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:   20 and -16? -320
    
2.   Add:   11 and -8? 3
    
3.   Divide:   -13 and -1? 13
    
4.   Substract:   16 and 9? 7
    
5.   Calculate: |-18 · -10 + 5 · 7| 215
    
6.   Simplify the following expressions:
  • 16x + 17x + -3x 30x
        
  • -3y + 4y + -9 + 10x -9+10x+1y
        
  • -18x – 17y + 13x – -17 + -20y + 11y 17-5x-26y
        
  • x-4 × y-3 × y3 x-4 × y0
        
  • x-6
    x12
    x-18
        
  • (4x2)9 262144x18
        
7.   Which of the following expressions show the associative property?
  • ( m + n ) × 3 = 3 × ( m + n )
  • -2 × 4 = 4 × -2
  • ( x + y ) + z = x + ( y + z )
  • x × ( y + 8 ) = xy + 8y
C
    
8.   Which properties are illustrated by the following three expressions?
  • (o + p) × -5 = -5 × (o + p)
  • 19 × -11 + -5 = -5 + 19 × -11
  • n + o + p + 0 = n + o + p
  • Commutative property of multiplication, Commutative property of addition and Identity property of addition
  • Identity property of multiplication, Identity property of addition and Associative property of addition
  • Commutative property of addition, Distributive property and Identity property of multiplication
  • Associative property of addition, Associative property of multiplication and Commutative property of multiplication
A
    
9.   Solve the following equations for x:
  • -9 = x + 30 x = -39
        
  • -
    13
    11
    =
    1
    11
    x x = -13
        
  • -82 = -55 + -9x x = 3
        
  • -c = -bx – ax x = c/(b+a)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x – 34 ≥ -30 x ≤ -4
        
  • x ≠ -81
  • -3 < x < -73
  • -
    24
    6
    x ≤ -24 x ≥ 6
        
11.   Convert the following numbers into scientific notation:
  • 0.000000151 1.51 × 10-7
        
  • 877000 8.77 × 105
        
12.   Add the following polynomials:
  • -4z10 + 4z4  and  -15z9 + -15z8 + 12z4 + 11z4 + 14z2
    -4z10 + -15z9 + -15z8 + 27z4 + 14z2
        
  • 5z14 + 10z11 + -12z10 + -12  and  14z14 + 6z13 + -3z11 + -6z10 + 9 19z14 + 6z13 + 7z11 + -18z10 + -3
        
13.   Multiply the following polynomials and simplify:
  • (4x3 + 2x2 - 10)9x4
    36x7 + 18x6 - 90x4
        
  • (6x2 + 7x)(1x3 + 9x2 - 1)
    6x5 + 61x4 + 63x3 - 6x2 - 7x
        
14.   Divide:
  • 5x2 + 20x + 15 / x + 3
    5x + 5
        
15.   Find the greatest common factor of the following terms:
  • 44, 90, 42
    2
        
  • 88x9y8, 54x9y2
    2x9y2
        
16.   Factor the following polynomials:
  • 3x3 + 6x2 + 3x
    3x(x + 1)(x + 1)
        
  • x2 + 9x + 14
    (x + 7)(x + 2)
        
  • x5 - 6x4 - 135x3
    x3(x - 15)(x + 9)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -7
    and
    -2


        
  • x =
    0
    ,
    15

    and
    -9
        
18.   How many ways can 3 people wait in line?
  • 6
        
19.   Use the following data to construct a box and whiskers plot:
  • 38, 35, 36, 7, 40, 29, 4, 1
        
20.   A bag contains 2 blue balls, 3 red balls, and 5 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    50.00%
        
  • A blue ball or red ball?
    50.00%
        
  • Two red balls?
    6.67%
        
  • A blue ball and a white ball?
    11.11%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -17
    x - y = 12
    A(-2.5,-14.5)
        
  • 3x - 10y = 2
    2x + 9y = 13

    B(3.15,0.74)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 1)7
    (x + 1)2
    (x + 1)5
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • x2 - 10x = 56
    x1 = 14,   x2 = -4
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.2535
    2510
    9900
        
25.   Solve the following equation:
  • 18
    x
    - 13 = 6
    x
    - 1
    x = 1
        
26.   Rationalize the denominator of each fraction below:
  • 15
    7 +
    15
    105 - 15
    15
    34
        
27.   Use a trigonometric ratio to find x:
x = 24.75 cm
    
28.   The sum of two consecutive odd integers is 60. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=29, b=31
    
29.   After you leave your house, you walk 12 blocks west and 5 blocks south. How far are you from your house?
  • I am
    13
    blocks from my house.
        
