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: -5 and -2? 10

2. Add: -13 and -1? -14

3. Divide: -11 and -11? 1

4. Substract: -14 and -6? -8

5. Calculate: |15 + 13 · -12 + 15| 126

6. Simplify the following expressions:

7x + 5x + -8x 4x
5y + -16x – 1y – -13y -16x+17y
6y – 1z – 11 + -10y – 16x -11-16x-4y-1z
y² × x¹⁶ × y² x¹⁶ × y⁴
x^-19
x^-2
x^-17
(2x²)⁵ 32x¹⁰

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

( x × y ) × z = x × ( y × z )
w × ( x + 6 ) = wx + 6x
( -9 × 10 ) + -5 = -5 + ( -9 × 10 )
0 + 9x = 9x

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

0 + 70 = 70
( h + 0 ) + g = h + ( 0 + g )
( -15 + 6) × 9 = -15 × 9 + 6 × 9

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

9. Solve the following equations for x:

x · 2 = 12 x = 6
16
11
= -
8
11
x x = -2
-8 = -7x – -27 x = 5
cx = -b – gx x = (-b)/(c+g)

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

3x – 5 ≤ -32 x ≤ -9

x ≠ 427
-95 ≥ x ≥ 61

36
12
x ≤ -
6
2
x ≤ -1

11. Convert the following numbers into scientific notation:

0.000000319 3.19 × 10^-7
5290000 5.29 × 10⁶

12. Add the following polynomials:

4z⁷ + -6z¹ and 2z⁷ + -12z⁴ + -4z¹

6z⁷ + -12z⁴ + -10z¹
13z¹⁷ + 5z¹³ + 7z⁸ + 5z⁵ + 2 and 13z⁵ + 7z¹ + 13 13z¹⁷ + 5z¹³ + 7z⁸ + 18z⁵ + 7z¹ + 15

13. Multiply the following polynomials and simplify:

10x⁵(6x⁵ + 2x³ + 9x²)

60x¹⁰ + 20x⁸ + 90x⁷
(7x⁴ + 3x² - 2)(6x² + 4x)

42x⁶ + 28x⁵ + 18x⁴ + 12x³ - 12x² - 8x

14. Divide:

6x² - 24x - 30 / 3x + 3
2x - 10

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

72, 42
6
15x³y⁴, 80x⁷y³, 75xy³
5xy³

16. Factor the following polynomials:

15x³ - 31x² + 2x
15x(x -
1
15
)(x - 2)
x² - 2x - 3
(x + 1)(x - 3)
x⁷ - 2x⁶ - 168x⁵
x⁵(x - 14)(x + 12)

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

x =
-1
and

3
x =
0
,
14

and
-12

18. You have 4 pants, 4 shirts, and 5 shoes. How many different ways can you dress?

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

26, 9, 10, 25, 13, 32, 31

20. A bag contains 3 blue balls, 6 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?

18.18%

A blue ball or red ball?

81.82%

Two red balls?

27.27%

A blue ball and a white ball?

5.45%

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

x + y = 13
x - y = -1

A(6,7)

9x - 9y = -6
2x + 9y = -9

B(-1.36,-0.7)

22. Write the following fractions in simplest form:

12x⁷y⁸
6x²y³

2x⁵y⁵

(x - 2)⁶
(x - 2)²

(x - 2)⁴

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

x = x² - 2
x₁ = 2, x₂ = -1

24. Convert the following repeating decimal into a fraction:

x = 0.21
21
99

25. Solve the following equation:

-14 +
3x + 10
= -1
x = 53

26. Rationalize the denominator of each fraction below:

21
3
+ 1

21
3
- 21
2

27. Use a trigonometric ratio to find x:

x = 29.00 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 north and 5 blocks west. How far are you from your house?

I am
13
blocks from my house.

30. A rectangle has a length 4 m greater than its width. The area of the rectangle is 192m². What are the length and width of the rectangle?

width = 12, length = 16

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