SAT Math How to Score a Perfect 800 [Plus a Downloadable Guide]

1 Who wants a perfect 800 score in SAT Math? Who wouldnt want that? Well, good news—that perfect 800 is within your reach. With the right prep, and the right understanding of SAT Math, anyone can get an 800, or something very close to it. Well share quick facts about SAT Math, steps you can take to get an 800, and share practice resources, including a free eBook filled with practice questions! Aside from the obvious appeal of seeing that beautiful 800 glowing on your score report, there are other benefits to scoring perfectly in SAT Math. Whether you feel more confident in SAT Math or the Reading/Writing Language sections of the test, a perfect Math score can keep your whole-test score high, making you a highly competitive applicant. Table of Contents SAT Math: Quick Facts What Does it Take to Get an 800 in SAT Math? What are Some Steps I can Take to Get an 800 in SAT Math? Step 1: Master content first, then pacing Step 2: Keep an error log Step 3: Try to solve problems in multiple ways Step 4: Master every one of your weak areas Step 5: Master even the rarest of SAT Math content Step 6: Repeat, repeat, repeat! Step 7: Understand, dont just memorize Step 8: Train yourself for minimal calculator use Step 9: Know and practice common strategies for SAT Math Step 10: Complete as many high quality practice questions as you can Where Else Can I Get SAT Math Practice? Frequently Asked Questions Get the Free Downloadable eBook! SAT Math: Quick Facts The first step toward SAT Math preparation is understanding. And by this, I mean you need to understand the basic structure of the test. Its an easy first step. Consult the quick facts list and the two tables below, and youll clearly see the whole picture. Fact #1: There are two sections of SAT Math: Calculator, and No Calculator. The third and fourth sections of the whole SAT exam focus on math. Section 3 of the test is the first math section, and is headed Math Test—No Calculator. As youd assume, you cant use a calculator in this section of the test. Section 4 of the exam, the second SAT Math section, is entitled Math Section—Calculator. And—you guessed it—you can use a calculator in this part of SAT Math. For full details on the differences between these two sections, check out the handy dandy table below: Test SectionMultiple Choice Questions"Grid-In" QuestionsTime Limit No Calculator (20 questions)15 questions5 questions25 minutes (average of 1 minute, 15 seconds per question) Calculator (38 questions)30 questions8 questions55 minutes (average of 1 minute, 27 seconds per question) Whole SAT Math Section (58 questions)45 questions13 questions80 minutes Fact #2: Questions are either multiple choice or grid-in. The majority of SAT Math questions are multiple choice. However, there is a smaller group of grid-in questions at the end of both SAT Math sections. Grid-in questions require test-takers to come up with the exact numerical answer themselves, and then enter the answer by filling in bubbles for the digits in the number. Fact #3: Each question is worth the same amount of points. Although there are two sections of SAT Math, the questions in these sections are equally weighted. A question missed in either section will have the exact same impact on your score. Moreover, you dont earn more points for one topic or another. Whether a question deals with stats, trig, compound interest, etc., it will be worth the same amount as any other question. (And of course, multiple choice and grid-in questions are worth the same amount of points as well.) Fact #4: Both sections focus on the same categories of math problems. The College Board puts SAT Math problems into four categories: Heart of Algebra, Problem Solving and Data Analysis, Passport to Advanced Math, and Additional Topics in Math. Questions from these subcategories are distributed equally across the Calculator and No Calculator sections of SAT Math. You can see the categories and their subcategories below: CategoryMath Topics CoveredNumber of questions per category Heart of Algebra-Linear equations and functions -Inequalities19 Problem Solving and Data Analysis-Ratios -Proportions -Percentages -Units of measurement -Quantitative data17 Passport to Advanced Math-Equivalent algebraic expressions -Quadratic equations -Exponents -Other nonlinear equations and functions (including expressions for lines on the coordinate plane)16 Additional Topics in Math-Geometry (2 dimensional and 3 dimensional) -Trigonometry (very basic trig)6 Fact #5: SAT Math is scored on a 200-800 scale. Once all of your right and wrong answers have been tallied up, the College Board will convert your performance into a score between 200 and 800. This 200-800 range scaled score is what youll see on your official score report. As you may have already realized, this 200-800 point range means that the two SAT Math sections (Calculator and No-Calculator) make up half of the 2 = 1,000 * 1.69. So the final amount is now $1,690 (A = 1,690). Thats a difference of approximately $0 D) 199 Here, if you used a calculator, youd have to start checking the math for each answer, multiplying every choice by 1.3 (the multiplier for a 30% increase). 