SAT Tip of the Week: The Most Useful Math Tip You Will Hear This Year

SAT Tip of the Week - FullIn the world of test prep, there are a number of promises made about “one trick” that will bring up your score 800 points with almost no effort!  This is almost always an oversimplification and the tips are either so broad they are  not useful, or much more complicated in practice than in theory.

This tip is not a panacea for all of your testing challenges, but for those who struggle with the math section of the SAT or ACT, this one technique has been extremely helpful for approaching difficult math problems. So what is this incredible technique?

Write down all the given information and plug it into an applicable equation.

This may sound like an obvious technique, but often times even advanced students don’t do this one extremely useful and beneficial step.  Let’s take a look at how this technique works in practice to see just how useful it can be:

Farmer Charmer is building a stable for his prize winning ponies. The length of the stable needs to be twice the width.  In the center of the stable, a circular area must be set apart with a separate fence, the diameter of which is one half the width of the stable.  If the area of the stable is 800 square feet, how much fencing is necessary to build an outer fence and the inner circular fence of the stable? 

This is a classic multistep problem.  The actual computations involved are simple (which is true for all math on the SAT and ACT), but in order to see what computations must take place, the somewhat complex verbiage needs to be re-written in a way that looks more like a traditional math problem.

Write down all the given information…

The problem says that the length of the stable is twice the width.

L = 2W

The problem also says the area of the stable is 800 square feet.  We can rewrite this given using the area formula.

L x W = 800

Finally the problem says the diameter of the circular fence is half the width of the stable.

D = ½W

We are solving for the perimeter of stable plus the circumference of the circle. This should be written out and marked with a star so that we know we are finished when it is solved.

*2L +2W +D(Pi) =

Now that we have all the givens written down, all we have to do is…

Plug it into an applicable equation.

All that is left to do is plug in all the variables into the applicable equations. Let’s start by substituting 2W for L in the area equation, and then plugging the solutions into all other previously written equations:

W x 2W = 800

2W^2 = 800

W^2 = 400

W = 20

L=2W

L = 2(20)

L = 40

D = ½ W

D = ½ (20)

D = 10

*2L + 2W + D(Pi)

2(40) + 2(20) + 10(Pi) = 120 + 10Pi

And voila! We have our solution.  Almost all computational problems on the SAT can be approached by writing the givens and then plugging the variables into the relevant equations.  Remember, this isn’t a cure-all for all of your math challenges, but it is one of the best tools to have in your tool belt.  Happy test taking!

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David Greenslade is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy. Read more of his articles here, including How I Scored in the 99th Percentile and How to Effectively Study for the SAT.