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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:   17 and 18? 306

2.   Add:   -19 and -2? -21

3.   Divide:   -8 and 2? -4

4.   Substract:   6 and 8? -2

5.   Calculate: |-4 + -5 · 9| 49

6.   Simplify the following expressions:
• -4x + 12x + 17 17+8x

• -14 – -6 + -17y – -20y -8+3y

• 5x + 3x + -15z – 11z – -7 7+8x-26z

• y6 × y2 × y-11 y-3

• x-15
x-16
x1

• (3x4)4 81x16

7.   Which of the following expressions show the associative property?
• -1 × -2 = -2 × -1
• v × ( w + 5 ) = vw + 5w
• -1x + 8 = 8 + -1x
• ( m × n ) × p = m × ( n × p )
D

8.   Which properties are illustrated by the following three expressions?
• 1 × -61 = -61
• -13 × -18 + 19 = 19 + -13 × -18
• -6 × -10 = -6 × -10
• Identity property of multiplication, Commutative property of addition and Commutative property of multiplication
• Identity property of addition, Associative property of addition and Commutative property of multiplication
• Identity property of addition, Associative property of multiplication and Distributive property
• Associative property of addition, Commutative property of multiplication and Associative property of multiplication
A

9.   Solve the following equations for x:
• 3 = -x – -58 x = 55

• 15
21
x =
30
21
x = 2

• 84 = -89 – -173x x = 1

• -a = bx x = -a/b

10.   Solve the following inequalities. Then graph a) on the number line
• -4x + -21 < -17 x > -1

• x ≠ 988
• -19 ≥ x < -77
• -
6
3
x <
6
3
x > -1

11.   Convert the following numbers into scientific notation:
• 0.00000000356 3.56 × 10-9

• 897000000 8.97 × 108

• 6z10 + -10z9 + 15z2  and  5z10 + 11z9 + 5z7 + -1
11z10 + 1z9 + 5z7 + 15z2 + -1

• 7z14 + 8z12 + -3z3 + -15z1 + -4  and  -6z14 + -3z12 + 5z1 + -4 1z14 + 5z12 + -3z3 + -10z1 + -8

13.   Multiply the following polynomials and simplify:
• 7x3(10x5 + 5x2)
70x8 + 35x5

• (6x5 + 6x4 + 2x2)(5x4 + 5x2 + 4x)
30x9 + 30x8 + 30x7 + 64x6 + 24x5 + 10x4 + 8x3

14.   Divide:
• 4x3 + 40x2 + 8x + 80 / x + 10
4x2 + 8

15.   Find the greatest common factor of the following terms:
• 90, 60, 84
6

• 18x8y, 36xy, 84x6y5
6xy

16.   Factor the following polynomials:
• 56x3 + 98x2 + 35x
56x(x +
5
4
)(x +
1
2
)

• x2 + 6x - 7
(x + 7)(x - 1)

• x6 - 3x5 - 108x4
x4(x - 12)(x + 9)

17.   For question 16, exercises b) and c), solve for x:
• x =
-7
and
1

• x =
0
,
12

and
-9

18.   You are seating 5 people on 5 chairs. How many different ways can those people sit?
• 120

19.   Use the following data to construct a box and whiskers plot:
• 40, 20, 31, 10, 4, 18, 15 20.   A bag contains 3 blue balls, 6 red balls, and 5 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
• A white ball?
35.71%

• A blue ball or red ball?
64.29%

• Two red balls?
18.37%

• A blue ball and a white ball?
7.65%

21.   Solve and graph the following systems of linear equations:
• x + y = 5
x - y = 13
A(9,-4)

• 6x - 6y = -7
5x + 4y = 2

B(-0.3,0.87)

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

• (x - 5)4
(x - 5)6
1
(x - 5)2

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• 15x = x2 + 50
x1 = 5,   x2 = 10

24.   Convert the following repeating decimal into a fraction:
• x = 0.1474
1460
9900

25.   Solve the following equation:
• 32
x
= 4
x = 2

26.   Rationalize the denominator of each fraction below:
• 21
5
+ 10
-
21
5
- 210
95

27.   Use a trigonometric ratio to find x: x = 13.50 cm

28.   The sum of two consecutive odd integers is 36. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=17, b=19

29.   After you leave your house, you walk 15 blocks east and 8 blocks north. How far are you from your house?
• I am
17
blocks from my house.

30.   A rectangle has an area of 330ft2. Its width is 7 ft less than its length. What are the dimensions of the rectangle?
• width = 15,  length = 22

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