IAAT - Iowa Algebra Aptitude Interpreting Mathematical Information Questions and Answers — Questions and Answers
Question 1: The graph below shows the number of books read by students in a book club over four months. Which of the following statements is best supported by the information in the graph?
[A bar graph shows 'Books Read by Book Club'. The x-axis is labeled 'Month' with bars for January, February, March, and April. The y-axis is labeled 'Number of Books' from 0 to 50 in increments of 10. January's bar reaches 25, February's reaches 35, March's reaches 30, and April's reaches 45.]
- The number of books read increased each month.
- The book club read more books in the first two months than in the last two months.
- The greatest increase in the number of books read occurred between March and April. (Correct answer)
- The average number of books read per month was 30.
Correct answer: The greatest increase in the number of books read occurred between March and April.
To find the correct statement, evaluate each option. A is incorrect because reading decreased from February (35) to March (30). B is incorrect because the first two months total 25+35=60 books, while the last two months total 30+45=75 books. C is correct because the increases were: Jan-Feb (35-25=10), Feb-Mar (a decrease), and Mar-Apr (45-30=15), making the March to April increase the largest. D is incorrect because the total is 25+35+30+45=135 books, and the average is 135/4 = 33.75.
Question 2: A new mathematical operation is defined as a © b = 2a + b^2. What is the value of 4 © 5?
- 18
- 28
- 33 (Correct answer)
- 39
Correct answer: 33
This question requires substituting the given numbers into the defined operation. In this case, 'a' is 4 and 'b' is 5. The operation is a © b = 2a + b^2. So, we calculate 2 * 4 + 5^2. This simplifies to 8 + 25, which equals 33.
Question 3: A recipe for a fruit smoothie requires 3 ounces of yogurt for every 5 ounces of mixed berries. Based on this relationship, which of the following tables correctly shows the amount of yogurt and berries needed for different quantities of the smoothie?
[Table A shows Yogurt(oz): 6, 9, 12 and Berries(oz): 10, 15, 20. Table B shows Yogurt(oz): 6, 8, 10 and Berries(oz): 10, 13, 16. Table C shows Yogurt(oz): 5, 10, 15 and Berries(oz): 3, 6, 9. Table D shows Yogurt(oz): 6, 9, 12 and Berries(oz): 8, 11, 14.]
- Table B
- Table A (Correct answer)
- Table D
- Table C
Correct answer: Table A
The problem states a ratio of 3 ounces of yogurt to 5 ounces of berries (3:5). We need to find the table where this ratio holds true for all entries. In Table A, the ratios are 6:10 (which simplifies to 3:5), 9:15 (simplifies to 3:5), and 12:20 (simplifies to 3:5). All pairs maintain the required 3:5 ratio. The other tables do not consistently follow this ratio.
Question 4: The total cost (C) of a pizza is determined by a base price of $12 plus $1.50 for each topping (t). Which equation correctly represents this relationship?
- C = 12t + 1.50
- C = 12 + 1.50t (Correct answer)
- C = 1.50(12 + t)
- C = 12 - 1.50t
Correct answer: C = 12 + 1.50t
The relationship described is a fixed cost plus a variable cost. The fixed cost, or base price, is $12. This is the starting value. The variable cost depends on the number of toppings, 't', at $1.50 each, which is represented as 1.50t. The total cost is the sum of the base price and the cost of the toppings, leading to the equation C = 12 + 1.50t.
Question 5: A middle school is tracking the number of students who participate in after-school sports. They find that the number of participants has increased by an average of 15 students per year since 2020, when there were 120 participants. If this trend continues, how many students will be participating in sports in 2026?
- 195
- 210 (Correct answer)
- 225
- 180
Correct answer: 210
First, determine the number of years that have passed from the start year (2020) to the target year (2026). This is 2026 - 2020 = 6 years. The number of participants increases by 15 students each year, so the total increase over 6 years is 6 * 15 = 90 students. To find the total number of participants in 2026, add this increase to the initial number of participants: 120 + 90 = 210 students.
Question 6: The formula for converting temperature from Celsius (C) to Fahrenheit (F) is F = (9/5)C + 32. A scientist records a temperature of 25°C. What is the equivalent temperature in Fahrenheit?
- 45°F
- 57°F
- 77°F (Correct answer)
- 102°F
Correct answer: 77°F
To solve this, substitute 25 for C in the given formula: F = (9/5) * 25 + 32. First, calculate (9/5) * 25. This simplifies to 9 * 5, which is 45. Then, add 32 to this result: F = 45 + 32. The final answer is 77°F.
