How to Overcome a Difficult Math Equation

By Carl F., IvyWise Master Tutor

We’ve all been there: staring at an “impossible” problem on the ACT or SAT, unsure how we will ever solve this test troll’s riddle and make it safely to the other side of the bridge. Worse, you’re absolutely positive that getting this question right is the difference between your goal score and the one that’ll have you miss the cut for your ideal college. All is lost, right? Far from it. Here are three easily repeatable steps to take if you ever find yourself in this position. 

Zoom Out, Retrace Your Steps (Literally)

By now, it should be no secret that tests like the SAT and ACT don’t actually test the most challenging math a high school student has seen, but rather, they take familiar concepts and ask about them in confusing ways. A lot of times, the reason you’re so confused about what to do is that you’ve missed a crucial piece of information, either because you didn’t read the question correctly, or maybe you didn’t read the question at all. Once students are in a groove, they often jump into the equation without stopping to check what it’s actually asking. 

When you feel like you’re stuck, that’s a perfect time to reread the question, pencil in hand. Take in every word, reevaluate what it means, and underline the most important pieces of information: units, values, and what the question is actually asking. Have you been trying to solve for x this whole time, all the while you’re being asked for y or x+y? Sometimes you might be trying to solve the wrong thing, and that’s why you’re so stuck. If the question is asking about a shape or graph, be sure to have drawn out that diagram, so you’re not sitting there trying to abstractly solve an invisible concept. You might be making it harder than it is. 

Reading the question word for word and underlining key terms might sound super basic, but it goes a long way toward minimizing avoidable errors and sometimes revealing that “impossible” problems may just have needed a more thorough look.

Reach Into Your Bag of Tricks

Once you’ve reread the question and underlined the key terms, think about all the tricks of the test prep trade. Try to solve the question in the easiest, most painless way possible. You may have many questions ahead of you, or in the case of the ACT, two full sections. Don’t burn yourself out here. Even on the SAT, remember that degree of difficulty resets when the test shifts to grid-in questions, so there may be a super easy question just around the corner.

Ask yourself a series of questions that might help. Can you plug in the answer choices? Might you pick a number to substitute for a variable? Can you backsolve your way to the answer? What concepts are being tested? Is there a trusty formula to use? Is that formula available in the reference table (for SAT only)?

Chances are, this question is one in a classic type of math question that has been asked hundreds of times or that you’ve seen before, and you just haven’t found the right approach. Remember that you don’t have to do it the “math class” way. See if you can turn algebra into arithmetic or simplify terms. Can the process of elimination help? You might do all the above, exhaust your creativity, and still not get it. If that happens…

Guess, Move On, Come Back If There’s Time

Often, the test-makers take advantage of our instincts to solve problems the “right” way, just like a good math student who shows all her work and never skips a step. In math class, if you show all your work, you may earn partial credit even if an error leads to an incorrect final answer. These tests offer no such grace. The little blue light that scans the choice you bubbled doesn’t care if you proved the quadratic equation on your way to your answer or if you blindly guessed. The right bubble gets a point, the wrong bubble gets no point, and at no point do you lose any points. So guess if you have to! There’s no shame in guessing! No one will ever know you did it. Don’t waste precious time in your timed exam belaboring a super challenging question. An easier one or four may be right around the corner, and you want to still have enough time to do those. So narrow it down if you can, guess, and live to fight another day.

It’s way more important to maintain your rhythm than it is to get this particular question right. They are all worth the same 1 point in your raw score. You get no extra points for degree of difficulty, and you earn no badge of honor for suffering for five minutes to solve a question that leaves you with less time to do the rest of the test. So make peace with the fact that you probably won’t win ‘em all, and save your energy for the questions you have a better chance at answering correctly. This way, you also increase the likelihood that you’ll have time at the end to come back to this question with fresh eyes and repeat steps one and two.

Whether you’re prepping for the SAT or ACT or working on your in-class mathematic skills, our expert team of IvyWise tutors can provide you with the guidance and tools necessary to be a high-achieving student in a plethora of subjects. For more information on IvyWise’s tutoring services, contact us today.