SAT Math: How to get an 800

nelkypie
Mon, 11 Jun 2012 16:12:00 +0000

I’ve been lurking on CC for a while and thought I’d try my hand at giving future test takers advice on how to ace the math section of the SAT. It would be prudent to mention that my story isn’t one of those “I started out getting 600s and then worked my way to an 800” narratives. Math has always been my best subject, but I still think my pointers would benefit those struggling on this section.

The Mentality- Start off by understanding the following: none of the math problems college board will throw at you are inherently labor intensive. There are easy ways to solve all of them, tricks that you’ll pick up as you continue practicing.

Before you start prepping…
Take a diagnostic in the blue book published by college board. Work through any one test, but here’s the catch: only do the three math sections and take as much time as you need, making sure to note your start and finish times at each part. I recommend that you do this because it allows you to gain insight on your natural math ability apart from the test’s constraints. This kind of nuanced diagnostic will allow you to identify the method of preparation best suited for you. For example, it’s useful to know that you have the ability to get all of the problems correct if you take two extra minutes on each section. In this case, you’d know not to review math concepts but instead work on learning quicker ways to solve the problems.

Crunch your score using the book’s guidelines.

If you score a 740+ within the time limit…
You’re well on your way to an 800. What may be keeping you from getting the perfect score is making careless mistakes. Combat this by marking the questions that have the biggest room for error (ones that require multiple calculations or more than one formula), and then go back at the end and redo them. If you don’t have enough time to look through the rest of the problems, prioritize checking multiple choice over grid ins (no penalty for incorrect answers on the latter.)
The Game Plan: You want to have enough time left over to check the entire section, so the majority of your prep efforts should be targeted towards solving problems more quickly while retaining accuracy. If moving quickly trips you up, do the opposite: go slowly, read each question intentionally, solve each problem carefully, and you shouldn’t have to check over your answers at all.

If you score a 740+ taking extra time…
The 800 is within reach, but you’re going to have to do some monotonous prep to attain it. First, you need to determine why you didn’t finish within time. Are there certain types of questions that you take a while on? Or do you solve math problems slowly in general? Peruse the solution methods referenced in the answer key and see whether yours were as efficient. Armed with this insight, go forth and multiply (math jokes, anyone? Okay I’ll stop.)
The Game Plan: Your goal is to finish on time. The best ways to accomplish this are a) Learn efficient solution methods and b) Learn to do easy problems quickly so you have time to work through the harder ones. My general rule of thumb is that if you can finish the first ten problems under 7 minutes, you’re good to go. Work towards this goal by doing practice problems, but DO NOT sacrifice accuracy for speed. If you make silly mistakes moving at this pace, slow down a little, read carefully, and bank on getting the correct answers the first time through.

If you score below a 740…
You might argue that two people who score 730 and 600, respectively, should be treated differently, but I’ve chosen not to. Why? Breaking the 750 barrier is almost as difficult as increasing your score by 150 points! If you’re scoring below a 740, chances are, you need to brush up on some math. The blue book summarizes the concepts tested on the SAT very well. Use it, love it. Also, refer to the strategies below to solve the types of problems that usually stump people!
The Game Plan: Whether you score a 730 or a 500 on the diagnostic, you can get an 800 so long as you’re willing to put in the work. By the way, when I say “put in the work,” I do not mean study 3+ hours a day, like many insist is necessary for improvement. 30 minutes a day should suffice if you’re preparing intelligently (that is, with your strengths and weaknesses in mind.) If you lack in one specific area (like geometry, for example), work on it. You can also master the section by doing one set of practice problems a day and noticing the patterns in the types of questions asked. Eventually, you’ll grow so accustomed to College Board questions that you’ll know how to approach almost all of them upon first sight. The questions are very repetitive in nature, so it’s important that you review each test you take and determine WHY you got each problem that you did wrong. Learn from your mistakes!

Strategies by Problem Type

Problems with DIAGRAMS- Always, always, always fill in diagrams with information you can derive based on what you’re given.

