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:   -94 and -69? 6486
    
2.   Add:   -96 and -27? -123
    
3.   Divide:   -76 and -76? 1
    
4.   Substract:   -21 and 66? -87
    
5.   Calculate: |13 · -80 + -52| 1092
    
6.   Simplify the following expressions:
  • 83x – 32 + -16 -48+83x
        
  • -36y – 11y – 93x – -5x -88x-47y
        
  • -27z – -67z + -38y + 56x – 95y + 65x 121x-133y+40z
        
  • x33 × y-6 x33 × y-6
        
  • x-13
    x75
    x-88
        
  • (10x2)2 100x4
        
7.   Which of the following expressions show the associative property?
  • ( m + n ) × 4 = 4 × ( m + n )
  • 5( 2 + 3 ) = 5×2 + 5×3
  • ( m × n ) × p = m × ( n × p )
  • 8 + 10t + 6
C
    
8.   Which properties are illustrated by the following three expressions?
  • (x + 6) × (y + 10) = (y + 10) × (x + 6)
  • 7 + ( -15 + 19 ) = ( 7 + -15 ) + 19
  • 38 × 1 = 38
  • Identity property of multiplication, Distributive property and Associative property of addition
  • Commutative property of multiplication, Identity property of addition and Commutative property of addition
  • Associative property of multiplication, Identity property of multiplication and Identity property of addition
  • Commutative property of multiplication, Associative property of addition and Identity property of multiplication
D
    
9.   Solve the following equations for x:
  • 27 = x + -71 x = 98
        
  • -
    17
    4
    =
    1
    4
    x x = -17
        
  • 95 = -70 – -3x x = 55
        
  • fx = -a – g x = (-a-g)/f
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -5x + 22 < 17 x > 1
        
  • x ≠ 749
  • 40 < x < 99
  • -
    40
    20
    x ≤ -
    18
    3
    x ≥ 3
        
11.   Convert the following numbers into scientific notation:
  • 0.000000190 1.9 × 10-7
        
  • 530000000 5.3 × 108
        
12.   Add the following polynomials:
  • -8z3 + -1z1  and  7z10 + 15z4 + 3z1
    7z10 + 15z4 + -8z3 + 2z1
        
  • 48z20 + -18z9 + -28z8 + -13z5 + 25z2  and  46z20 + -39z8 + -36z5 94z20 + -18z9 + -67z8 + -49z5 + 25z2
        
13.   Multiply the following polynomials and simplify:
  • (9x2 + 7x)(10x3 + 5x2 + 4x)
    90x5 + 115x4 + 71x3 + 28x2
        
  • (6x2 + 5)(4x4 + x3 - 8)
    24x6 + 6x5 + 20x4 + 5x3 - 48x2 - 40
        
14.   Divide:
  • 5x2 + 31x - 28 / x + 7
    5x - 4
        
15.   Find the greatest common factor of the following terms:
  • 390, 240, 405
    15
        
  • 468x6y, 288y10
    36y
        
16.   Factor the following polynomials:
  • 24x3 - 72x2 + 53x
    24x(x -
    18 +
    6
    12
    )(x -
    18 -
    6
    12
    )
        
  • x2 + 2x - 24
    (x + 6)(x - 4)
        
  • x9 - 13x8 + 22x7
    x7(x - 2)(x - 11)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -6
    and
    4


        
  • x =
    0
    ,
    2

    and
    11
        
18.   You have 3 books to read. How many different ways can you read your books?
  • 6
        
19.   Use the following data to construct a box and whiskers plot:
  • 27, 15, 4, 37, 1, 38, 39, 5, 19
        
20.   A bag contains 3 blue balls, 6 red balls, and 4 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    30.77%
        
  • A blue ball or red ball?
    69.23%
        
  • Two red balls?
    21.30%
        
  • A blue ball and a white ball?
    7.10%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -2
    x - y = -10
    A(-6,4)
        
  • 6x - 6y = 11
    3x + 7y = -9

    B(0.38,-1.45)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • x3(x - 8)
    x6 - 6x5 - 16x4
    1
    x(x + 2)
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • 29x = x2 + 78
    x1 = 26,   x2 = 3
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.486
    486
    999
        
25.   Solve the following equation:
  • 5
    x
    + 3 = 20
    x
    - 12
    x = 1
        
26.   Rationalize the denominator of each fraction below:
  • 7
    5
    15 +
    15
    3
    5
    -
    3
    6
        
27.   Use a trigonometric ratio to find x:
x = 24.25 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 4 blocks west and 3 blocks south. How far are you from your house?
  • I am
    5
    blocks from my house.
        
