Algebra test generator

Name _____________________ Date:_____________________

current difficulty level: Choose test difficulty: Easy Challenging
(current difficulty level: Easy)

Solve the following problems:

Important instructions

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1. Multiply: -8 and -14? 112

2. Add: 9 and 18? 27

3. Divide: -15 and 3? -5

4. Substract: -7 and 8? -15

5. Calculate: |5 · -14 + -7 · -2| 56

6. Simplify the following expressions:

2x + 7x + -13x -4x
-20x – 3x – 2y + 1 1-23x-2y
12x – -20 – 10z + 16 – 13x 36-1x-10z
y¹³ × x^-8 × y⁵ × x^-9 x^-17 × y¹⁸
x³
x³
x⁰
(5x³)⁸ 390625x²⁴

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

0 + -10x = -10x
u × ( v + 6 ) = uv + 6v
( m × n ) × 3 = m × ( n × 3 )
5 × ( y + 9 + 2 ) = 5×y + 5×9 + 5×2

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

( u + v ) × t = u × t + v × t
( w + x ) + v = w + ( x + v )
30 + -66 = 30 + -66

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

9. Solve the following equations for x:

-25 + x = 54 x = 79
21
12
= -
7
4
x x = -1
-108x + 20 = -88 x = 1
dx = -f x = -f/d

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

-2x + 35 ≥ -3 x ≤ 19

x ≠ 92
-86 < x ≤ 59

8
4
x ≤
32
4
x ≤ 4

11. Convert the following numbers into scientific notation:

0.00000000981 9.81 × 10^-9
94900000000 9.49 × 10¹⁰

12. Add the following polynomials:

5z⁹ + -2z⁷ + 1z⁵ + 5 and 12z⁹ + 9z⁵

17z⁹ + -2z⁷ + 10z⁵ + 5
-13z²⁰ + -11z¹⁸ + 1z¹⁶ + -7z⁸ and -12z²⁰ + -5z¹⁸ + 9z¹⁶ + -3z⁸ -25z²⁰ + -16z¹⁸ + 10z¹⁶ + -10z⁸

13. Multiply the following polynomials and simplify:

(3x² - 1)6x⁵

18x⁷ - 6x⁵
(7x³ + 7x² + 1)(4x⁵ - 6)

28x⁸ + 28x⁷ + 4x⁵ - 42x³ - 42x² - 6

14. Divide:

4x³ - 4x² + 8x - 8 / x - 1
4x² + 8

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

36, 52
4
45x⁹y⁸, 30x¹⁰y⁶, 50x⁷y⁹
5x⁷y⁶

16. Factor the following polynomials:

54x⁵ - 54x⁴ + 9x³
54x³(x -
3 +
3
6
)(x -
3 -
3
6
)
x² - 3x - 4
(x - 4)(x + 1)
x⁷ + 4x⁶ + 4x⁵
x⁵(x + 2)(x + 2)

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

x =
4
and

-1
x =
0
,
-2

and
-2

18. You have 4 CDs. How many different ways can you listen to them?

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

23, 14, 37, 11, 38, 34, 15

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

What is the probability of getting tails and 3?

2.50%

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

25%

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

12.5%

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

20%

What is the probability of not heads and not 15?

47.5%

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 = 11
x - y = 17

A(14,-3)

7x - 3y = 6
3x + 8y = 14

B(1.38,1.23)

22. Write the following fractions in simplest form:

48x⁴y⁴
16x⁷y⁸

3
x³y⁴

(x - 3)⁷
(x - 3)⁵

(x - 3)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 + 42 = 17x
x₁ = 14, x₂ = 3

24. Convert the following repeating decimal into a fraction:

x = 0.5
5
9

25. Solve the following equation:

10
x
= 1
x = 100

26. Rationalize the denominator of each fraction below:

14
7

2
7

27. Use a trigonometric ratio to find x:

x = 17.68 cm

28. The sum of two consecutive odd integers is 52. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=25, b=27

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

I am
10
blocks from my house.

30. A rectangle has an area of 144m². Its width is 10 m less than its length. What are the dimensions of the rectangle?

width = 8, length = 18

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