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:   65 and 93? 6045
    
2.   Add:   46 and -55? -9
    
3.   Divide:   77 and 1? 77
    
4.   Substract:   65 and -74? 139
    
5.   Calculate: |42 · -87 + 100 · 89| 5246
    
6.   Simplify the following expressions:
  • -40x – 33 + -7 -40-40x
        
  • -88x – 17 + -71x + 97y -17-159x+97y
        
  • 1x + 68x + 53z – 57z – 6 + -76x -6-7x-4z
        
  • y-57 × y-83 y-140
        
  • x54
    x83
    x-29
        
  • (3x5)8 6561x40
        
7.   Which of the following expressions show the associative property?
  • -8x + -3 = -3 + -8x
  • ( m + n ) × 7 = 7 × ( m + n )
  • ( m + n ) + 8 = m + ( n + 8 )
  • 8 + 4z + 5
C
    
8.   Which properties are illustrated by the following three expressions?
  • z + -6 × -2 = -6 × -2 + z
  • 18 + ( -10 + 14 ) = ( 18 + -10 ) + 14
  • 81 × 1 = 81
  • Associative property of addition, Identity property of addition and Associative property of multiplication
  • Distributive property, Commutative property of multiplication and Identity property of addition
  • Commutative property of addition, Associative property of addition and Identity property of multiplication
  • Associative property of addition, Commutative property of multiplication and Associative property of multiplication
C
    
9.   Solve the following equations for x:
  • x + -26 = -29 x = -3
        
  • -
    29
    7
    x =
    29
    7
    x = -1
        
  • -40x – 97 = -57 x = -1
        
  • fx + bx = -d x = (-d)/(f+b)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -7x + -11 > 3 x < -2
        
  • x ≠ -701
  • 3 ≥ x > -91
  • -
    32
    16
    x > -
    36
    2
    x < 9
        
11.   Convert the following numbers into scientific notation:
  • 0.000000649 6.49 × 10-7
        
  • 50700000 5.07 × 107
        
12.   Add the following polynomials:
  • -8z10 + -15z8 + -5z4  and  -15z10 + -1z4 + -17z4
    -23z10 + -15z8 + -23z4
        
  • 5z14 + 46z10 + -14z5 + 48  and  -11z16 + -26z14 + -15z10 + -41z7 + 5 -11z16 + -21z14 + 31z10 + -41z7 + -14z5 + 53
        
13.   Multiply the following polynomials and simplify:
  • (2x5 + 6x)2x3
    4x8 + 12x4
        
  • (3x3 + 3x2 + 2x)(9x4 + 3x + 3)
    27x7 + 27x6 + 18x5 + 9x4 + 18x3 + 15x2 + 6x
        
14.   Divide:
  • 8x2 + 26x - 45 / 4x - 5
    2x + 9
        
15.   Find the greatest common factor of the following terms:
  • 375, 180
    15
        
  • 450y8, 65x9y4, 336y4
    y4
        
16.   Factor the following polynomials:
  • 30x3 - 12x2 + 1x
    30x(x -
    6 +
    6
    30
    )(x -
    6 -
    6
    30
    )
        
  • x2 - 4x - 5
    (x - 5)(x + 1)
        
  • x5 - 8x4 + 7x3
    x3(x - 7)(x - 1)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    5
    and
    -1


        
  • x =
    0
    ,
    7

    and
    1
        
18.   You have 2 pants, 3 shirts, and 2 shoes. How many different ways can you dress?
  • 12
        
19.   Use the following data to construct a box and whiskers plot:
  • 18, 6, 21, 31, 30, 8, 29, 14, 20, 22
        
20.   A bag contains 3 blue balls, 6 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?
    22.73%
        
  • A blue ball and a white ball?
    6.82%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 17
    x - y = 10
    A(13.5,3.5)
        
  • 7x - 8y = -20
    4x + 8y = -4

    B(-2.18,0.59)
        
22.   Write the following fractions in simplest form:
  • 14x10y
    42x9y
    x
    3
        
  • (x + 2)2
    (x + 2)5
    1
    (x + 2)3
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -x2 = -4x - 12
    x1 = -2,   x2 = 6
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.573
    5680
    9900
        
25.   Solve the following equation:
  • -3
    x
    - 3 = -6
    x
    + 15
    x = 36
        
26.   Rationalize the denominator of each fraction below:
  • 6
    21
    + 3
    21
    - 3
    2
        
27.   Use a trigonometric ratio to find x:
x = 16.17 cm
    
28.   The sum of two consecutive odd integers is 40. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=19, b=21
    
29.   After you leave your house, you walk 8 blocks west and 6 blocks south. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   A rectangle has a width that is 3 m less than its length. The area of the rectangle is 180m2. What are the dimensions of the rectangle?
  • width = 12,  length = 15
        