30.   A rectangle has a length 8 m greater than its width. The area of the rectangle is 48m2. What are the length and width of the rectangle?
  • width = 4,  length = 12
        


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:   -37 and -89? 3293
    
2.   Add:   -91 and 99? 8
    
3.   Divide:   -80 and 1? -80
    
4.   Substract:   -18 and 30? -48
    
5.   Calculate: |-4 + -32 · 40| 1284
    
6.   Simplify the following expressions:
  • 33x + -91 + 25x -91+58x
        
  • 83x + -76x – -1x + 41 41+8x
        
  • 75z + -85 + 79 – -37x – -33x -6+70x+75z
        
  • x-98 × y-15 x-98 × y-15
        
  • x5
    x73
    x-68
        
  • (7x5)3 343x15
        
7.   Which of the following expressions show the associative property?
  • 2 + 8 = 8 + 2
  • p × ( q + 9 ) = pq + 9q
  • ( x + y ) + z = x + ( y + z )
  • ( 7 + -6 ) × 6 = 6 × ( 7 + -6 )
C
    
8.   Which properties are illustrated by the following three expressions?
  • 6 + ( 14 + 7 ) = ( 6 + 14 ) + 7
  • -2 × -10 + y = y + -2 × -10
  • 1 × (r + s + t) = r + s + t
  • Associative property of addition, Commutative property of addition and Identity property of multiplication
  • Identity property of multiplication, Identity property of addition and Associative property of multiplication
  • Associative property of multiplication, Commutative property of addition and Associative property of addition
  • Identity property of addition, Commutative property of multiplication and Identity property of multiplication
A
    
9.   Solve the following equations for x:
  • -x · 36 = 72 x = -2
        
  • -
    1
    6
    x = -
    22
    12
    x = 11
        
  • 79 = 87 – 8x x = 1
        
  • -d = -b + cx x = (-d+b)/c
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 5x – -4 > -21 x > -5
        
  • x ≠ -249
  • -75 > x ≥ -70
  • 6
    3
    x ≤
    20
    5
    x ≤ 2
        
11.   Convert the following numbers into scientific notation:
  • 0.00000000847 8.47 × 10-9
        
  • 1500000 1.5 × 106
        
12.   Add the following polynomials:
  • -11z7 + -8z5 + -19z4 + -10z3 + 5  and  13z10 + 11z7 + 10z5
    13z10 + 2z5 + -19z4 + -10z3 + 5
        
  • 30z16 + -9z14 + 30z11  and  -26z16 + -39z14 + -15z11 4z16 + -48z14 + 15z11
        
13.   Multiply the following polynomials and simplify:
  • (2x5 + 8x2)7x3
    14x8 + 56x5
        
  • (5x3 - 10)(9x5 + 7x + 7)
    45x8 - 90x5 + 35x4 + 35x3 - 70x - 70
        
14.   Divide:
  • 5x2 + 26x - 63 / 5x - 9
    x + 7
        
15.   Find the greatest common factor of the following terms:
  • 286, 180
    2
        
  • 48y6, 162x3y9
    6y6
        
16.   Factor the following polynomials:
  • 30x4 + 17x3 - 9x2
    30x2(x -
    1
    3
    )(x +
    9
    10
    )
        
  • x2 + 6x + 5
    (x + 1)(x + 5)
        
  • x4 - 10x3 + 21x2
    x2(x - 3)(x - 7)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -1
    and
    -5


        
  • x =
    0
    ,
    3

    and
    7
        
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:
  • 40, 31, 17, 15, 22, 38, 25, 16, 1, 20
        
20.   A bag contains 4 blue balls, 6 red balls, and 7 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
  • A white ball?
    41.18%
        
  • A blue ball or red ball?
    58.82%
        
  • Two red balls?
    11.03%
        
  • A blue ball and a white ball?
    10.29%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 2
    x - y = -1
    A(0.5,1.5)
        
  • 4x - 9y = 2
    7x + 3y = 3

    B(0.44,-0.03)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • x4(x + 8)
    x3 + 13x2 + 40x
    x3
    (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.
  • x2 + 14 = -15x
    x1 = -14,   x2 = -1
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.4
    4
    9
        
25.   Solve the following equation:
  • -13 +
    4x + 5
    = -10
    x = 1
        
26.   Rationalize the denominator of each fraction below:
  • 15
    7 -
    5
    105 + 15
    5
    44
        
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 8 blocks east 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 5 m less than its length. The area of the rectangle is 266m2. What are the dimensions of the rectangle?
  • width = 14,  length = 19
        


To print this algebra practice test, click here.



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