Algebra test generator. Unlimited practices. Sharpen your algebra skills! Answers and solutions.
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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 -12? -6

3.   Divide:   -15 and 15? -1

4.   Substract:   7 and 15? -8

5.   Calculate: |-10 + 14 · 1 + -8| 4

6.   Simplify the following expressions:
• 16x + 13x + -11 -11+29x

• -11y – -3 – 16x – -3x 3-13x-11y

• -9 + 3x – -11z – -17x – -15 6+20x+11z

• x-2 × y1 x-2 × y1

• x11
x-1
x12

• (4x)5 1024x5

7.   Which of the following expressions show the associative property?
• ( x × y ) + 6 = 6 + ( y × x )
• ( m + n ) + p = m + ( n + p )
• 9x + -1 = -1 + 9x
• a + b = b + a
B

8.   Which properties are illustrated by the following three expressions?
• y × ( z + 0 ) = y × z + y × 0
• 14 + v + w = v + w + 14
• 4 × (-6 + y) = (-6 + y) × 4
• Identity property of multiplication, Identity property of addition and Commutative property of multiplication
• Identity property of addition, Distributive property and Identity property of multiplication
• Distributive property, Commutative property of addition and Commutative property of multiplication
• Identity property of addition, Commutative property of addition and Associative property of multiplication
C

9.   Solve the following equations for x:
• 24 – x = -12 x = 36

• -
7
25
=
7
25
x x = -1

• 61x – -86 = 25 x = -1

• -ax = b – g x = (-b+g)/a

10.   Solve the following inequalities. Then graph a) on the number line
• 2x + 9 > 35 x > 13

• x ≠ -921
• -85 ≤ x < 86
• 32
16
x <
24
3
x < 4

11.   Convert the following numbers into scientific notation:
• 0.00000000329 3.29 × 10-9

• 77600000 7.76 × 107

• 14z10 + -15z9 + -11z5 + -7z2  and  6z10 + 12z9 + -10z5 + -13z4 + -5z1
20z10 + -3z9 + -21z5 + -13z4 + -7z2 + -5z1

• 7z7 + -1z4 + 14z3  and  1z7 + -4z4 + -12z3 8z7 + -5z4 + 2z3

13.   Multiply the following polynomials and simplify:
• -9(5x5 + 3x2 + x)
-45x5 - 27x2 - 9x

• (6x5 + 9)(10x4 + 9x3 + 4x2)
60x9 + 54x8 + 24x7 + 90x4 + 81x3 + 36x2

14.   Divide:
• 2x3 + 10x2 - 5x - 25 / x + 5
2x2 - 5

15.   Find the greatest common factor of the following terms:
• 66, 72, 39
3

• 88x5y3, 12x10y6
4x5y3

16.   Factor the following polynomials:
• 16x5 + 72x4 + 74x3
16x3(x -
-9 +
7
4
)(x -
-9 -
7
4
)

• x2 - 10x + 25
(x - 5)(x - 5)

• x9 + 0x8 - 25x7
x7(x - 5)(x + 5)

17.   For question 16, exercises b) and c), solve for x:
• x =
5
and
5

• x =
0
,
5

and
-5

18.   You have 5 CDs. How many different ways can you listen to them?
• 120

19.   Use the following data to construct a box and whiskers plot:
• 18, 15, 32, 39, 24, 34, 12

20.   A bag contains 2 blue balls, 2 red balls, and 3 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
• A white ball?
42.86%

• A blue ball or red ball?
57.14%

• Two red balls?
4.76%

• A blue ball and a white ball?
14.29%

21.   Solve and graph the following systems of linear equations:
• x + y = -13
x - y = -14
A(-13.5,0.5)

• 10x - 10y = -10
2x + 2y = -18

B(-5,-4)

22.   Write the following fractions in simplest form:
• 9x7y2
3x7y8
3
y6

• x(x - 2)
x6 - 7x5 + 10x4
1
x3(x - 5)

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• x2 + 15 = 16x
x1 = 1,   x2 = 15

24.   Convert the following repeating decimal into a fraction:
• x = 0.113
112
990

25.   Solve the following equation:
• 3
x
= 15
x =
9
225

26.   Rationalize the denominator of each fraction below:
• 15
5
- 6
-
15
5
+ 90
31

27.   Use a trigonometric ratio to find x:
x = 32.33 cm

28.   The sum of two consecutive even integers is 26. What are the integers? (Hint: use 2x as the first even integer)
a=12, b=14

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

30.   The length of a rectangle is 6 more than twice its width. The area of the rectangle is 308m2. What is the length and width of the rectangle?
• width = 11,  length = 28

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