# SAT / ACT Prep Online Guides and Tips

Are you scoring in the 600-750 range on SAT Math? Do you want to raise that score as high as possible—to a perfect 800?

Getting to an 800 SAT Math score isn't easy. It'll require perfection. But with hard work and my strategies below, you'll be able to do it. I've scored 800 on Math on all my SATs, and I know what it takes. Follow my advice, and you'll get a perfect score—or get very close.

Brief note: This article is suited for students already scoring a 600 on SAT math or above. If you're below this range, my "How to improve your SAT Math score" article is more appropriate for you. Follow the advice in that article, then come back to this one when you've reached a 600.

## Overview

A lot of SAT Math guides out there are pretty bad. They're written by people who don't have actual expertise in the test, or they contain vague advice that isn't helpful to the advanced student. You need better advice than simple SAT Math tips like "remember there's no guessing penalty!"

In contrast, I've written what I believe to be the best guide on getting an 800 available anywhere. I have confidence that these strategies work because I used them myself to score 800 on SAT Math, every time I've taken the SAT. They've also worked for thousands of my students at PrepScholar.

In this article, I'm going to discuss why scoring an 800 is a good idea, what it takes to score an 800, and then go into the 8 key SAT Math strategies so you know how to get an 800 on SAT Math.

Stick with me—as an advanced student, you probably already know that scoring high is good. But it's important to know why an 800 Math score is useful, since this will fuel your motivation to get a high score.

Finally, in this guide, I talk mainly about getting to a 800. But if your goal is a 700, these strategies still equally apply.

## Understand the Stakes: Why an 800 SAT Math?

Let's make something clear: for all intents and purposes, a 1530+ on an SAT is equivalent to a perfect 1600. No top college is going to give you more credit for a 1580 than a 1540. You've already crossed their score threshold, and whether you get in now depends on the rest of your application.

So if you're already scoring a 1540, don't waste your time studying trying to get a 1600. You're already set for the top colleges, and it's time to work on the rest of your application.

But if you're scoring a 1520 or below AND you want to go to a top 10 college, it's worth your time to push your score up to a 1530 or above. There's a big difference between a 1440 and a 1540, largely because it's easy to get a 1440 (and a lot more applicants do) and a lot harder to get a 1540.

A 1520 places you right around average at Harvard and Princeton, and being average is bad in terms of admissions, since the admissions rate is typically below 10%.

So why get an 800 on SAT Math? Because it helps you compensate for weaknesses in other sections. By and large, schools consider your composite score more than your individual section scores. If you can get an 800 in SAT Math, that means you only need a 730 in SAT Reading and Writing. This gives you a lot more flexibility.

MIT expects an 800 in SAT Math.

There are two other scenarios where an 800 in SAT Math is really important. First is if you're planning for a quantitative or science major (like math, physics, statistics, chemistry). The second is if you're applying to a highly selective technical school like MIT or Caltech.

Here's the reason: college admissions is all about comparisons between applicants. The school wants to admit the best, and you're competing with other people in the same "bucket" as you.

By applying as a math/science major, you're competing against other math/science folks: people for whom SAT Math is easy. Really easy.

Here are a few examples from schools. For Harvard, Princeton, MIT, Caltech, and even less selective schools like Carnegie Mellon, the 75th percentile SAT Math score is an 800. That means at least 25% of all students at these schools have an 800 in SAT Math.

Even more surprising: the 25th percentile score for SAT Math at MIT and Caltech are 780 and 790, respectively. This means if you score a 750 on your SAT Math, you're well below average for these schools!

I'm not going to lie. SAT Math was super easy for me. I got 800 on pretty much every practice test and official SAT I ever took. This was largely because I had a strong math background and competed in math competitions like AMC/AIME. I also worked hard and applied the strategies below to achieve perfection.

You're competing against people like me. And if you apply with a 700 on Math, schools like MIT, Harvard, and Princeton are going to doubt your ability. Because SAT Math is supposed to be trivially easy for you.

But if you can work your way to an 800, you show that you're at an equal level (at least on this metric). Even if it takes you a ton of work, all that matters is the score you achieve at the end.

## Know That You Can Do It

This isn't just some fuzzy feel-good message you see on the back of a Starbucks cup.

I mean, literally, you and every other reasonably intelligent student can score an 800 on SAT Math.

The reason most people don't is they don't try hard enough or they don't study the right way.

