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:   -12 and 7? -84

2.   Add:   -5 and -12? -17

3.   Divide:   4 and -4? -1

4.   Substract:   1 and 9? -8

5.   Calculate: |-10 + -15 · 10 + -10| 170

6.   Simplify the following expressions:
• -20x – 2x + 17x -5x

• 6y – -9y – -12x – 3y 12x+12y

• -9y + 16z – -8 – 16x – 6x – -7x 8-15x-9y+16z

• x-4 × x-16 × y-19 x-20 × y-19

• x1
x18
x-17

• (3x4)3 27x12

7.   Which of the following expressions show the associative property?
• 8 + 2w + 4
• 0 + 1x = 1x
• 5( 6 + 8 ) = 5×6 + 5×8
• ( m + n ) + 5 = m + ( n + 5 )
D

8.   Which properties are illustrated by the following three expressions?
• 0 + e + f + g = e + f + g
• (x + -10) × (y + 3) = (y + 3) × (x + -10)
• 9 + -5z = -5z + 9
• Identity property of multiplication, Identity property of addition and Associative property of addition
• Commutative property of addition, Associative property of addition and Distributive property
• Identity property of addition, Commutative property of multiplication and Commutative property of addition
• Associative property of multiplication, Identity property of multiplication and Commutative property of multiplication
C

9.   Solve the following equations for x:
• -x · -30 = -60 x = -2

• -
1
16
x =
6
16
x = -6

• -51 = -68x – -17 x = 1

• gx = -a x = -a/g

10.   Solve the following inequalities. Then graph a) on the number line
• 30x + -32 ≥ 28 x ≥ 2

• x ≠ 292
• 84 ≥ x ≥ 17
• -
26
13
x > 4 x < -2

11.   Convert the following numbers into scientific notation:
• 0.000000000622 6.22 × 10-10

• 407000000000 4.07 × 1011

• 2z10 + -15z5 + -5z3  and  11z5 + -9z3
2z10 + -4z5 + -14z3

• 4z18 + 1z16 + 13z14 + -11z2 + -14z1  and  14z18 + -6z16 + 15z14 + -9z5 + -11z2 18z18 + -5z16 + 28z14 + -9z5 + -22z2 + -14z1

13.   Multiply the following polynomials and simplify:
• (10x4 + 7x3)(4x5 + x4 - 5)
40x9 + 38x8 + 7x7 - 50x4 - 35x3

• (6x5 + 8x4)(4x4 + 2)
24x9 + 32x8 + 12x5 + 16x4

14.   Divide:
• 15x3 + 21x2 - 20x - 28 / 5x + 7
3x2 - 4

15.   Find the greatest common factor of the following terms:
• 78, 77, 36
1

• 72x10y10, 84y5, 99x6y3
3y3

16.   Factor the following polynomials:
• 28x3 + 92x2 + 24x
28x(x +
2
7
)(x + 3)

• x2 + 2x - 80
(x + 10)(x - 8)

• x5 - 10x4 + 21x3
x3(x - 3)(x - 7)

17.   For question 16, exercises b) and c), solve for x:
• x =
-10
and
8

• x =
0
,
3

and
7

18.   You can purchase your ice cream in a cup or a cone. Orders can be one, two, three, or four scoops. Flavors can be chocolate, vanilla or strawberry. How many choices do you have?
• 24

19.   Use the following data to construct a box and whiskers plot:
• 39, 7, 4, 6, 29, 40, 38, 11, 22

20.   Suppose you toss a coin and spin a spinner numbered 1 through 9
• What is the probability of getting tails and 7?
5.56%

• What is the probability of getting tails and an even number?
22.22%

• What is the probability of getting tails and a multiple of 2?
22.22%

• What is the probability of getting heads and a prime number?
22.22%

• What is the probability of not tails and not 6?
44.44%

• What is the probability of getting not heads 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 = 1
x - y = 20
A(10.5,-9.5)

• 3x - 9y = 7
10x + 4y = 9

B(1.07,-0.42)

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

• x6(x + 1)
x4 + 7x3 + 6x2
x4
(x + 6)

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• x2 - 10x = -9
x1 = 9,   x2 = 1

24.   Convert the following repeating decimal into a fraction:
• x = 0.158
143
900

25.   Solve the following equation:
• 5
x
- 8 = 2
x
+ 4
x = 16

26.   Rationalize the denominator of each fraction below:
• 7
15 +
5
105 - 7
5
220

27.   Use a trigonometric ratio to find x:
x = 24.25 cm

28.   The sum of two consecutive odd integers is 48. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=23, b=25

29.   After you leave your house, you walk 9 blocks south and 12 blocks west. How far are you from your house?
• I am
15
blocks from my house.

30.   A rectangle has a length 7 m greater than its width. The area of the rectangle is 78m2. What are the length and width of the rectangle?
• width = 6,  length = 13