Algebra test generator

Name _____________________ Date:_____________________

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

Solve the following problems:

Important instructions

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1. Multiply: -15 and 16? -240

2. Add: -16 and -1? -17

3. Divide: 11 and -11? -1

4. Substract: -15 and 10? -25

5. Calculate: |-7 · 7 + 15| 34

6. Simplify the following expressions:

5 – 20x + -20 -15-20x
4x + 17y – -13 + 8 21+4x+17y
17z + 11y – 12y – -1x + -9z 1x-1y+8z
x¹³ × x^-15 × y⁹ x^-2 × y⁹
x^-16
x¹⁷
x^-33
(9x⁵)⁸ 43046721x⁴⁰

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

0 + -9x = -9x
( 3 × 1 ) + -6 = -6 + ( 3 × 1 )
-2 × 1 = -2
( m × n ) × 3 = m × ( n × 3 )

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

( 19 × -10 ) × 4 = 19 × ( -10 × 4 )
( b + c ) + a = b + ( c + a )
-4 × -15 = -4 × -15

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

9. Solve the following equations for x:

-x + -31 = 2 x = -33
-
1
4
x = -
13
4
x = 13
13x + 3 = -36 x = -3
bx + gx = -f x = (-f)/(b+g)

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

12x + 19 ≤ -29 x ≤ -4

x ≠ 756
97 < x < -73

18
9
x < 34 x < 17

11. Convert the following numbers into scientific notation:

0.000870 8.7 × 10^-4
69800000 6.98 × 10⁷

12. Add the following polynomials:

-4z⁶ + 11 and -1z¹⁰ + 2z⁹ + -6z⁶ + -4z² + -2

-1z¹⁰ + 2z⁹ + -10z⁶ + -4z² + 9
2z¹⁷ + 4z¹³ + -5z¹¹ + -7z⁹ + -11 and 1z¹¹ + 1z⁹ + -1 2z¹⁷ + 4z¹³ + -4z¹¹ + -6z⁹ + -12

13. Multiply the following polynomials and simplify:

8x(5x⁴ + 8x)

40x⁵ + 64x²
(5x³ + 2x)(6x⁵ + x⁴ + 9x)

30x⁸ + 5x⁷ + 12x⁶ + 2x⁵ + 45x⁴ + 18x²

14. Divide:

6x² - 26x + 32 / 2x - 4
(3x - 7) with a remainder of 4

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

66, 60, 54
6
60x³y⁷, 84x⁹y¹⁰, 66x²y⁸
6x²y⁷

16. Factor the following polynomials:

6x⁵ + 21x⁴ - 66x³
6x³(x - 2)(x +
11
2
)
x² + 13x + 36
(x + 9)(x + 4)
x⁷ - 9x⁶ + 18x⁵
x⁵(x - 6)(x - 3)

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

x =
-9
and

-4
x =
0
,
6

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:

29, 33, 17, 9, 8, 12, 27, 32, 28, 14

20. A bag contains 7 blue balls, 2 red balls, and 7 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:

A white ball?

43.75%

A blue ball or red ball?

56.25%

Two red balls?

1.56%

A blue ball and a white ball?

19.14%

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

x + y = -16
x - y = -14

A(-15,-1)

2x - 3y = 9
6x + 7y = 9

B(2.81,-1.13)

22. Write the following fractions in simplest form:

20x²y⁴
5x⁴y

4y³
x²

(x² - 20x + 100)
(x - 10)

x - 10

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

-7x - 18 = -x²
x₁ = 9, x₂ = -2

24. Convert the following repeating decimal into a fraction:

x = 6.48
642
99

25. Solve the following equation:

-16
x
+ 19 = -7
x
+ 10
x = 1

26. Rationalize the denominator of each fraction below:

10
4 +
6

4 -
6

27. Use a trigonometric ratio to find x:

x = 30.00 cm

28. The sum of two consecutive odd integers is 60. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=29, b=31

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

I am
13
blocks from my house.

30. Each side of a square is decreased by 5 ft. The area of the newly created square is 400ft². What was the original length of one side of the square?

25 ft

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