IAAT - Iowa Algebra Aptitude Graph and Table Analysis Questions and Answers — Questions and Answers
Question 1: The line graph below shows the temperature in a city over a 12-hour period. During which two-hour interval did the temperature increase at the highest rate? [A line graph shows 'City Temperature'. The x-axis is 'Time of Day' from 6 AM to 6 PM in 2-hour increments. The y-axis is 'Temperature (°F)' from 40 to 70. The data points are: 6 AM at 45°F, 8 AM at 50°F, 10 AM at 60°F, 12 PM at 65°F, 2 PM at 68°F, 4 PM at 67°F, 6 PM at 62°F.]
- 6 AM to 8 AM
- 8 AM to 10 AM (Correct answer)
- 12 PM to 2 PM
- 4 PM to 6 PM
Correct answer: 8 AM to 10 AM
To find the highest rate of increase, look for the steepest upward slope on the graph. Calculate the temperature change for each interval: 6-8 AM: 50-45 = 5°F increase. 8-10 AM: 60-50 = 10°F increase. 12-2 PM: 68-65 = 3°F increase. 4-6 PM: 62-67 = 5°F decrease. The greatest increase was 10°F, which occurred between 8 AM and 10 AM.
Question 2: A community garden tracks the growth of a sunflower. The table below shows the height of the sunflower at the end of each week. If the pattern of growth continues, what will be the height of the sunflower at the end of Week 6? | Week (W) | Height (cm) | |---|---| | 1 | 15 | | 2 | 21 | | 3 | 27 | | 4 | 33 |
- 39 cm
- 42 cm
- 45 cm (Correct answer)
- 36 cm
Correct answer: 45 cm
By analyzing the table, we can see that the sunflower grows by 6 cm each week (21 - 15 = 6; 27 - 21 = 6). To find the height in Week 6, continue the pattern. Week 5 height would be 33 + 6 = 39 cm. Week 6 height would be 39 + 6 = 45 cm.
Question 3: A survey asked 300 middle school students to name their favorite after-school club. The results are displayed in the pie chart below. How many more students chose the Sports club than the Art club? [A pie chart titled 'Favorite After-School Club' is shown with the following percentages: Sports 40%, Music 25%, Art 20%, Drama 15%.]
- 120
- 60
- 20
- 60 (Correct answer)
Correct answer: 60
First, calculate the number of students who chose each club. Sports: 40% of 300 = 0.40 * 300 = 120 students. Art: 20% of 300 = 0.20 * 300 = 60 students. Then, find the difference between the two groups: 120 (Sports) - 60 (Art) = 60 students. Alternatively, find the difference in percentage points (40% - 20% = 20%) and then calculate that percentage of the total students (20% of 300 = 0.20 * 300 = 60).
Question 4: The scatter plot below shows the relationship between the number of hours a student sleeps the night before a test and their score on the test. A line of best fit is drawn. Based on the line of best fit, what is the best prediction for the score of a student who sleeps for 8 hours? [A scatter plot shows 'Test Score vs. Hours of Sleep'. The x-axis is 'Hours of Sleep' from 4 to 10. The y-axis is 'Test Score' from 50 to 100. Data points show a positive correlation. A line of best fit passes through approximately (5, 65) and (9, 85).]
- 70
- 95
- 80 (Correct answer)
- 60
Correct answer: 80
To make a prediction using the line of best fit, locate '8 hours' on the x-axis. Move vertically up to the line of best fit, and then move horizontally to the left to read the corresponding value on the y-axis. The line passes through approximately 80 on the y-axis for an x-value of 8.
Question 5: A company sells two products, Gadgets and Widgets. The bar chart shows the number of units sold for each product in a month, and the table shows the profit per unit. Which statement is best supported by the data? [A bar chart shows 'Units Sold'. For 'Gadgets', the bar reaches 150. For 'Widgets', the bar reaches 200.] | Product | Profit per Unit | |---|---| | Gadget | $8 | | Widget | $5 |
- The company sold more Gadgets than Widgets.
- The total profit from Widgets was greater than the total profit from Gadgets.
- The company made more profit from Gadgets than from Widgets. (Correct answer)
- The profit from Gadgets and Widgets was equal.
Correct answer: The company made more profit from Gadgets than from Widgets.
To determine the total profit for each product, multiply the units sold by the profit per unit. Profit from Gadgets: 150 units * $8/unit = $1200. Profit from Widgets: 200 units * $5/unit = $1000. Comparing the total profits, $1200 (Gadgets) is greater than $1000 (Widgets). Therefore, the company made more profit from Gadgets.
Question 6: The table below shows the cost for a plumbing service based on the number of hours worked. Which equation represents the relationship between the total cost (C) and the number of hours worked (h)? | Hours (h) | Total Cost (C) | |---|---| | 1 | $110 | | 2 | $170 | | 3 | $230 | | 4 | $290 |
- C = 110h
- C = 50h + 50
- C = 110h + 60
- C = 60h + 50 (Correct answer)
Correct answer: C = 60h + 50
First, find the hourly rate by calculating the difference in cost for each additional hour: $170 - $110 = $60; $230 - $170 = $60. This means the plumber charges $60 per hour (60h). Next, determine the fixed fee. Using the first hour: C = 60(1) + fixed fee = $110. Solving for the fixed fee gives $50. Therefore, the equation is C = 60h + 50. This can be verified with another point: for h=2, C = 60(2) + 50 = 120 + 50 = $170, which matches the table.
IAAT - Iowa Algebra Aptitude Graph and Table Analysis Questions and Answers
The line graph below shows the temperature in a city over a 12-hour period.
During which two-hour interval did the temperature increase at the highest rate?
[A line graph shows 'City Temperature'.
The x-axis is 'Time of Day' from 6 AM to 6 PM in 2-hour increments.
The y-axis is 'Temperature (°F)' from 40 to 70.
The data points are: 6 AM at 45°F, 8 AM at 50°F, 10 AM at 60°F, 12 PM at 65°F, 2 PM at 68°F, 4 PM at 67°F, 6 PM at 62°F.]
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