Even if math wasn't your strongest suit, or you got a B+ in Calculus, you're capable of this.

Because I know that more than anything else, your SAT score is a reflection of how hard you work and how smartly you study.

Here's why: the SAT is a weird test. When you take it, don't you get the sense that the questions are nothing like what you've seen in school?

It's purposely designed this way. The SAT can't test difficult concepts, because this would be unfair for students who never took AP Calculus. It can't ask you to solve Fermat's Last Theorem. The SAT is a national test, which means it needs a level playing field for all students around the country.

So it HAS to test concepts that all high school students will cover. Basic algebra (solving single-variable equations, word problems), advanced algebra (quadratic and exponential equations), geometry (x-y coordinate geometry, circles squares and triangles), and basic statistics.

You've learned all of this before in high school.

But the SAT still has to make the test difficult to differentiate student skill levels, so it needs to test these concepts in strange ways. This trips up students who don't prepare, but it rewards students who understand the test well.

Here's an example: Find the area of the shaded region below, if the radius of the circle is 5.

This is a classic SAT type question. You might already know how to solve it. But it's unlikely you ever ran into something like this in school.

The first time you see this, it might be confusing. How do you get the area of each of the shaded corners? It kind of looks like a triangle, but not really because of the curve region.

But you've learned all the concepts you need to solve this.

Notice that the shaded area is the area of the square, with the area of the circle punched out. To get to the answer quickly, this means that the area of a square is 10 x 10 = 100, and the area of a circle is πr2, or π * 5 * 5 = 25π.

So the area of the shaded region is 100—25π.

The SAT math section is full of weird examples like this, some of which get much more difficult.

To improve your score, you just need to:

• master the types of questions that the SAT tests, like the one above
• draw on the correct concepts you already know to solve the questions
• practice on a lot of questions so you learn from your mistakes

I'll go into more detail about exactly how to do this. First, let's see how many questions you need to get right an 800.

## What It Takes to Get An 800 in Math

If we have a target score in mind, it helps to understand what you need to get that score on the actual test. There are 58 questions in the Math section, and how many questions you miss determines your scaled score out of 800.

From the Official SAT Practice Tests, I've taken the raw score to scaled score conversion tables from four tests. (If you could use a refresher on how the SAT is scored and how raw scores are calculated, read this.)

 Raw Score Test 1 Test 2 Test 3 Test 4 58 800 800 800 800 57 790 790 790 800 56 780 780 780 790 55 760 770 770 790 54 750 760 750 780 53 740 750 740 770 52 730 740 730 760 51 710 730 720 750

Math has a really strict grading scale. On 3 out of 4 tests, if you just miss a single question, you get dropped down to a 790. That's it—no perfect score!

On one of these tests, you get an extra cushion of 1 question, but that's not much.

This all depends on how the particular test you're taking is scored. The harder the math questions are, the more likely you can miss one question and get an 800.

The safest thing to do is to aim for perfection. On every practice test, you need to aim for a perfect raw score for an 800.

Whatever you're scoring now, take note of the difference you need to get to a 800. For example, if you're scoring a 700 now, you need to answer 8-9 more questions right to get to an 800.

As a final example, here's a screenshot from my exact score report showing that I missed 0 questions and earned an 800.

(This was from the previous 2400 version of the SAT.)

OK—so we've covered why scoring a higher SAT math score is important, why you specifically are capable of improving your score, and the raw score you need to get to your target.

Now we'll actually get into actionable strategies that you should use in your own studying to maximize your score improvement.

## Strategies to Get an 800 on SAT Math

### Strategy 1: Understand Your High Level Weakness: Content or Time Management

Every student has different flaws in SAT Math. Some people aren't comfortable with the underlying math material. Others know the math material well, but can't solve questions quickly enough in the harsh time limit.

Here's how you can figure out which one applies more to you:

• For each section, use a timer and have it count down the time allotted for that section. Treat it like a real test.
• If time runs out for that section and you're 100% ready to move on, then move on. If you're not ready to move on, keep on working for as long as you need. For every new answer or answer that you change, mark it with a special note as "Extra Time."
• When you're ready, move on to the next section, and repeat the above until you finish the second math section.
• Grade your test using the answer key and score chart, but we want two scores: 1) The Realistic score you got under normal timing conditions, 2) The Extra Time score. This is why you marked the questions you answered or changed during Extra Time.

