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:   -70 and 46? -3220
    
2.   Add:   -61 and -90? -151
    
3.   Divide:   -18 and -1? 18
    
4.   Substract:   -39 and -15? -24
    
5.   Calculate: |4 + -68 · -91 + 15| 6207
    
6.   Simplify the following expressions:
  • -59x – -71 – 66 5-59x
        
  • -11y + 42 – 70 – 93x -28-93x-11y
        
  • 5 – 82x + 42y + 7z – 35 – -2 -28-82x+42y+7z
        
  • y-35 × x-96 × y-66 × x-4 x-100 × y-101
        
  • x21
    x-90
    x111
        
  • (4x)7 16384x7
        
7.   Which of the following expressions show the associative property?
  • 4x + 10 = 10 + 4x
  • ( 6 × -5 ) + 10 = 10 + ( 6 × -5 )
  • 3( 4 + 7 ) = 3×4 + 3×7
  • ( m × n ) × 8 = m × ( n × 8 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • (a + b + c) × 1 = a + b + c
  • 16 × -14 = 16 × -14
  • ( 20 × 2 ) × 19 = 20 × ( 2 × 19 )
  • Identity property of multiplication, Commutative property of multiplication and Associative property of multiplication
  • Identity property of addition, Identity property of multiplication and Associative property of addition
  • Distributive property, Commutative property of addition and Associative property of multiplication
  • Associative property of addition, Commutative property of multiplication and Associative property of multiplication
A
    
9.   Solve the following equations for x:
  • 70 + -x = -65 x = 135
        
  • -
    21
    17
    =
    1
    17
    x x = -21
        
  • 84 = -13x + 71 x = -1
        
  • dx = c – ex x = c/(d+e)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -15x + -25 ≤ 35 x ≥ -4
        
  • x ≠ -237
  • 26 ≥ x > 21
  • -
    8
    4
    x > -
    16
    2
    x < 4
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000000930 9.3 × 10-11
        
  • 646000 6.46 × 105
        
12.   Add the following polynomials:
  • -5z10 + 13z8 + 2z6 + 18z5 + 19z3  and  -13z10 + -9z6 + 9z3
    -18z10 + 13z8 + -7z6 + 18z5 + 28z3
        
  • 49z10 + -9z9 + -50z7 + 13z2  and  30z9 + -10z7 + -13z2 49z10 + 21z9 + -60z7
        
13.   Multiply the following polynomials and simplify:
  • (4x4 + 5x2 + 7x)(9x5 + 3x3)
    36x9 + 57x7 + 63x6 + 15x5 + 21x4
        
  • (6x4 + 7x)(5x3 + 9x2 + 6)
    30x7 + 54x6 + 71x4 + 63x3 + 42x
        
14.   Divide:
  • 10x2 - 45x + 35 / 5x - 5
    2x - 7
        
15.   Find the greatest common factor of the following terms:
  • 78, 180, 60
    6
        
  • 147xy7, 300y2
    3y2
        
16.   Factor the following polynomials:
  • 6x3 - 14x2 + 6x
    6x(x -
    7 +
    13
    6
    )(x -
    7 -
    13
    6
    )
        
  • x2 + 8x + 7
    (x + 7)(x + 1)
        
  • x5 - 19x4 + 70x3
    x3(x - 5)(x - 14)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -7
    and
    -1


        
  • x =
    0
    ,
    5

    and
    14
        
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:
  • 16, 10, 25, 7, 22, 26, 27, 31, 20
        
20.   A bag contains 6 blue balls, 4 red balls, and 4 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    28.57%
        
  • A blue ball or red ball?
    71.43%
        
  • Two red balls?
    6.59%
        
  • A blue ball and a white ball?
    13.19%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -20
    x - y = -15
    A(-17.5,-2.5)
        
  • 5x - 9y = 17
    6x + y = -6

    B(-0.63,-2.24)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 5)
    (x2 + 10x + 25)
    1
    x + 5
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 14 = x2 + 5x
    x1 = -7,   x2 = 2
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.5
    5
    9
        
25.   Solve the following equation:
  • 13
    x
    = 4
    x =
    169
    16
        
26.   Rationalize the denominator of each fraction below:
  • 10
    6
    5 +
    2
    50
    6
    - 20
    3
    23
        
27.   Use a trigonometric ratio to find x:
x = 15.59 cm
    
28.   The sum of two consecutive odd integers is 28. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=13, b=15
    
29.   After you leave your house, you walk 12 blocks south and 5 blocks east. How far are you from your house?
  • I am
    13
    blocks from my house.
        