30.   Each side of a square is lengthened by 2 ft. This makes the area of the square 49ft2. What is the original length of a side of the square?
  • 5 ft
        


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:   -16 and 2? -32
    
2.   Add:   -4 and -11? -15
    
3.   Divide:   -17 and -1? 17
    
4.   Substract:   6 and 7? -1
    
5.   Calculate: |1 · 20 + -1 · -4| 24
    
6.   Simplify the following expressions:
  • 12 + 20x + 11 23+20x
        
  • -4x + 12x – 11x + 7y -3x+7y
        
  • 13z + 5 – -9z + -6 – 5z – 1z -1+16z
        
  • x-3 × y15 × y-4 × x11 x8 × y11
        
  • x9
    x12
    x-3
        
  • (10x3)10 10000000000x30
        
7.   Which of the following expressions show the associative property?
  • ( m + n ) + 5 = m + ( n + 5 )
  • -7x + -2 = -2 + -7x
  • ( x × y ) + 8 = 8 + ( y × x )
  • i × ( j + 6 ) = ij + 6j
A
    
8.   Which properties are illustrated by the following three expressions?
  • -2 + -90 = -2 + -90
  • (r + s + t) × 1 = r + s + t
  • 0 + y + 18 = y + 18
  • Associative property of multiplication, Commutative property of multiplication and Commutative property of addition
  • Commutative property of addition, Identity property of multiplication and Identity property of addition
  • Commutative property of addition, Associative property of multiplication and Distributive property
  • Associative property of multiplication, Identity property of multiplication and Commutative property of addition
B
    
9.   Solve the following equations for x:
  • x – 78 = 98 x = 176
        
  • -
    29
    7
    x = -
    29
    7
    x = 1
        
  • -62 = -38 – 4x x = 6
        
  • -fx = c – a x = (-c+a)/f
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -46x + 18 < -28 x > 1
        
  • x ≠ -936
  • 29 < x < 55
  • 14
    7
    x ≤
    8
    4
    x ≤ 1
        
11.   Convert the following numbers into scientific notation:
  • 0.0000673 6.73 × 10-5
        
  • 20200000 2.02 × 107
        
12.   Add the following polynomials:
  • -15z10 + 15z9 + -13z7 + 1z5 + -3z3  and  -1z10 + 15z9 + -5z7 + 15
    -16z10 + 30z9 + -18z7 + 1z5 + -3z3 + 15
        
  • 2z18 + -2z13 + -9z8 + -15z3 + -12z1  and  14z20 + 9z19 + -14z18 + -14z13 + 12z9 14z20 + 9z19 + -12z18 + -16z13 + 12z9 + -9z8 + -15z3 + -12z1
        
13.   Multiply the following polynomials and simplify:
  • (2x5 + x4 + 9x3)9
    18x5 + 9x4 + 81x3
        
  • (8x5 + 7x4)(8x3 + 10x2 + 6x)
    64x8 + 136x7 + 118x6 + 42x5
        
14.   Divide:
  • 20x3 + 35x2 - 20x - 35 / 4x + 7
    5x2 - 5
        
15.   Find the greatest common factor of the following terms:
  • 48, 72, 24
    24
        
  • 60x2y2, 18x8y6, 90x4y6
    6x2y2
        
16.   Factor the following polynomials:
  • 40x4 - 56x3 + 12x2
    40x2(x -
    7 +
    19
    10
    )(x -
    7 -
    19
    10
    )
        
  • x2 - 12x + 32
    (x - 4)(x - 8)
        
  • x6 - 2x5 - 143x4
    x4(x + 11)(x - 13)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    4
    and
    8


        
  • x =
    0
    ,
    -11

    and
    13
        
18.   You can purchase your ice cream in a cup or a cone. Orders can be one, two, three, or four scoops. Flavors can be chocolate or vanilla. How many choices do you have?
  • 16
        
19.   Use the following data to construct a box and whiskers plot:
  • 37, 11, 40, 28, 24, 17, 18, 31, 26, 6
        
20.   A bag contains 7 blue balls, 2 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?
    1.82%
        
  • A blue ball and a white ball?
    12.73%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -14
    x - y = 17
    A(1.5,-15.5)
        
  • 2x - 4y = 10
    5x + 9y = -19

    B(0.37,-2.32)
        
22.   Write the following fractions in simplest form:
  • 3x6y7
    12x2y2
    x4y5
    4
        
  • (x - 7)7
    (x - 7)2
    (x - 7)5
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 55 = x2 + 6x
    x1 = 5,   x2 = -11
        
24.   Convert the following repeating decimal into a fraction:
  • x = 1.8
    17
    9
        
25.   Solve the following equation:
  • -
    9
    x
    = -7
    x =
    81
    49
        
26.   Rationalize the denominator of each fraction below:
  • 14
    10
    + 1
    14
    10
    - 14
    9
        
27.   Use a trigonometric ratio to find x:
x = 25.46 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 6 blocks east and 8 blocks north. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   The sides of a square are increased by 2 m. The area of the newly created square is 256m2. What was the original length of one side of the square?
  • 14 m
        


To print this algebra practice test, click here.



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