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Algebra test generator



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(current difficulty level: Challenging)

                           

Solve the following problems:

Important instructions

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1.   Multiply:   -33 and 57? -1881
    
2.   Add:   -80 and -85? -165
    
3.   Divide:   1 and -1? -1
    
4.   Substract:   -76 and -69? -7
    
5.   Calculate: |44 + -87 · -92 + -72| 7976
    
6.   Simplify the following expressions:
  • -73 + 57x + 48 -25+57x
        
  • -31 + -94y – -54y + 19x -31+19x-40y
        
  • 5x + -69 + 31x + 15y – -76 7+36x+15y
        
  • y97 × x23 x23 × y97
        
  • x20
    x41
    x-21
        
  • (2x)6 64x6
        
7.   Which of the following expressions show the associative property?
  • ( m + n ) + 9 = m + ( n + 9 )
  • ( x × y ) + 8 = 8 + ( y × x )
  • 0 + 8x = 8x
  • -4 + -9 = -9 + -4
A
    
8.   Which properties are illustrated by the following three expressions?
  • -11 + -8 × -13 = -8 × -13 + -11
  • 0 + 50 = 50
  • ( 13 + -6 ) + 15 = 13 + ( -6 + 15 )
  • Commutative property of addition, Identity property of addition and Associative property of addition
  • Identity property of multiplication, Commutative property of addition and Identity property of addition
  • Identity property of addition, Commutative property of addition and Distributive property
  • Identity property of multiplication, Commutative property of multiplication and Associative property of addition
A
    
9.   Solve the following equations for x:
  • 24 – -x = -7 x = -31
        
  • -
    28
    8
    =
    14
    8
    x x = -2
        
  • -1 = -16x – -95 x = 6
        
  • c – ax = fx x = c/(a+f)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x – -21 > 17 x < 4
        
  • x ≠ -411
  • 84 ≤ x > -9
  • 27
    9
    x < -12 x < -4
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000454 4.54 × 10-8
        
  • 17900000 1.79 × 107
        
12.   Add the following polynomials:
  • -6z8 + -17z4 + -5z2  and  -16z8 + 5z2 + 1
    -22z8 + -17z4 + 1
        
  • 6z15 + 48z13 + -43z6  and  -22z13 + -35z11 + -32z8 + 42z3 + -36z2 6z15 + 26z13 + -35z11 + -32z8 + -43z6 + 42z3 + -36z2
        
13.   Multiply the following polynomials and simplify:
  • (7x5 + 6x3 + 10x2)(7x4 + 6x)
    49x9 + 42x7 + 112x6 + 36x4 + 60x3
        
  • (1x3 + x)(10x3 + 10x + 1)
    10x6 + 20x4 + x3 + 10x2 + x
        
14.   Divide:
  • 15x3 - 18x2 - 40x + 48 / 5x - 6
    3x2 - 8
        
15.   Find the greatest common factor of the following terms:
  • 180, 252, 120
    12
        
  • 468x10y4, 140x6y9
    4x6y4
        
16.   Factor the following polynomials:
  • 2x5 + 15x4 + 26x3
    2x3(x -
    -15 +
    17
    4
    )(x -
    -15 -
    17
    4
    )
        
  • x2 - 5x + 4
    (x - 1)(x - 4)
        
  • x6 - 16x5 + 64x4
    x4(x - 8)(x - 8)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    1
    and
    4


        
  • x =
    0
    ,
    8

    and
    8
        
18.   You have 2 pants, 2 shirts, and 2 shoes. How many different ways can you dress?
  • 8
        
19.   Use the following data to construct a box and whiskers plot:
  • 5, 17, 6, 38, 13, 11, 7, 39
        
20.   A bag contains 3 blue balls, 4 red balls, and 6 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    46.15%
        
  • A blue ball or red ball?
    53.85%
        
  • Two red balls?
    9.47%
        
  • A blue ball and a white ball?
    10.65%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 14
    x - y = -19
    A(-2.5,16.5)
        
  • 8x - 4y = -10
    5x + 3y = 8

    B(0.05,2.59)
        
22.   Write the following fractions in simplest form:
  • 96x6y9
    24x7y8
    4y
    x
        
  • (x2 + 10x + 25)
    (x + 5)
    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.
  • 44 = x2 + 7x
    x1 = -11,   x2 = 4
        
24.   Convert the following repeating decimal into a fraction:
  • x = 6.442
    6378
    990
        
25.   Solve the following equation:
  • 24
    x
    = 2
    x = 6
        
26.   Rationalize the denominator of each fraction below:
  • 7
    2 -
    6
    -
    14 + 7
    6
    2
        
27.   Use a trigonometric ratio to find x:
x = 34.00 cm
    
28.   The sum of two consecutive even integers is 26. What are the integers? (Hint: use 2x as the first even integer)
a=12, b=14
    
29.   After you leave your house, you walk 12 blocks south and 9 blocks west. How far are you from your house?
  • I am
    15
    blocks from my house.
        
30.   The length of a rectangle is 4 more than twice its width. The area of the rectangle is 286m2. What is the length and width of the rectangle?
  • width = 11,  length = 26
        


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