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# Algebra test generator

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current difficulty level: Choose test difficulty:         Easy              Challenging
(current difficulty level: Challenging)

Solve the following problems:

Important instructions

1.   Multiply:   -78 and -30? 2340

2.   Add:   -37 and -92? -129

3.   Divide:   63 and 3? 21

4.   Substract:   -46 and 94? -140

5.   Calculate: |57 + 13 · 59 + -45| 779

6.   Simplify the following expressions:
• 5x + 18x – 87 -87+23x

• 71 + -73y – 27y – 13x 71-13x-100y

• 35z – -50x – -71 + -18y + -9x 71+41x-18y+35z

• y-38 × x40 × x58 × x-62 x36 × y-38

• x-75
x-14
x-61

• (10x3)10 10000000000x30

7.   Which of the following expressions show the associative property?
• -5x + 3 = 3 + -5x
• -7 × 1 = -7
• ( x + y ) + z = x + ( y + z )
• -2 + 6 = 6 + -2
C

8.   Which properties are illustrated by the following three expressions?
• 0 + 94 = 94
• 20 + l + m = l + m + 20
• ( y + 1 ) × x = y × x + 1 × x
• Identity property of addition, Commutative property of addition and Distributive property
• Associative property of multiplication, Associative property of addition and Identity property of multiplication
• Associative property of multiplication, Associative property of addition and Distributive property
• Associative property of multiplication, Commutative property of addition and Identity property of addition
A

9.   Solve the following equations for x:
• -33 + x = 56 x = 89

• -
2
12
= -
1
6
x x = 1

• 42x – -66 = 24 x = -1

• ex = -b x = -b/e

10.   Solve the following inequalities. Then graph a) on the number line
• 15x – 19 > -4 x > 1

• x ≠ 610
• -67 ≥ x < -61
• -
39
13
x < -
12
2
x > 2

11.   Convert the following numbers into scientific notation:
• 0.00000639 6.39 × 10-6

• 314000 3.14 × 105

• 19z10 + -15z8 + -8z7 + -11z1  and  -16z10 + -14z7 + -6z2 + 4z1 + 16z1
3z10 + -15z8 + -22z7 + -6z2 + 9z1

• 31z18 + -14z9 + 33z8 + -27z2 + 34  and  -37z18 + -22z10 + 48z8 + -17z2 + -31 -6z18 + -22z10 + -14z9 + 81z8 + -44z2 + 3

13.   Multiply the following polynomials and simplify:
• (9x4 + 10x2 - 3)(9x5 + 6x3 + 7x)
81x9 + 144x7 + 96x5 + 52x3 - 21x

• (2x5 + 8x + 2)(3x4 + 2x)
6x9 + 4x6 + 24x5 + 6x4 + 16x2 + 4x

14.   Divide:
• 10x3 - 12x2 + 10x - 12 / 5x - 6
2x2 + 2

15.   Find the greatest common factor of the following terms:
• 260, 378, 195
1

• 360, 110x7y8, 294x5y2
2

16.   Factor the following polynomials:
• 42x5 - 67x4 + 26x3
42x3(x -
13
14
)(x -
2
3
)

• x2 + 3x - 54
(x + 9)(x - 6)

• x5 + 3x4 - 40x3
x3(x - 5)(x + 8)

17.   For question 16, exercises b) and c), solve for x:
• x =
-9
and
6

• x =
0
,
5

and
-8

18.   You can purchase your ice cream in a cup or a cone. Orders can be one, two, or three scoops. Flavors can be chocolate, vanilla, strawberry or peach. How many choices do you have?
• 24

19.   Use the following data to construct a box and whiskers plot:
• 9, 8, 17, 36, 23, 2, 31, 11, 27, 5 20.   Suppose you toss a coin and spin a spinner numbered 1 through 10
• What is the probability of getting tails and 9?
5.00%

• What is the probability of getting tails and an even number?
25%

• What is the probability of getting tails and a multiple of 4?
10%

• What is the probability of getting heads and a prime number?
20%

• What is the probability of not heads and not 1?
45%

• 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 = 18
x - y = 7
A(12.5,5.5)

• 3x - y = -15
7x + 7y = 9

B(-3.43,4.71)

22.   Write the following fractions in simplest form:
• 22x6y7z4
44x7y9z2
z2
2xy2

• x6 - 7x5 - 18x4
x(x + 2)
x3(x - 9)

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• x2 + 84 = -20x
x1 = -14,   x2 = -6

24.   Convert the following repeating decimal into a fraction:
• x = 0.4457
4413
9900

25.   Solve the following equation:
• 40
x
= 2
x = 10

26.   Rationalize the denominator of each fraction below:
• 7
5 -
35
-
35 + 7
35
10

27.   Use a trigonometric ratio to find x: x = 34.00 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 6 blocks east and 8 blocks south. How far are you from your house?
• I am
10
blocks from my house.

30.   Each side of a square is decreased by 10 ft. The area of the newly created square is 4ft2. What was the original length of one side of the square?
• 8 ft

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