# Regents Recap — January 2014: Systems of Equations

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

Solving systems of equations is a fundamental mathematical skill. Systems come up in a variety of mathematical contexts, and so they play a natural role in all high school math courses.

It’s not surprising, then, that solving systems of equations appear on all New York math Regents exams. But what is surprising is how similar the questions on different exams are, given that the three exams span 3-4 years of mathematical learning.

For example, here is a problem from the Integrated Algebra exam.

Here is a problem from the Geometry exam.

And here is a problem from the Algebra 2 / Trig exam.

The question from the Integrated Algebra exam is actually harder than the question on the Geometry exam. Ironically, the directive on the algebra exam is to solve the equation *graphically*.

The system on the Algebra 2 / Trig exam involves rational expressions and a quadratic equation, but these are skills students are supposed to have in the Integrated Algebra course, which they take 2-3 years earlier.

I have written about this phenomenon before, but it continues to strike me as odd that over the span of 3-4 years of mathematics instruction, this is the growth these tests are looking for.

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