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Algebra test generator



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(current difficulty level: Easy)

                           

Solve the following problems:

Important instructions

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1.   Multiply:   -18 and -18? 324
    
2.   Add:   7 and 2? 9
    
3.   Divide:   11 and 1? 11
    
4.   Substract:   -1 and 18? -19
    
5.   Calculate: |8 · 15 + 10| 130
    
6.   Simplify the following expressions:
  • 5x – 17x – 17 -17-12x
        
  • 7x + 5y + -19x – 6y -12x-1y
        
  • 15 – -20x – 10x + -19x + 9z 15-9x+9z
        
  • x-18 × x-4 × x-18 × x8 x-32
        
  • x-3
    x13
    x-16
        
  • (2x2)8 256x16
        
7.   Which of the following expressions show the associative property?
  • ( x + y ) × 2 = 2 × ( y + x )
  • a + b = b + a
  • ( m × n ) + 6 = 6 + ( m × n )
  • ( m + n ) + 2 = m + ( n + 2 )
D
    
8.   Which properties are illustrated by the following three expressions?
  • 67 + 53 = 67 + 53
  • (t + u) × 1 = t + u
  • (z + -4) × (y + -3) = (y + -3) × (z + -4)
  • Identity property of addition, Commutative property of multiplication and Distributive property
  • Identity property of addition, Commutative property of multiplication and Commutative property of addition
  • Identity property of addition, Commutative property of addition and Identity property of multiplication
  • Commutative property of addition, Identity property of multiplication and Commutative property of multiplication
D
    
9.   Solve the following equations for x:
  • 12 + x = -2 x = -14
        
  • 23
    25
    =
    23
    25
    x x = 1
        
  • -60 = 28x + 52 x = -4
        
  • -f = bx – c x = (-f+c)/b
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -19x + -39 ≥ 37 x ≤ -4
        
  • x ≠ 587
  • 53 > x < -97
  • 26
    13
    x ≤ -
    30
    5
    x ≤ -3
        
11.   Convert the following numbers into scientific notation:
  • 0.000787 7.87 × 10-4
        
  • 48700000000 4.87 × 1010
        
12.   Add the following polynomials:
  • -3z10 + -15z9 + 13z8 + 9z6 + 3z4  and  -10z6 + -12z4
    -3z10 + -15z9 + 13z8 + -1z6 + -9z4
        
  • 3z10 + 1z7 + 10z6 + -8z5 + -6z5  and  -13z19 + 8z11 + 10z7 + -12z5 + -6z4 -13z19 + 8z11 + 3z10 + 11z7 + 10z6 + -26z5 + -6z4
        
13.   Multiply the following polynomials and simplify:
  • (5x5 + 6x4 - 6)(9x4 + x)
    45x9 + 54x8 + 5x6 + 6x5 - 54x4 - 6x
        
  • (1x4 + 9)(9x5 + 8x3 - 9)
    9x9 + 8x7 + 81x5 - 9x4 + 72x3 - 81
        
14.   Divide:
  • 16x2 - 4x - 56 / 4x + 7
    4x - 8
        
15.   Find the greatest common factor of the following terms:
  • 56, 28
    28
        
  • 90x9y5, 72x3y2, 75x2y7
    3x2y2
        
16.   Factor the following polynomials:
  • 3x3 + 65x2 - 22x
    3x(x -
    1
    3
    )(x + 22)
        
  • x2 + 10x + 21
    (x + 3)(x + 7)
        
  • x8 - 4x7 - 96x6
    x6(x + 8)(x - 12)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -3
    and
    -7


        
  • x =
    0
    ,
    -8

    and
    12
        
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:
  • 10, 38, 40, 9, 11, 31, 2, 17, 27, 35
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 20
  • What is the probability of getting heads and 11?
    2.50%
        
  • What is the probability of getting tails and an even number?
    25%
        
  • What is the probability of getting tails and a multiple of 5?
    10%
        
  • What is the probability of getting tails and a prime number?
    20%
        
  • What is the probability of not tails and not 7?
    47.5%
        
  • 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 = 15
    x - y = 14
    A(14.5,0.5)
        
  • 3x - 10y = -9
    10x + 3y = -4

    B(-0.61,0.72)
        
22.   Write the following fractions in simplest form:
  • 23x4y8
    46x8y4
    y4
    2x4
        
  • (x2 - 14x + 49)
    (x - 7)
    x - 7
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • x2 + 41x = -78
    x1 = -2,   x2 = -39
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.31
    28
    90
        
25.   Solve the following equation:
  • 13 -
    3x - 2
    = -6
    x = 121
        
26.   Rationalize the denominator of each fraction below:
  • 3
    2
    - 10
    -
    3
    2
    + 30
    98
        
27.   Use a trigonometric ratio to find x:
x = 36.37 cm
    
28.   The sum of two consecutive odd integers is 24. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=11, b=13
    
29.   After you leave your house, you walk 6 blocks south and 8 blocks east. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   A rectangle has a width that is 2 m less than its length. The area of the rectangle is 224m2. What are the dimensions of the rectangle?
  • width = 14,  length = 16
        


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