5 Quick Tricks to Improve Your Score on the SAT Math Section
The math section of the SAT is probably the most strategy-based section of the SAT. While the reading section depends a lot on your ability to read and understand the contents of a passage, your score on the math section is really just dependent on a lot of practice!
When you start doing more practice and UNDERSTANDING why you got certain questions wrong and why you got certain questions right, you’ll start to see your score skyrocket when the actual test rolls around!
Here are five of the tips that have helped me the most when trying to increase my score on this section. Along with consistent practice, these strategies can be life-changing.
This first SAT math tip I’ll introduce is what I like to call the plug-and-chug method. No matter how much you might find yourself complaining about standardized testing and the makers of those types of tests, they actually gave you one of the biggest advantages in the test-taking world by structuring the test the way they did. Can you guess what it is?
They made the test fully multiple choice! I cannot stress this enough. USE THIS FORMATTING TO YOUR ADVANTAGE!
One of your biggest advantages on the SAT is that since the test is multiple choice, it doesn’t so much test your ability to come up with the right answer as it does your ability to recognize the right answer.
Although these may seem like the same thing, they’re not. If you think about it, in a multiple choice test, the correct answer is right on the paper in front of you. Your only job is to recognize it.
This tip comes in handy on math questions that may ask you to find the value of a variable in an equation, and may give you the potential values for that unknown variable in the answer choices.
A pretty simple, yet effective example is given below:
Johnny ate 5 packages of apples and 2 packages of oranges. He then gave two apples to his sister. After this, he had eaten 16 fruits in total. Johnny’s sister originally ate 4 packages of apples and one package of oranges, but after eating the 2 apples from Johnny, she had eaten 13 fruits total. How many apples are in each individual package?
- 1 apple
- 2 apples
- 3 apples
- 4 apples
Let’s take a look at how we would solve this algebraically. We could develop the expression 5a + 2r = 16 for Johnny’s fruits, and 4a + r + 2 = 13 for his sister’s fruits, where a is the amount of apples in each package and r is the number of oranges in each package.
After combining like terms, the system of equations is as shown below:
4a + r = 11
5a + 2r = 16
Multiplying the first equation by -2, we get the following system:
-8a – 2r = -22
5a + 2r = 16
Adding the two equations gives us;
-3a = -6
a = 2
There are 2 apples in each package. The correct answer is B.
Now, if all this algebra sounds like a mess of complete confusion to you, don’t be discouraged. There is a much easier way to solve this question: a way that capitalizes on the fact that the entire test is multiple choice.
Instead of creating a whole system of equations and using addition of equations to figure out the missing variables, try plugging in the answer choices into the equations! Go down the list of answer choices (one by one from A to D), until you reach a numerical answer that satisfies all the conditions given in the problem.
In this example, we’d go down the list and see that nothing works with the question conditions until we get down to answer choice B. When we check this answer choice, we would see that if Johnny ate 5 packages, each made of 2 apples, he would have eaten 10 apples. If he eats 16 fruits total, that would mean that he ate 6 oranges.
Since the question gives us the fact that Johnny ate 2 orange packages, we conclude (based on the assumption that B is correct) that each orange package should have 3 oranges.
Now, we can see if this makes sense for Johnny’s sister’s case. If his sister eats 4 packages of apples, each containing 2 apples, this multiplies out to 8 apples. If she eats one more package of oranges, which presumptively contains 3 oranges, this brings us up to 11 fruits total. Then, she eats the 2 that Johnny gave her.
This comes out to 13 fruits total, which is the same number that the question provides us with. Since these numbers seem to satisfy all the question conditions, the correct answer would be B.
Now, it depends on which way you find easier. But a good rule of thumb is that if you find yourself struggling to figure out the algebra of a question and solve for unknown variables, don’t waste any more of your time!
Instead, begin to plug each of the answer choices into the problem. Plug and chug until you get an answer that fits. This way, you have a higher chance of getting it right and you won’t waste any more valuable time.
2. Know your special triangles
What are special triangles? While you may not have taken a trigonometry or even a Calculus class before, chances are you’ve heard the term “special triangle” in any basic algebra or geometry class at some point in your education. Here’s a quick refresher:
Right triangles are a special case of triangle in that if you know two of the side lengths of the triangle, you can figure out the third. Using the formula a2 + b2 = c2 – where a and b are the legs of the right triangle and c is the slanted side – it’s possible to substitute values and figure out the length of the remaining side.
