# 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:   19 and -2? -38

2.   Add:   -10 and 10? 0

3.   Divide:   2 and -2? -1

4.   Substract:   8 and 13? -5

5.   Calculate: |-7 · 19 + -19| 152

6.   Simplify the following expressions:
• -4x – 2 + -11x -2-15x

• -1 + -18y – -13y – -10x -1+10x-5y

• -5y – -14x + 14z + -15z + 18y 14x+13y-1z

• x-6 × y8 x-6 × y8

• x18
x10
x8

• (3x5)10 59049x50

7.   Which of the following expressions show the associative property?
• 1 × 1 = 1
• 0 + 8x = 8x
• q × ( r + 6 ) = qr + 6r
• ( 3 + 7 ) + 5 = 3 + ( 7 + 5 )
D

8.   Which properties are illustrated by the following three expressions?
• ( g × h ) × f = g × ( h × f )
• -1 × 1 + z = z + -1 × 1
• ( b + 0 ) + a = b + ( 0 + a )
• Identity property of addition, Associative property of addition and Distributive property
• Commutative property of multiplication, Identity property of addition and Commutative property of addition
• Associative property of multiplication, Commutative property of addition and Associative property of addition
• Associative property of addition, Commutative property of multiplication and Distributive property
C

9.   Solve the following equations for x:
• -x · 4 = -16 x = 4

• 19
15
= -
1
15
x x = -19

• 19 – 13x = 32 x = -1

• -cx = ax + b x = (-b)/(c+a)

10.   Solve the following inequalities. Then graph a) on the number line
• 8x – -16 < 24 x < 1

• x ≠ 887
• 98 < x ≥ -22
• -
40
10
x ≥ -
32
4
x ≤ 2

11.   Convert the following numbers into scientific notation:
• 0.0000758 7.58 × 10-5

• 1600000000 1.6 × 109

12.   Add the following polynomials:
• 10z10 + -3z7 + -1z6 + 5z3  and  -1z10 + 4z2
9z10 + -3z7 + -1z6 + 5z3 + 4z2

• -2z19 + 4z9 + 14z5  and  -4z19 + 13z11 + -9z9 + -10z5 -6z19 + 13z11 + -5z9 + 4z5

13.   Multiply the following polynomials and simplify:
• (4x + 3)(1x4 + 5x3 + 7x)
4x5 + 23x4 + 15x3 + 28x2 + 21x

• (6x4 + 10x2 + 7x)(7x5 + 3x3 + 10)
42x9 + 88x7 + 49x6 + 30x5 + 81x4 + 100x2 + 70x

14.   Divide:
• 15x2 - 4x - 6 / 3x - 5
(5x + 7) with a remainder of 29

15.   Find the greatest common factor of the following terms:
• 45, 49
1

• 36x2y8, 60xy9, 26x2y3
2xy3

16.   Factor the following polynomials:
• 21x4 - 48x3 + 12x2
21x2(x - 2)(x -
2
7
)

• x2 + 17x + 70
(x + 7)(x + 10)

• x7 + 10x6 + 21x5
x5(x + 7)(x + 3)

17.   For question 16, exercises b) and c), solve for x:
• x =
-7
and
-10

• x =
0
,
-7

and
-3

18.   You are seating 7 people on 7 chairs. How many different ways can those people sit?
• 5040

19.   Use the following data to construct a box and whiskers plot:
• 39, 27, 40, 7, 17, 21, 36, 6, 11 20.   A bag contains 5 blue balls, 4 red balls, and 6 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
• A white ball?
40.00%

• A blue ball or red ball?
60.00%

• Two red balls?
7.11%

• A blue ball and a white ball?
13.33%

21.   Solve and graph the following systems of linear equations:
• x + y = 11
x - y = -3
A(4,7)

• 5x - 9y = -10
2x + 6y = -4

B(-2,0)

22.   Write the following fractions in simplest form:
• 15x6y
30x10y7
1
2x4y6

• x8 - 1x7 - 6x6
x2(x - 3)
x4(x + 2)

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• 12x + 36 = -x2
x1 = -6,   x2 = -6

24.   Convert the following repeating decimal into a fraction:
• x = 0.15
14
90

25.   Solve the following equation:
• -11
x
+ 19 = 5
x
- 13
x = 4

26.   Rationalize the denominator of each fraction below:
• 6
10
10 +
7
20
10
- 2
70
31

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

28.   The sum of two consecutive odd integers is 56. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=27, b=29

29.   After you leave your house, you walk 12 blocks north and 16 blocks east. How far are you from your house?
• I am
20
blocks from my house.