Get what we're doing here? By marking which questions you did under Extra Time, we can figure out what score you got if you were given all the time you needed. This will help us figure out where your weaknesses lie.

If you didn't take any extra time, then your Extra Time score is the same as your Realistic score.

Was your Extra Time score a 700 or above?

If NO (Extra Time score < 700), then you have remaining content weaknesses. You might have weaknesses across a range of subjects, or a deep weakness in only a few subjects. (We'll cover this later). Your first plan of attack should be to develop more comfort with all SAT Math subjects.

If YES (Extra Time score > 700), then:

Was your Realistic score a 700 or above?

If NO (Extra Time score > 700, Realistic < 700), then that means you have a difference between your Extra Time score and your Realistic score. If this difference is more than 50 points, then you have some big problems with time management. We need to figure out why this is. Are you generally slow at math across most questions? Or did particular problems slow you down? Generally, doing a lot of practice questions and learning the most efficient solutions will help reduce your time. More on this later.

If YES (both Extra Time and Realistic scores > 700), then you have a really good shot at getting an 800. Compare your Extra Time and Realistic score—if they differed by more than 30 points, then you would benefit from learning how to solve questions more quickly. If not, then you likely can benefit from shoring up on your last content weaknesses and avoiding careless mistakes (more on this strategy later).

Hopefully that makes sense. Typically I see that students have both timing and content issues, but you might find that one is much more dominant for you than the other. For example, if you can get an 800 with extra time, but score a 700 in regular time, you know exactly that you need to work on time management to get an 800.

### Strategy 2: Do a ton of Practice, and Understand Every Single Mistake

On the path to perfection, you need to make sure every single one of your weak points is covered. Even one mistake on all of SAT Math will knock you down from an 800.

The first step is simply to do a ton of practice. If you're studying from free materials or from books, you have access to a lot of practice questions in bulk. As part of our PrepScholar program, we have over 7,000 SAT questions customized to each skill.

The second step—and the more important part—is to be ruthless about understanding your mistakes.

Every mistake you make on a test happens for a reason. If you don't understand exactly why you missed that question, you will make that mistake over and over again.

I've seen students who did 20 practice tests. They've solved over 3,000 questions, but they're still nowhere near an 800 on SAT Math.

Why? They never understood their mistakes. They just hit their heads against the wall over and over again.

Think of yourself as an exterminator, and your mistakes are cockroaches. You need to eliminate every single one—and find the source of each one—or else the restaurant you work for will be shut down.

Here's what you need to do:

• on every practice test or question set that you take, mark every question that you're even 20% unsure about

• when you grade your test or quiz, review EVERY single question that you marked, and every incorrect question. This way even if you guessed a question correctly, you'll make sure to review it.

• in a notebook, write down:
#1: the gist of the question
#2: why you missed it, and
#3: what you'll do to avoid that mistake in the future.
Have separate sections by subject and sub-topic (algebra—solving equations, data analysis—experimental interpretation, etc.)

It's not enough to just think about it and move on. It's not enough to just read the answer explanation. You have to think hard about why you specifically failed on this question.

By taking this structured approach to your mistakes, you'll now have a running log of every question you missed, and your reflection on why.

No excuses when it comes to your mistakes.

#### Always Go Deeper—WHY Did You Miss a Math Question?

Now, what are some common reasons that you missed a question? Don't just say, "I didn't get this question right." That's a cop out.

Always take it one step further—what specifically did you miss, and what do you have to improve in the future?

Here are some examples of common reasons you miss a question, and how you take the analysis one step further:

Content: I didn't learn the math skill or knowledge needed to answer this question.

One step further: What specific math skill do I need to learn, and how will I learn this skill?

Incorrect Approach: I knew the content, but I didn't know how to approach this question.

One step further: How do I solve the question? How will I solve questions like this in the future?

Careless Error: I misread what the question was asking for or solved for the wrong thing.

One step further: Why did I misread the question? What should I do in the future to avoid this?

Get the idea? You're really digging into understanding why you're missing questions.

Yes, this is hard, and it's draining, and it takes work. That's why most students who study ineffectively don't improve.

But you're different. Just by reading this guide, you're already proving that you care more than other students. And if you apply these principles and analyze your mistakes, you'll improve more than other students too.

Bonus: If all of this is making sense to you, you'd love our SAT prep program, PrepScholar.

