IAAT - Iowa Algebra Aptitude Using Algebraic Symbols Questions and Answers

Question 1

A student is saving for a new tablet that costs $350.
They already have $80 saved.
They earn $15 per week for chores.
Which inequality represents the number of weeks, `w`, the student must work to have at least enough money to buy the tablet?

Accepted Answer

80 + 15w ≥ 350

Answer

80 + 15w < 350

Answer

15w - 80 ≥ 350

Answer

80w + 15 ≤ 350

Question 2

The expression `100 - 8x` can be used to represent the amount of water, in gallons, remaining in a tank after `x` minutes. Which of the following statements best describes the meaning of the term `8x` in this context?

Accepted Answer

The total amount of water that has been drained from the tank after `x` minutes.

Answer

The tank started with 8 gallons of water.

Answer

Water is being added to the tank at a rate of 8 gallons per minute.

Answer

The tank is empty after 8 minutes.

Question 3

Which algebraic expression correctly represents the phrase 'five less than the product of a number, `n`, and the square of another number, `m`'?

Accepted Answer

nm² - 5

Answer

5 - nm²

Answer

(n + m²) - 5

Answer

5 - (n + m²)

Question 4

A coach buys `g` sports drinks for $2 each and `g` protein bars for $3 each for their team. The total cost can be represented by the expression `2g + 3g`. Which of the following expressions is NOT an equivalent way to represent the total cost?

Accepted Answer

5g²

Answer

5g

Answer

g(2 + 3)

Answer

(3 + 2)g

Question 5

A group of `f` friends wins a cash prize of `P` dollars. They agree to first donate $100 to a charity and then split the remaining amount equally among themselves. Which expression represents the amount of money each friend receives?

Accepted Answer

(P - 100) / f

Answer

P/f - 100

Answer

P / (f - 100)

Answer

100 - P/f

Question 6

Which verbal statement accurately describes the algebraic expression `(x + 4)³`?

Accepted Answer

The cube of the sum of a number and four.

Answer

The sum of a number cubed and four.

Answer

Four more than the cube of a number.

Answer

The product of a number and four, cubed.

A student is saving for a new tablet that costs $350.They already have $80 saved.They earn $15 per week for chores.Which inequality represents the number of weeks, `w`, the student must work to have *at least* enough money to buy the tablet?

A student is saving for a new tablet that costs $350.
They already have $80 saved.
They earn $15 per week for chores.
Which inequality represents the number of weeks, `w`, the student must work to have at least enough money to buy the tablet?