If you’re a current student of the SAT, you’re likely well-aware that SAT math can be a bear to master. Any math topics that you have ever studied, and even some you haven’t, are fair game on the SAT. It’s a difficult exam, especially so because it is vying for your very limited time. You have many competing priorities — school, family, friends, maybe a job, homework, sports activities, college applications. The pressure to meet all these commitments, plus studying for the SAT, can be overwhelming!
The good news is that there are many SAT math strategies that you can apply to make your SAT math studying more efficient. This article will cover 10 ultra-useful SAT math tips and tricks to help you prepare for the big day.
Here are the topics we’ll cover:
- Tip #1: Know the Exam
- Tip #2: Learn One Topic at a Time When Learning SAT Math
- Tip #3: Practice What You’ve Learned
- Tip #4: Leave Yourself Plenty of Time to Take Practice Tests Before Test Day
- Tip #5: Make Sure You Memorize Key Math Formulas
- Tip #6: Your Calculator Can Be Either Your Friend or Your Enemy on the SAT
- Tip #7: Don’t Leave Any Answers Blank
- Tip #8: Don’t Let Any One Math Question Be Your Downfall
- Tip #9: Use Your Answer Choices Strategically
- Tip #10: When You Are in a Pinch, Backsolve
- In Summary
- Frequently Asked Questions (FAQ)
- What’s Next?
To start, let’s look at the basics of SAT math.
Tip #1: Know the Exam
Before we discuss how to best learn SAT math, let’s briefly list the math topics tested on the SAT and discuss two steps to take before starting your test preparation.
Heart of Algebra:
- Solving Linear Equations
- Inequalities and Absolute Value
- Coordinate Geometry
- Linear Functions
- Systems of Linear Equations
Problem Solving and Data Analysis:
- General Word Problems
- Rates
- Unit Conversions
- Ratios
- Statistics
- Percents
Passport to Advanced Math:
- Exponents
- Roots
- Quadratic Equations
- Functions
- Coordinate Geometry
- Graph Interpretation
- Table Data
Additional Topics in Math:
- Geometry
- Trigonometry
- Complex Numbers
What you may notice from the above list is that the titles in bold are the College Board classification of SAT math topics. However, we have broken them down further so you can see what exactly is included under each math topic heading.
Establish Your Target Score and Your Baseline Score
Before you open a book or plan your study schedule, you have to know where you want to go and where you are. Therefore, you must know two numbers: your target score and your baseline score.
To know your target score, research the colleges to which you wish to apply. You can find the SAT score ranges for admitted students on most schools’ websites. More selective schools, such as MIT, will have SAT math score requirements in the 700s. Contrastingly, some less selective but still respectable state schools might want candidates to have SAT math scores in the mid-500s to mid-600s.
Once you have your target score, you’ll want to know your baseline score. To get your baseline score, take a free, official SAT practice test from the College Board. After you take it, you can compare your target math score with your practice test math score. You’ll get a feel for how much time and effort you’ll need to put in to get the score you want.
Now that we know the basics, let’s concentrate on putting our best foot forward by using the best study strategy available for mastering SAT math: topical learning.
Tip #2: Learn One Topic at a Time When Learning SAT Math
If you talk to any past SAT students, they may advise you to crack open the latest SAT book and start answering thousands of practice questions. While that may seem like a good move, it’s not. Random learning will not do you any favors! Instead, you need to make a point of focusing on just one topic at a time. Doing so lets you learn the ins and outs of just one topic, and then move to the next one, but not until you’ve mastered the current one.
For example, if you look at the topic list above, you can see that it would be helpful to do some dedicated studying of just geometry strategies, or just algebra strategies, or just trigonometry strategies, but definitely not all of them at once! By concentrating your energy on just one topic at a time, you’ll ensure that you climb the SAT math ladder one rung at a time!
TTP PRO TIP:
When studying SAT math, concentrate on learning one topic at a time.
Tip #3: Practice What You’ve Learned
Learning topics one at a time is critically important, but if you don’t practice what you have learned, it won’t stick! So part of topical learning is topical practice.
