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: -8 and -12? 96

2. Add: -20 and -7? -27

3. Divide: -12 and 1? -12

4. Substract: 8 and 20? -12

5. Calculate: |6 + 1 · -15| 9

6. Simplify the following expressions:

-3x + 11 – -6x 11+3x
-18y + 19x + 17x – -7y 36x-11y
-14 + 13y – 4y – -10z – -12 + -17x -2-17x+9y+10z
x¹⁴ × x¹⁷ × x¹⁸ x⁴⁹
x^-2
x²⁰
x^-22
(5x³)⁸ 390625x²⁴

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

10 × 2 = 2 × 10
5( 9 + 4 ) = 5×9 + 5×4
( m × n ) × 8 = m × ( n × 8 )
( 6 × 1 ) + 10 = 10 + ( 6 × 1 )

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

(o + p) × 1 = 1 × (o + p)
f + g + h + 0 = f + g + h
1 × (h + i + j) = h + i + j

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

9. Solve the following equations for x:

-41 + -x = 55 x = -96
-
7
9
= -
7
9
x x = 1
2x – 65 = 41 x = 53
b = ax x = b/a

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

23x – -32 ≤ 9 x ≤ -1

x ≠ 297
53 ≤ x < 23

-
24
6
x ≤
28
7
x ≥ -1

11. Convert the following numbers into scientific notation:

0.000000949 9.49 × 10^-7
907000 9.07 × 10⁵

12. Add the following polynomials:

10z⁸ + -8z⁴ + 3z³ + 3z¹ and -7z⁹ + -10z⁸ + 7z³

-7z⁹ + -8z⁴ + 10z³ + 3z¹
-4z¹⁷ + 7z¹⁵ + -3z¹³ + -13z⁴ + -8z¹ and -14z¹⁷ + 5z¹³ + -11z⁴ + 8z³ + -7z¹ -18z¹⁷ + 7z¹⁵ + 2z¹³ + -24z⁴ + 8z³ + -15z¹

13. Multiply the following polynomials and simplify:

(2x³ + 10x)2

4x³ + 20x
(10x⁵ + 2x⁴ + 8x³)(10x⁵ + 7x³)

100x¹⁰ + 20x⁹ + 150x⁸ + 14x⁷ + 56x⁶

14. Divide:

8x³ + 12x² - 12x - 18 / 4x + 6
2x² - 3

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

30, 54, 52
2
78y¹⁰, 72x³y⁵, 24x⁸y²
6y²

16. Factor the following polynomials:

3x⁵ - 7x⁴ - 10x³
3x³(x + 1)(x -
10
3
)
x² - 4x - 21
(x + 3)(x - 7)
x⁹ + 17x⁸ + 30x⁷
x⁷(x + 2)(x + 15)

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

x =
-3
and

7
x =
0
,
-2

and
-15

18. You can purchase your ice cream in a cup or a cone. Orders can be one, two, or three scoops. Flavors can be chocolate, vanilla or strawberry. How many choices do you have?

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

17, 18, 37, 29, 9, 40, 13, 30

20. Suppose you toss a coin and spin a spinner numbered 1 through 10

What is the probability of getting tails and 1?

5.00%

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

25%

What is the probability of getting heads and a multiple of 4?

10%

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

20%

What is the probability of not tails and not 8?

45%

What is the probability of getting not tails 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 = 1
x - y = -16

A(-7.5,8.5)

3x - 3y = -11
x + 3y = 7

B(-1,2.67)

22. Write the following fractions in simplest form:

22x⁶y⁷z⁴
44x⁷y⁹z²

z²
2xy²

(x + 10)³
(x + 10)

(x + 10)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 = 13x + 30
x₁ = -10, x₂ = -3

24. Convert the following repeating decimal into a fraction:

x = 0.5817
5812
9990

25. Solve the following equation:

5 -
2x - 10
= -3
x = 37

26. Rationalize the denominator of each fraction below:

3
14

3
14
14

27. Use a trigonometric ratio to find x:

x = 16.17 cm

28. The sum of two consecutive odd integers is 48. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=23, b=25

29. After you leave your house, you walk 6 blocks west and 8 blocks north. How far are you from your house?

I am
10
blocks from my house.

30. Each side of a square is lengthened by 2 ft. This makes the area of the square 100ft². What is the original length of a side of the square?

8 ft

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