All About the Redesigned SAT: Systems of Equations

The New SAT - The Redesigned SAT - Math - Systems of Equations

When a test like the SAT undergoes a major redesign, changes come in a variety of forms. Big changes like those to the essay structure are easier to spot, but subtle changes can be just as interesting.

Consider the pair of similar-looking questions above. On the left we have a question that could appear on the current SAT Reasoning Test. On the right we have a question that could appear on the redesigned SAT.

So what is different? The question on the left has five answer choices; the question on the right has four answer choices. The question on the left has three variables and two equations; the question on the right has two variables and two equations. But is that it? Are we looking at two superficially different yet largely equivalent questions?

The key different between these two questions is not how they look but how they are solved. On the left, we have a system with more variables than equations.

Can we solve for y? No. Can we solve for z? No. Do we need to? No.

We don’t need to solve for y or z, we just need to find the sum of y and z. And if we subtract the second equation from the first equation, we get y​+​z​=​4. How did we know to subtract the second the equation from the first equation? Because the SAT Reasoning Test is looking for clever manipulations of these equations (in this case, simple subtraction) to get the desired result without solving the whole system.

But what about the question on the right? Here we are asked for the actual solution. So we have two simple approaches: we can solve this system like any beginning algebra student by eliminating one of the variables, or we can find the solution by plugging in the pairs given in the answer choices.

Neither of these solutions works on the question on the left: we can’t solve the system, and we can’t directly plug in numbers for y​+​z.

Why does this matter? Well, this change showcases one of the main differences between the math sections on the SAT Reasoning Test and the redesigned SAT. The math on the current test focuses more on problem-solving skills, while the math on the new test focuses more on skills with the kinds of questions given in school.

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Posted on November 24, 2015 and filed under SAT.