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:   -18 and 20? -360
    
2.   Add:   10 and -18? -8
    
3.   Divide:   13 and 13? 1
    
4.   Substract:   -20 and -9? -11
    
5.   Calculate: |10 + -7 · -14| 108
    
6.   Simplify the following expressions:
  • 7 – -17x + 18 25+17x
        
  • 1x – 4x – -1x – 11 -11-2x
        
  • -13x + -19 + 20z – -14x + -5x + 11y -19-4x+11y+20z
        
  • y-12 × x17 × y12 × y-8 x17 × y-8
        
  • x-1
    x20
    x-21
        
  • (7x)9 40353607x9
        
7.   Which of the following expressions show the associative property?
  • h × ( i + 2 ) = hi + 2i
  • a + b = b + a
  • -3 × 1 = -3
  • ( 9 + 4 ) + 7 = 9 + ( 4 + 7 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • y × ( 16 + -2 ) = y × 16 + y × -2
  • i + 10 + 0 = i + 10
  • 6 × (-7 + x) = (-7 + x) × 6
  • Commutative property of multiplication, Associative property of addition and Identity property of addition
  • Identity property of multiplication, Associative property of multiplication and Distributive property
  • Commutative property of multiplication, Distributive property and Associative property of multiplication
  • Distributive property, Identity property of addition and Commutative property of multiplication
D
    
9.   Solve the following equations for x:
  • -73 = x + -84 x = 11
        
  • -
    30
    25
    = -
    1
    25
    x x = 30
        
  • -22 = -15 – -7x x = -1
        
  • -f = ax + e x = (f+e)/(-a)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x – -27 ≤ 23 x ≥ 4
        
  • x ≠ -432
  • -2 < x > -89
  • 33
    11
    x ≤ 6 x ≤ 2
        
11.   Convert the following numbers into scientific notation:
  • 0.0000446 4.46 × 10-5
        
  • 45700000000 4.57 × 1010
        
12.   Add the following polynomials:
  • 11z10 + 12z7 + 3z5 + 13z4 + -2z1  and  11z10 + 1z5 + 2z1
    22z10 + 12z7 + 4z5 + 13z4
        
  • -3z9 + -10z8 + -7z5 + 3  and  -2z9 + -5z5 + -13 -5z9 + -10z8 + -12z5 + -10
        
13.   Multiply the following polynomials and simplify:
  • (2x5 + 6x3 + 8x2)(1x5 + 7x4 + 4)
    2x10 + 14x9 + 6x8 + 50x7 + 56x6 + 8x5 + 24x3 + 32x2
        
  • (5x4 + 5x3 + 10x2)(7x5 - 1)
    35x9 + 35x8 + 70x7 - 5x4 - 5x3 - 10x2
        
14.   Divide:
  • 4x3 - 9x2 - 40x + 90 / 4x - 9
    x2 - 10
        
15.   Find the greatest common factor of the following terms:
  • 45, 24
    3
        
  • 54x8y3, 90y
    18y
        
16.   Factor the following polynomials:
  • 26x5 + 20x4 - 6x3
    26x3(x -
    3
    13
    )(x + 1)
        
  • x2 + x - 56
    (x + 8)(x - 7)
        
  • x7 + 10x6 + 16x5
    x5(x + 2)(x + 8)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -8
    and
    7


        
  • x =
    0
    ,
    -2

    and
    -8
        
18.   You have 7 CDs. How many different ways can you listen to them?
  • 5040
        
19.   Use the following data to construct a box and whiskers plot:
  • 28, 36, 39, 9, 38, 13, 18, 30, 22
        
20.   A bag contains 7 blue balls, 3 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?
    41.18%
        
  • A blue ball or red ball?
    58.82%
        
  • Two red balls?
    3.11%
        
  • A blue ball and a white ball?
    16.96%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 14
    x - y = 9
    A(11.5,2.5)
        
  • 8x - y = 17
    9x + 7y = -5

    B(1.75,-2.97)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 8)
    (x2 + 16x + 64)
    1
    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.
  • 37x - 78 = -x2
    x1 = -39,   x2 = 2
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.175
    158
    900
        
25.   Solve the following equation:
  • 3x - 2
    - 4 = 13
    x = 97
        
26.   Rationalize the denominator of each fraction below:
  • 2
    49 -
    7
    49 +
    7
    1197
        
27.   Use a trigonometric ratio to find x:
x = 26.87 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 12 blocks west and 16 blocks south. How far are you from your house?
  • I am
    20
    blocks from my house.
        
