You Don't Need To Solve All the Problems

Sharp eyes, or lucky guesses?

Whether it is a school math test or a state exam, chances are that you would guess on a problem if you are stumped, in hopes of getting an extra point. That's great and all, but you might want to reconsider using that strategy on the SAT.

If you haven't heard of it already, the SAT takes off a quarter of a point for every problem you answer incorrectly. Mind you, that you lose 0.25 point for every question you answer incorrectly, and then you lose ANOTHER point for not getting the correct answer. Meaning that the total amount of points you lose for answering incorrectly is 1.25. Answer 4 questions incorrectly, blech, 5 points down the drain.

The SAT discourages guessing to prevent students from earning points "wrongfully". But since guessing is a totally different topic, we'll discuss it some other time. Right now, let's talk about how you don't need to solve all the problems. Boom.

UNIVERSE!!!

After checking 3 actual previously administered SAT Math exams, and 7 other practice exams, I have concluded that you can score at least 600 by solving all of the easy and medium questions correctly, and skipping all of the hard questions. We're talking about 600 here, that is usually about the top 25% out of all test takers. (Of course, if you're aiming for over a 700, then disregard this post. You're going to need all of the correctly answered problems as possible.)

Sound crazy? I know, right? For those who can't believe this insane fact, check it out yourself. 

Click Here

I'll save you the trouble:

1. There are 16 hard problems (Level 4's and Level 5's)
2. And there is a total of 54 problems.
3. Subtract 54 by 16 (remember, we are skipping the hard problems, so we don't lose an extra quarter point)
4. Which equals 38.
5. What is the scaled score for a raw score of 38?
6. 610 (OMG)

TLDR: If you skip all the hard problems and get the all easy and medium questions correct, you'll get at least a 600.

Where do you find the hard questions?

Here's a link.

Happy SAT prep.

Should I Memorize Formulas For the SAT Math?

Chill, I got 800 and I don't even know any of these. (Okay, maybe two of them.)

Every math class makes you memorize or at least gives you a sheet full of formulas to use for tests. Since the SAT Math is a math test, you'll need to memorize formulas, right?

Err— sort of...? Kind of...?

"So do I have to memorize formulas for the SAT??"

What the heck?

The test makers give you a list of formulas and math facts at the beginning of every math section. How nice are they? You don't have to memorize any formulas after all!

If only things were that simple... 

Have you ever wondered why practically every student has to take the SAT (or ACT), a test that includes MATH? If you're going to major in English, why do you have to take a MATH test?

Because the SAT Math was intended to be a test for EVERY student, whether he/she is pursuing a STEM major or not.

Also, the SAT is designed so that students from virtually any sort of background can solve. For example, not every high school provides AP Calculus. And what if the SAT were to test on calculus? Students who couldn't take calculus are at a huge disadvantage. 

To make the SAT "accessible" to pretty much every student, it tests on basic math concepts taught in Algebra and Geometry, courses that almost every high school student must take. 

Did I mention how the SAT is meant for EVERY student? STEM major or not? (I did.)

That's because the SAT Math is testing more on your math "ability" than your math "knowledge". (For more depth into this topic, click here.)

Formulas are things that you know or do not know. It doesn't necessarily indicate intelligence. An average high school math student can memorize the Law of Sines because he took Trigonometry and Pre-calculus, but can't solve the sum of the first 100 whole numbers quickly, when a 7 year old did it over 200 years ago. (Curious? Click here.)

But is it true that the SAT Math is meant for every student? Err— IDK. That's not really important.

What's important is that the SAT Math doesn't expect you to memorize a bunch of crazy formulas. 

"Then what is it? Do I have to memorize formulas or not??"

I don't even...

Short answer: yes, you do have to memorize some formulas.

HOWEVER, you do have to know more math facts than formulas for the SAT. You need to know your order of operations, number properties, geometry properties, etc.

But this post is about formulas, so let's talk about math facts some other time.

Let's start with the formulas you are given at the beginning of every math section. Memorize those cold. You might think that it's a waste of time to memorize formulas that are given to you, but the SAT is a time deprived test. You'll be wasting precious seconds for every time you turn over your testing paper to look up a formula. Not to mention that those formulas aren't too hard to memorize, so why not commit those to memory?

Are there any formulas that aren't given?

Yes, there are some formulas the SAT expects you to know ahead of time. You'll need to know how to solve percentages, percent change, distance, probability, averages, etc.

Although, those formulas are rather easy and you've should know them already. After all, those have been used occasionally, if not frequently in your math classes. 

If you don't know them, or can't remember them, that's alright. You can always look them up on the internet. 

"Did you memorize formulas for the SAT Math?"

Other than obvious and easy formulas such as the reference sheet, percentage, percent change, probability, distance = rate x time, averages, etc. I didn't memorize many formulas. (Maybe (n-2) x 180?)

