IAAT - Iowa Algebra Aptitude Formulating Rules from Data 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?

Accepted Answer

y = x² + 2

Answer

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?

Accepted Answer

C = 40 + 10(g - 5)

Answer

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?

Accepted Answer

15

Answer

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?

Accepted Answer

As review time increases, the exam score tends to increase.

Answer

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?

Accepted Answer

5 games

Answer

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.

IAAT - Iowa Algebra Aptitude Test Practice Test

IAAT - Iowa Algebra Aptitude Test Practice Test

IAAT - Iowa Algebra Aptitude Formulating Rules from Data Questions and Answers