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Formulating Rules from Data Flashcards

6 cards from real IAAT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. The table below shows a relationship between an input, x, and an output, y. Which equation correctly describes this relationship?

    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.

  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?

    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).

  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?

    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.

  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?

    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.

  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?

    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.

  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?

    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.