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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:   13 and 10? 130

2.   Add:   -1 and -10? -11

3.   Divide:   -6 and -6? 1

4.   Substract:   3 and -6? 9

5.   Calculate: |15 + -16 · -13 + -9| 214

6.   Simplify the following expressions:
• 7x + 2x – 19x -10x

• -10x – -14 + -8 – -12y 6-10x+12y

• -17z + 11 + -3y + -3z – -12z 11-3y-8z

• x-19 × y15 × x-14 × x7 x-26 × y15

• x8
x2
x6

• (9x5)7 4782969x35

7.   Which of the following expressions show the associative property?
• 0 + 3x = 3x
• 5 + 4 = 4 + 5
• ( m × n ) × p = m × ( n × p )
• 5 × 1 = 5
C

8.   Which properties are illustrated by the following three expressions?
• x × (v + w) = (v + w) × x
• ( g × h ) × f = g × ( h × f )
• 1 × (r + s) = r + s
• Associative property of multiplication, Associative property of addition and Identity property of multiplication
• Distributive property, Commutative property of addition and Commutative property of multiplication
• Distributive property, Identity property of multiplication and Identity property of addition
• Commutative property of multiplication, Associative property of multiplication and Identity property of multiplication
D

9.   Solve the following equations for x:
• -x + -22 = -28 x = 6

• 5
25
=
5
25
x x = 1

• 71 = 4x – 77 x = 37

• cx = e x = e/c

10.   Solve the following inequalities. Then graph a) on the number line
• -20x – 1 < -21 x > 1

• x ≠ 13
• 92 < x ≥ -52
• 14
7
x < -
32
2
x < -8

11.   Convert the following numbers into scientific notation:
• 0.0000000811 8.11 × 10-8

• 16800000 1.68 × 107

• -12z9 + -4z7 + -8z6 + -5z4 + 11z2  and  5z9 + -1z7 + -4z2 + 11z1
-7z9 + -5z7 + -8z6 + -5z4 + 7z2 + 11z1

• 12z13 + 4z6 + 2z3  and  -7z13 + -11z6 + 3z3 5z13 + -7z6 + 5z3

13.   Multiply the following polynomials and simplify:
• (5x5 + 10x3)9x5
45x10 + 90x8

• (6x2 + 6)(6x3 + 5x)
36x5 + 66x3 + 30x

14.   Divide:
• 12x2 - 62x + 81 / 4x - 10
(3x - 8) with a remainder of 1

15.   Find the greatest common factor of the following terms:
• 90, 54
18

• 63xy5, 84y10, 48x5y9
3y5

16.   Factor the following polynomials:
• 28x4 - 4x3 - 32x2
28x2(x + 1)(x -
8
7
)

• x2 - 4x - 12
(x + 2)(x - 6)

• x8 - 2x7 - 195x6
x6(x - 15)(x + 13)

17.   For question 16, exercises b) and c), solve for x:
• x =
-2
and
6

• x =
0
,
15

and
-13

18.   You have 7 CDs. How many different ways can you listen to them?
• 5040

19.   Use the following data to construct a box and whiskers plot:
• 33, 14, 36, 1, 15, 28, 13 20.   A bag contains 5 blue balls, 2 red balls, and 2 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
• A white ball?
22.22%

• A blue ball or red ball?
77.78%

• Two red balls?
4.94%

• A blue ball and a white ball?
12.35%

21.   Solve and graph the following systems of linear equations:
• x + y = -10
x - y = -19
A(-14.5,4.5)

• 3x - 7y = -14
10x + 10y = 11

B(-0.63,1.73)

22.   Write the following fractions in simplest form:
• 5x10y2
15x10y10
1
3y8

• x(x + 8)
x5 + 16x4 + 64x3
1
x2(x + 8)

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• x2 + 7x = 78
x1 = 6,   x2 = -13

24.   Convert the following repeating decimal into a fraction:
• x = 1.545
1530
990

25.   Solve the following equation:
• -
12
x
= -12
x = 1

26.   Rationalize the denominator of each fraction below:
• 21
14 +
6
294 - 21
6
190

27.   Use a trigonometric ratio to find x: x = 38.18 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 12 blocks south and 5 blocks west. How far are you from your house?
• I am
13
blocks from my house.

30.   The length of a rectangle is 6 more than twice its width. The area of the rectangle is 216m2. What is the length and width of the rectangle?
• width = 9,  length = 24

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