Algebra test generator



Name _____________________                                        Date:_____________________


Current difficulty level: Choose test difficulty:         Easy              Challenging
(current difficulty level: Challenging)

                           

Solve the following problems:

Important instructions

(or click here to generate a new test)
1.   Multiply:   53 and 61? 3233
    
2.   Add:   -58 and 83? 25
    
3.   Divide:   67 and 67? 1
    
4.   Substract:   5 and 16? -11
    
5.   Calculate: |16 · -5 + 6 · 57| 262
    
6.   Simplify the following expressions:
  • 15x – 46 + -89 -135+15x
        
  • 25x + -86x + -92x + 43y -153x+43y
        
  • 34y – 76z + 11z – 91z + -76y – 65 -65-42y-156z
        
  • y-15 × x70 × x16 x86 × y-15
        
  • x18
    x-12
    x30
        
  • (4x3)8 65536x24
        
7.   Which of the following expressions show the associative property?
  • ( -5 × 10 ) + -4 = -4 + ( -5 × 10 )
  • 0 + -3x = -3x
  • ( m × n ) × 9 = m × ( n × 9 )
  • 5 + 9 = 9 + 5
C
    
8.   Which properties are illustrated by the following three expressions?
  • z + 4 × -1 = 4 × -1 + z
  • (v + w) × 3 = 3 × (v + w)
  • ( 7 + 20 ) + 3 = 7 + ( 20 + 3 )
  • Commutative property of addition, Associative property of multiplication and Identity property of addition
  • Commutative property of addition, Associative property of multiplication and Associative property of addition
  • Commutative property of addition, Commutative property of multiplication and Associative property of addition
  • Distributive property, Identity property of multiplication and Identity property of addition
C
    
9.   Solve the following equations for x:
  • -86 – -x = -57 x = 29
        
  • -
    9
    16
    x =
    9
    16
    x = -1
        
  • 39 – 14x = 95 x = -4
        
  • ax = f + c x = (f+c)/a
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -5x + 30 ≥ 5 x ≤ 5
        
  • x ≠ -354
  • -48 < x ≤ -67
  • 5x ≤
    15
    3
    x ≤ 1
        
11.   Convert the following numbers into scientific notation:
  • 0.0000680 6.8 × 10-5
        
  • 9950000 9.95 × 106
        
12.   Add the following polynomials:
  • -3z7 + -11z1  and  14z7 + 19z4 + 7z3 + 12z1 + -1
    11z7 + 19z4 + 7z3 + 1z1 + -1
        
  • -44z18 + 26z6 + 25z4 + 33z2  and  50z18 + -27z7 + 5z6 + 6z4 + 12z2 6z18 + -27z7 + 31z6 + 31z4 + 45z2
        
13.   Multiply the following polynomials and simplify:
  • (9x3 + x + 4)(5x4 + 2x3 + 4x2)
    45x7 + 18x6 + 41x5 + 22x4 + 12x3 + 16x2
        
  • (4x5 + 6x2 + 9)(10x4 + 6x2)
    40x9 + 24x7 + 60x6 + 126x4 + 54x2
        
14.   Divide:
  • 6x2 - 24x + 18 / 3x - 9
    2x - 2
        
15.   Find the greatest common factor of the following terms:
  • 176, 300, 390
    2
        
  • 364x10, 324x5y7
    4x5
        
16.   Factor the following polynomials:
  • 2x3 + 43x2 - 22x
    2x(x + 22)(x -
    1
    2
    )
        
  • x2 - 15x + 50
    (x - 5)(x - 10)
        
  • x5 + x4 - 20x3
    x3(x + 5)(x - 4)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    5
    and
    10


        
  • x =
    0
    ,
    -5

    and
    4
        
18.   You are seating 6 people on 6 chairs. How many different ways can those people sit?
  • 720
        
19.   Use the following data to construct a box and whiskers plot:
  • 35, 26, 33, 15, 8, 23, 30, 21, 11
        
20.   A bag contains 7 blue balls, 4 red balls, and 5 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    31.25%
        
  • A blue ball or red ball?
    68.75%
        
  • Two red balls?
    6.25%
        
  • A blue ball and a white ball?
    13.67%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 3
    x - y = 6
    A(4.5,-1.5)
        
  • 8x - 10y = 19
    x + 9y = 12

    B(3.55,0.94)
        
22.   Write the following fractions in simplest form:
  • 10xy5
    40x8y2
    y3
    4x7
        
  • (x - 4)
    (x - 4)7
    1
    (x - 4)6
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 8x - 9 = -x2
    x1 = -9,   x2 = 1
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.338
    305
    900
        
25.   Solve the following equation:
  • 18
    x
    = 3
    x = 2
        
26.   Rationalize the denominator of each fraction below:
  • 5
    3
    9 +
    21
    3
    3
    -
    7
    4
        
27.   Use a trigonometric ratio to find x:
x = 20.51 cm
    
28.   The sum of two consecutive odd integers is 24. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=11, b=13
    
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.   The sides of a square are increased by 6 m. The area of the newly created square is 256m2. What was the original length of one side of the square?
  • 10 m
        


To print this algebra practice test, click here.



