IAAT - Iowa Algebra Aptitude Evaluating Simple Expressions Questions and Answers

Question 1

What is the value of the expression 3x² - 2y + 5 when x = 4 and y = 7?

Accepted Answer

39

Answer

Substitute x=4 and y=7 into the expression. Following the order of operations (PEMDAS/BODMAS), first evaluate the exponent: 4² = 16. Then, perform multiplication: 3 × 16 = 48 and 2 × 7 = 14. The expression becomes 48 - 14 + 5. Finally, perform subtraction and addition from left to right: 48 - 14 = 34, and 34 + 5 = 39.

Question 2

A gamer starts a level with 1500 points. In the first minute, they lose 80 points. In the second minute, they find a treasure that triples their current score. In the third minute, they use a power-up that costs 250 points. What is the gamer's final score?

Accepted Answer

4010

Answer

First, calculate the score after the first minute: 1500 - 80 = 1420. Next, triple this new score: 1420 × 3 = 4260. Finally, subtract the cost of the power-up: 4260 - 250 = 4010. The final score is 4010.

Question 3

What is the value of the expression 10 + 8 × (1/4) - 6 ÷ 2?

Accepted Answer

9

Answer

According to the order of operations (PEMDAS/BODMAS), perform multiplication and division from left to right before addition and subtraction. First, 8 × (1/4) = 2. Then, 6 ÷ 2 = 3. The expression simplifies to 10 + 2 - 3. Finally, perform addition and subtraction from left to right: 10 + 2 = 12, and 12 - 3 = 9.

Question 4

Which of the following expressions has the greatest value?

Accepted Answer

(5 + 3) × 6

Answer

To find the expression with the greatest value, we must evaluate each one correctly using the order of operations.
A) 5 + 3 × 6 = 5 + 18 = 23.
B) (5 + 3) × 6 = 8 × 6 = 48.
C) 6 + 3 × 5 = 6 + 15 = 21.
D) 5 × (6 - 3) = 5 × 3 = 15.
Comparing the results (23, 48, 21, 15), the greatest value is 48.

Question 5

A student is asked to evaluate the expression 5 - 2(9 - 4)². Their work is shown below. In which step did the student make the first mistake?

Step 1: 3(9 - 4)²
Step 2: 3(5)²
Step 3: 3(25)
Step 4: 75

Accepted Answer

Step 1

Answer

The student made a mistake in Step 1. According to the order of operations (PEMDAS), operations inside parentheses and multiplication should be performed before subtraction. Instead of evaluating (9 - 4) or handling the multiplication of 2 by the parenthetical expression, the student incorrectly performed the subtraction 5 - 2 first. The correct first step is to evaluate the expression inside the parentheses: 5 - 2(5)².

IAAT - Iowa Algebra Aptitude Test Practice Test

IAAT - Iowa Algebra Aptitude Test Practice Test

IAAT - Iowa Algebra Aptitude Evaluating Simple Expressions Questions and Answers