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:   19 and -2? -38
    
2.   Add:   -10 and 10? 0
    
3.   Divide:   2 and -2? -1
    
4.   Substract:   8 and 13? -5
    
5.   Calculate: |-7 · 19 + -19| 152
    
6.   Simplify the following expressions:
  • -4x – 2 + -11x -2-15x
        
  • -1 + -18y – -13y – -10x -1+10x-5y
        
  • -5y – -14x + 14z + -15z + 18y 14x+13y-1z
        
  • x-6 × y8 x-6 × y8
        
  • x18
    x10
    x8
        
  • (3x5)10 59049x50
        
7.   Which of the following expressions show the associative property?
  • 1 × 1 = 1
  • 0 + 8x = 8x
  • q × ( r + 6 ) = qr + 6r
  • ( 3 + 7 ) + 5 = 3 + ( 7 + 5 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • ( g × h ) × f = g × ( h × f )
  • -1 × 1 + z = z + -1 × 1
  • ( b + 0 ) + a = b + ( 0 + a )
  • Identity property of addition, Associative property of addition and Distributive property
  • Commutative property of multiplication, Identity property of addition and Commutative property of addition
  • Associative property of multiplication, Commutative property of addition and Associative property of addition
  • Associative property of addition, Commutative property of multiplication and Distributive property
C
    
9.   Solve the following equations for x:
  • -x · 4 = -16 x = 4
        
  • 19
    15
    = -
    1
    15
    x x = -19
        
  • 19 – 13x = 32 x = -1
        
  • -cx = ax + b x = (-b)/(c+a)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 8x – -16 < 24 x < 1
        
  • x ≠ 887
  • 98 < x ≥ -22
  • -
    40
    10
    x ≥ -
    32
    4
    x ≤ 2
        
11.   Convert the following numbers into scientific notation:
  • 0.0000758 7.58 × 10-5
        
  • 1600000000 1.6 × 109
        
12.   Add the following polynomials:
  • 10z10 + -3z7 + -1z6 + 5z3  and  -1z10 + 4z2
    9z10 + -3z7 + -1z6 + 5z3 + 4z2
        
  • -2z19 + 4z9 + 14z5  and  -4z19 + 13z11 + -9z9 + -10z5 -6z19 + 13z11 + -5z9 + 4z5
        
13.   Multiply the following polynomials and simplify:
  • (4x + 3)(1x4 + 5x3 + 7x)
    4x5 + 23x4 + 15x3 + 28x2 + 21x
        
  • (6x4 + 10x2 + 7x)(7x5 + 3x3 + 10)
    42x9 + 88x7 + 49x6 + 30x5 + 81x4 + 100x2 + 70x
        
14.   Divide:
  • 15x2 - 4x - 6 / 3x - 5
    (5x + 7) with a remainder of 29
        
15.   Find the greatest common factor of the following terms:
  • 45, 49
    1
        
  • 36x2y8, 60xy9, 26x2y3
    2xy3
        
16.   Factor the following polynomials:
  • 21x4 - 48x3 + 12x2
    21x2(x - 2)(x -
    2
    7
    )
        
  • x2 + 17x + 70
    (x + 7)(x + 10)
        
  • x7 + 10x6 + 21x5
    x5(x + 7)(x + 3)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -7
    and
    -10


        
  • x =
    0
    ,
    -7

    and
    -3
        
18.   You are seating 7 people on 7 chairs. How many different ways can those people sit?
  • 5040
        
19.   Use the following data to construct a box and whiskers plot:
  • 39, 27, 40, 7, 17, 21, 36, 6, 11
        
20.   A bag contains 5 blue balls, 4 red balls, and 6 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    40.00%
        
  • A blue ball or red ball?
    60.00%
        
  • Two red balls?
    7.11%
        
  • A blue ball and a white ball?
    13.33%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 11
    x - y = -3
    A(4,7)
        
  • 5x - 9y = -10
    2x + 6y = -4

    B(-2,0)
        
22.   Write the following fractions in simplest form:
  • 15x6y
    30x10y7
    1
    2x4y6
        
  • x8 - 1x7 - 6x6
    x2(x - 3)
    x4(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.
  • 12x + 36 = -x2
    x1 = -6,   x2 = -6
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.15
    14
    90
        
25.   Solve the following equation:
  • -11
    x
    + 19 = 5
    x
    - 13
    x = 4
        
26.   Rationalize the denominator of each fraction below:
  • 6
    10
    10 +
    7
    20
    10
    - 2
    70
    31
        
27.   Use a trigonometric ratio to find x:
x = 15.56 cm
    
28.   The sum of two consecutive odd integers is 56. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=27, b=29
    
29.   After you leave your house, you walk 12 blocks north and 16 blocks east. How far are you from your house?
  • I am
    20
    blocks from my house.
        