Name _____________________                                        Date:_____________________


Current difficulty level: Choose test difficulty:         Easy              Challenging
(current difficulty level: Challenging)

                           

Solve the following problems:

Important instructions

(or click here to generate a new test)
1.   Multiply:   -61 and -29? 1769
    
2.   Add:   -65 and 73? 8
    
3.   Divide:   -98 and -14? 7
    
4.   Substract:   92 and -46? 138
    
5.   Calculate: |90 · -20 + 28 · -72| 3816
    
6.   Simplify the following expressions:
  • -39x – 72 + -11 -83-39x
        
  • -66x – -19x – -54x + -50x -43x
        
  • 41 + -61y – -80z + 32y + -88z – -11y 41-18y-8z
        
  • y53 × y-55 × x13 x13 × y-2
        
  • x-41
    x32
    x-73
        
  • (2x2)8 256x16
        
7.   Which of the following expressions show the associative property?
  • 2 × 1 = 2
  • 4x + 5 = 5 + 4x
  • ( m + n ) + p = m + ( n + p )
  • ( 4 + 2 ) × 3 = 3 × ( 4 + 2 )
C
    
8.   Which properties are illustrated by the following three expressions?
  • ( u + v ) + t = u + ( v + t )
  • o + p + q + 0 = o + p + q
  • k × ( l × 1 ) = ( k × l ) × 1
  • Distributive property, Associative property of addition and Associative property of multiplication
  • Associative property of addition, Identity property of addition and Associative property of multiplication
  • Identity property of addition, Identity property of multiplication and Associative property of addition
  • Associative property of multiplication, Identity property of addition and Commutative property of addition
B
    
9.   Solve the following equations for x:
  • -x · 39 = 78 x = -2
        
  • 2
    28
    x =
    8
    28
    x = 4
        
  • 30 – 7x = -5 x = 5
        
  • -a = b – ex x = (a+b)/e
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x – 17 > -34 x < 17
        
  • x ≠ -517
  • 49 < x ≤ -81
  • 30
    6
    x ≥ -
    40
    8
    x ≥ -1
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000000984 9.84 × 10-11
        
  • 128000000000 1.28 × 1011
        
12.   Add the following polynomials:
  • 17z7 + -3  and  -2z10 + 10z9 + -19z7 + -9
    -2z10 + 10z9 + -2z7 + -12
        
  • 33z19 + -23z15 + -49z14 + -21z13 + -50  and  -27z19 + 26z13 + -20 6z19 + -23z15 + -49z14 + 5z13 + -70
        
13.   Multiply the following polynomials and simplify:
  • 7x5(8x + 5)
    56x6 + 35x5
        
  • (1x5 + x2)(7x3 + 7x + 8)
    7x8 + 7x6 + 15x5 + 7x3 + 8x2
        
14.   Divide:
  • 12x2 + 29x + 15 / 4x + 3
    3x + 5
        
15.   Find the greatest common factor of the following terms:
  • 189, 273
    21
        
  • 300x10y2, 234x5y10
    6x5y2
        
16.   Factor the following polynomials:
  • 48x5 + 69x4 + 24x3
    48x3(x -
    -23 +
    17
    32
    )(x -
    -23 -
    17
    32
    )
        
  • x2 + 20x + 100
    (x + 10)(x + 10)
        
  • x5 + 3x4 - 10x3
    x3(x + 5)(x - 2)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -10
    and
    -10


        
  • x =
    0
    ,
    -5

    and
    2
        
18.   You can purchase your ice cream in a cup or a cone. Orders can be one or two scoops. Flavors can be chocolate, vanilla, strawberry, peach or kiwi. How many choices do you have?
  • 20
        
19.   Use the following data to construct a box and whiskers plot:
  • 15, 22, 31, 7, 24, 30, 37, 18, 6
        
20.   A bag contains 5 blue balls, 4 red balls, and 3 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    25.00%
        
  • A blue ball or red ball?
    75.00%
        
  • Two red balls?
    9.09%
        
  • A blue ball and a white ball?
    11.36%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 17
    x - y = -4
    A(6.5,10.5)
        
  • 3x - 8y = -12
    3x + 13y = -12

    B(-4,0)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 9)
    (x2 + 18x + 81)
    1
    x + 9
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -78 = x2 + 41x
    x1 = -2,   x2 = -39
        
24.   Convert the following repeating decimal into a fraction:
  • x = 9.4
    85
    9
        
25.   Solve the following equation:
  • 19 -
    x - 5
    = 2
    x = 294
        
26.   Rationalize the denominator of each fraction below:
  • 6
    10
    - 5
    -
    2
    10
    + 10
    5
        
27.   Use a trigonometric ratio to find x:
x = 12.12 cm
    
28.   The sum of two consecutive odd integers is 36. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=17, b=19
    
29.   After you leave your house, you walk 16 blocks north and 12 blocks east. How far are you from your house?
  • I am
    20
    blocks from my house.
        
30.   The sides of a square are increased by 8 ft. The area of the newly created square is 169ft2. What was the original length of one side of the square?
  • 5 ft
        


To print this algebra practice test, click here.



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