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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:   -12 and 5? -60

2.   Add:   16 and -3? 13

3.   Divide:   10 and -5? -2

4.   Substract:   -6 and 5? -11

5.   Calculate: |1 + -1 · -7 + -11| 3

6.   Simplify the following expressions:
• -8x – 4 + 2 -2-8x

• -12x + -6 + 11 – 18x 5-30x

• -7x + -10 – -17x – -3y + -12y – 3x -10+7x-9y

• y-1 × y18 × y0 × y-6 y11

• x12
x11
x1

• (3x2)6 729x12

7.   Which of the following expressions show the associative property?
• 6x + 4 = 4 + 6x
• 9 × -9 = -9 × 9
• 6 + 10u + 5
• ( x + y ) + z = x + ( y + z )
D

8.   Which properties are illustrated by the following three expressions?
• d + 15 + 0 = d + 15
• ( x × y ) × w = x × ( y × w )
• u + ( v + w ) = ( u + v ) + w
• Distributive property, Identity property of addition and Commutative property of addition
• Identity property of addition, Distributive property and Commutative property of multiplication
• Distributive property, Identity property of multiplication and Associative property of addition
• Identity property of addition, Associative property of multiplication and Associative property of addition
D

9.   Solve the following equations for x:
• -67 – -x = 15 x = 82

• 6
4
= -
1
2
x x = -3

• -19x + -3 = -60 x = 3

• g = -cx x = -g/c

10.   Solve the following inequalities. Then graph a) on the number line
• -4x – 1 ≥ -21 x ≤ 5

• x ≠ 75
• -33 > x ≥ 29
• 20
2
x <
40
2
x < 2

11.   Convert the following numbers into scientific notation:
• 0.00000593 5.93 × 10-6

• 48700 4.87 × 104

• -15z10 + 6z9 + 9z8 + -9z7 + 5z2  and  -2z9 + 4z8 + 2z7 + 2z3 + 14z2
-15z10 + 4z9 + 13z8 + -7z7 + 2z3 + 19z2

• -13z13 + -9z7 + -5z2 + 7z1  and  -4z16 + -8z13 + 9z7 + 11z2 + 13z1 -4z16 + -21z13 + 6z2 + 20z1

13.   Multiply the following polynomials and simplify:
• (1x4 + 9)5x5
5x9 + 45x5

• (4x5 + 6x2)(7x5 + 4x4)
28x10 + 16x9 + 42x7 + 24x6

14.   Divide:
• 20x3 - 36x2 - 45x + 81 / 5x - 9
4x2 - 9

15.   Find the greatest common factor of the following terms:
• 52, 78, 36
2

• 54x6y, 78x5y2
6x5y

16.   Factor the following polynomials:
• 34x5 + 69x4 + 27x3
34x3(x +
9
17
)(x +
3
2
)

• x2 - 8x + 12
(x - 2)(x - 6)

• x8 + 20x7 + 96x6
x6(x + 12)(x + 8)

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

• x =
0
,
-12

and
-8

18.   How many ways can 8 people wait in line?
• 40320

19.   Use the following data to construct a box and whiskers plot:
• 18, 25, 5, 17, 29, 14, 13, 32, 22 20.   A bag contains 6 blue balls, 5 red balls, and 6 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
• A white ball?
35.29%

• A blue ball or red ball?
64.71%

• Two red balls?
7.35%

• A blue ball and a white ball?
13.24%

21.   Solve and graph the following systems of linear equations:
• x + y = 8
x - y = 6
A(7,1)

• 2x - 3y = -19
2x + 6y = 5

B(-5.5,2.67)

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

• x5(x + 7)
x3 + 14x2 + 49x
x4
(x + 7)

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• -x = x2 - 20
x1 = -5,   x2 = 4

24.   Convert the following repeating decimal into a fraction:
• x = 0.1224
1223
9990

25.   Solve the following equation:
• -
10
x
= -4
x =
100
16

26.   Rationalize the denominator of each fraction below:
• 35
2
35
2
2

27.   Use a trigonometric ratio to find x: x = 15.00 cm

28.   The sum of two consecutive odd integers is 32. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=15, b=17

29.   After you leave your house, you walk 5 blocks south and 12 blocks west. How far are you from your house?
• I am
13
blocks from my house.

30.   Each side of a square is lengthened by 6 ft. This makes the area of the square 196ft2. What is the original length of a side of the square?
• 8 ft

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