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 12? -60

2. Add: -11 and 9? -2

3. Divide: -3 and 3? -1

4. Substract: 4 and 5? -1

5. Calculate: |3 · -18 + -9| 63

6. Simplify the following expressions:

19x + 17 – -5 22+19x
10 – 2x – -6 – -13x 16+11x
7y – 6y – 12x + -19x + 10y -31x+11y
x³ × x²⁰ × x⁴ × y⁵ x²⁷ × y⁵
x¹⁸
x^-9
x²⁷
(7x²)¹⁰ 282475249x²⁰

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

-4x + 1 = 1 + -4x
0 + 8x = 8x
9 × 2 = 2 × 9
( 9 + 3 ) + 4 = 9 + ( 3 + 4 )

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

z + 4 × -6 = 4 × -6 + z
11 × ( 19 × -18 ) = ( 11 × 19 ) × -18
( -3 + -17 ) × y = -3 × y + -17 × y

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

9. Solve the following equations for x:

-40 = 35 + x x = -75
-
5
25
x = -
20
25
x = 4
-35 + 8x = -19 x = 2
gx + ax = -c x = (-c)/(g+a)

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

23x – -13 ≤ -10 x ≤ -1

x ≠ 924
-37 > x ≤ 95

-
18
9
x <
24
12
x > -1

11. Convert the following numbers into scientific notation:

0.00000000977 9.77 × 10^-9
74100000 7.41 × 10⁷

12. Add the following polynomials:

-1z¹⁰ + 7z⁸ + -9z⁵ + 12z³ + 1z¹ and 15z¹⁰ + -11z⁸ + -10z⁵ + 13z³ + 1z¹

14z¹⁰ + -4z⁸ + -19z⁵ + 25z³ + 2z¹
9z¹⁷ + 8z⁸ + 3z⁴ and -2z²⁰ + -13z¹⁷ + 5z⁸ + -7z⁷ -2z²⁰ + -4z¹⁷ + 13z⁸ + -7z⁷ + 3z⁴

13. Multiply the following polynomials and simplify:

(8x³ + 3x²)(6x⁵ + 6x⁴ + 7)

48x⁸ + 66x⁷ + 18x⁶ + 56x³ + 21x²
(2x⁵ + 7x² + 9x)(7x³ + 7x²)

14x⁸ + 14x⁷ + 49x⁵ + 112x⁴ + 63x³

14. Divide:

10x² - 3x + 7 / 2x - 3
(5x + 6) with a remainder of 25

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

75, 56
1
27x⁴y, 45x²y⁵, 22y
y

16. Factor the following polynomials:

20x³ - 100x² + 60x
20x(x -
5 +
13
2
)(x -
5 -
13
2
)
x² - 8x - 9
(x - 9)(x + 1)
x⁶ + 11x⁵ + 24x⁴
x⁴(x + 3)(x + 8)

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

x =
9
and

-1
x =
0
,
-3

and
-8

18. You have 2 pants, 2 shirts, and 3 shoes. How many different ways can you dress?

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

24, 30, 35, 5, 40, 25, 34, 33, 37, 31

20. Suppose you toss a coin and spin a spinner numbered 1 through 5

What is the probability of getting tails and 5?

10.00%

What is the probability of getting heads and an odd number?

20%

What is the probability of getting tails and a multiple of 2?

20%

What is the probability of getting tails and a prime number?

30%

What is the probability of not heads and not 5?

40%

What is the probability of getting not heads and not a whole number?

0%

What is the probability of heads or tails and a whole number?

100%

What is the probability of getting tails?

50%

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

x + y = 10
x - y = -13

A(-1.5,11.5)

2x - 9y = -10
7x + 7y = -7

B(-1.73,0.73)

22. Write the following fractions in simplest form:

22x⁶y⁷z⁴
44x⁷y⁹z²

z²
2xy²

x⁵ - 5x⁴ - 6x³
x(x + 1)

x²(x - 6)

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

-11x + 28 = -x²
x₁ = 4, x₂ = 7

24. Convert the following repeating decimal into a fraction:

x = 0.53
48
90

25. Solve the following equation:

4x + 1
- 18 = -5
x = 42

26. Rationalize the denominator of each fraction below:

4
2
3 +
21

-
3
2
-
42
3

27. Use a trigonometric ratio to find x:

x = 27.58 cm

28. The sum of two consecutive odd integers is 44. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=21, b=23

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. Each side of a square is lengthened by 8 m. This makes the area of the square 289m². What is the original length of a side of the square?

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