We designed our program around the concepts in this article, because they actually work. When you start with PrepScholar, you'll take a diagnostic that will determine your weaknesses in over forty SAT skills. PrepScholar then creates a study program specifically customized for you.

To improve each skill, you'll take focused lessons dedicated to each skill, with over 20 practice questions per skill. This will train you for your specific area weaknesses, so your time is always spent most effectively to raise your score.

We also force you to focus on understanding your mistakes and learning from them. If you make the same mistake over and over again, we'll call you out on it.

There's no other prep system out there that does it this way, which is why we get better score results than any other program on the market.

Check it out today with a 5-day free trial:

### Strategy 3: If You Have Math Content Gaps, Be Ruthless About Filling Them

Within SAT Math, you have to master a lot of subjects. At the high level, you need to know basic algebra, advanced algebra, data analysis, and geometry. Even further, within algebra, you need to know how to solve equations, how to deal with word problems, properties of functions, etc.

Here's our complete mapping of all 24 skills you need in SAT Math:

• Basic Algebra
• Linear functions
• Single variable equations
• Systems of linear equations
• Absolute value
• Manipulating polynomials
• Dividing polynomials
• Exponential functions
• Function notation
• Solving exponential equations
• Systems of equations with nonlinear equations
• Problem Solving and Data Analysis
• Ratios and proportions
• Scatterplots and graphs
• Categorical data and probabilities
• Experimental interpretation
• Mean, median, mode, standard deviation
• Coordinate geometry—lines and slopes
• Coordinate geometry—nonlinear functions
• Geometry—circles
• Geometry—lines and angles
• Geometry—solid geometry
• Geometry—triangles and polygons
• Trigonometry
• Complex numbers

Whew! That's a handful. This might be a greater breakdown of skills then you're used to, but at PrepScholar we believe in grouping questions by specific skill so you can train most effectively. In our program, we break down all our SAT Math content into these detailed skills so you can train your specific weaknesses in focused groups.

Unless you're a math whiz and are already scoring a 750-800, it's unlikely that you've mastered all of these evenly. You probably have different strengths and weaknesses across these subjects.

If from the analysis of mistakes above you find that you have a content problem, you need to improve your understanding of that content.

By Content problem, I mean that you're not comfortable with the underlying math concepts in a subject. Maybe you forgot how to solve a type of problem, or you forgot a formula to use, or you just don't remember the subject material.

If you've identified one of these issues, you've spotted an opportunity for yourself to improve your score.

Fill in the potholes of your understanding.

Think of a mistake like discovering a cavity in your mouth. When your dentist fills in a cavity, he doesn't just patch up the hole right away. He cleans out the entire cavity, sterilizes it, then adds a filling.

Content mistakes are similar—you have a weakness in a subject, say x-y coordinate geometry. This probably means you have a lot of other weaknesses in that subject other than the one identified by that question. Don't just focus on understanding that one question you missed.

Take the opportunity to research that subject and get more practice in it. You need to find a way to get lesson material to teach yourself the main concepts that you're forgetting. Then you need to find more practice questions for this skill so you can drill your mistakes.

In our SAT prep program PrepScholar, we do that work for you by splitting up our 7,000+ practice questions by skill and difficulty. If you're weak in algebra—solving equations, you get 20+ questions in a quiz dealing specifically with that skill. This repetitive practice fills up your content gap far better than any other method I know.

### Strategy 4: If You Miss a Question, Try It Again Before Reading the Explanation

When you're doing practice questions, the first thing you probably do is read the answer explanation and at most reflect on it a little.

This is a little too easy. I consider this passive learning—you're not actively engaging with the mistake you made.

Instead, try something different—find the correct answer choice (A-D), but don't look at the explanation. Instead, try to re-solve the question once over again and try to get the correct answer.

This will often be hard. You couldn't solve it the first time, so why could you solve it the second time around?

But this time, with less time pressure, you might spot a new strategy, or something else will pop up. Something will just "click" for you.

When this happens, what you learned will stick with you for 20 times longer than if you just read an answer explanation. I know this from personal experience. Because you've struggled with it and reached a breakthrough, you retain that information far better than if you just passively absorbed the information.

It's too easy to just read an answer explanation and have it go in one ear and out the other. You won't actually learn from your mistake, and you'll make that mistake over and over again.

