Carless errors on the math portion of the SAT and ACT can be major point killers. To illustrate just how drastically mistakes can affect your score, let’s look at the first SAT in the blue book. If you were able to correctly solve every math question but one, you’d score an 800. Let’s say you miss two additional questions, however, because of avoidable mistakes. Your score just dropped 70 points! Because of the incorrect answer penalty, your raw score has gone from a 53 (rounded up from a 52.75) to a 50 (rounded down from a 50.25). Two simple, avoidable errors just cost you the difference between a 730 and an 800. That’s huge.
Things don’t get any better when we look at the ACT. On an official ACT practice test from 2003, missing three math questions because of careless errors, i.e. lowering your raw score from a 60 to a 57, would drop your math score from a perfect 36 down to a 33. That’s just as substantial as going from an 800 to a 730.
Why Should I Worry About A Few Mistakes?
Why is the difference between a 730 and an 800 or a 33 and a 36 so huge? Even if 70 or 3 points is a big difference, a 730 or a 33 are still both great scores, right? While these are very high scores, at some schools an 800 or 36 can make you a much more competitive applicant in terms of admission and scholarship opportunities than someone with a 730 or 33.
At elite engineering schools like MIT and Caltech, for instance, nearly all accepted students have perfect or near-perfect scores. The 75th percentile of SAT scores for accepted students at both is 800, while the 25th percentile is 750 at MIT and 770 at Caltech. MIT’s 75th percentile for ACT Math is 36, but a 33 would put you below the 25th percentile of 34. Submitting an application with scores below the 50th percentile—let alone below the 25th—would make your application considerably less competitive than those of your perfect or near-perfect scoring peers. That’s the damage a few silly mistakes can make!
OK, you might be saying, but I’m not applying to the nation’s most elite engineering schools. What do I care about a couple points on the math section? Because you ideally want to aim for the median SAT or ACT score or above at a particular college to submit a competitive application, picking up as little as 30 points by avoiding just one careless mistake can sometimes give you the boost you need to get there.
Avoiding a single careless error can also pay off big in terms of scholarships. This is because many schools employ score cutoffs to determine scholarship eligibility. One study revealed that half of all states surveyed used specific test scores as cutoffs to determine merit-based aid. At Louisiana State University, falling even a single point short of a 1250 on the SAT or a 28 on the ACT—only one careless error—could cost you up to $7,600 per year, or $30,400 over four years. $30,400 is a lot to lose over one careless mistake!
What Can I Do?
Unfortunately, avoidable mistakes happen with great frequency on SAT and ACT math. The truth is that it’s difficult to answer 54-60 challenging math questions in a 60-70 minute, high-pressured scenario without making any mistakes. The good news, however, is that there are many things you can and should be doing to minimize if not eliminate trivial errors on this part of the test.
So, what exactly can you do to avoid making mistakes on SAT and ACT math? First, you need to figure out why you’re making careless mistakes. Often, the reason is simply working too quickly on a section.
You Don’t Need To Rush
While it is true that there is very real time pressure on the SAT and (to an even greater degree) on the ACT, this does not mean that you should rush through the questions. The test makers have deliberately built enough time into the test for you to solve each question without rushing.
How can you tell if you’re rushing? On any given SAT or ACT math section, take the total amount of time allotted and divide it by the number of questions. This will give you the average amount of time you have for each question. You should, on average, spend a little less than this on the early questions (which are easier) and a little bit more on the later questions (which are more difficult). If you’re spending less time than this and making a lot of careless mistakes, then it’s probably time to slow down.
What if you’re unable to complete the section on time when you don’t rush? If this is the case, you either haven’t learned the best way of solving the problems yet or you just need more practice to help speed things up. Many problems have two solutions: a fast one and a lengthy one. This is true on both exams, although the SAT typically features more shortcuts than the ACT. Once you learn the methods for solving these problems quickly and begin to look for shortcuts, you’ll cut down on the amount of work and time you need to get through the questions.
One caveat: don’t spend too long on any given problem. While it’s important to take your time and avoid careless errors, you also want to avoid burning all your time on a single question. If you haven’t figured out a way to solve a problem after a little more than the allotted amount of time per problem, mark the question so that you can come back to it if you have time at the end and move on to the next question.
Ease Any Anxiety
Another problem closely related to rushing is anxiety. The SAT and ACT cause everyone to experience a little anxiety, but if you’re overwhelmed with it then it might be causing you to make mistakes. It’s easy to make careless errors when your thoughts are elsewhere and your heart is racing.
