SAT / ACT Prep Online Guides and Tips

How to Guess Strategically on SAT Math

Posted by Courtney Montgomery | Nov 11, 2015 9:00:00 AM

SAT Math

 

feature_question_mark

The SAT gives negative penalties for guessing, so you shouldn’t even bother to guess on the SAT math section...right? Well yes and no.

Guessing requires strategy for a test like the SAT, but it is possible (and indeed we recommend that you do so!) when you can do it smartly. In this guide, we’ll go through when and how to guess strategically on the SAT math section and show you examples of it in action.

 

Refresher on SAT Math Scoring and Organization

The SAT is a standardized test, which means that each SAT must look and feel like every other SAT as much as possible. The individual questions may vary, but the patterns in how the test-makers design both the questions and the answer choices will be as similar as can be. With time and practice, you can learn to not only recognize these patterns when you see them, but also use the clues in both the question and the answer choices to help you find your right answer (or at least narrow down your options!).

To refresh your understanding of how the SAT math test is structured, let’s look at how it is scored. For each multiple choice question, you will get: +1 point for every correct answer, 0 points for every blank answer, and -0.25 points for every incorrect answer.

For each math grid-in question, you will get: +1 point for every correct answer and 0 points for every blank OR incorrect answer. There is no negative penalty for an incorrect grid-in answer.

There will be a total of 54 math questions on the test, 44 multiple choice and 10 grid-in.

[Note: if you receive an extra math section on the day of the test, it will be because this is your “experimental” section. If this happens, you will have a total of 74 math questions--64 multiple choice and 10 grid-in. There will never be any additional grid-in questions in the experimental section.]

 

Developing a Target Score

Because the SAT delivers a penalty for incorrect answers, your strategy for how to approach the SAT math section will depend on your target score and will change as your score goals change.

First, take a practice test, and try to slow down a little more than might feel natural as you work through your test. In addition, come up with different ways to mark your questions--one mark for questions you don't know how to do, and another mark for questions you're only somewhat confident about. You may even want to create a third marker for questions that you know how to do, but will take a long time or will require multiple steps, so must be done carefully to avoid error. This way, you can save them for last (though this is optional).

For now, use your best judgment on whether to skip or guess the questions you've marked, but do make sure that you can identify which problems were which later. These marks will help you when you go to analyze your answers (and your guessing strategy) in the next section. 

Once you're done with your practice test, check out our guide to developing your ideal target score, based on your current scores and the schools you want to get into. 

 

body_target-1

Don't worry if you're a little off your target right now. A little strategy and practice will soon get you much closer to where you want to be (if not right on the bull's eye!).

 

Guessing Based on Target Score

After you find your target curved score, see how that translates to your raw score. How many questions must you answer correctly to get that target score? Keep that number in your head and then plan to answer a few more questions than that target. Why? You are leaving yourself room to get a few questions wrong.

For example, if your target SAT math score is 600, you’ll need a raw score of about 37. But to get a raw 37, you must answer 37 questions correctly and absolutely no questions wrong. Since this is difficult for most students, you should aim to answer somewhere in the range of 44 questions. This would allow you to miss up to 6 questions and still get a raw score of 37.

How? If you answered 38 questions correctly and missed 6, you would have a score of:

$38 + 6(-0.25)$

$38 - 1.5$

$36.5$

The SAT rounds up any score ending in 0.5 or 0.75, so your raw score would be rounded to 37. Success!

Once you’ve scored your test, look back on the questions you marked. How accurate is your guessing right now? Did you mostly get questions right or wrong that you marked as "didn't know" or "kind of knew," or did you leave most of these blank? Is there a pattern in your missed guesses?

But what happens if you're currently well under your target raw score? If this is the case, then you're going to want to establish a two-tonged study approach of brushing up on the individual math topics you're struggling in right now and learning how to guess more effectively. 

So now that you’ve seen how you’re guessing strategies have worked so far (even if that means you haven't been guessing at all), let’s talk best guessing strategies for SAT math. 

 

body_plan-1

The more you practice, the more refined and honed your study skills and guessing abilities will become.

 

SAT Math Guessing Strategies

The SAT math section is designed to test how well you can recognize and figure out how to apply familiar mathematical concepts to new situations. But though the scenarios may be unusual, each and every math topic on the test is one that you are likely familiar with and have studied for a number of years.

This is all to say that you likely have a better understanding of the questions than you may think, even if you don’t know how to actually solve the problem. Often (though not always), a little strategy will allow you to eliminate at least one or two answer choices and make an educated guess.

Note: this may seem apparent, but only use your guessing strategies when you don't know how to solve a problem or are not confident about your answer. Guessing often takes a little more time than a straight-solve, so if you know the answer, great! Move on to the next problem. Only stop and take the time to guess if you're stuck.

We’ve laid out three of the most important rules of thumb that go into making an educated guess on an SAT math problem. Most of the time you will use a combination of these three techniques on any given problem, so they are less individual strategy than they are a combination of thought processes that you should go through every time you make a guess.

