IAAT - Iowa Algebra Aptitude Representing Relationships Questions and Answers

Question 1

A pizza restaurant charges a flat fee of $3 for delivery and $11 for each pizza ordered. Which equation can be used to find the total cost (C) for any number of pizzas (p)?

Accepted Answer

C = 11p + 3

Answer

The total cost (C) is the sum of the cost of the pizzas and the delivery fee. The cost of the pizzas is $11 times the number of pizzas (p), which is 11p. The delivery fee is a constant $3. Therefore, the correct equation is C = 11p + 3.

Question 2

The table below shows the relationship between the number of hours a student spends studying (h) and the score they receive on a test (S). Which rule describes this relationship?

| Hours (h) | Score (S) |
|---|---|
| 0 | 65 |
| 1 | 72 |
| 2 | 79 |
| 3 | 86 |

Accepted Answer

S = 7h + 65

Answer

The score (S) starts at 65 when the hours (h) are 0. For each additional hour of studying, the score increases by 7. This can be represented by the equation S = 7h + 65. Let's test it: for h=2, S = 7(2) + 65 = 14 + 65 = 79, which matches the table.

Question 3

Which of the following verbal statements correctly represents the algebraic expression 2(n - 5)?

Accepted Answer

Twice the difference of a number and five.

Answer

The expression (n - 5) represents 'the difference of a number and five'. The number 2 outside the parentheses indicates that this entire difference is multiplied by two, or 'twice' the difference.

Question 4

A taxi company charges $2.50 for the first mile and $0.75 for each additional mile. If 'm' represents the total number of miles traveled, which expression represents the total cost for a ride that is more than one mile?

Accepted Answer

2.50 + 0.75(m - 1)

Answer

The cost includes a flat fee of $2.50 for the first mile. The variable 'm' is the total miles. Since the first mile is already paid for by the $2.50 fee, the additional charge of $0.75 applies only to the remaining miles, which is represented by (m - 1). Thus, the total cost is 2.50 + 0.75(m - 1).

Question 5

The perimeter of a rectangle is found using the formula P = 2L + 2W, where L is the length and W is the width. If the length of a rectangle is 4 units more than its width (W), which equation represents the perimeter in terms of only its width?

Accepted Answer

P = 2(W + 4) + 2W

Answer

The problem states that L = W + 4. To write the perimeter formula in terms of only W, we substitute (W + 4) for L in the original formula: P = 2(W + 4) + 2W.

IAAT - Iowa Algebra Aptitude Test Practice Test

IAAT - Iowa Algebra Aptitude Test Practice Test

IAAT - Iowa Algebra Aptitude Representing Relationships Questions and Answers