If you think anxiety might be distracting you, you can combat it by taking practice tests often and under realistic conditions. Take these tests as they are officially administered – timed, whole, and with the officially allotted amount of breaks. Practice taking the test at the same time you’ll actually be taking it on test day. For paper tests, use an official bubble sheet to fill in your answers and the same type of pencil you’ll be using on the test. Try taking some of the practice tests in unfamiliar locations. The more you’ve simulated the pressures of test day, the better prepared you’ll be to handle them.
There are a number of other techniques you can use to help combat testing anxiety. If you’re still feeling overwhelmed or you suffer from severe anxiety, consider discussing your anxiety with a psychiatrist or other health care professional.
Don’t Do Mental Math, aka, Increase Your Cognitive Horsepower
Even if you’re not anxious or rushing, it’s easy to make careless errors on the SAT and ACT when you don’t do things like writing out your work. Not only does this make you more likely to make a careless mistake, but it also makes it more difficult to solve a problem. By writing your work down on paper, you free up short-term memory (a limited resource), thereby increasing the amount of cognitive horsepower you have available at any given time.
Instead of solving problems in your head, always write each step of your work down, making sure that your writing is legible, clearly ordered and easy to follow. It’s just too easy to make mistakes by attempting to solve problems all or in part through mental calculations. Also, if you find that your answer isn’t the correct one, having a clear record of your work will allow you to quickly backtrack and see where you may have made a mistake.
Along these same lines, don’t be afraid to use your calculator. All too often students feel that in order to save time they need to do the math in their head rather than on the calculator. This often results in calculation errors that could have been easily avoided. The actual time it takes to enter an operation into the calculator is usually very little. Use the calculator for all but the simplest of calculations. If you do find yourself making mental mistakes on basic operations however, such as 3×3, then you should be using your calculator for these as well.
Force Yourself To Pay More Attention To The Questions
SAT and ACT math questions can be trickily worded, and it’s the wording that often leads test takers into avoidable mistakes. If you find yourself missing questions because you misread them, then underline all key pieces of information in the question. The makers of the SAT and ACT love to sneak important details into the questions that are easy to overlook. (That said, don’t forget that the test writers will also occasionally include useless information in order to mislead you.) As soon as you start reading, you should begin underlining all important words, values and conditions. This also helps get your brain into high gear and forces you to tackle the question with focus and critical awareness. Make sure to underline each individual piece of important information separately – if you are asked to find a “positive integer,” for example, make sure to use two distinct dashes, one for “positive” and one for “integer.” Otherwise, you risk only looking for an “integer” or a “positive” answer choice. The test makers often hide important details this way. Lastly, don’t avoid underlining key information just because you’re going to be copying that information into a geometric figure or transcribing it into algebra. It can be even easier to make mistakes when transcribing is involved, so it’s important to always underline the specified values and conditions first.
Keep Things Organized
If you can’t make sense of your own notes, chances are you’re going to have a problem at some point during the exam. Keep your work structured and organized. This goes for all problems, but it’s especially relevant on geometry problems. When solving a geometry problem, label all relevant values on the geometric figures, even if this involves repetition. It’s very easy to make mistakes on geometric figures if they are not thoroughly labeled, especially because they must often be broken down into smaller, more complex figures.
If there are multiple possibilities for the values or arrangement of a geometrical figure, draw out the various possibilities rather than relying on the sole illustration provided in the question. Often the correct answer will be hidden in a second iteration of the figure that the test makers haven’t shown you.
Check Your Work
If there is time at the end of a section, always check your work. Work backward from the last question to the first. Because the later questions are more difficult than the first ones, there is both more room for error and more hidden tricks on these problems. Because you may not have enough time to review the entire section, you want to make sure that these mistake-prone questions get reviewed before the others. The more practice you do, the more likely you’ll be able to finish sections with additional time left over. This is the ideal to aim for, if possible.
You can also check your answers by trying to solve the problems a different way and checking to see if you end up with the same solution. This can be time consuming, but it can also help ensure that you’ve found the right answer.
Learn From Your Mistakes – Even Careless Ones
This might seem counterintuitive since these types of mistakes are only careless, but you can actually learn from them. When reviewing questions, always study the questions you missed because of mental errors and mistakes. That means that you should always make a note of questions you miss because of mistakes, and make sure to include what the mistake was. Re-work these problems each time you review the material you’ve already covered. This will both highlight your mistake patterns (you’d be surprised at what you’ll find) and reduce the likelihood that you will repeat the mistakes you’re prone to make.
Careless errors on SAT and ACT math can cost you valuable points and dollars. If you find yourself making them, first try to figure out what’s causing them: is it rushing, anxiety, mental math, or something else? Once you know the problem, implement the relevant suggestions in this article to minimize them. You’ll be glad you did.