SAT Crash Course
Page 3: SAT Math Strategies
If you want higher SAT math scores, you need to use my two most powerful math concepts:
1. Always use the answers to your advantage.
2. Math is always easiest when you use real numbers.
These concepts are extremely basic, and that’s the whole idea – the simpler your strategy is, the more easy it is to employ. Let’s take a closer look at both strategies to see how they can help you immediately.
1. Use the answers whenever possible. The SAT is a (mostly) multiple-choice exam. Inherent in any multiple-choice exam is a beautiful advantage:
The right answer to every single question is already provided for you!
Sure, it might be surrounded by three wrong answers, but that doesn’t change the fact that the right answer is staring you in the face. Even better, the wrong answers provided by the SAT provide invaluable clues that you can use to help solve each problem.
Here are four ways to start using the provided answers to your immediate advantage:
A) Always look at answer “form” before doing any calculations. Before you start doing any actual math, you should always look at the “form” that the answers take.
Do all the answers contain radicals? Are they all in ratio form? Do they all have pi in them? Are they all in exponent form? Do they contain variables within them? Are they all below 1? Negative? Is there a “this is not possible to deduce” option?
All of this information is essential. The form of the answers can provide insights into the proper way to solve each problem. Most importantly, taking a peek at the answer choices can prevent you from wasting time, and can give you a much better idea of what “Point B” looks like. For instance, if you know that every answer choice is in ratio format, you can start solving for a ratio rather than for a particular variable. If the answer choices are in in “2^x” format, you can find out how many times to multiply 2 by itself, rather than finding an actual number. From this point forward, never start to solve a problem without first looking at the answer choices provided (except, of course, in the case of open-response questions).
B) Rather than doing any math yourself, try plugging in the answer choices. Imagine that a question asks you: “what is one possible solution to the following equation?” You can either solve the equation yourself, or you can just steal the answer choices and plug them in until one works.
This strategy can get you incredibly far. If the question asks you what the largest possible number is that will work in a given situation, start with the largest answer choice provided and work your way down – the first answer that fits is correct (and vice versa for the smallest possible answer). If a question asks you “which number could be the median of this set,” line up all the other numbers from lowest to highest, plug in the answer choices, and see which one falls in the middle.
Using the provided answer choices as problem-solving tools is fast, flawless, and just plain smart. If you’re always looking for opportunities to use this strategy, you’ll always be aware of the times when it will help you.
It takes practice to use this strategy as effectively as possible, but you always need to practice with this strategy in mind.
C) When you’re stuck, look at the answers for clues. If you have no clue how to solve a particular problem, look at the answers for help. Do half of them contain root 3? Then perhaps there’s a 30/60/90 triangle you don’t see yet. Are they all negative? Perhaps you forgot to take negative integers into account. Do they all contain the constant “k” within them? Then perhaps it’s impossible to find “k,” and you need to solve the problem without it. Reviewing the answers when you do not know how to proceed might help you figure out how to solve the problem.
D) Use the answers to save time on calculations. SAT math isn’t particularly difficult – figuring out what math you need to do is tough. Once you’ve figured out what a problem is actually asking of you, the math is usually very straightforward. Once you’ve figured out what you need to do on each problem, take a quick peek at the answers and see if there are any shortcuts. For instance, if you know your answer is going to be odd, see if there’s only one odd answer choice. If you know that your answer is going to be greater than 25,000, see if the other answer choices are all tiny (and one answer choice is massive). Eliminating wrong answers can be very effective, and can save you a lot of time.
Additionally, there are some problems that can only be solved by elimination and use of the existing answer choices. For instance, if a question asks you: “Which of the following graphs represents the following equation: Y=5X-4?”, you know that the graphed line will have a steep, positive slope and a Y intercept of negative 4. Just cross out the answer choices that don’t match and you’ll end up with the right answer.
I teach my students to obsess over the given answers on the math section. They’re big, fat clues just waiting to be used by any student savvy enough to employ them.
