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: -11 and 20? -220

2. Add: 10 and 17? 27

3. Divide: 16 and 8? 2

4. Substract: -9 and 1? -10

5. Calculate: |10 · -19 + -13 · 4| 242

6. Simplify the following expressions:

11 + -6x – -2 13-6x
11y – -15y – -11y – 5 -5+37y
19z – -7y + -4 – -6x + 20x – -11y -4+26x+18y+19z
x¹⁶ × x⁷ × y^-16 × y^-7 x²³ × y^-23
x¹⁹
x^-5
x²⁴
(7x²)⁸ 5764801x¹⁶

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

0 + 9x = 9x
7 + 2q + 3
a + b = b + a
( 3 + 8 ) + 2 = 3 + ( 8 + 2 )

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

(r + s) × t = t × (r + s)
h × ( i × j ) = ( h × i ) × j
z + -4 × -9 = -4 × -9 + z

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

9. Solve the following equations for x:

-x + 46 = -83 x = 129
-
4
24
= -
1
24
x x = 4
-94 = 19 + -113x x = 1
c = -dx x = -c/d

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

x – -32 ≤ -20 x ≤ -52

x ≠ 422
68 > x < -51

21
7
x ≥ 3 x ≥ 1

11. Convert the following numbers into scientific notation:

0.000683 6.83 × 10^-4
1500000 1.5 × 10⁶

12. Add the following polynomials:

-3z⁹ + 9z² and 12z¹⁰ + -11z⁹ + -12z⁴ + -4z²

12z¹⁰ + -14z⁹ + -12z⁴ + 5z²
-11z¹³ + -1z⁹ + 10z⁸ + 6z² and 9z⁹ + -14z⁸ + 15z² -11z¹³ + 8z⁹ + -4z⁸ + 21z²

13. Multiply the following polynomials and simplify:

(9x⁴ + 7x² - 5)(4x³ + 3x² - 6)

36x⁷ + 27x⁶ + 28x⁵ - 33x⁴ - 20x³ - 57x² + 30
(8x⁵ + x²)(2x⁵ + 7x⁴)

16x¹⁰ + 56x⁹ + 2x⁷ + 7x⁶

14. Divide:

6x³ + 3x² - 6x - 1 / 2x + 1
(3x² - 3) with a remainder of 2

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

77, 36, 10
1
45x⁴y, 30x⁶y, 54x⁷y⁶
3x⁴y

16. Factor the following polynomials:

12x⁵ + 54x⁴ + 60x³
12x³(x +
5
2
)(x + 2)
x² - 4x - 32
(x + 4)(x - 8)
x⁴ - 15x³ + 26x²
x²(x - 2)(x - 13)

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

x =
-4
and

8
x =
0
,
2

and
13

18. You have 6 books to read. How many different ways can you read your books?

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

17, 19, 9, 11, 16, 22, 2, 20

20. A bag contains 5 blue balls, 7 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?

29.41%

A blue ball or red ball?

70.59%

Two red balls?

15.44%

A blue ball and a white ball?

9.19%

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

x + y = 3
x - y = -16

A(-6.5,9.5)

3x - 8y = 10
7x + 6y = -1

B(0.7,-0.99)

22. Write the following fractions in simplest form:

66x⁶y⁹
22x¹⁰y⁸

3y
x⁴

(x + 2)²
(x + 2)

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.

-x² = 7x - 78
x₁ = 6, x₂ = -13

24. Convert the following repeating decimal into a fraction:

x = 0.522
470
900

25. Solve the following equation:

-
3x - 2
+ 13 = 8
x = 9

26. Rationalize the denominator of each fraction below:

25
5
1 +
7

-
25
5
- 25
35
6

27. Use a trigonometric ratio to find x:

x = 22.63 cm

28. The sum of two consecutive even integers is 58. What are the integers? (Hint: use 2x as the first even integer)

a=28, b=30

29. After you leave your house, you walk 4 blocks south and 3 blocks west. How far are you from your house?

I am
5
blocks from my house.

30. The length of a rectangle is 3 more than thrice its width. The area of the rectangle is 270ft². What is the length and width of the rectangle?

width = 9, length = 30

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