30.   The length of a rectangle is 3 less than 3 times the width. What are the dimensions of the rectangle if the area is 270m2?
  • width = 10,  length = 27
        


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:   -5 and -14? 70
    
2.   Add:   19 and 4? 23
    
3.   Divide:   -17 and 1? -17
    
4.   Substract:   11 and -6? 17
    
5.   Calculate: |12 · 20 + -1| 239
    
6.   Simplify the following expressions:
  • -20x + 19x + -11x -12x
        
  • -9y – -12y + -3x + 12x 9x+3y
        
  • 12z – -15z + -1x + -14x – 10 -10-15x+27z
        
  • x17 × x-2 x15
        
  • x3
    x-13
    x16
        
  • (7x2)5 16807x10
        
7.   Which of the following expressions show the associative property?
  • a + b = b + a
  • ( m × n ) × 5 = m × ( n × 5 )
  • 5 × ( z + 6 + 9 ) = 5×z + 5×6 + 5×9
  • 7x + 9 = 9 + 7x
B
    
8.   Which properties are illustrated by the following three expressions?
  • -18 × 12 = -18 × 12
  • 1 × (x + 10) = x + 10
  • 26 + 79 = 26 + 79
  • Commutative property of multiplication, Identity property of multiplication and Commutative property of addition
  • Identity property of multiplication, Associative property of multiplication and Associative property of addition
  • Identity property of multiplication, Distributive property and Commutative property of addition
  • Associative property of multiplication, Commutative property of multiplication and Identity property of multiplication
A
    
9.   Solve the following equations for x:
  • 65 + x = 72 x = 7
        
  • 26
    20
    =
    2
    20
    x x = 13
        
  • 89 + 4x = 77 x = -3
        
  • -a – e = -cx x = (a+e)/c
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -58x – -23 ≤ -35 x ≥ 1
        
  • x ≠ -309
  • 59 > x ≤ -9
  • 36
    12
    x ≤
    15
    5
    x ≤ 1
        
11.   Convert the following numbers into scientific notation:
  • 0.00000995 9.95 × 10-6
        
  • 243000000000 2.43 × 1011
        
12.   Add the following polynomials:
  • -10z8 + 6z6 + 5z4 + -3  and  11z10 + 15z5 + -10z4 + 2 + 9
    11z10 + -10z8 + 6z6 + 15z5 + -5z4 + 8
        
  • 12z19 + 6z18 + 12z15 + 3z5 + 6z1  and  15z15 + -14z5 + 8z1 12z19 + 6z18 + 27z15 + -11z5 + 14z1
        
13.   Multiply the following polynomials and simplify:
  • (6x5 + 10x4 + 7x)7x3
    42x8 + 70x7 + 49x4
        
  • (1x5 + 8x)(9x5 + 4x4 + 6x2)
    9x10 + 4x9 + 6x7 + 72x6 + 32x5 + 48x3
        
14.   Divide:
  • 4x2 + 2x + 17 / 2x + 4
    (2x - 3) with a remainder of 29
        
15.   Find the greatest common factor of the following terms:
  • 42, 52
    2
        
  • 54x4y7, 18x10y8, 15x3y8
    3x3y7
        
16.   Factor the following polynomials:
  • 30x3 + 35x2 + 5x
    30x(x + 1)(x +
    1
    6
    )
        
  • x2 + 6x + 9
    (x + 3)(x + 3)
        
  • x7 + 9x6 - 90x5
    x5(x + 15)(x - 6)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -3
    and
    -3


        
  • x =
    0
    ,
    -15

    and
    6
        
18.   You have 4 pants, 2 shirts, and 3 shoes. How many different ways can you dress?
  • 24
        
19.   Use the following data to construct a box and whiskers plot:
  • 4, 39, 12, 21, 40, 30, 8, 34, 2
        
20.   A bag contains 3 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?
    25.00%
        
  • A blue ball or red ball?
    75.00%
        
  • Two red balls?
    25.00%
        
  • A blue ball and a white ball?
    6.25%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -14
    x - y = -17
    A(-15.5,1.5)
        
  • 7x - 11y = 18
    11x + 2y = 9

    B(1,-1)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x2 + 16x + 64)
    (x + 8)
    x + 8
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 98 = x2 + 7x
    x1 = -14,   x2 = 7
        
24.   Convert the following repeating decimal into a fraction:
  • x = 8.469
    7623
    900
        
25.   Solve the following equation:
  • -6
    x
    + 11 = 1
    x
    - 3
    x = 4
        
26.   Rationalize the denominator of each fraction below:
  • 2
    5
    - 7
    -
    5
    + 7
    22
        
27.   Use a trigonometric ratio to find x:
x = 33.77 cm
    
28.   The sum of two consecutive even integers is 34. What are the integers? (Hint: use 2x as the first even integer)
a=16, b=18
    
29.   After you leave your house, you walk 16 blocks east and 12 blocks south. How far are you from your house?
  • I am
    20
    blocks from my house.
        
30.   The sides of a square are increased by 3 ft. The area of the newly created square is 256ft2. What was the original length of one side of the square?
  • 13 ft
        


To print this algebra practice test, click here.



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