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: 13 and 10? 130

2. Add: -1 and -10? -11

3. Divide: -6 and -6? 1

4. Substract: 3 and -6? 9

5. Calculate: |15 + -16 · -13 + -9| 214

6. Simplify the following expressions:

7x + 2x – 19x -10x
-10x – -14 + -8 – -12y 6-10x+12y
-17z + 11 + -3y + -3z – -12z 11-3y-8z
x^-19 × y¹⁵ × x^-14 × x⁷ x^-26 × y¹⁵
x⁸
x²
x⁶
(9x⁵)⁷ 4782969x³⁵

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

0 + 3x = 3x
5 + 4 = 4 + 5
( m × n ) × p = m × ( n × p )
5 × 1 = 5

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

x × (v + w) = (v + w) × x
( g × h ) × f = g × ( h × f )
1 × (r + s) = r + s

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

9. Solve the following equations for x:

-x + -22 = -28 x = 6
5
25
=
5
25
x x = 1
71 = 4x – 77 x = 37
cx = e x = e/c

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

-20x – 1 < -21 x > 1

x ≠ 13
92 < x ≥ -52

14
7
x < -
32
2
x < -8

11. Convert the following numbers into scientific notation:

0.0000000811 8.11 × 10^-8
16800000 1.68 × 10⁷

12. Add the following polynomials:

-12z⁹ + -4z⁷ + -8z⁶ + -5z⁴ + 11z² and 5z⁹ + -1z⁷ + -4z² + 11z¹

-7z⁹ + -5z⁷ + -8z⁶ + -5z⁴ + 7z² + 11z¹
12z¹³ + 4z⁶ + 2z³ and -7z¹³ + -11z⁶ + 3z³ 5z¹³ + -7z⁶ + 5z³

13. Multiply the following polynomials and simplify:

(5x⁵ + 10x³)9x⁵

45x¹⁰ + 90x⁸
(6x² + 6)(6x³ + 5x)

36x⁵ + 66x³ + 30x

14. Divide:

12x² - 62x + 81 / 4x - 10
(3x - 8) with a remainder of 1

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

90, 54
18
63xy⁵, 84y¹⁰, 48x⁵y⁹
3y⁵

16. Factor the following polynomials:

28x⁴ - 4x³ - 32x²
28x²(x + 1)(x -
8
7
)
x² - 4x - 12
(x + 2)(x - 6)
x⁸ - 2x⁷ - 195x⁶
x⁶(x - 15)(x + 13)

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

x =
-2
and

6
x =
0
,
15

and
-13

18. You have 7 CDs. How many different ways can you listen to them?

5040

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

33, 14, 36, 1, 15, 28, 13

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

A white ball?

22.22%

A blue ball or red ball?

77.78%

Two red balls?

4.94%

A blue ball and a white ball?

12.35%

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

x + y = -10
x - y = -19

A(-14.5,4.5)

3x - 7y = -14
10x + 10y = 11

B(-0.63,1.73)

22. Write the following fractions in simplest form:

5x¹⁰y²
15x¹⁰y¹⁰

1
3y⁸

x(x + 8)
x⁵ + 16x⁴ + 64x³

1
x²(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.

x² + 7x = 78
x₁ = 6, x₂ = -13

24. Convert the following repeating decimal into a fraction:

x = 1.545
1530
990

25. Solve the following equation:

-
12
x
= -12
x = 1

26. Rationalize the denominator of each fraction below:

21
14 +
6

294 - 21
6
190

27. Use a trigonometric ratio to find x:

x = 38.18 cm

28. The sum of two consecutive odd integers is 36. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=17, b=19

29. After you leave your house, you walk 12 blocks south and 5 blocks west. How far are you from your house?

I am
13
blocks from my house.

30. The length of a rectangle is 6 more than twice its width. The area of the rectangle is 216m². What is the length and width of the rectangle?

width = 9, length = 24

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