Algebra Air Test Practice

What is the simplified form of the following expression?

• (2y⁵) ÷ (x⁵)
• (22y²) ÷ (x⁷)
• (2y²) ÷ (x⁷)
• (22y⁵) ÷ (x⁵)

What is √27x⁹y³z⁶ written in simplest radical form?

• 3x³yz³√3y
• 3x⁴yz³√3xy
• 3x³yz²
• 3x³yz²√9xyz

When completely factored, what does 4x² - 11x + 6 equal?

• (2x + 2)(2x + 3)
• (2x - 2)(2x - 3)
• (x + 2)(4x + 3)
• (4x - 3)(x - 2)

Hillary is looking to purchase a piece of land to build a library.The rectangular plot of land has a length (∫) that is 25 feet longer than its width (w). The total area of the land is 6600 square feet. Which of the following best models the scenario?

• ∫ + w = 6600
• ∫ ⋅ (∫ + 25) = 6600
• 2 ⋅ (w + 25) = 6600
• w ⋅ (w + 25) = 6600

Find the quotient of (18x² + 15x - 18) and (3x - 2).

• 6x² + 9
• 3(2x + 3)
• (2x + 3)(3x - 2)
• 6x² + 5x - 6

What is the simplified form of the following?
[(-2x³) ÷ (y²)]^-3

• - [(y⁶) ÷ (8x⁹)]
• (6y⁵) ÷ (x⁶)
• - [(y⁵) ÷ (6x⁶)]
• - [(8x⁹) ÷ (y⁶)]

Which of the following verbal expressions could represent ¹/₂ (√x + 3) - 5y?

• one half the square root of three times a number x less the product of 5 and y
• one half the square root of three more than a number x less the product of 5 and y
• the difference of 5 and a number y and one half of x and three squared
• one half the square of a number x and three less the product of 5 and y

A paving company is paving the rectangular student parking lot at Hamilton High School. 
⋅ The length of the parking lot can be represented as (5p - 7)
⋅ The width of the parking lot can be represented as (3p + 4)
Which expression represents the area of the parking lot?

• 15p² - 41p - 28
• 8p² + 41p - 3
• 8p² - p - 3
• 15p² - p - 28

Simplify: ∛? = 3∛5

• 32
• 135
• 45
• 27

This is Charlie's model. 
Which of the following is equivalent to Charlie's model?

• (2x - 12)(3x + 2)
• (7x²+3x+7)-(x²+5x+7)
• (4x²-x+3)+(2x²+x+3)
• (36x² - 12x + 6x) ÷ (6x)