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: 3 and 20? 60

2. Add: 3 and -6? -3

3. Divide: -15 and 5? -3

4. Substract: -5 and -7? 2

5. Calculate: |-17 · -17 + -6 · 14| 205

6. Simplify the following expressions:

19x + 18x – 7x 30x
20x – 16 + -13x + -8y -16+7x-8y
-2y – -3y – -14y + 18x + 3z 18x+15y+3z
x^-8 × y¹⁴ x^-8 × y¹⁴
x³
x⁶
x^-3
(5x³)² 25x⁶

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

( -8 × -6 ) + -7 = -7 + ( -8 × -6 )
( 7 × 4 ) × 9 = 7 × ( 4 × 9 )
5 + 1 = 1 + 5
a + b = b + a

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

15 + -4x = -4x + 15
(d + e) × 8 = 8 × (d + e)
(j + k + l) × 1 = j + k + l

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

9. Solve the following equations for x:

-89 + -x = 91 x = -180
1
22
x =
3
22
x = 3
-17 = 53x – 70 x = 1
ex = d x = d/e

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

-23x + 27 ≤ 4 x ≥ 1

x ≠ -561
-90 ≤ x ≥ 15

-
40
10
x ≤ -28 x ≥ 7

11. Convert the following numbers into scientific notation:

0.000000000353 3.53 × 10^-10
81700 8.17 × 10⁴

12. Add the following polynomials:

-3z⁹ + 12z⁷ + -14z² + 7 and -13z⁹ + -1z⁷ + 11z² + 6

-16z⁹ + 11z⁷ + -3z² + 13
-10z¹⁶ + -13z¹⁴ + -15z¹³ + -15z⁶ and 10z¹⁶ + -1z¹⁴ + -10z¹³ + 6z¹⁰ + 10z⁶ -14z¹⁴ + -25z¹³ + 6z¹⁰ + -5z⁶

13. Multiply the following polynomials and simplify:

(7x⁵ + 5x⁴)4x³

28x⁸ + 20x⁷
(4x⁴ + 2x³ + 6)(7x⁵ + 10)

28x⁹ + 14x⁸ + 42x⁵ + 40x⁴ + 20x³ + 60

14. Divide:

8x³ - 14x² + 12x - 21 / 4x - 7
2x² + 3

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

15, 36, 45
3
30x⁵y, 39x³, 22x³
x³

16. Factor the following polynomials:

20x³ + 16x² + 1x
20x(x -
-4 +
11
10
)(x -
-4 -
11
10
)
x² - 17x + 70
(x - 7)(x - 10)
x⁸ - 8x⁷ + 12x⁶
x⁶(x - 2)(x - 6)

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

x =
7
and

10
x =
0
,
2

and
6

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:

37, 24, 23, 21, 18, 30, 36, 32

20. A bag contains 2 blue balls, 7 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?

38.18%

A blue ball and a white ball?

3.64%

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

x + y = 10
x - y = 19

A(14.5,-4.5)

10x - 2y = -2
2x + y = -14

B(-2.14,-9.71)

22. Write the following fractions in simplest form:

5x⁷y²
15x¹⁰y

y
3x³

(x² - 2x + 1)
(x - 1)

x - 1

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

-15 = x² + 16x
x₁ = -1, x₂ = -15

24. Convert the following repeating decimal into a fraction:

x = 0.39
39
99

25. Solve the following equation:

-17
x
- 10 = -20
x
+ 8
x = 36

26. Rationalize the denominator of each fraction below:

10
2 -
10

-
10 + 5
10
3

27. Use a trigonometric ratio to find x:

x = 16.50 cm

28. The sum of two consecutive even integers is 46. What are the integers? (Hint: use 2x as the first even integer)

a=22, b=24

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

I am
5
blocks from my house.

30. Each side of a square is lengthened by 3 ft. This makes the area of the square 361ft². What is the original length of a side of the square?

16 ft

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