Here is another installment in my series reviewing the NY State Regents exams in mathematics.

The following question appeared on the 2014 Integrated Algebra exam.

My question is this: what, exactly, is an “absolute value equation”? According to the scoring key, the correct answer to this question is (2). This suggests that the exam writers believe an “absolute value equation” to be some transformation of .

But “absolute value equation” is not a precise description of what the exam writers seem to be looking for. It would be hard to argue that is not an “absolute value equation”, but that appears to be the graph depicted in (1). With some work, all the given graphs could be represented as equations involving absolute values (an exercise left to the reader).

I doubt this imprecision caused any student to get this question wrong, but as I have argued again and again, these exams should stand as exemplars of mathematical precision. These exams should not model imprecise language, poor notation, and improper terminology. We do our students a great disservice by constantly asking them to guess what the exam writers were trying to say.