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:   -72 and 99? -7128
    
2.   Add:   -51 and -13? -64
    
3.   Divide:   3 and -1? -3
    
4.   Substract:   76 and 15? 61
    
5.   Calculate: |-81 + -83 · -13| 998
    
6.   Simplify the following expressions:
  • -32 – 48x – 47x -32-95x
        
  • 67x – 96y + -76 + 91x -76+158x-96y
        
  • 28 + -84y + -89 + -29y + 76 – 66x 15-66x-113y
        
  • y31 × y54 y85
        
  • x-29
    x75
    x-104
        
  • (9x)4 6561x4
        
7.   Which of the following expressions show the associative property?
  • n × ( o + 8 ) = no + 8o
  • ( -3 × 10 ) + 5 = 5 + ( -3 × 10 )
  • ( 3 + 9 ) + 2 = 3 + ( 9 + 2 )
  • 6 + 7b + 10
C
    
8.   Which properties are illustrated by the following three expressions?
  • 0 + -35 = -35
  • 20 × -7 = 20 × -7
  • k + ( l + m ) = ( k + l ) + m
  • Identity property of addition, Commutative property of multiplication and Associative property of addition
  • Commutative property of multiplication, Identity property of multiplication and Identity property of addition
  • Associative property of multiplication, Commutative property of addition and Distributive property
  • Distributive property, Associative property of addition and Identity property of multiplication
A
    
9.   Solve the following equations for x:
  • x · 28 = -28 x = -1
        
  • -
    21
    25
    = -
    7
    25
    x x = 3
        
  • -64 = 4 – -17x x = -4
        
  • c – bx = g x = (c-g)/b
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x + -12 < 34 x > -46
        
  • x ≠ -208
  • -83 > x > -81
  • -
    16
    8
    x > -
    28
    7
    x < 2
        
11.   Convert the following numbers into scientific notation:
  • 0.000000530 5.3 × 10-7
        
  • 75200000 7.52 × 107
        
12.   Add the following polynomials:
  • -6z6 + 15z5  and  1z8 + -8z6 + -18z5 + -14z4 + 12z3
    1z8 + -14z6 + -3z5 + -14z4 + 12z3
        
  • -43z20 + 36z15 + -5z13 + -46z6 + -4z2  and  24z20 + 29z13 + -18z6 + -48z2 -19z20 + 36z15 + 24z13 + -64z6 + -52z2
        
13.   Multiply the following polynomials and simplify:
  • 3x5(7x5 + 6x2 + 6x)
    21x10 + 18x7 + 18x6
        
  • (1x5 + 4x4 + 5)(1x5 + 3x4)
    x10 + 7x9 + 12x8 + 5x5 + 15x4
        
14.   Divide:
  • 8x2 - 28x + 22 / 2x - 5
    (4x - 4) with a remainder of 2
        
15.   Find the greatest common factor of the following terms:
  • 270, 120
    30
        
  • 468x5y6, 180x6y3
    36x5y3
        
16.   Factor the following polynomials:
  • 18x4 + 10x3 + 1x2
    18x2(x -
    -5 +
    7
    18
    )(x -
    -5 -
    7
    18
    )
        
  • x2 + 9x - 10
    (x - 1)(x + 10)
        
  • x4 + 0x3 - 25x2
    x2(x + 5)(x - 5)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    1
    and
    -10


        
  • x =
    0
    ,
    -5

    and
    5
        
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:
  • 23, 21, 26, 17, 34, 37, 7
        
20.   A bag contains 5 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?
    35.71%
        
  • A blue ball or red ball?
    64.29%
        
  • Two red balls?
    8.16%
        
  • A blue ball and a white ball?
    12.76%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 2
    x - y = -11
    A(-4.5,6.5)
        
  • 5x - 10y = -10
    8x + y = 4

    B(0.35,1.18)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 1)5
    (x + 1)6
    1
    x + 1
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • x2 + 2x = 3
    x1 = -3,   x2 = 1
        
24.   Convert the following repeating decimal into a fraction:
  • x = 6.41
    577
    90
        
25.   Solve the following equation:
  • 5
    x
    - 18 = 4
    x
    + 10
    x = 784
        
26.   Rationalize the denominator of each fraction below:
  • 10
    6
    - 6
    -
    6
    + 6
    3
        
27.   Use a trigonometric ratio to find x:
x = 13.86 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 east and 9 blocks south. How far are you from your house?
  • I am
    15
    blocks from my house.
        
30.   A rectangle has an area of 228m2. Its width is 7 m less than its length. What are the dimensions of the rectangle?
  • width = 12,  length = 19
        


To print this algebra practice test, click here.



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