30.   The length of a rectangle is 3 less than 3 times the width. What are the dimensions of the rectangle if the area is 270m2?
• width = 10,  length = 27

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:   -5 and -14? 70

2.   Add:   19 and 4? 23

3.   Divide:   -17 and 1? -17

4.   Substract:   11 and -6? 17

5.   Calculate: |12 · 20 + -1| 239

6.   Simplify the following expressions:
• -20x + 19x + -11x -12x

• -9y – -12y + -3x + 12x 9x+3y

• 12z – -15z + -1x + -14x – 10 -10-15x+27z

• x17 × x-2 x15

• x3
x-13
x16

• (7x2)5 16807x10

7.   Which of the following expressions show the associative property?
• a + b = b + a
• ( m × n ) × 5 = m × ( n × 5 )
• 5 × ( z + 6 + 9 ) = 5×z + 5×6 + 5×9
• 7x + 9 = 9 + 7x
B

8.   Which properties are illustrated by the following three expressions?
• -18 × 12 = -18 × 12
• 1 × (x + 10) = x + 10
• 26 + 79 = 26 + 79
• Commutative property of multiplication, Identity property of multiplication and Commutative property of addition
• Identity property of multiplication, Associative property of multiplication and Associative property of addition
• Identity property of multiplication, Distributive property and Commutative property of addition
• Associative property of multiplication, Commutative property of multiplication and Identity property of multiplication
A

9.   Solve the following equations for x:
• 65 + x = 72 x = 7

• 26
20
=
2
20
x x = 13

• 89 + 4x = 77 x = -3

• -a – e = -cx x = (a+e)/c

10.   Solve the following inequalities. Then graph a) on the number line
• -58x – -23 ≤ -35 x ≥ 1

• x ≠ -309
• 59 > x ≤ -9
• 36
12
x ≤
15
5
x ≤ 1

11.   Convert the following numbers into scientific notation:
• 0.00000995 9.95 × 10-6

• 243000000000 2.43 × 1011

12.   Add the following polynomials:
• -10z8 + 6z6 + 5z4 + -3  and  11z10 + 15z5 + -10z4 + 2 + 9
11z10 + -10z8 + 6z6 + 15z5 + -5z4 + 8

• 12z19 + 6z18 + 12z15 + 3z5 + 6z1  and  15z15 + -14z5 + 8z1 12z19 + 6z18 + 27z15 + -11z5 + 14z1

13.   Multiply the following polynomials and simplify:
• (6x5 + 10x4 + 7x)7x3
42x8 + 70x7 + 49x4

• (1x5 + 8x)(9x5 + 4x4 + 6x2)
9x10 + 4x9 + 6x7 + 72x6 + 32x5 + 48x3

14.   Divide:
• 4x2 + 2x + 17 / 2x + 4
(2x - 3) with a remainder of 29

15.   Find the greatest common factor of the following terms:
• 42, 52
2

• 54x4y7, 18x10y8, 15x3y8
3x3y7

16.   Factor the following polynomials:
• 30x3 + 35x2 + 5x
30x(x + 1)(x +
1
6
)

• x2 + 6x + 9
(x + 3)(x + 3)

• x7 + 9x6 - 90x5
x5(x + 15)(x - 6)

17.   For question 16, exercises b) and c), solve for x:
• x =
-3
and
-3

• x =
0
,
-15

and
6

18.   You have 4 pants, 2 shirts, and 3 shoes. How many different ways can you dress?
• 24

19.   Use the following data to construct a box and whiskers plot:
• 4, 39, 12, 21, 40, 30, 8, 34, 2 20.   A bag contains 3 blue balls, 6 red balls, and 3 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
• A white ball?
25.00%

• A blue ball or red ball?
75.00%

• Two red balls?
25.00%

• A blue ball and a white ball?
6.25%

21.   Solve and graph the following systems of linear equations:
• x + y = -14
x - y = -17
A(-15.5,1.5)

• 7x - 11y = 18
11x + 2y = 9

B(1,-1)

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

• (x2 + 16x + 64)
(x + 8)
x + 8

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• 98 = x2 + 7x
x1 = -14,   x2 = 7

24.   Convert the following repeating decimal into a fraction:
• x = 8.469
7623
900

25.   Solve the following equation:
• -6
x
+ 11 = 1
x
- 3
x = 4

26.   Rationalize the denominator of each fraction below:
• 2
5
- 7
-
5
+ 7
22

27.   Use a trigonometric ratio to find x: x = 33.77 cm

28.   The sum of two consecutive even integers is 34. What are the integers? (Hint: use 2x as the first even integer)
a=16, b=18

29.   After you leave your house, you walk 16 blocks east and 12 blocks south. How far are you from your house?
• I am
20
blocks from my house.

30.   The sides of a square are increased by 3 ft. The area of the newly created square is 256ft2. What was the original length of one side of the square?
• 13 ft

To print this algebra practice test, click here.

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