30.   The length of a rectangle is 4 less than 2 times the width. What are the dimensions of the rectangle if the area is 16m2?
  • width = 4,  length = 4
        


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:   -13 and -8? 104
    
2.   Add:   13 and 7? 20
    
3.   Divide:   6 and 3? 2
    
4.   Substract:   17 and -4? 21
    
5.   Calculate: |13 · 20 + -11 · -19| 469
    
6.   Simplify the following expressions:
  • -18x + -12x + 15x -15x
        
  • -4x – 3 – 7 – 13x -10-17x
        
  • -2x – -6x + 10y + -17 + -12x -17-8x+10y
        
  • x-17 × x3 × x15 × x-13 x-12
        
  • x17
    x-3
    x20
        
  • (5x)6 15625x6
        
7.   Which of the following expressions show the associative property?
  • ( x × y ) + 4 = 4 + ( y × x )
  • 8( 7 + 6 ) = 8×7 + 8×6
  • -2x + -9 = -9 + -2x
  • ( 7 × 5 ) × 3 = 7 × ( 5 × 3 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • ( k + 0 ) + j = k + ( 0 + j )
  • 1 × -30 = -30
  • (q + r) × -9 = -9 × (q + r)
  • Commutative property of multiplication, Associative property of multiplication and Associative property of addition
  • Commutative property of multiplication, Identity property of addition and Distributive property
  • Identity property of multiplication, Distributive property and Commutative property of multiplication
  • Associative property of addition, Identity property of multiplication and Commutative property of multiplication
D
    
9.   Solve the following equations for x:
  • -61 + -x = -87 x = 26
        
  • -
    12
    9
    = -
    6
    9
    x x = 2
        
  • 70 – -115x = -45 x = -1
        
  • -bx = a x = -a/b
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 53x – 15 > 38 x > 1
        
  • x ≠ -697
  • -36 > x > -19
  • 10
    5
    x <
    12
    6
    x < 1
        
11.   Convert the following numbers into scientific notation:
  • 0.000315 3.15 × 10-4
        
  • 982000000000 9.82 × 1011
        
12.   Add the following polynomials:
  • 10z10 + 13z6  and  -6z10 + -3z9 + -10z6 + 1z1
    4z10 + -3z9 + 3z6 + 1z1
        
  • -13z20 + 4z19 + -5z10 + -14z1  and  -10z20 + -10z19 + 2z10 + 10z9 -23z20 + -6z19 + -3z10 + 10z9 + -14z1
        
13.   Multiply the following polynomials and simplify:
  • (2x3 + 8)(7x5 + 7x2)
    14x8 + 70x5 + 56x2
        
  • (6x3 + 7x2 - 5)(10x4 + 3x)
    60x7 + 70x6 - 32x4 + 21x3 - 15x
        
14.   Divide:
  • 20x2 + 24x + 4 / 5x + 1
    4x + 4
        
15.   Find the greatest common factor of the following terms:
  • 45, 84
    3
        
  • 9x4y8, 78x2y3
    3x2y3
        
16.   Factor the following polynomials:
  • 12x4 + 19x3 + 4x2
    12x2(x +
    1
    4
    )(x +
    4
    3
    )
        
  • x2 - 7x - 8
    (x - 8)(x + 1)
        
  • x8 - 6x7 - 16x6
    x6(x - 8)(x + 2)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    8
    and
    -1


        
  • x =
    0
    ,
    8

    and
    -2
        
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:
  • 11, 31, 13, 40, 22, 6, 14
        
20.   A bag contains 4 blue balls, 5 red balls, and 2 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    18.18%
        
  • A blue ball or red ball?
    81.82%
        
  • Two red balls?
    18.18%
        
  • A blue ball and a white ball?
    7.27%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -17
    x - y = -5
    A(-11,-6)
        
  • 3x - 6y = 18
    11x + 8y = 6

    B(2,-2)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x - 10)
    (x - 10)7
    1
    (x - 10)6
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 9x - 90 = -x2
    x1 = 6,   x2 = -15
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.447
    443
    990
        
25.   Solve the following equation:
  • -16
    x
    - 19 = -17
    x
    - 18
    x = 1
        
26.   Rationalize the denominator of each fraction below:
  • 6
    21 +
    14
    126 - 6
    14
    427
        
27.   Use a trigonometric ratio to find x:
x = 10.50 cm
    
28.   The sum of two consecutive even integers is 30. What are the integers? (Hint: use 2x as the first even integer)
a=14, b=16
    
29.   After you leave your house, you walk 3 blocks north and 4 blocks west. How far are you from your house?
  • I am
    5
    blocks from my house.
        
30.   A rectangle has an area of 9ft2. Its width is 8 ft less than its length. What are the dimensions of the rectangle?
  • width = 1,  length = 9
        


To print this algebra practice test, click here.



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