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: Challenging)

Solve the following problems:

Important instructions

1.   Multiply:   -40 and 61? -2440

2.   Add:   -85 and -97? -182

3.   Divide:   45 and -15? -3

4.   Substract:   -1 and 16? -17

5.   Calculate: |32 · -11 + -4| 356

6.   Simplify the following expressions:
• -44x – 43x – 98x -185x

• -81y + 75 + 79 – -8y 154-73y

• -98 + 46 + 13y – 7y – -72y -52+78y

• x46 × y81 × y81 x46 × y162

• x86
x-38
x124

• (9x5)10 3486784401x50

7.   Which of the following expressions show the associative property?
• 5 × 1 = 5
• ( x × y ) + 9 = 9 + ( y × x )
• ( 9 × 3 ) × 6 = 9 × ( 3 × 6 )
• -1x + 2 = 2 + -1x
C

8.   Which properties are illustrated by the following three expressions?
• 1 × (g + 15) = g + 15
• ( -13 + -6 ) × z = -13 × z + -6 × z
• o + 10 + 0 = o + 10
• Commutative property of addition, Identity property of addition and Identity property of multiplication
• Identity property of multiplication, Distributive property and Identity property of addition
• Associative property of addition, Identity property of addition and Identity property of multiplication
• Commutative property of multiplication, Identity property of addition and Distributive property
B

9.   Solve the following equations for x:
• 12 = -x · -4 x = 3

• -
10
11
= -
5
11
x x = 2

• 89 + 111x = -22 x = -1

• a = -bx x = -a/b

10.   Solve the following inequalities. Then graph a) on the number line
• x – 14 ≥ 33 x ≥ 47

• x ≠ 75
• -17 > x > -23
• -
12
6
x < -
34
17
x > 1

11.   Convert the following numbers into scientific notation:
• 0.00000000323 3.23 × 10-9

• 41800000000 4.18 × 1010

• 15z9 + -1  and  19z9 + 20z8 + 6z7 + -8z6
34z9 + 20z8 + 6z7 + -8z6 + -1

• 19z17 + -4z15 + -33z12 + -28  and  -7z17 + 46z15 + -49z12 12z17 + 42z15 + -82z12 + -28

13.   Multiply the following polynomials and simplify:
• (6x4 + 8x3 + 8x)(3x4 + 6x2 + x)
18x8 + 24x7 + 36x6 + 78x5 + 8x4 + 48x3 + 8x2

• (6x4 + 4x2 + 10x)(1x4 + 10x3 + 2)
6x8 + 60x7 + 4x6 + 50x5 + 112x4 + 8x2 + 20x

14.   Divide:
• 16x2 - 36x + 20 / 4x - 5
4x - 4

15.   Find the greatest common factor of the following terms:
• 135, 108, 252
9

• 384x4y2, 180x2y
12x2y

16.   Factor the following polynomials:
• 64x4 + 92x3 + 32x2
64x2(x -
-23 +
17
32
)(x -
-23 -
17
32
)

• x2 + 2x - 24
(x + 6)(x - 4)

• x8 - x7 - 156x6
x6(x - 13)(x + 12)

17.   For question 16, exercises b) and c), solve for x:
• x =
-6
and
4

• x =
0
,
13

and
-12

• 5040

19.   Use the following data to construct a box and whiskers plot:
• 13, 36, 6, 34, 32, 5, 22, 1, 12, 26

20.   Suppose you toss a coin and spin a spinner numbered 1 through 7
• What is the probability of getting tails and 3?
7.14%

• What is the probability of getting tails and an odd number?
21.43%

• What is the probability of getting heads and a multiple of 3?
14.29%

• What is the probability of getting heads and a prime number?
28.57%

• What is the probability of not heads and not 5?
42.86%

• What is the probability of getting not tails and not a whole number?
0%

• What is the probability of heads or tails and a whole number?
100%

• What is the probability of getting heads?
50%

21.   Solve and graph the following systems of linear equations:
• x + y = 4
x - y = 8
A(6,-2)

• 10x - 2y = -11
x + 9y = 17

B(-0.71,1.97)

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

• (x - 10)
(x2 - 20x + 100)
1
x - 10

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• 7x + 10 = -x2
x1 = -2,   x2 = -5

24.   Convert the following repeating decimal into a fraction:
• x = 0.4
4
9

25.   Solve the following equation:
• x - 7
- 20 = 4
x = 583

26.   Rationalize the denominator of each fraction below:
• 14
9
5
18
7
2
5

27.   Use a trigonometric ratio to find x:
x = 23.33 cm

28.   The sum of two consecutive odd integers is 28. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=13, b=15

29.   After you leave your house, you walk 15 blocks north and 8 blocks east. How far are you from your house?
• I am
17
blocks from my house.

30.   Each side of a square is decreased by 2 m. The area of the newly created square is 361m2. What was the original length of one side of the square?
• 21 m