Treat each wrong question like a puzzle. Struggle with each wrong answer for up to 10 minutes. Only then if you don't get it should you read the answer explanation.

### Strategy 5: Master Every SAT Math Skill—Even the Rare Ones

The SAT has an uneven balance of questions by skill. Algebra dominates the test, taking up over 50% of the test. This is somewhat good news, in that if you're an Algebra whiz, you'll do well on the bulk of SAT math.

The bad news is that there's a long tail of straggling skills that show up just a few times a test. We've done a careful analysis of every math question on every official SAT test, and here are the LEAST common skills in SAT math. I'll show you the frequency of appearance, as well as the expected # of questions per test for that skill.

 Skill Frequency Expected Questions Per Test Dividing polynomials 1.72% 1 Trigonometry, radians 1.72% 1 Absolute value 1.29% 0.75 Complex numbers 1.29% 0.75 Experimental interpretation 0.86% 0.5 Lines and angles 0.86% 0.5 Solid geometry 0.86% 0.5 Systems of equations with nonlinear equations 0.86% 0.5 Function notation 0.43% 0.25

This might surprise you. Some of these skills have an expected # of questions lower than one.

That's right: sometimes you might not even get a complex number or solid geometry question. But you have to know it anyway. You have to know it all.

In some ways, this is really extreme. You have to know a lot of topics in trigonometry, just to answer that one question per test. Here's an example:

You need knowledge of radians and standard triangles to answer this question. To solve the question, you can realize that if the x length is √3, and the height is 1, then you know that this is a 30-60-90 triangle lying on its long side. Thus the angle is 30 degrees.

Then, because π radians is 180 degrees, then the angle is π/6 radians, so a = 6.

But notice that you weren't tested on any other items in standard trigonometry—SOH CAH TOA, graphing functions like cos (90 + 2x), and converting between sin and cos. Yet you still need to know this, because you can't predict what they're going to test.

This is also true of complex numbers, solid geometry (volumes, surface areas), absolute value, dividing polynomials, etc.

This is the challenge of the 800 Math scorer—you need a wide BREADTH of knowledge as well as DEPTH of mastery in each one. No single test is going to test the entire breadth of your knowledge, but you must be prepared anyway.

The way we handle this at PrepScholar, which is based on how I mastered the SAT myself, is to give you detailed lessons and quizzes for all 24 Math skills, and all Reading/Writing skills. For even the least common skills like complex numbers and solid geometry, you'll get dozens of questions to practice with and master the skill. You'll leave no stone unturned, which is why top scoring students love us.

If you don't use PrepScholar, then you need to find great sources of practice content yourself, and to structure your study time optimally so you get both breadth and depth.

### Strategy 6: Finish With Extra Time and Double Check

Your goal at the end of all this work is to get so good at SAT Math that you solve every question and have extra time left over at the end of the section to recheck your work.

In high school and even now, I can finish SAT Math sections in about 60% of the time allotted. This means I finish a 25 minute section in 15 minutes or less, and a 55 minute section in 35 minutes. This gives me a ton of time to recheck my answers two times over and make sure I make no careless mistakes.

How can I finish a section this quickly? It comes down to mastery of the math skills and a LOT of experience with the test. When I see a question, I usually know exactly what the College Board is asking for, and I've seen so many such questions that I know exactly how to solve it in the fewest steps needed.

It comes from hard work and perseverance. If you're pretty far from this time benchmark, don't fret—it took me a lot of training and experience to get to this level. (After all, I've seen thousands of questions in my own SAT prep and when designing our PrepScholar SAT program).

So let's say you finish a section ahead of time. What do you do with all that extra time?

Don't rest and don't put your head down. Use this valuable time to double-check, even triple-check your work. Remember, even one question missed will bring you down from an 800—you need to achieve perfection.

What's the best way to double-check your work? I have a reliable method that I follow:

• Re-read the question again. Question your assumption about what the question is about. If the question asks for a specific variable, make sure you're solving for that variable!

• Try to resolve the question another way. If I solved a question algebraically, I can recheck it by plugging in the solution.
• If I'm 100% sure I'm right on a question, I draw a huge check mark in the test book and never look at the question again. Even if I feel just a little twinge of remaining doubt, I'll come back to it on the third pass.
• At least two minutes before time's up, I rapidly double-check that I bubbled the answers correctly. I try to do this all at once so as not to waste time looking back and forth between the test book and the answer sheet. Go 5 at a time ("A D A C B") for more speed.

