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: 6 and 5? 30

2. Add: 1 and -17? -16

3. Divide: 19 and 1? 19

4. Substract: 5 and 2? 3

5. Calculate: |9 · -7 + 9| 54

6. Simplify the following expressions:

11x + 9 – 13 -4+11x
-2 + 3y + -14y + 13x -2+13x-11y
-20x + -9x – 20z + -2z + -17y -29x-17y-22z
y^-8 × x² × y^-19 x² × y^-27
x¹⁰
x⁸
x²
(6x²)⁶ 46656x¹²

7. Which of the following expressions show the associative property?

( x × y ) × z = x × ( y × z )
3( 8 + 6 ) = 3×8 + 3×6
( m + n ) × 6 = 6 × ( m + n )
8 + 7v + 2

8. Which properties are illustrated by the following three expressions?

12 × ( -9 × 3 ) = ( 12 × -9 ) × 3
w × (u + v) = (u + v) × w
1 × (l + 17) = l + 17

Identity property of multiplication, Commutative property of addition and Associative property of addition
Associative property of multiplication, Commutative property of multiplication and Identity property of multiplication
Distributive property, Identity property of multiplication and Commutative property of addition
Identity property of addition, Commutative property of addition and Commutative property of multiplication

9. Solve the following equations for x:

x · 10 = 100 x = 10
-
14
28
=
1
4
x x = -2
-48 = 66 – 3x x = 38
cx = e x = e/c

10. Solve the following inequalities. Then graph a) on the number line

20x – -27 < -33 x < -3

x ≠ -695
61 < x < -63

-
20
5
x <
16
2
x > -2

11. Convert the following numbers into scientific notation:

0.0000000613 6.13 × 10^-8
7590000000 7.59 × 10⁹

12. Add the following polynomials:

13z⁹ + 4z¹ and -2z¹⁰ + 15z⁹ + -15z⁷ + -4z³ + -6z¹

-2z¹⁰ + 28z⁹ + -15z⁷ + -4z³ + -2z¹
6z¹⁹ + 11z¹⁶ + -5z¹³ + 15z⁷ + -9z⁶ and 5z⁸ + 6z⁷ + -15z⁶ + 7z¹ 6z¹⁹ + 11z¹⁶ + -5z¹³ + 5z⁸ + 21z⁷ + -24z⁶ + 7z¹

13. Multiply the following polynomials and simplify:

1x⁵(6x⁴ + 6x³ - 8)

6x⁹ + 6x⁸ - 8x⁵
(8x³ + 6x + 4)(3x⁵ + 6x⁴ + 8)

24x⁸ + 48x⁷ + 18x⁶ + 48x⁵ + 24x⁴ + 64x³ + 48x + 32

14. Divide:

16x² + 12x + 24 / 4x + 4
(4x - 1) with a remainder of 28

15. Find the greatest common factor of the following terms:

18, 90, 28
2
66x¹⁰y⁴, 21x⁴y⁶, 80x⁸y⁵
x⁴y⁴

16. Factor the following polynomials:

2x⁵ - 21x⁴ + 40x³
2x³(x - 8)(x -
5
2
)
x² - 11x + 18
(x - 9)(x - 2)
x⁴ - 9x³ - 36x²
x²(x - 12)(x + 3)

17. For question 16, exercises b) and c), solve for x:

x =
9
and

2
x =
0
,
12

and
-3

18. You have 3 pants, 5 shirts, and 3 shoes. How many different ways can you dress?

19. Use the following data to construct a box and whiskers plot:

13, 39, 8, 12, 20, 18, 15, 24, 14, 30

20. A bag contains 2 blue balls, 5 red balls, and 5 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:

A white ball?

41.67%

A blue ball or red ball?

58.33%

Two red balls?

15.15%

A blue ball and a white ball?

7.58%

21. Solve and graph the following systems of linear equations:

x + y = 17
x - y = 6

A(11.5,5.5)

9x - y = 3
5x + 10y = -18

B(0.13,-1.86)

22. Write the following fractions in simplest form:

22x⁶y⁷z⁴
44x⁷y⁹z²

z²
2xy²

x³ - 6x² + 8x
x⁵(x - 4)

(x - 2)
x⁴

23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.

x² + 6 = -7x
x₁ = -6, x₂ = -1

24. Convert the following repeating decimal into a fraction:

x = 0.47
43
90

25. Solve the following equation:

12
x
= 10
x =
144
100

26. Rationalize the denominator of each fraction below:

1
2 -
21

-
2 +
21
17

27. Use a trigonometric ratio to find x:

x = 26.87 cm

28. The sum of two consecutive even integers is 62. What are the integers? (Hint: use 2x as the first even integer)

a=30, b=32

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

I am
20
blocks from my house.

30. The length of a rectangle is 2 more than twice its width. The area of the rectangle is 312ft². What is the length and width of the rectangle?

width = 12, length = 26

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