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: -6 and -1? 6

2. Add: -6 and -19? -25

3. Divide: 20 and 10? 2

4. Substract: 8 and -5? 13

5. Calculate: |-6 · 16 + -7 · -7| 47

6. Simplify the following expressions:

-6x + -13x + 19x
-5y + 5x + 3 + -7 -4+5x-5y
-4x – 18x + -6y + -20y + 13y – 9x -31x-13y
x¹⁵ × x^-1 × x^-16 x^-2
x⁸
x^-4
x¹²
(4x²)¹⁰ 1048576x²⁰

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

0 + -9x = -9x
( -10 × 7 ) + -2 = -2 + ( -10 × 7 )
( m + n ) + 8 = m + ( n + 8 )
( x × y ) + 7 = 7 + ( y × x )

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

( z + 0 ) × y = z × y + 0 × y
g + ( h + 0 ) = ( g + h ) + 0
( 16 × -8 ) × 12 = 16 × ( -8 × 12 )

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

9. Solve the following equations for x:

x – -30 = -23 x = -53
-
9
25
x =
9
25
x = -1
45 = 7 – 2x x = -19
ax = f x = f/a

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

-x – 1 > -19 x < 18

x ≠ 839
-92 > x ≤ 31

-17x ≤ -34 x ≥ 2

11. Convert the following numbers into scientific notation:

0.000000000182 1.82 × 10^-10
832000000 8.32 × 10⁸

12. Add the following polynomials:

3z⁹ + 9z⁵ + 2z⁴ and 3z⁴ + 9z² + -5z¹

3z⁹ + 9z⁵ + 5z⁴ + 9z² + -5z¹
2z¹⁷ + -8z¹³ + -14z¹¹ + -8z¹⁰ and 8z¹³ + -10z¹⁰ + 15z⁶ 2z¹⁷ + -14z¹¹ + -18z¹⁰ + 15z⁶

13. Multiply the following polynomials and simplify:

8x³(2x⁵ + 8x⁴)

16x⁸ + 64x⁷
(10x⁵ + 3x³ + 2x²)(4x⁵ + 8x)

40x¹⁰ + 12x⁸ + 8x⁷ + 80x⁶ + 24x⁴ + 16x³

14. Divide:

10x² + 24x - 7 / 2x + 6
(5x - 3) with a remainder of 11

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

22, 39, 90
1
20x⁵y³, 84x³y¹⁰, 63x⁹
x³

16. Factor the following polynomials:

22x⁴ + 20x³ - 2x²
22x²(x -
1
11
)(x + 1)
x² + 18x + 80
(x + 10)(x + 8)
x⁵ - 3x⁴ - 180x³
x³(x + 12)(x - 15)

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

x =
-10
and

-8
x =
0
,
-12

and
15

18. How many ways can 6 people wait in line?

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

16, 34, 31, 18, 35, 14, 40, 33, 29

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 tails 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 tails and not 2?

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 heads?

50%

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

x + y = 11
x - y = -20

A(-4.5,15.5)

4x - 10y = 7
8x + 6y = 10

B(1.37,-0.15)

22. Write the following fractions in simplest form:

84xy⁸
21x⁵y⁴

4y⁴
x⁴

(x + 2)
(x² + 4x + 4)

1
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 + 24 = -10x
x₁ = -4, x₂ = -6

24. Convert the following repeating decimal into a fraction:

x = 4.218
3797
900

25. Solve the following equation:

18 -
5x + 4
= 1
x = 57

26. Rationalize the denominator of each fraction below:

10
14 +
15

140 - 10
15
181

27. Use a trigonometric ratio to find x:

x = 33.94 cm

28. The sum of two consecutive odd integers is 20. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=9, b=11

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

I am
5
blocks from my house.

30. Each side of a square is decreased by 8 m. The area of the newly created square is 1m². What was the original length of one side of the square?

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