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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:   -45 and -91? 4095
    
2.   Add:   -38 and -85? -123
    
3.   Divide:   -61 and 1? -61
    
4.   Substract:   21 and 5? 16
    
5.   Calculate: |-81 · 51 + 96| 4035
    
6.   Simplify the following expressions:
  • 62x – 85x – -48x 25x
        
  • 93y – -25x + 52x + -51y 77x+42y
        
  • 46y – 8z + 49x + -32z – 65y – -25y 49x+6y-40z
        
  • x-69 × x-61 × y-41 × y-25 x-130 × y-66
        
  • x-31
    x-67
    x36
        
  • (8x)3 512x3
        
7.   Which of the following expressions show the associative property?
  • n × ( o + 2 ) = no + 2o
  • 7( 1 + 9 ) = 7×1 + 7×9
  • ( x + y ) + z = x + ( y + z )
  • 6 + 5d + 3
C
    
8.   Which properties are illustrated by the following three expressions?
  • ( r × s ) × q = r × ( s × q )
  • n × ( o + p ) = n × o + n × p
  • (b + 7) × 1 = b + 7
  • Identity property of addition, Associative property of multiplication and Commutative property of addition
  • Associative property of addition, Commutative property of multiplication and Commutative property of addition
  • Associative property of multiplication, Distributive property and Identity property of multiplication
  • Commutative property of multiplication, Commutative property of addition and Identity property of multiplication
C
    
9.   Solve the following equations for x:
  • 78 = -78 · -x x = 1
        
  • 25
    22
    x =
    25
    22
    x = 1
        
  • 6 – 2x = -96 x = 51
        
  • -g + dx = -fx x = g/(d+f)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x – 29 < 18 x > -47
        
  • x ≠ -348
  • 52 ≤ x < -24
  • -
    36
    18
    x >
    18
    9
    x < -1
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000177 1.77 × 10-8
        
  • 407000 4.07 × 105
        
12.   Add the following polynomials:
  • -7z7 + 9z3 + -3  and  -11z9 + 15z7 + 18z6 + 12z3 + 3z1
    -11z9 + 8z7 + 18z6 + 21z3 + 3z1 + -3
        
  • -2z9 + 7z8 + 49z6  and  3z9 + -4z8 + -12z7 1z9 + 3z8 + -12z7 + 49z6
        
13.   Multiply the following polynomials and simplify:
  • 10x(4x3 + 5x2)
    40x4 + 50x3
        
  • (8x3 + 9x2 + 2)(9x2 + 3x)
    72x5 + 105x4 + 27x3 + 18x2 + 6x
        
14.   Divide:
  • 3x2 - 16x - 60 / x - 8
    (3x + 8) with a remainder of 4
        
15.   Find the greatest common factor of the following terms:
  • 66, 50
    2
        
  • 450x4y7, 495x5y2, 330x5y9
    15x4y2
        
16.   Factor the following polynomials:
  • 12x3 + 54x2 + 57x
    12x(x -
    -9 +
    5
    4
    )(x -
    -9 -
    5
    4
    )
        
  • x2 + 3x - 28
    (x + 7)(x - 4)
        
  • x9 - x8 - 90x7
    x7(x - 10)(x + 9)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -7
    and
    4


        
  • x =
    0
    ,
    10

    and
    -9
        
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:
  • 35, 12, 21, 13, 39, 2, 18, 28
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 16
  • What is the probability of getting heads and 15?
    3.13%
        
  • What is the probability of getting heads and an odd number?
    25%
        
  • What is the probability of getting heads and a multiple of 7?
    6.25%
        
  • What is the probability of getting tails and a prime number?
    18.75%
        
  • What is the probability of not heads and not 5?
    46.88%
        
  • What is the probability of getting not heads and not a whole number?
    0%
        
  • What is the probability of heads or tails and a whole number?
    100%
        
  • What is the probability of getting tails?
    50%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -1
    x - y = -8
    A(-4.5,3.5)
        
  • x - 9y = 8
    8x + y = -10

    B(-1.12,-1.01)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 4)
    (x2 + 8x + 16)
    1
    x + 4
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -8x - 33 = -x2
    x1 = -3,   x2 = 11
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.53
    48
    90
        
25.   Solve the following equation:
  • 15
    x
    = 1
    x = 225
        
26.   Rationalize the denominator of each fraction below:
  • 7
    30
    7
    30
    30
        
27.   Use a trigonometric ratio to find x:
x = 17.32 cm
    
28.   The sum of two consecutive even integers is 42. What are the integers? (Hint: use 2x as the first even integer)
a=20, b=22
    
29.   After you leave your house, you walk 15 blocks south and 8 blocks west. How far are you from your house?
  • I am
    17
    blocks from my house.
        
30.   The length of a rectangle is 8 more than twice its width. The area of the rectangle is 120m2. What is the length and width of the rectangle?
  • width = 6,  length = 20
        


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