 + 21x5 + 21x4 + 21x3 + 27x + 27
        
14.   Divide:
  • 10x2 + x - 24 / 5x + 8
    2x - 3
        
15.   Find the greatest common factor of the following terms:
  • 30, 90, 15
    15
        
  • 36x4y3, 60x5y6, 45y10
    3y3
        
16.   Factor the following polynomials:
  • 36x4 + 71x3 - 2x2
    36x2(x + 2)(x -
    1
    36
    )
        
  • x2 - 12x + 35
    (x - 5)(x - 7)
        
  • x4 + 16x3 + 60x2
    x2(x + 10)(x + 6)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    5
    and
    7


        
  • x =
    0
    ,
    -10

    and
    -6
        
18.   You have 5 CDs. How many different ways can you listen to them?
  • 120
        
19.   Use the following data to construct a box and whiskers plot:
  • 8, 26, 37, 13, 3, 18, 12
        
20.   A bag contains 4 blue balls, 6 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?
    23.08%
        
  • A blue ball or red ball?
    76.92%
        
  • Two red balls?
    21.30%
        
  • A blue ball and a white ball?
    7.10%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 18
    x - y = -20
    A(-1,19)
        
  • 8x - 6y = 11
    9x + 3y = -9

    B(-0.27,-2.19)
        
22.   Write the following fractions in simplest form:
  • 72x4y5
    24x5y5
    3
    x
        
  • x3 - 5x2 + 4x
    x3(x - 1)
    (x - 4)
    x2
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 28x + 52 = -x2
    x1 = -26,   x2 = -2
        
24.   Convert the following repeating decimal into a fraction:
  • x = 5.851
    5846
    999
        
25.   Solve the following equation:
  • 3
    x
    = 14
    x =
    9
    196
        
26.   Rationalize the denominator of each fraction below:
  • 3
    35 -
    7
    35 +
    7
    406
        
27.   Use a trigonometric ratio to find x:
x = 24.00 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 12 blocks south and 16 blocks east. How far are you from your house?
  • I am
    20
    blocks from my house.
        
30.   A rectangle has a width that is 4 ft less than its length. The area of the rectangle is 357ft2. What are the dimensions of the rectangle?
  • width = 17,  length = 21
        


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:   -3 and -12? 36
    
2.   Add:   3 and 19? 22
    
3.   Divide:   -19 and -19? 1
    
4.   Substract:   -10 and 13? -23
    
5.   Calculate: |6 + -17 · -12| 210
    
6.   Simplify the following expressions:
  • -14x – 18 + -3 -21-14x
        
  • 3y + 5y – -10x + -4 -4+10x+8y
        
  • -8 + -16y + -11y + -3 – 18y – 17y -11-62y
        
  • x15 × x-11 × y1 × y-16 x4 × y-15
        
  • x2
    x4
    x-2
        
  • (4x3)8 65536x24
        
7.   Which of the following expressions show the associative property?
  • ( -2 + -3 ) × 2 = 2 × ( -2 + -3 )
  • a + b = b + a
  • ( m × n ) × 5 = m × ( n × 5 )
  • -10 × ( y + 4 + 8 ) = -10×y + -10×4 + -10×8
C
    
8.   Which properties are illustrated by the following three expressions?
  • 1 × -9 = -9
  • i × (g + h) = (g + h) × i
  • h × ( i + j ) = h × i + h × j
  • Distributive property, Associative property of multiplication and Commutative property of multiplication
  • Identity property of multiplication, Commutative property of multiplication and Distributive property
  • Commutative property of addition, Identity property of multiplication and Associative property of multiplication
  • Distributive property, Identity property of addition and Commutative property of multiplication
B
    
9.   Solve the following equations for x:
  • 72 = 27 + -x x = -45
        
  • 5
    13
    = -
    5
    13
    x x = -1
        
  • 26 = 8x – -34 x = -1
        
  • d = cx x = d/c
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -2x + 31 ≤ -15 x ≥ 23
        
  • x ≠ 617
  • 73 ≥ x ≤ -20
  • -
    26
    2
    x ≤ 13 x ≥ -1
        
11.   Convert the following numbers into scientific notation:
  • 0.0000785 7.85 × 10-5
        
  • 7890000000 7.89 × 109
        
12.   Add the following polynomials:
  • -4z10 + 2z8 + -7z6 + 6z4 + 1  and  9z8 + 6z6 + 8z5 + 12z2
    -4z10 + 11z8 + -1z6 + 8z5 + 6z4 + 12z2 + 1
        
  • -8z15 + 2z12 + 13z4 + 14  and  2z15 + 12z12 + -12z4 + 13 -6z15 + 14z12 + 1z4 + 27
        
13.   Multiply the following polynomials and simplify:
  • (8x5 + 5x)(2x4 + 3x2 + 4x)
    16x9 + 24x7 + 32x6 + 10x5 + 15x3 + 20x2
        
  • (2x4 + 2x)(6x5 + 9x3 + 10)
    12x9 + 18x7 + 12x6 + 38x4 + 20x
        
14.   Divide:
  • 15x3 - 6x2 + 15x - 4 / 5x - 2
    (3x2 + 3) with a remainder of 2
        
15.   Find the greatest common factor of the following terms:
  • 36, 11
    1
        
  • 40x4y4, 63x5y10, 72x10y10
    x4y4
        
16.   Factor the following polynomials:
  • 16x4 + 52x3 + 41x2
    16x2(x -
    -13 +
    5
    8
    )(x -
    -13 -
    5
    8
    )
        
  • x2 - 5x - 24
    (x - 8)(x + 3)
        
  • x4 + 16x3 + 28x2
    x2(x + 14)(x + 2)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    8
    and
    -3


        
  • x =
    0
    ,
    -14

    and
    -2
        
18.   How many ways can 8 people wait in line?
  • 40320
        
19.   Use the following data to construct a box and whiskers plot:
  • 19, 1, 22, 34, 18, 23, 32
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 17
  • What is the probability of getting heads and 15?
    2.94%
        
  • What is the probability of getting tails and an even number?
    23.53%
        
  • What is the probability of getting tails and a multiple of 4?
    11.76%
        
  • What is the probability of getting heads and a prime number?
    20.59%
        
  • What is the probability of not tails and not 12?
    47.06%
        
  • 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 = -20
    A(-3.5,16.5)
        
  • 2x - 2y = 10
    2x + 5y = 3

    B(4,-1)
        
22.   Write the following fractions in simplest form:
  • 11x3y10
    44x3y7
    y3
    4
        
  • (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 = -56
    x1 = 14,   x2 = 4
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.370
    367
    990
        
25.   Solve the following equation:
  • -8 -
    2x - 5
    = -13
    x = 15
        
26.   Rationalize the denominator of each fraction below:
  • 35
    30
    7
    30
    6
        
27.   Use a trigonometric ratio to find x:
x = 52.00 cm
    
28.   The sum of two consecutive odd integers is 48. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=23, b=25
    
29.   After you leave your house, you walk 16 blocks east and 12 blocks north. How far are you from your house?
  • I am
    20
    blocks from my house.
        
30.   The length of a rectangle is 2 more than twice its width. The area of the rectangle is 364m2. What is the length and width of the rectangle?
  • width = 13,  length = 28
        


To print this algebra practice test, click here.



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