105*1.3 = 136.5, 122*1.3 = 158.6, and 130*1.3 = 169. So youd be able to stop at the third choice and select it. But lets see how much easier it is without a calculator, relying on mental math techniques. In that case, you would probably start with a shortcut for calculating 30%. Youd realize that 30% is 1/10 times 3. So to figure out what 30% of any answer choice is, youd need to divide the answer choice by 10 and then multiply that 1/10 of the answer by 3. From there, a quick glance at the answer choices reveals something interesting. Because (C) is the only answer that ends in 0, (C) is the only answer where 10% is a whole number. So its the only answer where 30%, or a 30% increase, would also be a whole number. Since a 30% increase leads to the whole number 169, youve just eliminated answers (A), (B), and (D) effortlessly. If you have a keen understanding of mental math shortcuts, you can get to the answer almost instantly without a single calculator keystroke. Here, the calculator could have wasted 15-20 seconds or so of your time. Think about how much that wasted time will add up if you needlessly use the calculator on 10, 20, or even 30 of your SAT Math Calculator problems. Calculator downside 2: Keying in mistakes Its pretty difficult to write down the wrong number on a piece of scrap paper completely by accident. I mean, how often have you intended to write down, say, a 9, and accidentally written a 6 or 5 instead, without even noticing that you did that? I cant imagine thats happened very often to anyone. If you look at your calculator keypad, youll know why Im bringing this up. The 5 is diagonal from the 9 on most calculators, and the 6 is right below the 9. So these kinds of mistakes are easy to make on a calculator, yet wholly avoidable with mental math and pencil/paper. However, theres also a less obvious way that calculators facilitate careless mistakes. To see how else the SAT Math Calculator section can lure you into keypad mistakes, lets take a look at this problem: Based on the histogram above, which of the following is the closest to the average (arithmetic mean) number of people per household? A) 3 B) 4 C) 5 D) 6 Because there are so many numbers, its tempting to try to use a calculator to keep track of them all. You need to divide the total number of people on the block by the number of households. Now, there are 17 households total; this is easy enough to add up with or without a calculator. But what about the total number of people? To get that with a calculator, youd enter this operation: (4*1) + (4*2) + (5*4) + (2*5) + 7 + 8 = 57 Unfortunately, when you use a calculator to deal with info from a graph, youre not focusing much on the full meaning of the graph. Instead, your energies are devoted to transferring numbers from the visual to the calculator. So you could easily transfer numbers that you shouldnt. For example, you might accidentally include a 3 and a 6 in the figure for total people among the households. In our haste to copy numbers from the chart to the calculator, you may not think about the fact that there are zero households with those numbers of people. In that case, your calculation would incorrectly look like this: (4*1) + (4*2) + 3 + (5*4) + (2*5) + 6 + 7 + 8 = 66 With that mistake, you get 66/17 instead of 57/17. 66/17 leads you to a number that rounds up to 4 (an incorrect answer), while 57/17 would round down to the correct answer of 3. It would actually be far safer to use scrap paper or mental math for just about every step in this problem. The only point at which a calculator might be useful is the very end, when you actually divide the number of people by the number of households. Otherwise, the calculator really is a trap that can cause you to miss an otherwise manageable question. How to train yourself to use the calculator less Basically, you need to treat every Calculator problem as a challenge. The challenge is to do the entire problem, or as many steps as possible, without a calculator. Be creative! Think of shortcuts you can take to skip steps, make other steps go faster, and get to that answer quickly, just through brain power. And speaking of shortcuts, that brings us to Step 9 on your path to an 800 in SAT Math Step 9: Know and practice common strategies for SAT Math Strategies are the lifeblood of your SAT Math performance. On problems where its useful, be sure to try backsolving—starting with the answer choices, and then seeing which answer choice best works for the question. (You saw this in the first example problem in Step 8 above.) Be sure to use other common strategies as needed, too. Sometimes estimation will get you to the right answer choice quickly. Other times, replacing the variables with numbers youve picked will make it easier for you to understand an algebra operation in SAT Math. In general, you want to cultivate a strong number sense, so that you can identify and use the right mental math tricks for various questions in SAT Math. For more instruction on this, with lots of tips and examples, check out the downloadable eBook! Step 10: Complete as many high quality practice questions as you can When it comes to getting an 800 in SAT Math, practice makes perfect. But not just any practice. There are plenty of low-quality SAT Math practice questions out there. Poorly designed SAT Math practice wont match whats actually on the exam, and can leave you unprepared for the real test. Be sure to seek out high quality resources from reputable companies. This blog is a good place to start. Here, youll find excellent SAT Math practice in our free resources, such as the Guide to a Perfect 800 in SAT Math eBook. Where Else Can I Get SAT Math Practice? There are quite a few places to get good SAT Math practice. Check out the lists below. Magoosh SAT Math Practice In addition to the eBooks I mentioned in the previous section, you can also practice SAT Math with: Magooshs free SAT Practice Test PDF Magooshs Public SAT Video Lessons Magoosh SAT Premium (approximately 350 practice SAT Math questions, well over 100 SAT Math video lessons) College Board SAT Practice The College Board, the company that makes the real SAT exam, offers a generous amount of free practice in SAT Math, along with practice questions for the rest of the exam. Official SAT Practice Tests (free online resource, includes 8 full tests in PDF, with essay questions and answer explanations) SAT Sample Questions (additional free online test questions for SAT Math, SAT