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:   -17 and 2? -34

2.   Add:   17 and 16? 33

3.   Divide:   12 and 3? 4

4.   Substract:   10 and 4? 6

5.   Calculate: |-6 + 20 · -8| 166

6.   Simplify the following expressions:
• -8x – -5x + -13 -13-3x

• -18x + -12y + -20x – 17y -38x-29y

• 17z + -14z – 17y – -1y – -7 7-16y+3z

• y19 × y5 × y-14 × x-7 x-7 × y10

• x-3
x1
x-4

• (6x2)5 7776x10

7.   Which of the following expressions show the associative property?
• ( m × n ) × 8 = m × ( n × 8 )
• -6 + -5 = -5 + -6
• 4x + 6 = 6 + 4x
• 0 + 8x = 8x
A

8.   Which properties are illustrated by the following three expressions?
• 0 + 28 = 28
• -17 × 9 + -11 = -11 + -17 × 9
• 1 × 17 = 17
• Commutative property of addition, Associative property of multiplication and Distributive property
• Commutative property of addition, Associative property of multiplication and Identity property of multiplication
• Identity property of multiplication, Identity property of addition and Commutative property of multiplication
• Identity property of addition, Commutative property of addition and Identity property of multiplication
D

9.   Solve the following equations for x:
• -8 + x = 13 x = 21

• 12
30
= -
6
30
x x = -2

• -63 = 43 + 2x x = -53

• -gx = -e + c x = (e-c)/g

10.   Solve the following inequalities. Then graph a) on the number line
• -17x – 21 < 30 x > -3

• x ≠ -581
• -54 < x < 98
• 30
10
x ≥ -
12
4
x ≥ -1

11.   Convert the following numbers into scientific notation:
• 0.000000795 7.95 × 10-7

• 849000000 8.49 × 108

• 8z8 + -4z5  and  -9z7 + -9z6 + -9z5 + 3z3 + 10z1
8z8 + -9z7 + -9z6 + -13z5 + 3z3 + 10z1

• -10z17 + 12z12 + -13z5 + -14z3  and  -1z12 + -3z10 + -7z3 -10z17 + 11z12 + -3z10 + -13z5 + -21z3

13.   Multiply the following polynomials and simplify:
• (4x3 + 9x - 5)6x5
24x8 + 54x6 - 30x5

• (7x3 + 7x + 6)(3x4 + 6x + 9)
21x7 + 21x5 + 60x4 + 63x3 + 42x2 + 99x + 54

14.   Divide:
• 20x3 - 5x2 - 16x + 4 / 4x - 1
5x2 - 4

15.   Find the greatest common factor of the following terms:
• 42, 90, 72
6

• 39y5, 90x9y7, 40x9y6
y5

16.   Factor the following polynomials:
• 26x4 + 5x3 - 51x2
26x2(x +
3
2
)(x -
17
13
)

• x2 - 2x - 35
(x - 7)(x + 5)

• x4 + 4x3 + 3x2
x2(x + 1)(x + 3)

17.   For question 16, exercises b) and c), solve for x:
• x =
7
and
-5

• x =
0
,
-1

and
-3

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:
• 2, 33, 9, 19, 31, 6, 38, 26, 23

20.   A bag contains 4 blue balls, 5 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?
12.76%

• A blue ball and a white ball?
10.20%

21.   Solve and graph the following systems of linear equations:
• x + y = -3
x - y = 18
A(7.5,-10.5)

• 3x - 7y = 3
13x + 5y = 13

B(1,0)

22.   Write the following fractions in simplest form:
• 11x3y
44x3y8
1
4y7

• (x + 3)5
(x + 3)6
1
x + 3

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• x2 + 22 = 23x
x1 = 22,   x2 = 1

24.   Convert the following repeating decimal into a fraction:
• x = 0.952
952
999

25.   Solve the following equation:
• 2
x
+ 14 = 11
x
- 4
x = 4

26.   Rationalize the denominator of each fraction below:
• 7
3 -
14
-
21 + 7
14
5

27.   Use a trigonometric ratio to find x:
x = 35.36 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 12 blocks east and 16 blocks north. How far are you from your house?
• I am
20
blocks from my house.

30.   A rectangle has an area of 8m2. Its width is 7 m less than its length. What are the dimensions of the rectangle?
• width = 1,  length = 8