Algebra 2 PARCC: imaginary number arithmetic

The following fill-in-the-number question, explained here in hopes of helping algebra 2 students and their parents in Maryland prepare for the PARCC test near the end of this school year, appears on the released version of the PARCC Algebra 2 sample test released following the 2016 test (#5).

In the table shown, i represents the imaginary unit. Select all cells in the table for which the product of the row value and the column value is a real number.

Value –3 –2i 5 i2
i __ __ __ __
–4 __ __ __ __
Correct answer and references
Sample solution strategy (there are others)

Analysis of this question and online accessibility

The question can be delivered online or on paper. However, because students have to make multiple selections, a multiple-choice presentation might have slightly different performance statistics from the online version of the item.

The question is aligned to the Common Core math standard to which it purports to align, but the use of the word “cell” to describe a table element may make the question less accessible for some students who have a limited proficiency in English, as this word has multiple meanings with very different translations into whatever may be their native language. These errors are considered minor, since the interaction is clear, but a better word choice would have made the question more accessible to the broader population.

No special accommodation challenges can be identified with this question, so the question is considered fair.

About the Author

Paul Katula
Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.

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