*by Christina Varner*

It’s hard to guess what math will and won’t show up on an SAT. The topics can range from anything a student is supposed to have learned in Algebra 1 to Geometry to Algebra 2.

While the math can seem all over the place, there is a repeated structure for some questions that we can use to our advantage. Understanding what a question is asking in advance can save you time and trouble on the test.

#### Let’s look at one of the question structures that is used repeatedly on the test:

The problems involve an equation or two, but in the places where we usually see numbers, they have used letters, in this case ‘a’ and ‘b’. The directions tell us that those particular letters (a and b) are “constants”. At this point, we have 4 different variables in our equations but two of them are meant to stay letters and two are not.

What?!

When they say “a and b are constants” they are telling us that those are the letters that should be replaced with numbers. ‘x’ and ‘y’ will remain as the variables, which is helpful because they’re the ones we are used to always seeing in equations.

So how are we supposed to decide what number to replace ‘a’ and ‘b’ with?

The question will also provide you the information you need to figure that out. You just have to know how to look for what that information is.

In the case of this particular problem, they already gave us the information we need when they state that the system would have “infinitely many” solutions.

If a system has infinite solutions, that means that both our equations represent the same function. We should look at the bottom equation as though it was originally the top equation and was multiplied by something. Since they gave us the coefficients of both ‘y’s (5 and 10), we can tell we must have multiplied by 2. Thus the original coefficient of x (2) should be multiplied by the same thing. And working backwards, ‘a’ on the other side of the equal sign should be half the value of -8.

#### Here is the same structure being used for a quadratics based problem:

Again, we are supposed to complete the equation by figuring out what numbers to replace ‘a’ and ‘b’ with. The trick is figuring out how to use the additional information they have given us to do so! In this case, they have given us a table of values to work with. And what is a table of values but a list of points on the function? Each column represents an (x,y) or (x,f(x)) that is included in our function. The second column of the table tells us that when x=0, we should expect an output of -2. Now we can replace ‘x’ and ‘f(x)’ in the equation with these values and solve for ‘b’. Once we know what number to use for ‘b’, we can pull a second point from the table (1,3) and replace ‘x’ and ‘f(x)’ again to solve for ‘a’.

The concept they base the question on may change but the structure remains the same. By telling us that letters other than ‘x’ and ‘y’ (or ‘f(x)’) are “constants” they are telling us they should be numbers and it’s our job to use what they have given us to figure out what numbers they should be.

Knowing that this is the aim of this kind of question will save you time figuring out the directions and give you a sense of where to begin in a question that looks rather bare and complicated.

The more exposure you have to practice problems, the more experience you will have with these repeated structures so feel free to spend a little time each day working on practice tests. Besides, just attempting the math is forming connections in your brain that improve understanding, even if you’re getting the problems wrong!

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