Reading, and SAT Writing and Language) The Official SAT Study Guide (The practice tests in this book are also available online, through the above-linked Official SAT Practice tests. However, this book also offers additional model practice questions and tutorials, as well as a chance to practice the SAT in paper form, like you would on test day.) Khan Academy SAT Prep Khan Academy has worked closely with the College Board to create additional official prep for SAT Math. (And for the other parts of the exam, of course!) Here is what they have to offer: SAT Math Practice (The practice problems come in video form, with a video lesson on how to solve each problem; there are 79 video lessons in all. This is a companion practice set to Khan Academys similar SAT Reading and Writing practice.) Full-length SAT (in addition to the full-length practice tests from Magoosh and College Board, Khan provides one of their own) Other sources of SAT Math practice I definitely recommend Magoosh, College Board, and Khan Academy as the very best sources of SAT Math practice. But needless to say, these three sources arent the only ones out there. Should you try any additional publishers and companies? You just might want to. Read Magooshs SAT book reviews and decide for yourself. Getting an 800 in SAT Math: Frequently Asked Questions If you want the very top score in SAT Math, there are a few important things you need to know. Here are some answers to ambitious SAT Math students frequently asked questions. What is the math on the SAT? This is a great question. As Ive mentioned before, you really do need to know every possible math topic on the SAT if you want to get an 800. The College Board puts SAT Math into four categories: Heart of Algebra, Problem Solving and Data Analysis, Passport to Advanced Math, and Additional Topics in Math. But obviously, these sometimes poetic-sounding category names dont tell the whole story. Lets take a closer look at what kind of math is actually in these categories. Heart of Algebra deals with regular algebraic equations, and with functions, by which I mean the problems that use the notation f(x) to indicate a certain type of algebraic function. Heart of Algebra also deals with algebraic inequalities in addition to regular equations. Problem Solving and Data Analysis is dominated by word problems and infographics. Youll need to calculate proportions and rations of different things to each other. Youll also deal a lot with percentage changes, units of measurement, and other types of quantitative data. Passport to Advanced Math is the next step up from Heart of Algebra, in terms of difficulty. Here, youll solve systems of algebraic equations, and algebraic equations where there is more than one possible answer. This category of SAT Math also includes quadratics and other algebraic equations where one or more of the variables is a square or exponent. Expect to deal with many exponent-related problems, and many problems where x, y, or other variables have two possible values, or sometimes more. So, what are Additional Topics in Math, exactly? While the College Board-given name implies this is a generic mix of extra math, there is in fact a common theme: geometry. Expect to deal with coordinate geometry, three-dimensional geometry (volume, surface measurements for physical objects, etc.) and two-dimensional geometry (area, angles, shape, and so on). Here, youll also see some trigonometry, advanced mathematics in 2D geometry, focusing on the properties of triangles and circles. Is there any calculus on the SAT? There are no calculus math problems on the SAT. However, within the Passport to Advanced Math category of questions, there are some math problems that could be thought of as pre-calculus. The more advanced math problems on the SAT will include complex algebraic expressions and functions that might also be seen in some easier calculus problems. However, what you do with those functions on the SAT will be different from what youd do with them in calculus. You wont be using calculus methods to evaluate functions, and the answer choices wont be the kinds of results youd typically get in a calculus math problem. What is the highest level of math on the SAT? This question is a little tricky. In terms of the typical high school learning sequence for math, trigonometry is probably the most advanced content in SAT Math. However, not everyone learns math in the same sequence at their high school. More importantly, not everyone finds the same kinds of math to be hard or easy. When students ask what the highest level of SAT Math is, they are usually really trying to figure out what the hardest SAT math is. And for that, your individual mileage may vary. Typically, SAT test takers find trig and the complex systems of algebraic equations to be the hardest. However, Ive also talked to plenty of students who are reasonably comfortable with trig and Passport to Advanced Math, but find something else to be really challenging. (This something else could be a certain type of word problem, a certain aspect of the exponential growth formula, specific kinds of shapes in geometry, and so on.) Anyone aspiring to a perfect 800 in SAT Math should work diligently to discover and address their own personal weaknesses. Free Downloadable eBook: The How to Get a Perfect 800 in SAT Math PDF Hopefully the information and steps in this article can guide you as you work toward your perfect score. But were not done yet! Magoosh has also made an eBook to help you along the way. This eBook lists the strategies you should practice and the formulas you should truly understand. Weve also given you 20 practice questions (with answer explanations) so you can actively use those strategies and formulas. These questions cover all of the math content youll see on the test. Good luck, and heres to a perfect 800!