To illustrate this idea, let’s imagine you were learning about quadratic equations. In the learning portion of your study plan, you would learn all you can about that SAT math topic. You would learn concepts such as FOILing quadratic equations, factoring quadratic equations, the quadratic formula, graphs of quadratic equations, etc.
Once you have learned those concepts, you must practice what you have learned. Choose any number of questions you feel comfortable with. You may prefer a smaller set of 20 SAT math questions or a larger one of 38 SAT math questions. Whatever number you choose, treat these practice sets like mini SAT math practice tests to get the most accurate results possible.
By practicing, you’ll clearly understand where you are strong and where you’re weak. Then, you can go back to your prep materials to fill any knowledge gaps you find.
Finally, once you have practiced and reviewed all you can from quadratic equations, you can move to the next math topic in your study plan.
TTP PRO TIP:
Topical learning is a start, but you also must engage in topical practice.
Tip #4: Leave Yourself Plenty of Time to Take Practice Tests Before Test Day
Thus far, we have discussed how topical learning and practice are essential when learning SAT math. However, once you have all that knowledge stored in your brain, you need to apply it by taking official SAT practice exams. The College Board offers eight practice tests. We recommend shooting to take at least five before test day, in addition to the one you took to establish your baseline score.
Practice tests require a lot of time and effort, so you must be strategic about when you take them, meaning also that you must leave plenty of time to take them before test day. Taking practice exams will help prepare you mentally for the rigors of test day and help you identify your strong and weak areas. Armed with that information, you can make any necessary tweaks before test day.
TTP PRO TIP:
Take at least five official SAT practice tests before your SAT.
Now let’s begin our discussion of some test-taking strategies, such as memorizing and using SAT quant formulas on the SAT.
Tip #5: Make Sure You Memorize Key Math Formulas
If I’m being honest, you need to learn many formulas and concepts to solve SAT math problems effectively. Sure, you have the SAT equation sheet provided in your test booklet. However, constantly referring to that sheet will waste time. Also, there is not much on it! Short of mainly geometry formulas, there is not much you can use it for. So, rather than rely on the half-baked equation sheet, you will benefit significantly from memorizing key SAT math shortcuts, formulas, and math problem-solving strategies. In fact, the more formulas and strategies you have in your quick-recall memory, the better you’ll perform!
For example, if you see a coordinate geometry problem, wouldn’t it be a relief knowing that you have the slope formula down cold, or for a trig question, that the cosine of an angle in quadrant 2 is negative? The result would be that you feel totally confident about getting the question right, and you’d save valuable time by not having to think hard to recall the needed information.
TTP PRO TIP:
Memorize important SAT math concepts and formulas.
So, now the question becomes, how do you get all of these SAT tips and tricks memorized?
Flashcard Use Is Key for Memorization
There is a lot you need to know to succeed in SAT math. I also recognize that you are not thinking about SAT math 24 hours a day, seven days a week! So, how can we bridge the gap between what you need to memorize and how long it will take you to memorize that info? With flashcards!
Flashcards are an amazing tool. You can create your own set or use a pre-made deck online (such as what we have in the Target Test Prep online SAT course). Your flashcards can consist of anything you think would be helpful to memorize—concepts such as the difference of squares in quadratics or the sum of exterior angles in geometry.
Once you have your flashcards made, try to do a little flashcard review each day, whether you have a few minutes before class or you can use a free period to study. Sit down with your flashcards and quiz yourself.
TTP PRO TIP:
Using flashcards is a great way to memorize SAT math concepts and formulas.
For example, for the SAT, we need to know some facts about the discriminant, which are shown below:
- The discriminant of the quadratic equation ax2 + bx + c = 0 is b2 – 4ac.
| If the value of the discriminant b2 – 4ac is: | Then the number and type of roots is: |
|---|---|
| Positive | 2 real roots |
| 0 | 1 real root (repeated) |
| Negative | No real roots (2 complex roots) |
Getting everything above memorized would be extremely helpful for the following problem.
Memorized Facts: Example 1
x2 + 3 = (19/4)x has how many real solutions?
