The SAT Mathematics Solution Guide©

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Instead, write your answers on a piece of paper as you take the "test. While the newest practice tests will be most useful for your prep, you can also use any of these four old pre SAT practice tests. You might notice that there are some missing years e. In other words, the four tests linked above are the only free SAT tests available from the past 10 years excluding the newest ones. What's more, its tests use the old pre version of the SAT , so expect minor differences in math content and form. No need to weigh the pros and cons here—all of the resources we recommend are guaranteed to help you get a great SAT Math score!

Browse our SAT Math guides below to get started!

All guides are arranged by topic. Fractions, Ratios, and Proportions. Statistics Mean, Median, Mode. Reflections, Translations, and Rotations. In addition, we have strategy guides that will help you solve numerous SAT Math problems across the board: Our program assesses your current strengths and weaknesses and adapts based on your progress.

It gives you practice questions tailored to your areas of needed improvement and provides answer explanations for all questions. All our questions are based off of real SAT test questions and, though the full program is not free, we guarantee your money back if you do not improve by points.

SAT / ACT Prep Online Guides and Tips

Rather, it's best to use this website after you've exhausted all the official SAT resources above. What's especially nice about this website is its organization: However, they're not perfect. Some of the questions on the Math sections are a little too easy and not as similar to those on the SAT as they could be. It's just as important to know how to best utilize your SAT study materials as it is to know how to access them.

These six tips will help you achieve your highest SAT Math score on test day. You're probably mostly concerned about your SAT Math score, but it's still important to take a full SAT practice test so you can see how you'll fare on test day. And exhaustion can lead anyone to make mistakes! So before you dedicate your focus to the SAT Math section, take an official SAT practice test to see how your Math score fits into the larger test-taking picture.

Make sure to take the whole test in one sitting; this will help you build endurance for test day.

Step-by-Step Math Video Solution Guide to the New Official SAT Study Guide Textbook

As you take SAT practice tests and any Math-specific sections, be sure to use the same time limits you'll have on test day. The chart below shows how much time you'll have on each SAT section as well as how much time you should approximately spend per question:. You'll have about 75 seconds per question on No Calculator Math section, and 87 seconds per question on the Calculator Math section.

Some questions might take you less or more time, but keep practicing so that you're not consistently spending too long on a single math question. Remember that accuracy is only half the battle—you have to actually finish the questions within the time limits if you want to get a high Math score! This is completely normal and gives you a starting point from which you can later improve.

It's one thing to take an SAT Math test, but you also need to look over your results and identify any patterns in your correct and incorrect answers. Do you tend to get the last few questions wrong on each Math section? Do function questions just seem to throw you for a loop? First, figure out what went wrong.

Remember that each Math question, no matter its difficulty, is worth the same number of points!

Choose Your Test

Once you've pinpointed patterns in the errors you make, it's time to dig deeper and examine your biggest weaknesses. Your ultimate goal will be to tailor your studying so that you can focus on improving the areas you struggle with the most. Since your overall objective is to answer as many questions as accurately as possible, you'll want to dedicate the majority of your study time to improving your weaknesses, rather than to reviewing material you already know well. Refreshing your known material again and again might make you feel productive and confident, but it doesn't do a whole lot to improve your score.

Your best bet is to focus on your problem areas by practicing and expanding your knowledge base. You might have a busy schedule and feel as if your only option is to cram for the SAT, but improvement really happens over time. We generally advise giving yourself at least three to six months to study for the SAT. No matter how much time you've got for studying, it is possible to come up with a balanced SAT study plan. First, calculate the amount of time you have before your test date. For example, say you've got a month before your test.

In this case, try to fit in at least one or two practice tests wherever you can. 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 , don't waste your time studying trying to get a You're already set for the top colleges, and it's time to work on the rest of your application. There's a big difference between a and a , largely because it's easy to get a and a lot more applicants do and a lot harder to get a So why get an on SAT Math?

Because it helps you compensate for weaknesses in other sections. By and large, schools consider your composite score moreso than your individual section scores. This gives you a lot more flexibility. There are two other scenarios where an 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. The school wants to admit the best, and you're competing with other people in the same "bucket" as you.

Here are a few examples from schools. I'm not going to lie. SAT Math was super easy for me. I got on pretty much every practice test and official SAT I ever took. I also worked hard and applied the strategies below to achieve perfection. You're competing against people like me. Because SAT Math is supposed to be trivially easy for you.

But if you can work your way to an , 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. I mean, literally, you and every other reasonably intelligent student can score an on SAT Math.

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. 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.


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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. 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. Notice that the shaded area is the area of the square, with the area of the circle punched out. The SAT math section is full of weird examples like this, some of which get much more difficult. 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 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 If you could use a refresher on how the SAT is scored and how raw scores are calculated, read this. On 3 out of 4 tests, if you just miss a single question, you get dropped down to a That's it - no perfect score! 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 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 Whatever you're scoring now, take note of the difference you need to get to a For example, if you're scoring a now, you need to answer more questions right to get to an As a final example, here's a screenshot from my exact score report showing that I missed 0 questions and earned an 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.

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. 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. 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 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. 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.

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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 with extra time, but score a in regular time, you know exactly that you need to work on time management to get an 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 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. 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, questions, but they're still nowhere near an on SAT Math. 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. 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. Now, what are some common reasons that you missed a question?

Don't just say, "I didn't get this question right. 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:. I didn't learn the math skill or knowledge needed to answer this question. What specific math skill do I need to learn, and how will I learn this skill? I knew the content, but I didn't know how to approach this question. How do I solve the question?

How will I solve questions like this in the future? I misread what the question was asking for or solved for the wrong thing. Why did I misread the question? What should I do in the future to avoid this? 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. 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.

Complex numbers — Harder example

We designed our program around the concepts in this article, because they actually work. PrepScholar then creates a study program specifically customized for you. 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. 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. 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 , 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. 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.

This repetitive practice fills up your content gap far better than any other method I know. 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. 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.

Complete List of FREE SAT Math Practice Problems

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. The SAT has an uneven balance of questions by skill. 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. I'll show you the frequency of appearance, as well as the expected of questions per test for that skill. But you have to know it anyway. You have to know it all.

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