Here's an example of solving a question two ways:

First way: My natural instinct is to solve this algebraically. I know I can plug in numbers, but I feel that's slower and more error prone than getting a definitive answer through solving the equation.

3x - 5 ≥ 4x - 3

I can rearrange in my head in one step like so:

-2 ≥ x

(if you make careless mistakes, like the College Board expects you to do, it's worthwhile splitting it up into smaller steps)

OK, so the solution set is numbers less than or equal to -2. This leaves answer A as NOT the solution.

Double-check way: Now that I know answer A should be correct, I'm going to verify by plugging that value back in and expecting the inequality to fail:

3x - 5 ≥ 4x - 3

-3 - 5 ≥ -4 -3

-8 ≥ -7

That's obviously false, so I can verify that A is the right answer. At this point I'm confident enough that I can move on and not check this question again.

Another time management tip: If you notice yourself spending more than 30 seconds on a problem and aren't clear how you'll get to the answer, skip and go to the next question. Even though you need a perfect raw score for an 800, don't be afraid to skip. You can come back to it later, and on your first pass it's more important to get as many points as possible.

Here's a bubbling tip that will save you 2 minutes per section.

When I first started test taking in high school, I did what many students do: after I finished one question, I went to the bubble sheet and filled it in. Then I solved the next question. Finish question 1, bubble in answer 1. Finish question 2, bubble in answer 2. And so forth.

This actually wastes a lot of time. You're distracting yourself between two distinct tasks—solving questions and bubbling in answers. This costs you time in both mental switching costs and in physically moving your hand and eyes to different areas of the test.

Here's a better method: solve all your questions first in the book, then bubble all of them in at once.

This has several huge advantages: you focus on each task one at a time, rather than switching between two different tasks. You also eliminate careless entry errors, like if you skip question 7 and bubble in question 8's answer into question 7's slot.

By saving just 10 seconds per question, you get back 200 seconds on a section that has 20 questions. This is huge.

Note: If you use this strategy, you should already be finishing the section with ample extra time to spare. Otherwise, you might run out of time before you have the chance to bubble in the answer choices all at once. 5 minutes before the section ends, make sure you bubble in the answers you already have.

### Strategy 7: Eliminate Careless Mistakes

Careless mistakes are one of the most frustrating types of errors to make, and nearly everyone makes them, especially on Math.

You know the underlying material, you know how to solve the question, and you're feeling good. But then you grade the quiz, and you find a careless mistake.

Oops—the question asked for the perimeter of the circle and not the area, which is what you calculated.

These types of errors are the most costly and frustrating. You've already put in a ton of work to master the underlying material, and here a question has tricked you into losing a point.

This is why finishing the test early, like I mention above, is so helpful. You get extra time to take a breather and double-check your answers.

If you find that careless mistakes are a recurring problem for you, here are some strategies to get rid of them:

• In the question, underline what the question is specifically asking you to solve for. It's so easy for the SAT to trick you into solving the wrong thing.
• If you're solving for a particular value (like length, area, etc), write the units down in the scratch space.
• Be careful with calculator entry. A missing parentheses makes a big difference. "4 + 9 / 2" is completely different from "(4 + 9) / 2"
• Avoid bubbling errors by using the Quick Tip above.

Here's an example:

This question is asking us to solve for y + z. Not x, y, or any other combination of variables.

To make sure I remember this, I underline y + z, and I also write "y + z = ?" in the work space so that I remember what I'm solving for.

You can bet that in many answer choices, the SAT will have trap answers for other things you can solve for, like x. (This one happens not to, but it's very common).

Memorize the SAT Math Formulas.

### Strategy 8: Memorize the Formulas and Common Math Facts

If you're still flipping to the front of the section to look at the math formulas, you haven't gotten to understand SAT Math well enough yet.

Not only does this cost you time, it also indicates that you haven't practiced enough with SAT Math to have the required formulas come to you fluidly.

Memorize the formulas at the front of the section and these common math facts:

• calculating slope from two points (rise over run)
• remainder when dividing a polynomial
• common right triangles:
• by angles
• 45-45-90 (1-1-√2)
• 30-60-90 (1-2-√3)
• by sides
• 3-4-5
• 5-12-13
• formula for volumes, surface areas

We have a complete list of SAT Math formulas here.

