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# Algebra test generator

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   -6 and -1? 6

2.   Add:   -6 and -19? -25

3.   Divide:   20 and 10? 2

4.   Substract:   8 and -5? 13

5.   Calculate: |-6 · 16 + -7 · -7| 47

6.   Simplify the following expressions:
• -6x + -13x + 19x

• -5y + 5x + 3 + -7 -4+5x-5y

• -4x – 18x + -6y + -20y + 13y – 9x -31x-13y

• x15 × x-1 × x-16 x-2

• x8
x-4
x12

• (4x2)10 1048576x20

7.   Which of the following expressions show the associative property?
• 0 + -9x = -9x
• ( -10 × 7 ) + -2 = -2 + ( -10 × 7 )
• ( m + n ) + 8 = m + ( n + 8 )
• ( x × y ) + 7 = 7 + ( y × x )
C

8.   Which properties are illustrated by the following three expressions?
• ( z + 0 ) × y = z × y + 0 × y
• g + ( h + 0 ) = ( g + h ) + 0
• ( 16 × -8 ) × 12 = 16 × ( -8 × 12 )
• Commutative property of addition, Associative property of addition and Distributive property
• Distributive property, Associative property of addition and Associative property of multiplication
• Associative property of multiplication, Commutative property of addition and Distributive property
• Distributive property, Commutative property of addition and Commutative property of multiplication
B

9.   Solve the following equations for x:
• x – -30 = -23 x = -53

• -
9
25
x =
9
25
x = -1

• 45 = 7 – 2x x = -19

• ax = f x = f/a

10.   Solve the following inequalities. Then graph a) on the number line
• -x – 1 > -19 x < 18

• x ≠ 839
• -92 > x ≤ 31
• -17x ≤ -34 x ≥ 2

11.   Convert the following numbers into scientific notation:
• 0.000000000182 1.82 × 10-10

• 832000000 8.32 × 108

• 3z9 + 9z5 + 2z4  and  3z4 + 9z2 + -5z1
3z9 + 9z5 + 5z4 + 9z2 + -5z1

• 2z17 + -8z13 + -14z11 + -8z10  and  8z13 + -10z10 + 15z6 2z17 + -14z11 + -18z10 + 15z6

13.   Multiply the following polynomials and simplify:
• 8x3(2x5 + 8x4)
16x8 + 64x7

• (10x5 + 3x3 + 2x2)(4x5 + 8x)
40x10 + 12x8 + 8x7 + 80x6 + 24x4 + 16x3

14.   Divide:
• 10x2 + 24x - 7 / 2x + 6
(5x - 3) with a remainder of 11

15.   Find the greatest common factor of the following terms:
• 22, 39, 90
1

• 20x5y3, 84x3y10, 63x9
x3

16.   Factor the following polynomials:
• 22x4 + 20x3 - 2x2
22x2(x -
1
11
)(x + 1)

• x2 + 18x + 80
(x + 10)(x + 8)

• x5 - 3x4 - 180x3
x3(x + 12)(x - 15)

17.   For question 16, exercises b) and c), solve for x:
• x =
-10
and
-8

• x =
0
,
-12

and
15

18.   How many ways can 6 people wait in line?
• 720

19.   Use the following data to construct a box and whiskers plot:
• 16, 34, 31, 18, 35, 14, 40, 33, 29 20.   Suppose you toss a coin and spin a spinner numbered 1 through 5
• What is the probability of getting tails and 5?
10.00%

• What is the probability of getting tails and an odd number?
20%

• What is the probability of getting tails and a multiple of 2?
20%

• What is the probability of getting tails and a prime number?
30%

• What is the probability of not tails and not 2?
40%

• 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 heads?
50%

21.   Solve and graph the following systems of linear equations:
• x + y = 11
x - y = -20
A(-4.5,15.5)

• 4x - 10y = 7
8x + 6y = 10

B(1.37,-0.15)

22.   Write the following fractions in simplest form:
• 84xy8
21x5y4
4y4
x4

• (x + 2)
(x2 + 4x + 4)
1
x + 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 + 24 = -10x
x1 = -4,   x2 = -6

24.   Convert the following repeating decimal into a fraction:
• x = 4.218
3797
900

25.   Solve the following equation:
• 18 -
5x + 4
= 1
x = 57

26.   Rationalize the denominator of each fraction below:
• 10
14 +
15
140 - 10
15
181

27.   Use a trigonometric ratio to find x: x = 33.94 cm

28.   The sum of two consecutive odd integers is 20. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=9, b=11

29.   After you leave your house, you walk 4 blocks west and 3 blocks north. How far are you from your house?
• I am
5
blocks from my house.

30.   Each side of a square is decreased by 8 m. The area of the newly created square is 1m2. What was the original length of one side of the square?
• 9 m

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