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Algebra test generator



Name _____________________                                        Date:_____________________


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(current difficulty level: Challenging)

                           

Solve the following problems:

Important instructions

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1.   Multiply:   -92 and 20? -1840
    
2.   Add:   93 and -44? 49
    
3.   Divide:   77 and 7? 11
    
4.   Substract:   -9 and 70? -79
    
5.   Calculate: |96 · 20 + -69 · 10| 1230
    
6.   Simplify the following expressions:
  • -14 – -1x – 10 -24+1x
        
  • -65x + -51 – 5y + -42 -93-65x-5y
        
  • 22z + 57 + -87z – -57 – -64z 114-1z
        
  • y54 × x-58 × x19 × y98 x-39 × y152
        
  • x-10
    x31
    x-41
        
  • (6x2)8 1679616x16
        
7.   Which of the following expressions show the associative property?
  • ( 1 + -1 ) × 2 = 2 × ( 1 + -1 )
  • ( m × n ) × 6 = m × ( n × 6 )
  • q × ( r + 8 ) = qr + 8r
  • ( x + y ) × 8 = 8 × ( y + x )
B
    
8.   Which properties are illustrated by the following three expressions?
  • -17 + ( -16 + -20 ) = ( -17 + -16 ) + -20
  • n + o + 0 = n + o
  • (i + j) × 1 = i + j
  • Associative property of multiplication, Identity property of addition and Commutative property of multiplication
  • Associative property of addition, Identity property of addition and Identity property of multiplication
  • Identity property of multiplication, Associative property of multiplication and Distributive property
  • Commutative property of addition, Identity property of addition and Commutative property of multiplication
B
    
9.   Solve the following equations for x:
  • -100 = -x – 58 x = 42
        
  • -
    19
    17
    x = -
    19
    17
    x = 1
        
  • 87 = -35 + -61x x = -2
        
  • -bx – f = -gx x = f/(-b+g)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x – -26 ≥ 40 x ≤ -14
        
  • x ≠ -76
  • 41 ≤ x ≤ -80
  • 24
    8
    x ≥ -
    27
    3
    x ≥ -3
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000000895 8.95 × 10-11
        
  • 203000000 2.03 × 108
        
12.   Add the following polynomials:
  • -4z9 + -5z5  and  -20z5 + 4z2 + 6z1
    -4z9 + -25z5 + 4z2 + 6z1
        
  • 20z19 + 16z18 + 46z8 + 1z6 + 2z5  and  32z19 + 25z18 + -36z8 + 5z6 + -49z5 52z19 + 41z18 + 10z8 + 6z6 + -47z5
        
13.   Multiply the following polynomials and simplify:
  • (7x4 + 8x)(3x4 + 5x + 4)
    21x8 + 59x5 + 28x4 + 40x2 + 32x
        
  • (2x3 - 10)(7x5 + 5x2 - 4)
    14x8 - 60x5 - 8x3 - 50x2 + 40
        
14.   Divide:
  • 16x2 + 28x + 33 / 4x + 6
    (4x + 1) with a remainder of 27
        
15.   Find the greatest common factor of the following terms:
  • 252, 108, 440
    4
        
  • 300x7y6, 117x5y, 351xy2
    3xy
        
16.   Factor the following polynomials:
  • 28x4 - 29x3 - 80x2
    28x2(x -
    16
    7
    )(x +
    5
    4
    )
        
  • x2 + 6x + 5
    (x + 1)(x + 5)
        
  • x5 + 27x4 + 180x3
    x3(x + 12)(x + 15)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -1
    and
    -5


        
  • x =
    0
    ,
    -12

    and
    -15
        
18.   You have 4 CDs. How many different ways can you listen to them?
  • 24
        
19.   Use the following data to construct a box and whiskers plot:
  • 32, 11, 1, 13, 25, 33, 31, 39, 29, 28
        
20.   A bag contains 4 blue balls, 4 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?
    20.00%
        
  • A blue ball or red ball?
    80.00%
        
  • Two red balls?
    13.33%
        
  • A blue ball and a white ball?
    8.89%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -9
    x - y = 8
    A(-0.5,-8.5)
        
  • 10x - 2y = -3
    6x + 5y = -8

    B(-0.5,-1)
        
22.   Write the following fractions in simplest form:
  • 96x3y4
    24x8y9
    4
    x5y5
        
  • (x - 3)7
    (x - 3)2
    (x - 3)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 + 7x = 78
    x1 = 6,   x2 = -13
        
24.   Convert the following repeating decimal into a fraction:
  • x = 5.52
    547
    99
        
25.   Solve the following equation:
  • -3
    x
    + 3 = -5
    x
    + 17
    x = 49
        
26.   Rationalize the denominator of each fraction below:
  • 7
    5
    1 +
    15
    -
    5
    - 5
    3
    2
        
27.   Use a trigonometric ratio to find x:
x = 15.56 cm
    
28.   The sum of two consecutive even integers is 30. What are the integers? (Hint: use 2x as the first even integer)
a=14, b=16
    
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 length of a rectangle is 2 more than twice its width. The area of the rectangle is 84m2. What is the length and width of the rectangle?
  • width = 6,  length = 14
        


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