30.   The sides of a square are increased by 6 ft. The area of the newly created square is 361ft2. What was the original length of one side of the square?
  • 13 ft
        


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:   -20 and 4? -80
    
2.   Add:   -39 and -38? -77
    
3.   Divide:   88 and -22? -4
    
4.   Substract:   -27 and 99? -126
    
5.   Calculate: |83 · 3 + -48| 201
    
6.   Simplify the following expressions:
  • 70x + -72x – -74 74-2x
        
  • -96x – 68y – -62y – 71x -167x-6y
        
  • -2y + 77y – 49 – 19x + 57x + 24 -25+38x+75y
        
  • x-17 × y-87 × y-92 x-17 × y-179
        
  • x-96
    x44
    x-140
        
  • (10x)4 10000x4
        
7.   Which of the following expressions show the associative property?
  • ( 9 × 6 ) × 4 = 9 × ( 6 × 4 )
  • a + b = b + a
  • ( x × y ) + 6 = 6 + ( y × x )
  • -4 + -10 = -10 + -4
A
    
8.   Which properties are illustrated by the following three expressions?
  • (h + i) × 2 = 2 × (h + i)
  • 0 + e + 4 = e + 4
  • a × ( b × 1 ) = ( a × b ) × 1
  • Commutative property of multiplication, Associative property of multiplication and Identity property of multiplication
  • Commutative property of multiplication, Identity property of addition and Associative property of multiplication
  • Commutative property of addition, Commutative property of multiplication and Identity property of addition
  • Associative property of addition, Associative property of multiplication and Identity property of multiplication
B
    
9.   Solve the following equations for x:
  • 10 = x · 10 x = 1
        
  • -
    8
    17
    = -
    2
    17
    x x = 4
        
  • 89 + -29x = 60 x = 1
        
  • cx = -a x = -a/c
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x + -24 < 29 x > -53
        
  • x ≠ -449
  • -83 ≤ x ≤ 41
  • -5x > 10 x < -2
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000000214 2.14 × 10-11
        
  • 92600000000 9.26 × 1010
        
12.   Add the following polynomials:
  • 10z8 + -14z5 + 3z3 + 2z1  and  4z9 + -13z8 + 16z5 + -10z3 + 11z1
    4z9 + -3z8 + 2z5 + -7z3 + 13z1
        
  • 2z13 + 18z8 + 47z4 + 29  and  40z8 + -43z6 + -40z4 + -4z1 + 1 2z13 + 58z8 + -43z6 + 7z4 + -4z1 + 30
        
13.   Multiply the following polynomials and simplify:
  • (5x4 + 3)3x4
    15x8 + 9x4
        
  • (9x4 + 7)(4x4 + x)
    36x8 + 9x5 + 28x4 + 7x
        
14.   Divide:
  • 20x2 - 45x + 25 / 4x - 5
    5x - 5
        
15.   Find the greatest common factor of the following terms:
  • 200, 390
    10
        
  • 468x2y8, 264x6y2, 252x5y3
    12x2y2
        
16.   Factor the following polynomials:
  • 21x5 - 21x4 - 42x3
    21x3(x + 1)(x - 2)
        
  • x2 - 6x - 27
    (x + 3)(x - 9)
        
  • x4 - 10x3 - 75x2
    x2(x - 15)(x + 5)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -3
    and
    9


        
  • x =
    0
    ,
    15

    and
    -5
        
18.   You are seating 8 people on 8 chairs. How many different ways can those people sit?
  • 40320
        
19.   Use the following data to construct a box and whiskers plot:
  • 20, 25, 39, 21, 14, 11, 2
        
20.   A bag contains 2 blue balls, 6 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?
    38.46%
        
  • A blue ball or red ball?
    61.54%
        
  • Two red balls?
    21.30%
        
  • A blue ball and a white ball?
    5.92%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -11
    x - y = -10
    A(-10.5,-0.5)
        
  • 6x - 3y = 14
    6x + 7y = 16

    B(2.43,0.2)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x - 1)6
    (x - 1)
    (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.
  • 4x - 60 = -x2
    x1 = -10,   x2 = 6
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.35
    35
    99
        
25.   Solve the following equation:
  • 4
    x
    = 8
    x =
    16
    64
        
26.   Rationalize the denominator of each fraction below:
  • 15
    27
    5
    3
    3
        
27.   Use a trigonometric ratio to find x:
x = 13.28 cm
    
28.   The sum of two consecutive even integers is 54. What are the integers? (Hint: use 2x as the first even integer)
a=26, b=28
    
29.   After you leave your house, you walk 12 blocks north and 5 blocks west. How far are you from your house?
  • I am
    13
    blocks from my house.
        
30.   The length of a rectangle is 10 less than 2 times the width. What are the dimensions of the rectangle if the area is 252ft2?
  • width = 14,  length = 18
        


To print this algebra practice test, click here.



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