- 0
- 1
- 2
- More than 2
Solution:
Let’s first express the given equation in general form:
x2 – (19/4)x + 3 = 0
So, a = 1, b = -19/4, and c = 3. Thus, for this equation, the discriminant is:
b2 – 4ac = (-19/4)2 – 4(1)(3) = 22.5625 – 12 = 10.5625
The discriminant’s value is positive. From our memorized flashcard, we know there are 2 real roots to the quadratic equation.
Answer: C
As you can see, memorizing the information about using the value of the discriminant to determine the number and type of roots of a quadratic was critical to correctly and efficiently solving the problem above!
Tip #6: Your Calculator Can Be Either Your Friend or Your Enemy on the SAT
There are some important calculator strategies to consider when preparing for your SAT. How you use your calculator plays a big part in your strategies for multiple-choice math questions and for grid-in questions.
For starters, you should use the same calculator that you have been using to prepare for the SAT math section of the exam. So, don’t switch out your calculator two days before your SAT.
Knowing when to utilize your calculator is another crucial aspect of preparation. Because the SAT is a timed exam, you must be sure that using a calculator adds value to your timing strategy rather than detracting from it.
Additionally, as you likely know, you need to get as many questions correct as possible, so your calculator use also has to positively affect your strategies for selecting correct answers on SAT math.
So, just be thoughtful when pulling out your calculator! For instance, don’t use a calculator to determine the product of 10 and 3 or the sum of 8 and 13. After all, the non-calculator math component will still require you to perform these types of manual calculations. Therefore, you shouldn’t waste your time on simple calculations such as these in the calculator section!
TTP PRO TIP:
Be well-acquainted with your SAT calculator prior to test day.
Know Your Calculator!
PEMDAS
All calculators perform the basic functions of addition, subtraction, multiplication, division, and taking square roots. One thing to practice ahead of time, even with a very basic calculator, is the way your calculator performs PEMDAS operations. Make sure that your calculator gives the correct answers to the following questions:
3 + 2 x 4 / 11 = 3.727272…
6 / 2(1+2) = 9
And make sure that YOU know how to calculate these by hand, too!
Special Functions
In addition to performing basic functions, many calculators allow you to evaluate trigonometric functions (sine, cosine, tangent, and their inverses). Also, calculators may reduce fractions automatically or find the lowest common denominator with one or two button presses. They might evaluate factorials, combinations, or permutations easily, saving you time and ensuring accuracy.
Additionally, some advanced calculators might have special built-in apps that help you evaluate conic sections (circles, parabolas, ellipses, and hyperbolas) and graph them. Some might help you find the roots of polynomials or even solve simultaneous equations.
If you decide to use any of these special functions, be forewarned that they take a bit of time to learn. And sometimes, using your brain or even basic algebra can be faster than using your calculator for some SAT questions. But, in a pinch, a calculator could provide a correct answer that you might not have otherwise been able to determine.
Tip #7: Don’t Leave Any Answers Blank
A great component of the SAT is that, within any section, you can jump back and forth between questions. What is also great is that there are no deductions for wrong answers on the SAT.
You must also understand that leaving answers blank in any SAT section is unwise. When you leave a question blank, there is a 100 percent chance of getting it wrong. But even if you randomly guess, you have a 25 percent chance of getting it right!
Even for questions that you are not 100 percent certain about, use your estimation strategies for math problems, take a guess, and keep moving! Remember, you can always return to a problem if you have time. So, for those problems you have guessed on, leave a big “x” next to the problem, so you know to come back to it, time permitting.
TTP PRO TIP:
Even if you have to guess, answer every SAT math question in a section.
Smart Guessing on Grid-In Questions
Grid-in questions are those for which you fill in a blank, so there are no answer choices provided. Even so, you can randomly guess intelligently on a grid-in question!
First, realize that if you don’t know the answer to a grid-in question, you probably won’t randomly guess the correct answer. There are thousands of possible answers that can be bubbled into those 4-space grids. Nevertheless, here are some answering strategies that might give you an edge.
- A grid-in answer will NEVER be negative. It is impossible to bubble in a negative sign, so if you calculate a negative answer, try again!
- Choose an answer based on the problem’s context. If you are asked how many apples Sally bought, for example, you should guess a reasonable number, maybe an integer between 5 and 15. Or for a geometry question about the height of a full-sized rocket, make a reasonable guess, perhaps 100 to 150 feet.