### Strategy 9: Don't Overly Depend on the Calculator

As you likely already know, Section 3 is a Math section forbidding the use of calculator, with 20 questions. Section 4 is a Math section that allows calculator, with 38 questions.

The calculator is really useful for certain questions that require complex calculations, like multiplying decimals together or taking square roots of weird numbers.

However, in many other situations, it's too much of a crutch, and it can make you soft. Learning to solve questions without the use of a calculator will strengthen your math intuition and force you to understand the underlying math, rather than relying on a calculator.

Actually, every question on the SAT is solvable without a calculator. Because the College Board cares a lot about equality, it doesn't want to give an unfair advantage to students who have grown up with graphing calculators compared to students who can't afford them or never used them in school. So it designs questions that don't require advanced calculators to solve.

Practically, this is important because some of the no-calculator questions are solvable with a calculator, and you need to wean yourself off of the calc. Here's an example:

Yes—you can solve this by plugging it into your graphing calculator's systems of equations tool. But this appears on the no calculator section, so you have to get used to solving this with pen and paper.

The second reason to depend less on the calculator is because solving without a calculator is actually faster in many cases. Here's an example:

The calculator way to solve this would be to solve for the quadratic formula, 0 = -4.9 t2 + 25t. You can plug it in and the calculator will spit out two values for t.

How I would naturally approach is to factor first:

0 = t (-4.9t + 25)

Obviously t = 0 is one solution, but the other solution is pretty easy to find too. I don't even need to use the calculator—I know 4.9 is close to 5, so I can see that t is close to 5. This is answer D.

For me, the second way is faster and feels more robust than the first. I know I've solved for t definitively, and I'm confident in my answer choice. Whereas if I used a calculator, I don't have a "feel" for the solution—I'm purely trusting the calculator and what I entered into the calculator as correct.

Now, when I double-check (Strategy 6), I might solve it a different way by plugging in the answer choices. I'll try plugging in answer choices C and D, and it'll be clear that D is the better answer. But this is reserved for answer checking, rather than the first time I solve it.

Being able to solve SAT Math questions without a calculator will train your SAT Math skills more rigorously. This is important when you're aiming for a perfect math score.

### Strategy 10: Keep a Calm Mind During the Test, No Matter What

Now you know what it takes to achieve perfection on SAT Math.

You know that it's critical to get a perfect raw score, or you might score a 780.

This makes a lot of students freak out during the test.

"I can't solve this question...my 800 is gone...I'm getting more nervous and I have to skip the next question too..."

You can see how quickly you can unravel like this. Before you know it, you're scoring way worse than you ever did on a practice test.

You need to learn to be mentally strong, like an athlete on game day.

Yes, you might have to skip a question on the first pass through. Maybe even two in a row.

But you've practiced hard up to this point. You know this stuff, and you'll come back to those questions and get it later.

You need to keep up a positive mindset during the test, or you'll crumble.

And in the worst case, maybe you won't get an 800. But if you've consistently been getting 800's on the practice tests, you likely won't go much lower than 750—and that's still really good.

## Recap: How to Get a Perfect SAT Math Score

Those are the main strategies I have for you to improve your SAT math score to an 800. If you're scoring above a 600 right now, with hard work and smart studying, you can raise it to a perfect SAT Math score.

Notice that I didn't actually teach you that much math content. I didn't point to any specific math solutions that will instantly raise your score.

That's because these one-size-fits-all, guaranteed strategies don't really exist. (And anyone who tells you this is deceiving you). Every student is different.

Instead, you need to understand where you're falling short, and drill those weaknesses continuously. You also need to be thoughtful about your mistakes and leave no mistake ignored.

If you want to go back and review any strategies, here are quick links to them:

Keep reading for more resources on how to boost your SAT score.

## What's Next?

We have a lot more useful guides to raise your SAT score.

Read our complete guide to a perfect SAT score, written by me, a perfect scorer.

Are you aiming for a top school like Harvard or the Ivy Leagues? Here's my famous guide, How to Get Into Harvard.

Learn how to write a perfect-scoring SAT essay, step by step.

Want to improve your SAT score by 160 points? We have the industry's leading SAT prep program. Built by Harvard grads and SAT full scorers, the program learns your strengths and weaknesses through advanced statistics, then customizes your prep program to you so you get the most effective prep possible.

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Allen Cheng