IAAT - Iowa Algebra Aptitude Evaluating Simple Expressions Questions and Answers — Questions and Answers
Question 1: What is the value of the expression 3x² - 2y + 5 when x = 4 and y = 7?
- 135
- 39 (Correct answer)
- 29
- 15
Correct answer: 39
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?
- 4170
- 3510
- 4510
- 4010 (Correct answer)
Correct answer: 4010
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?
- 9 (Correct answer)
- 3
- 1.5
- -0.75
Correct answer: 9
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?
- 5 + 3 × 6
- (5 + 3) × 6 (Correct answer)
- 6 + 3 × 5
- 5 × (6 - 3)
Correct answer: (5 + 3) × 6
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
- Step 4
- Step 3
- Step 2
- Step 1 (Correct answer)
Correct answer: Step 1
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.
Question 6: The formula to convert a temperature from Celsius (C) to Fahrenheit (F) is F = (9/5)C + 32. A meteorologist reports a temperature of 25° C. What is this temperature in degrees Fahrenheit?
- 57° F
- 103° F
- 77° F (Correct answer)
- 46° F
Correct answer: 77° F
To find the temperature in Fahrenheit, substitute C = 25 into the formula F = (9/5)C + 32. This gives F = (9/5) × 25 + 32. Following the order of operations, perform the multiplication first: (9/5) × 25 = 9 × 5 = 45. Then, perform the addition: 45 + 32 = 77. The temperature is 77° F.
IAAT - Iowa Algebra Aptitude Evaluating Simple Expressions Questions and Answers
What is the value of the expression 3x² - 2y + 5 when x = 4 and y = 7?