- If context doesn’t help, then you might simply guess a whole number between 1 and 10, inclusive. Research has shown that a surprising number of correct SAT grid-in questions include these integer values.
- If the answer is a fractional value, guess the more common fractions, such as 1/2, 1/4, or 3/4. Again, these fractions are more often the correct answers to fraction problems.
If you think these tips about grid-in guessing are just made up, think again. The SAT question-writers have certain restrictions in writing grid-in questions. As a result, some answers will be correct more often than others, just based on limitations on the types of questions that can be posed and the math that must be used to correctly answer them.
Tip #8: Don’t Let Any One Math Question Be Your Downfall
Consider the following scenario. You are midway through an SAT math section when you come across a question that makes you smile. In other words, you are familiar with this question type, and you already know you can correctly answer it. But after a minute and 30 seconds of working on it, something doesn’t make sense. Your answer is not one of the answer choices, and you’re thinking you’ll have to start over because you must have made an arithmetic or simple algebra mistake somewhere in the solution.
Even though every bone in your body is telling you to redo the entire problem, trust me when I say that the right thing to do is to take a guess and move on! After all, overextending yourself and spending another minute and a half to eventually get that problem correct may have disastrous effects on your ability to answer later problems in the section, because you may run out of time. So, take your best shot at an answer, put a big “X” on the problem to remind yourself to come back to it later if time permits, but move on to the rest of the questions. Don’t let pride or stubbornness lead to a potentially disastrous result.
TTP PRO TIP:
Don’t let a single SAT math question be your downfall.
Tip #9: Use Your Answer Choices Strategically
Thus far in the article, we have covered many SAT math tips, tricks, and strategies that will help you maximize your SAT score. Another consideration is strategically using your answer choices when solving SAT math problems.
For certain questions, you can quickly eliminate one or more answer choices based on the nature of the given question. This strategy is helpful for solving the problem quickly if you are running out of time. Eliminating answer choices is helpful with all types of SAT math questions, especially when dealing with algebraic equations on SAT math.
Consider the following question:
Strategically Eliminating Answer Choices: Example 1
What are the roots of the equation 10x^2 + 41x + 21 = 0?
- -3/5 and -7/2
- 3/5 and -7/2
- -3/5 and 7/2
- 3/5 and 7/2
Solution:
Before you try to factor this quadratic equation or jump into using the quadratic formula to find the roots, look at the answer choices. A quick stroll down memory lane from Algebra I should help you considerably. In fact, you can get this problem correct in about 30 seconds without doing any calculations whatsoever!
Recall that the value of the constant (21) in the equation is positive, meaning that the two roots must multiply to give us a positive value. Thus, we can immediately eliminate answer choices B and C. Each of these two choices contains one positive and one negative number, and thus the product of each positive/negative pair would be negative.
This leaves us with a 50-50 chance of answering correctly. And we’ve spent maybe 10 seconds on the problem. We could stop here and randomly guess either A or D, and move to the next question. Or, we could spend another 15 seconds using some elementary math logic to ensure that we pick the correct answer.
Take a look at choice D, which has both roots as positive. Now take a look at the original equation. If we plugged in any positive number whatsoever into the original equation of 10x^2 + 41x + 21 = 0, we could NEVER get 0 as the answer! If x is a positive number, then 10x^2 is positive, 41x is positive, and 21 is positive, and when we add three positive values, we for sure will NOT get 0 as the sum! So, case closed. Eliminate D.
Note that you could have gotten the correct answer by using the quadratic formula. We did, but it took 2 minutes and 14 seconds. Your choice.
Answer: A
TTP PRO TIP:
When possible, strategically eliminate answer choices.
Tip #10: When You Are in a Pinch, Backsolve
Backsolving is the process of substituting each answer choice into the original problem to see which one makes a true statement. You may have used backsolving in the past when you were stumped on a multiple-choice question that had numerical answers and you had no idea what the correct answer was.
Backsolving is both good and bad. It is good because it allows you to get a correct answer to a question that you have no idea how to solve. It is bad because it can take an inordinate amount of time to get that answer. Use the technique smartly and only when necessary.
