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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:   -4 and 6? -24

2.   Add:   10 and 7? 17

3.   Divide:   10 and -5? -2

4.   Substract:   -20 and -17? -3

5.   Calculate: |16 + 16 · 7 + 8| 136

6.   Simplify the following expressions:
• -7 – -8 + 3x 1+3x

• 9y – -12y – 4x + -6y -4x+15y

• 7x – 8z – -9x – -6z + 1y 16x+1y-2z

• x15 × y8 × y-13 × y10 x15 × y5

• x-7
x10
x-17

• (3x2)6 729x12

7.   Which of the following expressions show the associative property?
• -10 + 1 = 1 + -10
• 5 × 1 = 5
• -7x + -7 = -7 + -7x
• ( 9 × 2 ) × 7 = 9 × ( 2 × 7 )
D

8.   Which properties are illustrated by the following three expressions?
• ( -12 × -18 ) × 6 = -12 × ( -18 × 6 )
• x + 2 × 10 = 2 × 10 + x
• 0 + e + f = e + f
• Distributive property, Associative property of multiplication and Commutative property of multiplication
• Commutative property of multiplication, Commutative property of addition and Identity property of addition
• Distributive property, Associative property of addition and Identity property of multiplication
• Associative property of multiplication, Commutative property of addition and Identity property of addition
D

9.   Solve the following equations for x:
• -96 = -x – 67 x = 29

• 3
22
=
3
22
x x = 1

• -14 = -3x + -56 x = -14

• -d = ex + fx x = (-d)/(e+f)

10.   Solve the following inequalities. Then graph a) on the number line
• 15x – -4 ≤ 34 x ≤ 2

• x ≠ -275
• 81 ≤ x > -37
• 6
3
x ≤ -
18
3
x ≤ -3

11.   Convert the following numbers into scientific notation:
• 0.0000000000566 5.66 × 10-11

• 9530000 9.53 × 106

• 9z10 + 14z7 + -6z4 + -15z3 + -8z2  and  -9z9 + 8z7 + -5z4 + -2z2
9z10 + -9z9 + 22z7 + -11z4 + -15z3 + -10z2

• 12z15 + 15z8 + -13  and  -15z15 + 6z8 + -15 -3z15 + 21z8 + -28

13.   Multiply the following polynomials and simplify:
• (5x3 + 6x2 + 4x)(8x3 - 3)
40x6 + 48x5 + 32x4 - 15x3 - 18x2 - 12x

• (1x2 + 2x)(8x3 + 2x)
8x5 + 16x4 + 2x3 + 4x2

14.   Divide:
• x2 - 3x - 70 / x + 7
x - 10

15.   Find the greatest common factor of the following terms:
• 30, 45, 66
3

• 90x8y, 52x9y6, 72x8y3
2x8y

16.   Factor the following polynomials:
• 30x5 - 12x4 - 18x3
30x3(x +
3
5
)(x - 1)

• x2 - 9x + 14
(x - 7)(x - 2)

• x4 + 2x3 - 195x2
x2(x - 13)(x + 15)

17.   For question 16, exercises b) and c), solve for x:
• x =
7
and
2

• x =
0
,
13

and
-15

18.   You have 2 pants, 5 shirts, and 5 shoes. How many different ways can you dress?
• 50

19.   Use the following data to construct a box and whiskers plot:
• 25, 6, 24, 22, 1, 29, 37 20.   A bag contains 4 blue balls, 5 red balls, and 3 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
• A white ball?
25.00%

• A blue ball or red ball?
75.00%

• Two red balls?
17.36%

• A blue ball and a white ball?
8.33%

21.   Solve and graph the following systems of linear equations:
• x + y = 7
x - y = -2
A(2.5,4.5)

• 8x - 2y = 18
11x + 4y = 18

B(2,-1)

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

• (x + 8)
(x2 + 16x + 64)
1
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 - 34x = -33
x1 = 1,   x2 = 33

24.   Convert the following repeating decimal into a fraction:
• x = 0.309
309
999

25.   Solve the following equation:
• -20 +
x + 1
= -2
x = 323

26.   Rationalize the denominator of each fraction below:
• 4
6 -
10
12 + 2
10
13

27.   Use a trigonometric ratio to find x: x = 24.25 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 15 blocks west and 8 blocks north. How far are you from your house?
• I am
17
blocks from my house.

30.   A rectangle has a length 9 ft greater than its width. The area of the rectangle is 190ft2. What are the length and width of the rectangle?
• width = 10,  length = 19

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