What if only one side of the right triangle is given to you in the question? Turns out this is probably a special right triangle. There’s really no other way you can solve the length of another side of a right triangle given only one side. If it’s not a special triangle, you need at least two.
Special right triangles come in two varieties. The first is the 30-60-90 triangle and the second type is the 45-45-90 triangle. What these numbers stand for is actually the angles joining the different sides of the triangle.
In the first, the triangle consists of one right angle, one 30 degree angle, and one 60 degree angle. In the second scenario, the triangle consists of one right angle and the other two are 45 degree angles.
You may be wondering what exactly is so special about these triangles; why do we refer to them as “special?”
The reason is that in these triangles, you only need one side to figure out the other two! If you know that the angles of a triangle are 30 degrees, 60 degrees, and 90 degrees, then you can use the formulas x, x√3, and 2x to figure out the lengths of the sides. If the shortest side is x, then the longer side must automatically be the shorter side times √3, and the slanted side must be the shorter side times 2.
If the shorter side length– for example–is 2 units long, then the longer side will be 2√3 units, and the slant will be 4 units. Similarly if the problem gives you the angles 45, 45, and 90, the side lengths will both be x, and the slanted side length will be x√2. For example, if one of the side lengths is 4 units long, then the other side will also be 4 units and the slant will be 4√2 units long.
Let’s do a quick example.
Ricky the construction man wants to climb up to the roof of a house that he must fix. The roof of the house is 10 feet off the ground and his ladder length is adjustable. For safety reasons, he wants the ladder to make a 30 degree incline with the ground. What length should he adjust his ladder to?
Ready to check your answer? We know that this is a 30-60-90 triangle. How? One angle is 30 degrees, as given by the question. The angle between the horizontal ground and vertical ground is obviously 90 degrees, because…well…that’s just the way the world works.
We know that the angles of a triangle always add up to 180 degrees total. That would mean that the third angle of the triangle should automatically be 180 – 90 – 30 – 60 degrees! This makes it a special 30-60-90 triangle.
If the ladder has a 30 degree incline with reference to the ground, that would mean the side of the house is the short side of the right triangle, or x. This would mean that the distance from the base of the ladder to the house is the side opposite the 60 degree angle, or x√3.
Since x is 10 feet, the longer side of the triangle should be 10√3. The slanted side of the triangle (i.e. the length of the ladder) should be 20. So the answer should be D!
You may be wondering if it’s even worth it to memorize these short and quick expressions. Would it be more convenient just to do the trigonometry on the spot and use what you know about functions like sin, cos, and tan?
The answer is probably not! From the experience of someone who’s taken practice tests time and time again, I can tell you that this “special triangle” concept shows up more than you may think. It usually shows up on the non-calculator section where you don’t necessarily have the luxury of a calculator that can do some quick trigonometry for you.
While it may seem like a lot of work to memorize at first, committing these few simple formulas to memory can help you unbelievably on the SAT with not only time management, but also maximizing your score on the math section.
3. Know your formulas
It’s ALWAYS a good idea to memorize your formulas in the math section. Now, you may be thinking: doesn’t the SAT give you all the formulas you’ll need?
Yes, the formulas will be given to you in the beginning of the test booklet. Yes, you could very well look them up there every time you encounter a question that requires one. Yes, you could flip back and forth and plug the numbers in the question into the formulas at the beginning.
But wouldn’t it be easier just to memorize the formulas? Absolutely!
As I’ve mentioned many times through this strategy guide, time is of the essence on the SAT. Flipping back and forth in the test booklet, although it doesn’t seem like too time-consuming of a task, actually takes more time than you think.
Especially if it’s unnecessary flipping, you’ll more than likely perform better on the SAT if you commit the formulas to memory and use them as you work through the questions.
4. Recheck your answers at the end!
This one comes in handy if you find yourself with some extra time at the end. If you end up taking the entire time on the first round of the test, don’t sweat this one. If you happen to have some spare time at the end, try this instead of putting your head down and going to sleep for the rest of the time.