So let’s look at all three techniques needed to best make guesses (and when to do so!) on the SAT math section.

 

Guessing Strategy 1: Process of Elimination

Being able to eliminate questions SAT is arguably a more important skill than even being able to solve questions (or at least equally as important). Most of the SAT math questions are multiple choice, which means that the correct answer is always there amongst the answer choices. This may seem obvious, but it means that you have two options to get the right answer--you can solve the problem for the correct answer, or you can simply eliminate four wrong answers. Whatever remains must be correct. Either option you choose will each get you to the right answer in the end.

For example, is it impossible that the answer to a certain problem be negative? Do you know the parabola must open upwards, even if you don't know how it's positioned horizontally? Even knowing just a tiny bit about the problem or its possible answer will often be enough to eliminate a few answer choices. 

But what if don't know enough about the problem to know that four answers are wrong? Is eliminating just one or two answer choices enough? When, exactly, should you make a guess?

 

Eliminating 0 Answer Choices

So you’ve come to a question and you can’t eliminate any answer choices at all--should you guess? Definitely not!

The test is designed to make random guessing (quite literally) pointless. With the -0.25 point penalty and 5 answer choices for each question, random guessing will balance out to 0 points earned over time. Why? A one-in-five chance of a right answer will get you one right answer and four wrong answers for every five questions. This gives you:

$1 + 4(-0.25)$

$1 - 1$

$0$ points for every five questions. Better to leave it blank and move on. 

 

Eliminating 1 Answer Choice

All right, let’s say you can eliminate one answer choice, but no others--should you guess now? Unfortunately, the answer is: it depends.

If you can eliminate one answer choice, then you will have a one-in-four chance of getting the right answer. Over the course of several questions, you will earn:

$1 + 3(-0.25)$

$1 - 0.75$

$0.25$ points for every four questions you can answer this way.

As you can see, technically, if you can eliminate one answer, then it is to your benefit to guess. But this only works over the long-term and, even then, only if you make your final selection at random. Since human beings are not random, our advice is only to guess when you can eliminate two or more answer choices.

 

Eliminating 2 Answer Choices (Now We’re Getting Somewhere!)

You’ve eliminated two answer choices that you know have to be wrong and are now down to three possibilities. This is the time to start guessing.

Though eliminating one answer and making a guess might be worth it in the long-term (as in, you must do so over the course of several questions), you should really only make a guess when you can eliminate two or more answer choices. This will give you a one-in-three chance of guessing the right answer, which will earn you:

$1 + 2(-0.25)$

$1 - 0.5$

$0.5$ points for every three questions you can answer this way.

[Note: getting 0.5 points has an extra bonus in that raw scores on the SAT are rounded up at the 0.5 mark. So if you have a raw score of 41.5, you will actually end up with a final raw score of 42!]


Eliminating 3 Answer Choices

If you can eliminate three answer choices, you’re in a great place! This will give you a one-in-two shot of choosing the correct answer, which, over time will get you:

$1 + 1(-0.25)$

$1 - 0.25$

$0.75$ points for every two questions you can answer this way. Go you!

 

Eliminating 4 Answer Choices

If you can confidently eliminate four answer options, then celebrate! No need for guessing here--you’ve found the correct answer.

 

But how exactly do you go about eliminating answer choices? Let’s take a look.

  

Guessing Strategy 2: Approximating

If you have even a general idea of what the right answer might be (even a ballpark figure will do), you will often be able to eliminate one or two of the most blatant outliers. Though the answer choices are most often generated based on common student errors or closely related values, there will still generally be answer choices that are way far afield.

Let’s take a look at this in action. Don’t worry about actually solving the problem, just give yourself enough of a ballpark to see if you can eliminate one or two answer choices.

body_approx_example_1

Garcia won by a ratio of 5:3, which means that Pérez must have lost, but not by a landslide. First, let’s divide the total number of votes in half.

${120,000}/2$

$60,000$

Pérez received fewer than half the total votes, but again, not by too terribly much. At a rough estimate, let's say that Pérez probably received about 40,000 votes. Again, less than 60,000 (half), but not nearly so small as 15,000. 

Just with this ballpark figure, we can eliminate answer choices A, D, and E. We are left with answer choices B and C. Even if you didn’t understand how to work with ratios, you would still be in a good place to guess at this point. You now have a 50-50 chance of getting the right answer between the two options just from approximating what the correct answer might be. 

[Note: the correct answer is C, 45,000.]


You can also approximate answers on geometric figures on the test. Unless noted otherwise, all figures will be to scale, and you can make a ballpark guess as to their size and angles.

 body_approx_example_2

Because there is no note to indicate otherwise, we know the figure must be to scale. Just by glancing at the triangle ABO, we can see that angle ABO must be larger than 15° and less than 90°. We can definitively eliminate two answer choices, which leaves us with three--B, C, and D. This is enough to make a guess.

But we can even go further. Considering all the angles in the triangle look about the same, we can make an educated guess between our three options. Angle ABO looks about equal to angles BAO and BOA, and we know that there are 180° in a triangle. Knowing this, we can make a guess that the answer is D, 60°, without making any bit of effort to actually solve the problem.