As you practice more and more, you’ll start to get a feel for which answers can be used, and which answers can’t. It takes a lot of practice and refinement to nail this down, but it’s very worth the effort! If you want a step-by-step program that’ll teach you how to use this strategy in every imaginable scenario, my online programs are a great pace to start.
Whether or not you use my programs, I can promise you this: if you start to pay more attention to the answer choices, rather than doing math on your own without their assistance, you’ll immediately start to solve problems that may have seemed impossible beforehand.
2. Math is easiest with real numbers. It’s funny how obvious this fact is, but how rarely students think to put it into practice. Math problems are easy to solve when you have the right numbers in your hands. On the other hand, they’re practically impossible to solve when you don’t have any numbers in place. So how do you make sure you’re always doing your math with real numbers?
REFUSE to do math without them!
This is easier said than done, but there are two key strategies that can help you out:
A) If you don’t need to know what something is worth, MAKE IT UP! Making up numbers is, by far, the most powerful strategy you can use to turn extremely challenging problems into extremelyeasy ones. For instance, let’s say a problem asks you the following:
“What happens to the area of a circle when its radius is doubled?”
You have two options:
1. Do a bunch of algebra using variables and conceptual math (ugh).
2. Make up a radius and find out for yourself.
Let’s say that my original circle has a radius of 1. That means its area will be Pi. If I double the radius, I’ll have a radius of 2, and thus an area of 4Pi. That means that “the area quadruples” is the answer. If it works for one number, it works for ALL numbers (if you don’t believe me, try picking a different original and final radius and see if your result is different).
Every time you look at a problem, you should ask yourself the following:
Is there an exact value for X? X can be defined as “any element of the problem that could have a numerical value,” from the number of students in a school to the side length of a triangle to the value of some variable, “n.”
Some problems won’t let you make up numbers. For instance, if a problem asks you “what the value of X is,” you can’t just make it up – it has a specific, defined value that needs to be discovered. However, if the problem says that “there are twice as many boys as girls in a school. What’s the ratio of…..” and you don’t need to know exactly how many boys or girls there are, then why not have 20 boys and 10 girls? Now you can do real math!
Again, using this strategy takes practice. It’s not just something you can hear and then use perfectly. However, if you know to always look for numbers to make up, and do so during all your practice sessions, you’ll be able to use the strategy when it’s most appropriate.
B) If you need to do algebra with an unknown value, assign it a variable! Algebra is amazing because it never lies. If you need to find a certain set value (i.e. if you’re not allowed to make it up), and it hasn’t been assigned a variable, give it one!
For instance, imagine that a certain interior angle of a triangle is unknown, but necessary to help you find another angle within a diagram. You could either stare at it longingly, or you could just label it “Y.” Once you’ve given it a “placeholder,” you’ll be able to use that placeholder within algebraic equations, which will show you concrete and unfailing relative values between that placeholder and every other value within the diagram (the three angles inside the triangle – Y, X, and Z will add up to 180, which will help you to set up algebraic equations).
If a problem states that a girl reads two times as many Italian books as she does French books, and you need to find out how many of each she read, just say that she read F French books and 2F Italian books! Now you can do algebra with the problem, whereas before it was just a “floating” concept – an idea of math, but not actual math (remember – you shouldn’t consider it math unless you’re using numbers or algebra).
At the end of the day, your mission is to create tools which you can use to solve math the way it should be solved: with numbers and variables. If you’re stuck on a problem, it means you haven’t figured out what math to do, and if you haven’t figured out what math to do, it probably means that you don’t have the numbers or variables necessary to create an algebraic equation.
Start using both of these strategies TODAY, and use them on EVERY problem you solve. Eventually, these math tactics will become second nature to you and your scores will reflect your effort!
There are tons of math rules, formulas, and figures that you need to memorize, but anyone can learn and memorize these with time. The SAT isn’t hard because of the math – it’s hard because it makes you use math in a strange way. When you use these strategies, you cut through the BS and end up with clear, solvable problems every single time.
Now that we have math out of the way, let’s tackle “the final frontier” of the SAT – the Writing+Language section. For that, move on to the next guide: