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How the MAT Tests Math, Part 3: Algebra

MAT Algebra

In the past two posts, we’ve looked at the fundamentals of MAT math, covering both arithmetic and some basic number theory. This post picks back up with algebra, another important part of the Mathematics content area. As you might expect, MAT algebra problems can be tricky, since you have limited information to help you along. The good news is that MAT algebra is also “distraction-free,” with no weird charts or word-problem padding to obscure the answer.

MAT Algebra: Just the Facts

Some MAT algebra questions are just stripped-down versions of what you’d see on other standardized tests. The following practice problem, for example, would be turned into a big production on the GRE, with a paragraph of distracting information about factory output or the dimensions of a layer cake. On the MAT, for better or for worse, we get only the bare mathematical details:

x – 2 : 7 :: (x + 1)3 : _________

(A) 512
(B) 729
(C) 1000
(D) 1331

In this case, the “analogy” is actually an equation, or more accurately, a pair of equations:

If x – 2 = 7, then (x + 1)3 = _________

Solving for x is the way to proceed here:

x – 2 = 7
x = 2 + 7
x = 9

Then we plug our newfound value of x into the more complicated expression in slot 3:

(x + 1)3 = (9 + 1)3
= (10)3
= 1000

The algebra topics on the MAT are overwhelmingly ones you’d encounter in a standard high-school Algebra I course. You might, for example, have to multiply together a pair of binomials (i.e., “FOIL” them) or factor a quadratic expression. (If those terms make you uneasy, you can find a quick review in the Algebra section of our GRE Math eBook.) But many of the hardest-hitting algebra problem types, such as systems of equations or systems of inequalities, are off-limits for the MAT. The question format simply doesn’t leave room for such problems.

Vocab in Disguise

Now, a handful of MAT algebra questions, perhaps one or two per exam, will be purely terminological. Consider the following example:

x2: quadratic :: _________ : quintic

(A) x3
(B) x5
(C) x7
(D) x8

There’s no actual algebra required in this problem. Instead, the question asks us about the naming conventions for different powers of a variable. You may already know that an expression with an x2 term in it is a quadratic expression. You might even recognize that an expression with an x3 term is cubic. But what happens for powers larger than three? Here, we fall back on Latin ordinal prefixes: quartic (think “quartet”) means “fourth-degree,” and quintic (think “quintuplets”) means “fifth-degree.”

The analogy here goes something like this: “Just as x2 is a (very simple) quadratic expression, x5 is a (very simple) quintic expression.” In case you’re wondering, the usual terms for higher-degree expressions (or polynomials or functions) are sextic for sixth-degree, septic for seventh-degree, and octic for eighth-degree. Beyond that, even the mathematicians don’t care enough to have a consistent naming scheme.

The upshot is that “MAT algebra,” like “MAT chemistry” or “MAT history,” often boils down to specialized vocabulary. In the cramped multiple-choice format of the exam, there’s not much else they can test.

Notice, by the way, that the above question works even if the variable x is never mentioned. A more abstract, slightly more difficult version might read as follows:

2 : quadratic :: _________ : quintic

(A) 3
(B) 5
(C) 7
(D) 8

Here, we can state the governing analogy nice and compactly: “Quadratic expressions include terms of degree 2, but no higher; quintic expressions include terms of degree 5, but no higher.”


Like other posts in this series, the above is a brief sketch of the main ways in which the MAT deploys algebraic terms, concepts, and principles. If you feel that your grasp of those basics is shaky, I again recommend our GRE Math Formula eBook as a starting point for figuring out what you need to review. My goal here, as throughout the series, is to prime you to recognize the types of relationships that the MAT favors in its math problems.

With that in mind, we’ll be moving on to geometry in the next post. See you there!

About Michael

A fan of logic games, classic RPGs, and espresso (in no particular order), Michael likes to think of standardized tests as puzzles to be pulled apart and analyzed. He delights in showing students the trapdoors, pitfalls, and shortcuts that lurk in even the simplest of questions. When he isn't helping students navigate the GRE, GMAT, or MAT, Michael enjoys writing poetry, tinkering with microcontrollers, and taking long, leisurely hikes in the woods.

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