[Note: the correct answer is indeed D, 60°.]

 

body_odds

The more you can whittle away obviously wrong answers, the better the odds will be of you grabbing that right answer choice. 

 

Guessing Strategy 3: Avoiding Temptation

The test is designed around the statistically average student, and many of the answer choices are generated based on common student errors. People have a tendency to fall into predictable thinking patterns, and the SAT is, in part, designed to lure you to fall for traps that the average student falls for again and again.

Often, what makes an answer difficult is the wording and the bait answer choices, rather than the difficulty of the mathematical material being tested. So if you look at a question in the medium or difficult range that looks easy or--even worse--obvious, it may just be too good to be true.

If an answer choice seems immediately appealing, especially on a difficult question, it’s likely a trap. Think about how many other students would have felt the same way on trial tests. Don’t be that person and try not to let yourself fall for the booby traps.

body_tempt_ex_1

This question is near the end of a math section, which means that the test-makers consider it “medium-difficult.” Knowing this, the answer is probably NOT going to be simple or obvious.

If you don’t have a clue as to how to solve the problem, you can still narrow down your answer choices. Consider that we are working with the difference of 4 people vs. 3 people, which means that it is highly unlikely that the correct answer will be $x/4$ or $x/3$. Those answers look too obvious and tempting to be trusted.

We can probably also discard answer choice E, $7x$. Not always but most of the time, if an answer doesn’t look anything like the other answer choices, there’s a very good chance it is incorrect, and you can discard it. The rest of our answers are in fractions and E is the only answer that is purely a multiple. Let us, therefore, get rid of it.

By discarding both the tempting answer choices and the outlier, we are left with two options, answer choices A and D. This gives us a 50-50 chance of getting the right answer and is a good time to guess.

[Note: the correct answer is A, $x/12$.]

 

Let's take a look at another example.

body_tempt_ex_3

This is the last question in a math section, which means it is the hardest question (or one of the hardest questions) on the test. With that in mind, the correct answer will NOT be the most obvious.

There are two X-marked offices and four offices total. The X’s, therefore, make up half of the total number of offices, which is something we can see right at a glance. This means that the answer is NOT going to be E, $1/2$--that is way too obvious to be correct.

Considering there are four offices total, it is also safe to guess that the answer is not D, $1/4$ either, as that is still too obvious an answer for question 20 of 20. To solve any problem that is last on a math section, we will need to go through at least two or three math steps. We therefore know the problem will be more complex than simply using the number of offices as the denominator.

Even without knowing anything about probabilities, we have narrowed down our options to A, B, or C. It is now a safe time to guess, so we can go ahead and pick an answer.

[Note: the correct answer is C, $1/6$]

 

body_celebrate-1You did it! Now go forth and conquer.

 

The Take-Aways

Though it is very useful to know how to actually solve your SAT math problems, we’ve seen that it is not always necessary. Though you shouldn’t guess on every SAT math question, it can help your scores to do so on occasion.

Just remember to always employ your guessing strategies when you are forced to make a guess, and take a deep breath. Sometimes you will be able to eliminate enough answer choices to make a final guess and sometimes you'll have to leave the question blank, and that's okay.

You probably know more about the math topic in question than you think, and you probably know enough to at least eliminate an answer choice or two, even if you’re feeling overwhelmed. Don’t force yourself to answer questions you don’t feel comfortable answering, but don’t doubt your skills to eliminate possible answer choices either. Pretty soon you’ll be beating the odds and boosting your scores more than ever before.

 

What’s Next?

Still not satisfied with your SAT math scores? Improve your individual SAT math topic skills by working through our individual math topic guides. In each guide, we will walk you through the definitions of each topic, the formulas you'll need, and how you'll see the questions on the SAT math section, as well as give you real SAT math problems (and answer explanations) for you to practice your skills on.

Been procrastinating on your SAT prep? If you've found yourself in a procrastination rut, check out our guide on how to stop procrastinating so you can get back on that study wagon. 

Aiming for a perfect score? If you're looking to score a perfect 800 on your SAT math section, then look no further than our guide to getting an 800 on the SAT math, written by a perfect-scorer.

Want to improve your SAT score by 240 points? 

Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 240 points or more.

Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next.

Check out our 5-day free trial:

SAT Free Signup

 

Have friends who also need help with test prep? Share this article!
Courtney Montgomery
About the Author

Courtney scored in the 99th percentile on the SAT in high school and went on to graduate from Stanford University with a degree in Cultural and Social Anthropology. She is passionate about bringing education and the tools to succeed to students from all backgrounds and walks of life, as she believes open education is one of the great societal equalizers. She has years of tutoring experience and writes creative works in her free time.



Get Free Guides to Boost Your SAT/ACT
100% Privacy. No spam ever.

You should definitely follow us on social media. You'll get updates on our latest articles right on your feed. Follow us on all 3 of our social networks:

Twitter and Google+



Ask a Question Below

Have any questions about this article or other topics? Ask below and we'll reply!