# Algebra test generator

Name _____________________                                        Date:_____________________

Current difficulty level: Choose test difficulty:         Easy              Challenging
(current difficulty level: Easy)

Solve the following problems:

Important instructions

(or click here to generate a new test)
1.   Multiply:   8 and -17? -136

2.   Add:   -12 and 5? -7

3.   Divide:   -3 and -3? 1

4.   Substract:   8 and 4? 4

5.   Calculate: |4 · -4 + 8| 8

6.   Simplify the following expressions:
• -8x – -15 + 5 20-8x

• 19 + -10y – -11y – -12x 19+12x+1y

• 2 + 10z – 14 – 9x + -2z -12-9x+8z

• y-16 × x5 × x12 x17 × y-16

• x15
x5
x10

• (6x5)10 60466176x50

7.   Which of the following expressions show the associative property?
• 0 + 10x = 10x
• a + b = b + a
• e × ( f + 7 ) = ef + 7f
• ( m × n ) × 2 = m × ( n × 2 )
D

8.   Which properties are illustrated by the following three expressions?
• g × ( h + i ) = g × h + g × i
• e + f + 6 = 6 + e + f
• 5 + ( -12 + 19 ) = ( 5 + -12 ) + 19
• Distributive property, Commutative property of addition and Associative property of addition
• Commutative property of addition, Commutative property of multiplication and Associative property of addition
• Commutative property of multiplication, Identity property of addition and Distributive property
• Commutative property of multiplication, Distributive property and Associative property of multiplication
A

9.   Solve the following equations for x:
• 60 = -49 + x x = 109

• -
10
13
=
1
13
x x = -10

• 4x + 55 = 47 x = -2

• f + ax = -e x = (-f-e)/a

10.   Solve the following inequalities. Then graph a) on the number line
• -x – -18 ≤ -20 x ≥ 38

• x ≠ 250
• 1 ≥ x ≤ 21
• 33
11
x >
36
3
x > 4

11.   Convert the following numbers into scientific notation:
• 0.00000366 3.66 × 10-6

• 40500 4.05 × 104

12.   Add the following polynomials:
• -9z10 + -6z7 + -6z4 + 13z1  and  9z10 + 13z7 + -7z4
7z7 + -13z4 + 13z1

• 11z12 + 4z11 + 10z4  and  -5z12 + 13z11 + 12z4 6z12 + 17z11 + 22z4

13.   Multiply the following polynomials and simplify:
• 7x3(10x4 + 8x - 9)
70x7 + 56x4 - 63x3

• (10x2 + 10x + 8)(8x3 + 6x2 + x)
80x5 + 140x4 + 134x3 + 58x2 + 8x

14.   Divide:
• 4x3 - 24x2 + x + 4 / x - 6
(4x2 + 1) with a remainder of 10

15.   Find the greatest common factor of the following terms:
• 72, 42, 45
3

• 55x6y8, 100x8
5x6

16.   Factor the following polynomials:
• 16x3 + 32x2 + 14x
16x(x -
-4 +
2
4
)(x -
-4 -
2
4
)

• x2 - 8x + 7
(x - 1)(x - 7)

• x5 + 2x4 - 195x3
x3(x + 15)(x - 13)

17.   For question 16, exercises b) and c), solve for x:
• x =
1
and
7

• x =
0
,
-15

and
13

18.   You have 2 pants, 4 shirts, and 2 shoes. How many different ways can you dress?
• 16

19.   Use the following data to construct a box and whiskers plot:
• 18, 11, 9, 40, 27, 21, 23, 39 20.   Suppose you toss a coin and spin a spinner numbered 1 through 6
• What is the probability of getting tails and 5?
8.33%

• What is the probability of getting heads and an odd number?
25%

• What is the probability of getting heads and a multiple of 2?
25%

• What is the probability of getting heads and a prime number?
25%

• What is the probability of not heads and not 4?
41.67%

• 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 tails?
50%

21.   Solve and graph the following systems of linear equations:
• x + y = 9
x - y = 18
A(13.5,-4.5)

• 3x - 2y = 10
4x + 3y = -1

B(1.65,-2.53)

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

• (x2 + 2x + 1)
(x + 1)
x + 1

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• x2 - 12 = x
x1 = 4,   x2 = -3

24.   Convert the following repeating decimal into a fraction:
• x = 0.43
39
90

25.   Solve the following equation:
• 14
x
= 12
x =
196
144

26.   Rationalize the denominator of each fraction below:
• 35
30
9
12
35
10
18

27.   Use a trigonometric ratio to find x: x = 28.28 cm

28.   The sum of two consecutive odd integers is 16. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=7, b=9

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

30.   A rectangle has a width that is 7 ft less than its length. The area of the rectangle is 8ft2. What are the dimensions of the rectangle?
• width = 1,  length = 8

To print this algebra practice test, click here.

