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: 11 and 11? 121

2. Add: 16 and -20? -4

3. Divide: 2 and -2? -1

4. Substract: -5 and -11? 6

5. Calculate: |12 · 10 + 16 · 5| 200

6. Simplify the following expressions:

-19x – 11x – 14x -44x
-18y – -16x – 20y – -13y 16x-25y
-7 – 1x + -18z – -17x – 4y -7+16x-4y-18z
y^-9 × y^-15 × x²⁰ x²⁰ × y^-24
x¹⁸
x⁹
x⁹
(7x⁴)⁷ 823543x²⁸

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

( x × y ) × z = x × ( y × z )
( m × n ) + 8 = 8 + ( m × n )
a + b = b + a
-4 × ( y + 6 + 6 ) = -4×y + -4×6 + -4×6

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

1 × -79 = -79
b × ( c × d ) = ( b × c ) × d
6 + n + o = n + o + 6

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

9. Solve the following equations for x:

-94 + x = 28 x = 122
1
7
x =
24
7
x = 24
-58 = -15x + -43 x = 1
e + f = -gx x = (-e-f)/g

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

-x + 7 > -29 x < 36

x ≠ 663
-1 ≥ x ≤ 17

20
4
x < -
20
2
x < -2

11. Convert the following numbers into scientific notation:

0.000000000804 8.04 × 10^-10
69900000 6.99 × 10⁷

12. Add the following polynomials:

-2z⁹ + -14z⁶ and 14z⁹ + -1z⁶

12z⁹ + -15z⁶
7z¹⁶ + 1z¹⁵ + -6z¹² + 11z⁶ and -1z¹⁶ + -14z¹⁵ + -5z¹² 6z¹⁶ + -13z¹⁵ + -11z¹² + 11z⁶

13. Multiply the following polynomials and simplify:

1x(1x⁵ + 6x⁴ + 5x²)

x⁶ + 6x⁵ + 5x³
(10x⁴ + 4x)(2x⁵ + 8x³ + 5x²)

20x⁹ + 80x⁷ + 58x⁶ + 32x⁴ + 20x³

14. Divide:

5x³ + 35x² + 5x + 35 / x + 7
5x² + 5

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

77, 72
1
60xy⁴, 54xy
6xy

16. Factor the following polynomials:

25x³ + 45x² + 14x
25x(x +
2
5
)(x +
7
5
)
x² - 5x - 50
(x - 10)(x + 5)
x⁵ + 28x⁴ + 195x³
x³(x + 15)(x + 13)

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

x =
10
and

-5
x =
0
,
-15

and
-13

18. You have 5 pants, 4 shirts, and 3 shoes. How many different ways can you dress?

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

5, 7, 30, 10, 20, 33, 26, 4, 28

20. Suppose you toss a coin and spin a spinner numbered 1 through 18

What is the probability of getting heads and 3?

2.78%

What is the probability of getting tails and an even number?

25%

What is the probability of getting tails and a multiple of 5?

8.33%

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

19.44%

What is the probability of not heads and not 11?

47.22%

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 = 4
x - y = -2

A(1,3)

x - 9y = 19
9x + 9y = -8

B(1.1,-1.99)

22. Write the following fractions in simplest form:

22x⁶y⁷z⁴
44x⁷y⁹z²

z²
2xy²

x³ - 4x² - 21x
x⁴(x - 7)

(x + 3)
x³

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

9x = x² - 22
x₁ = -2, x₂ = 11

24. Convert the following repeating decimal into a fraction:

x = 0.35
32
90

25. Solve the following equation:

-9
x
+ 20 = 11
x
- 20
x = 4

26. Rationalize the denominator of each fraction below:

5
15
15 +
5

15
15
- 5
3
44

27. Use a trigonometric ratio to find x:

x = 39.84 cm

28. The sum of two consecutive even integers is 30. What are the integers? (Hint: use 2x as the first even integer)

a=14, b=16

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

I am
5
blocks from my house.

30. Each side of a square is lengthened by 4 m. This makes the area of the square 225m². What is the original length of a side of the square?

11 m

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