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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:   -1 and 70? -70
    
2.   Add:   -97 and -87? -184
    
3.   Divide:   -42 and 6? -7
    
4.   Substract:   -94 and -45? -49
    
5.   Calculate: |42 + -71 · -99 + -95| 6976
    
6.   Simplify the following expressions:
  • 19x + -73x + -46 -46-54x
        
  • -81x – 66x – 51y + 41y -147x-10y
        
  • -51z + -96y + -44 + -36y – 72 – -17y -116-115y-51z
        
  • x77 × y-53 × x30 × x20 x127 × y-53
        
  • x23
    x-58
    x81
        
  • (4x)8 65536x8
        
7.   Which of the following expressions show the associative property?
  • ( -4 + -9 ) × -10 = -10 × ( -4 + -9 )
  • 0 + 6x = 6x
  • ( x × y ) + 4 = 4 + ( y × x )
  • ( m + n ) + 4 = m + ( n + 4 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • 87 + 0 = 87
  • h + ( i + 0 ) = ( h + i ) + 0
  • ( z + 1 ) × y = z × y + 1 × y
  • Associative property of multiplication, Identity property of multiplication and Distributive property
  • Commutative property of addition, Commutative property of multiplication and Associative property of addition
  • Identity property of addition, Associative property of addition and Distributive property
  • Commutative property of multiplication, Associative property of addition and Identity property of addition
C
    
9.   Solve the following equations for x:
  • 61 · x = 61 x = 1
        
  • 7
    28
    x = -
    7
    28
    x = -1
        
  • 63 = -51x + 12 x = -1
        
  • -b + ex = -c x = (b-c)/e
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 5x – 40 ≥ -20 x ≥ 4
        
  • x ≠ 796
  • -93 ≤ x ≤ -48
  • -34x ≥ -34 x ≤ 1
        
11.   Convert the following numbers into scientific notation:
  • 0.0000432 4.32 × 10-5
        
  • 125000 1.25 × 105
        
12.   Add the following polynomials:
  • 14z5 + -13z2 + 1z1  and  2z9 + 11z5 + -2z4 + -8z2 + 9
    2z9 + 25z5 + -2z4 + -21z2 + 1z1 + 9
        
  • -33z17 + 10z4 + 23z1  and  -2z17 + 16z9 + -22z7 + -31z4 + -10 -35z17 + 16z9 + -22z7 + -21z4 + 23z1 + -10
        
13.   Multiply the following polynomials and simplify:
  • (7x4 + 10x3 + 9x)(1x5 + 3x4 + 10x3)
    7x9 + 31x8 + 100x7 + 109x6 + 27x5 + 90x4
        
  • (5x4 - 2)(1x5 + 4x4)
    5x9 + 20x8 - 2x5 - 8x4
        
14.   Divide:
  • 10x3 + 35x2 + 20x + 73 / 2x + 7
    (5x2 + 10) with a remainder of 3
        
15.   Find the greatest common factor of the following terms:
  • 468, 260, 300
    4
        
  • 260x3y4, 390x5, 108x7y5
    2x3
        
16.   Factor the following polynomials:
  • 3x5 - 45x4 + 42x3
    3x3(x - 1)(x - 14)
        
  • x2 - 7x + 10
    (x - 5)(x - 2)
        
  • x5 + 22x4 + 105x3
    x3(x + 15)(x + 7)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    5
    and
    2


        
  • x =
    0
    ,
    -15

    and
    -7
        
18.   You have 2 pants, 2 shirts, and 4 shoes. How many different ways can you dress?
  • 16
        
19.   Use the following data to construct a box and whiskers plot:
  • 26, 36, 29, 1, 19, 20, 4, 14, 28, 12
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 12
  • What is the probability of getting heads and 7?
    4.17%
        
  • What is the probability of getting tails and an even number?
    25%
        
  • What is the probability of getting heads and a multiple of 3?
    16.67%
        
  • What is the probability of getting tails and a prime number?
    20.83%
        
  • What is the probability of not tails and not 4?
    45.83%
        
  • What is the probability of getting not tails 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 = -12
    x - y = -19
    A(-15.5,3.5)
        
  • x - 6y = 14
    x + 5y = -7

    B(2.55,-1.91)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 1)5
    (x + 1)3
    (x + 1)2
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • x2 + 90 = -21x
    x1 = -15,   x2 = -6
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.6820
    6752
    9900
        
25.   Solve the following equation:
  • -1 -
    x + 9
    = -9
    x = 55
        
26.   Rationalize the denominator of each fraction below:
  • 4
    10
    2
    10
    5
        
27.   Use a trigonometric ratio to find x:
x = 22.00 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 12 blocks south and 16 blocks east. How far are you from your house?
  • I am
    20
    blocks from my house.
        
30.   The length of a rectangle is 3 more than thrice its width. The area of the rectangle is 216ft2. What is the length and width of the rectangle?
  • width = 8,  length = 27
        


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