On your first go of the math section of the test, it might be helpful to go through and star or circle the questions that you found difficult: perhaps those that didn’t initially make sense, or those that you answered, but as more of a guess than a resolute answer.
If you finish the test with time left, skim back through and find the questions that you had starred the first time through. Try using a different strategy to re-solve the problem.
Instead of starting with the question, try starting with the answer. Start with the answer you chose as the right answer the first time through and plug it into the problem. Does it make sense? If so, congrats! You got the question right the first time. If not, congrats still! You successfully found a mistake.
Either way, you have a reason to celebrate. In the case that re-checking your work lands you at a different answer, try solving the problem again. When you land at a new answer, check that one.
If there’s one thing I learned from taking the SAT so many times through high school, it’s that silly mistakes are your worst enemy. The only thing worse than getting a difficult question wrong because you don’t know the answer is getting an easy question wrong even though you know the answer.
There’s never such a thing as checking your answers too many times. You never know where and when you’ll find mistakes.
5. Recognize patterns
This last one is unbelievably important. Why? Because the SAT is designed to confuse you. If the test makers purposely made the test easy, everyone would be scoring perfect scores. That would devalue the very SAT as a whole. The makers of the test can’t have that happen.
There will be many problems you’ll run into on the SAT math section that seem impossible to solve. You may spend 5, 10, or even 15 minutes stuck on a question, not knowing where to start. What this likely means is that there’s some hidden pattern.
If there’s ever a question that seems impossible to solve, chances are that it is! It’s probably a pattern-based question, and the makers of the test are likely testing your logical reasoning skills when it comes to recognizing patterns.
If this concept seems confusing at first, maybe an example will help:
What is the value of 7 to the power of 14?
“Easy!” You may be thinking. All you have to do is plug 7 to the power of 14 into a calculator, and you should get the answer, right?
Well, not exactly. In fact, let’s assume that you saw this question on the non-calculator portion of the SAT. What would you do now?!
Lucky for you, you’re reading this article right now and will know exactly what to do if and when the time comes on the SAT.
The number one thing I would say about questions like these that simply seem impossible to solve is that if you can’t solve a question on the math section, you’re missing some kind of pattern!
Whether that pattern is a special triangle pattern, an exponential pattern, or some other recurring mathematical trend, none of the questions on the SAT are impossible to solve. Every question has to have some type of solution.
If you can’t get to the solution through normal mathematics, it is pretty likely that you have to get there by recognizing the numerical pattern.
For this question, it may help to start writing out the exponents of 7 to see if there’s any kind of pattern that you see in the numbers.
You know that 7 to the power of 1 is 7. Seven to the power of 2 is 49, and 7 to the power of 3 is 343 (might take you some quick math, but bear with me).
Let’s continue. 7 to the power of 4 is 2401, 7 to the power of 5 is 16807, 7 to the power of 6 is 117649, and 7 to the power of 7 is 823543. You may be starting to see a pattern. If you look at the last digits of each number that we solved for, it looks like there’s a trend.
The last digit goes from 7 to 9 to 3 to 1. So every 4 powers cycles through these four numbers, from 7 to 9 to 3 to 1. This would mean 71 through 74 is one cycle, 75 through 78 is the second cycle, 79 through 712 is the third cycle, and 713 through 715 is the fourth cycle.
Within this fourth cycle, we can see that 713 must end in 7, 714 must end in 9, 715 must end in 3, and 716 must end in 1. If you look back at the answer choices, you’ll notice that the only answer choice that ends in a 9 is D!
By process of elimination, we can conclude that D is the answer. As you can see, we weren’t actually able to figure out the mathematical answer to this question. That would have likely taken a lot of time (and multiplying skills!).
Rather, we were able to use the mathematical patterns relevant to the question to figure out the answer! Cool, right?
Now, as in the other sections of the SAT, some strategies work better for some students. Different strategies work better for others. That’s why practice is so important, too.
By practicing while using the strategies detailed in this article, you are figuring out what exactly works best for you and what works best for your specific test taking style. Everyone has different ways of approaching the SAT test and that’s completely okay!
Remember, especially when it comes to the math section, practice combined with strategy is an unbeatable combination.
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