Name _____________________                                        Date:_____________________

Current difficulty level: Choose test difficulty:         Easy              Challenging
(current difficulty level: Easy)

Solve the following problems:

Important instructions

(or click here to generate a new test)
1.   Multiply:   -20 and 8? -160

2.   Add:   12 and 3? 15

3.   Divide:   -20 and 10? -2

4.   Substract:   -8 and -15? 7

5.   Calculate: |-11 + 8 · 1| 3

6.   Simplify the following expressions:
• 19 + 2x + -9x 19-7x

• -18 + 2y + 14 – -3x -4+3x+2y

• -4x + 13 – 8x + -5z – -2z 13-12x-3z

• x-7 × x-3 × x-8 × x-9 x-27

• x5
x3
x2

• (3x3)7 2187x21

7.   Which of the following expressions show the associative property?
• ( 2 × -1 ) + 7 = 7 + ( 2 × -1 )
• ( m + n ) + 5 = m + ( n + 5 )
• a + b = b + a
• 0 + -10x = -10x
B

8.   Which properties are illustrated by the following three expressions?
• -15 + 0 = -15
• r × ( s × t ) = ( r × s ) × t
• -4 × 19 + 8 = 8 + -4 × 19
• Identity property of addition, Associative property of multiplication and Commutative property of addition
• Distributive property, Commutative property of addition and Identity property of addition
• Commutative property of multiplication, Distributive property and Identity property of addition
• Distributive property, Commutative property of addition and Commutative property of multiplication
A

9.   Solve the following equations for x:
• x · -2 = -76 x = 38

• 3
12
x = -
6
24
x = -1

• 99 + -73x = 26 x = 1

• e = fx x = e/f

10.   Solve the following inequalities. Then graph a) on the number line
• x – -25 ≤ 27 x ≤ 2

• x ≠ -611
• -35 > x < -23
• 38
19
x ≤ -18 x ≤ -9

11.   Convert the following numbers into scientific notation:
• 0.00000000442 4.42 × 10-9

• 828000000 8.28 × 108

12.   Add the following polynomials:
• 4z6 + 3z1 + -14  and  -12z6 + 1z5 + 1z3 + 3z1 + 13
-8z6 + 1z5 + 1z3 + 6z1 + -1

• 4z18 + -13z17 + 5z4 + -15z1 + -6  and  14z18 + 11z17 + 6z3 + -2 18z18 + -2z17 + 5z4 + 6z3 + -15z1 + -8

13.   Multiply the following polynomials and simplify:
• (2x4 + 5x3)(8x5 + 10x - 7)
16x9 + 40x8 + 20x5 + 36x4 - 35x3

• (10x5 + 10x3)(10x4 + 5x2 + 10x)
100x9 + 150x7 + 100x6 + 50x5 + 100x4

14.   Divide:
• 10x2 - 49x + 18 / 2x - 9
5x - 2

15.   Find the greatest common factor of the following terms:
• 50, 60, 45
5

• 44x10y, 84x9y10
4x9y

16.   Factor the following polynomials:
• 16x4 + 68x3 + 69x2
16x2(x -
-17 +
13
8
)(x -
-17 -
13
8
)

• x2 + 10x + 9
(x + 1)(x + 9)

• x4 + 9x3 + 20x2
x2(x + 4)(x + 5)

17.   For question 16, exercises b) and c), solve for x:
• x =
-1
and
-9

• x =
0
,
-4

and
-5

18.   You have 7 books to read. How many different ways can you read your books?
• 5040

19.   Use the following data to construct a box and whiskers plot:
• 28, 21, 29, 40, 30, 16, 11, 32 20.   A bag contains 4 blue balls, 7 red balls, and 2 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
• A white ball?
15.38%

• A blue ball or red ball?
84.62%

• Two red balls?
26.92%

• A blue ball and a white ball?
5.13%

21.   Solve and graph the following systems of linear equations:
• x + y = 11
x - y = 16
A(13.5,-2.5)

• x - 3y = 2
9x + 5y = 6

B(0.88,-0.38)

22.   Write the following fractions in simplest form:
• 16x9y3
32x10y4
1
2xy

• x7 + 2x6 - 3x5
x(x - 1)
x4(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.
• 7x = x2 + 6
x1 = 1,   x2 = 6

24.   Convert the following repeating decimal into a fraction:
• x = 0.13
12
90

25.   Solve the following equation:
• -13
x
+ 2 = -20
x
+ 9
x = 1

26.   Rationalize the denominator of each fraction below:
• 5
15 +
21
75 - 5
21
204

27.   Use a trigonometric ratio to find x: x = 15.56 cm

28.   The sum of two consecutive even integers is 14. What are the integers? (Hint: use 2x as the first even integer)
a=6, b=8

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

30.   Each side of a square is decreased by 7 ft. The area of the newly created square is 9ft2. What was the original length of one side of the square?
• 10 ft

To print this algebra practice test, click here.

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