Let’s look at an example in which backsolving may save the day.
Backsolving: Example 1
Given the equation 7 + sqrt [(3/4) (x^2) + 13] = 12, what is the value of x?
- 1
- 2
- 4
- 8
Solution:
We are given answer choices with the numbers in ascending order. In a traditional five-choice multiple-choice question, we would choose the middle option (choice C) as our first guess for backsolving. Why? Well, if choice C yields an answer that is too small, then we can eliminate choices A and B, as well as choice C. Then, we would have only choices D and E to consider. Or, if C works, then we are done, and if choice C gives us too great an answer, then we have to consider only A or B.
When we have four answer choices, as is the case on the SAT, we first choose either B or C. Let’s choose B and test it.
If x = 2, we substitute as follows:
7 + sqrt [(3/4) (2^2) + 13] = 12
7 + sqrt [(3/4) (4) + 13] = 12
7 + sqrt [3 + 13] = 12
7 + sqrt (16] = 12
7+ 4 = 12
11 = 12
This is false, and our answer when x = 2 is too small. Therefore, we can eliminate both A and B.
Let’s now test choice C, x = 4.
7 + sqrt [(3/4) (4^2) + 13] = 12
7 + sqrt [(3/4) (16) + 13] = 12
7 + sqrt (12 + 13) = 12
7 + 5 = 12
12 = 12
We see that choice C is correct.
Note: Had choice C not given us an equality, then we would have eliminated C and chosen choice D immediately. And we would not waste time doing any calculations with choice D. We would know that by previously eliminating A and B, and then showing that C did not produce equality, the only possible correct answer choice is D. Bubble it in and move on!
Answer: C
TTP PRO TIP:
Judicious use of backsolving can help you answer tough SAT math questions.
In Summary
In this article, we have covered 10 SAT tips and tricks for enhancing your preparation for this tough exam.
- Know the Exam – Know what is on the SAT and establish your target and baseline scores.
- Learn One Topic at a Time When Learning SAT Math – Topical learning is the most efficient way to prepare.
- Practice What You’ve Learned – Do lots of practice questions after you have learned the material.
- Leave Yourself Plenty of Time to Take Practice Tests Before Test Day – Practice exams from the College Board provide a realistic way to identify any weak areas that need to be remedied. They also assess your readiness to take the exam.
- Make Sure You Memorize Key Math Formulas – Use flashcards to help you learn them.
- Your Calculator Can Be Either Your Friend or Your Enemy on the SAT – Know when you should and should not use your calculator. And know your calculator’s special features and functions.
- Don’t Leave Any Answers Blank – Even if you must randomly guess, you have a measurable chance of getting a question correct. Use strategic numbers if you randomly guess on a grid-in question.
- Don’t Let Any One Math Question Be Your Downfall – Don’t spend too much time on any one problem at the expense of being able to solve others.
- Use Your Answer Choices Strategically – Realize that many problems can be solved by strategically eliminating some answer choices.
- When You Are in a Pinch, Backsolve – You can sometimes plug the answer choices into the problem to find the correct answer. Use this technique judiciously.
Frequently Asked Questions (FAQ)
How Can I Improve My Math for SAT Test Day?
The key to improving your SAT math score is to use topical learning and to study consistently throughout the months leading up to your exam date.
How Do I Get an 800 in Math on the SAT?
Topical learning is the best study strategy for getting a perfect SAT math score. Master each topic by studying and answering practice questions. Use the results of the practice questions to identify and fix any weaknesses. Rinse and repeat for every SAT topic listed in Tip #1 in this article, and you should be prepared to earn your best possible math score.
What Is the Hardest Part of SAT Math?
The hardest aspect of SAT math is the huge number of topics that can be tested. If you look at the topics listed in Tip #1 of this article, you will see that you have a lot of math to review or learn. If you can keep focused and stay disciplined in your preparation, you should be able to overcome any deficits in your math skills and perform extremely well on SAT math.
What’s Next?
We’ve looked at a number of tips and strategies for doing well on the math sections of the SAT. You can get some additional help by reading this article about improving your SAT math score.
Arm yourself with as much information as you can, and your SAT math score will be in the stratosphere!
Good luck!