TRIANGLES: The sum of the angles in a triangle is 180. If you are given two angles in a triangle, even if they are expressed algebraically, denote the last angle as “180 - measure of angle 1 - measure of angle 2.”
Memorize the pythagorean theorem. If you have a triangle with a right angle in it and are given two different sides, you can calculate the length of the third. Then write it into the diagram.
Memorize the special right triangle side ratios. These are ALWAYS tested, ALWAYS. It helps to have them committed to memory. If you know the length of one side of a special right triangle (a triangle that has angles of 30-60-90 or 45-45-90), then you know the length of all three. The second you see a right triangle an angle of 30, 45, or 60 in it, you should know to whip out these ratios. Mark anything relevant on the diagram.

ANGLES: Know the relationships between the angles formed when parallel lines are intersected by a transversal. If given one angle, you know all of the angles.
If you have two intersecting lines, the angles opposite each other will be congruent. The measures of the angles next to each other will add up to 180. Mark these relationships on the diagram, if relevant.
If you have a triangle with two congruent sides, then the angles opposite those sides will also be congruent. Mark these relationships on the diagram, if relevant.

CIRCLES: Given the area or circumference of a circle, you can solve for its radius by setting 2(pi)r=circumference or (pi)r^2=area. Mark the length of the radius on the diagram, if relevant.
If a triangle is inscribed into a circle, its longest side is the circle’s diameter, and its other two sides are formed by connecting the two ends of the diameter to a single point on the circle’s circumference, then this triangle is a right triangle. Mark this right angle on the diagram, if relevant.

Most diagram problems on the SAT will require you to use a combination of these methods to get the answer. Focus on the angle relationships, as they are the most universally applicable. (Note: I rarely come across a diagram problem which has an obvious solution method. You just have to fill in missing values and the answer reveals itself sooner or later.)

Questions involving STATISTICS- Depending on the kind of person you are, these problems are either score boosters or the bane of your existence.

LISTS OF VALUES: If College Board hits you with a problem in which you’re given the maximum, minimum, and median of a data set, write down these values in ascending order, leaving blank spaces for values in between (well, you don’t have to, but sometimes it helps to visualize these things.) Provided that the data set is supposed to be a five number set (and it usually is, unless they give you more values), the mean will be minimized if data point 2 equals the minimum and data point 4 equals the median. Conversely, the mean will be maximized if data point 2 equals the median and data point 4 equals the maximum.

MEANS: If you know the mean of a data set, you know the sum of the numbers, because mean= (sum)/number of values. Do not underestimate this formula’s usefulness. You can use it to solve problems in which you’re asked to determine the value of a certain data point (in which you’re also provided with the average/sum of the points excluding the desired value.) You can also use it to solve more complicated problems, like one that asks you to find the average of a 12 number set given the average of the first 6 values and the sum of the last 6.

General Tips- These apply to everyone.

1. Don’t be intimidated by variables. If an angle in a diagram is expressed in a variable quantity, label as if it were a number. If you get a question along the lines of “Given the even integer “x,” which of the following must be odd,” assign x a value and plug it into the expressions given.

2. Use your calculator if you need it. I rarely pick up mine during a math section because I trust my mental math more than my ability to type numbers into a machine, but if you’re not good with numbers, know that your calculator is there to support you.

3. Take each score you get with a grain of salt. An anecdote: the first time I took the SAT, I was twelve, and I scored an 800 on the math section. However, I just took the June test, and I know I got at least one problem wrong! The fact that I’m not going to get an 800 does not mean that I have gotten worse at math or that my abilities are deteriorating. Every person has a performance range, and so long as you’re consistently scoring at and around 800 on practice tests, you’re doing great.

4. SAT questions of the day are your friends. Get a College Board account and get them emailed to you. They’re good practice.

5. Only use College Board tests. I know there are other prep books out there, but no one does it quite like College Board does. You want an accurate portrayal of the kinds of questions that’ll be asked on the exam, not someone’s best guess.

I wish all of you starting to prep for the SAT luck! Please private message me if you have any questions, need any advice, or would like me to elaborate upon any of the strategies that I’ve outlined in my guide.

~N