IAAT - Iowa Algebra Aptitude Formulating Rules from Data Questions and Answers — Questions and Answers
Question 1: The table below shows a relationship between an input, x, and an output, y. Which equation correctly describes this relationship?
- y = 4x - 1
- y = 2x + 1
- y = x² + 2 (Correct answer)
- y = 3x
Correct answer: y = x² + 2
By testing each input value (x) in the proposed equations, only y = x² + 2 correctly produces the corresponding output value (y) for all pairs in the table. For x=1, 1²+2=3. For x=2, 2²+2=6. For x=3, 3²+2=11. For x=4, 4²+2=18.
Question 2: A cell phone plan costs $40 per month, which includes 5 GB of data. Any additional data costs $10 per GB. Which equation represents the total monthly cost (C) for a user who uses 'g' gigabytes of data, where g is greater than 5?
- C = 40 + 10(g - 5) (Correct answer)
- C = 40 + 10g
- C = 10(g - 5)
- C = 50g
Correct answer: C = 40 + 10(g - 5)
The total cost (C) is the base fee of $40 plus the cost for extra data. The amount of extra data is the total data used (g) minus the included amount (5), which is represented as (g - 5). The cost for this extra data is $10 per GB, so the extra charge is 10(g - 5). Therefore, the complete equation is C = 40 + 10(g - 5).
Question 3: A function machine follows the rule: 'multiply the input by 4, then subtract 7'. If the output of the machine is 53, what was the input?
- 13.25
- 15 (Correct answer)
- 205
- 11
Correct answer: 15
To find the input, you must perform the inverse operations in reverse order. Start with the output, 53. The reverse of 'subtract 7' is 'add 7', so 53 + 7 = 60. The reverse of 'multiply by 4' is 'divide by 4', so 60 / 4 = 15. The input was 15.
Question 4: The scatter plot shows the relationship between the number of hours students spent reviewing for a science exam and their exam scores. Which statement best describes the relationship shown in the data?
- There is no relationship between review time and exam score.
- Spending more time reviewing causes exam scores to decrease.
- As review time increases, the exam score tends to increase. (Correct answer)
- All students who reviewed for 4 hours got the same score.
Correct answer: As review time increases, the exam score tends to increase.
The points on the scatter plot generally trend from the lower-left to the upper-right. This pattern indicates a positive correlation, which means that as the value on the x-axis (Hours Reviewing) increases, the value on the y-axis (Exam Score) also tends to increase.
Question 5: Two rival companies offer video game streaming services. Company X charges a $10 monthly fee and $3 per game downloaded. Company Y charges a flat fee of $25 per month for unlimited game downloads. For what number of games downloaded per month is the cost of both services exactly the same?
- 3 games
- 4 games
- 6 games
- 5 games (Correct answer)
Correct answer: 5 games
Let 'g' be the number of games. The cost for Company X is C = 3g + 10. The cost for Company Y is C = 25. To find when the costs are equal, set the expressions equal to each other: 3g + 10 = 25. Subtract 10 from both sides: 3g = 15. Divide by 3: g = 5. At 5 games, the cost for both services is $25.
Question 6: A pattern is built with square tiles. Figure 1 has 2 tiles, Figure 2 has 5 tiles, and Figure 3 has 10 tiles. Which rule can be used to find the number of tiles, T, in any Figure, n?
- T = 3n - 1
- T = n + 1
- T = 2n² - 1
- T = n² + 1 (Correct answer)
Correct answer: T = n² + 1
Let's test the rule T = n² + 1. For Figure 1 (n=1), T = 1² + 1 = 2. This is correct. For Figure 2 (n=2), T = 2² + 1 = 5. This is correct. For Figure 3 (n=3), T = 3² + 1 = 10. This is also correct. The rule holds for all given figures.
IAAT - Iowa Algebra Aptitude Formulating Rules from Data Questions and Answers
The table below shows a relationship between an input, x, and an output, y.
Which equation correctly describes this relationship?