There are certainly formulas that you can use to solve for an answer quickly, such as the Harmonic Mean formula, or the Generalized Pythagorean Theorem. But I still found the answers to such problems without them. Meaning that I derived the answer by using MATH. Although it might be nice to know them because it can save you some time. (I didn't even know they existed until AFTER I finished my last SAT. Darn it.)

In short, I used a combination of memorizing the essential easy formulas, and did the rest by doing math.

TLDR: You must memorize formulas that are essential to solving a question. 

Here are some links to formulas/facts you (might) need to know for the SAT Math.

http://www.erikthered.com/tutor/facts-and-formulas-0.pdf

http://satprepget800.com/sat-math-formulas-memorize/

http://magoosh.resources.s3.amazonaws.com/SAT_Math_Formula_eBook.pdf

"Impossible" SAT Math Problem: Jumbo Size #'s & Their Remainders

Every problem on the SAT can be solved without a calculator. That is what the College Board tells us, and I agree. Pretty much every single problem on the SAT can be done by your head/hand. Of course, you would like to have a calculator, and you should. Calculators make most calculations quicker, so you save time, and time is scarce on the SAT.

However, the SAT is always going to throw you a problem that cannot be done by (only) the use of a calculator. 

Here's one:

Source

I've never seen such a big number...

OMG, what the heck is this problem? 3 to the 200th power?? That's a super large number. If you were to plug that in your calculator you'll get: 2.656139889E95.

As awesome a number that may be, chances are that you won't know what to do after that. Even if you divide that thing with 5, you'll still get a complicated huge number: 5.312279778E94.

In order to solve this problem, you'll need to know how to notice a pattern.

But before that, here's how to find the remainder in the calculator (or your hand):

1. If your quotient is a whole number, the "remainder" is 0.

2. If your quotient has a decimal, take out ONLY the decimal and multiply it with whatever number you've divided with.

3. You can use your graphing calculator's remainder function, but it won't work on this problem. I won't go over this because it's not today's lesson.

Now, for the actual tutorial:

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First, notice the first few powers of 3:

3¹ = 3

3² = 9

3³ = 27

3⁴ = 81

3⁵ = 243

3⁶ = 729

3⁷ = 2187

3⁸ = 6561

Pay attention to the units digit (ones place). Every four numbers follow the pattern: 3, 9, 7, 1. This sequence will continue on forever as the power of 3 increases. And because the units digit will always follow this pattern, when you divide each power of 3 by 5, your remainder will have a pattern as well. (Except for 3, because 3 is smaller than 5.)

Mind you that you can certainly solve the problem using the pattern of the remainders, however you can save time by just using the pattern of the powers of 3. All you need to know about the remainder pattern is just its existence.

In order to find the remainder of 3^200, we need to divide the exponent by the number of numbers in our pattern of 3, 9, 7, 1. Which is 4.

If we divide 200 by 4, we get 50, a whole number, meaning that the fourth/last number of our pattern shall be the unit digit of 3^200, which is 1.

If you didn't follow, then let's divide 199 by 4. What's the remainder? 3. Be careful because this 3 only means that 3^199's units digit is the third number in our pattern: 7.

198/4 's remainder is 2, meaning that 3^198 's unit digit is the second number in our pattern: 9.

197/4 's remainder is 1, meaning that 3^197 's unit digit is the first number in our pattern: 3.


Any number that is bigger than 5 and has a units digit of 1 divided by 5 is 1. Why? Just look at the following outcomes:

11 divided by 5: remainder is 1

21 divided by 5: remainder is 1

31 divided by 5: remainder is 1

41 divided by 5: remainder is 1

51 divided by 5: remainder is 1

and infinitely so on.


I know. I don't know what's crazier: the infinite pattern of numbers, or how we just found the remainder of 3^200 divided by 5 (a huge number) without actually dividing 3^200 at all.

Why does this work? Because math.

OMG it's a miracle...

Hopefully, my little guide made sense to you. There are things in math that make sense in my head, but I don't know if I can explain it to others while making sense at the same time. After all, we are dealing with numbers, cycles, remainders, and a bunch of other arithmetic stuff, so it would be hard to explain. 

If my tutorial made no sense (hopefully it did make sense), please leave a comment below as you explain with some detail as to why my explanation didn't make sense.

Oh, and if you find any errors in my post, be it mathematical, grammatical, spelling, please tell me. 

Anyways, thanks for reading. 

"Average" Averages On the SAT (Pun Totally Intended)

The average person would know how to calculate averages. (Pun Intended.) Since you would obviously know how to find the average of something, I wouldn't need to show you the average (arithmetic mean) formula. But since I am a nice guy, here you go:

WTH is this thing?

If you are freaking out at how complicated the "average formula" is– don't worry, this is just a fancy alternative for the "average formula". Here's the one we are all familiar with:

Better? Why did I show you an obscure version of the "average formula"? Because I can, and I like to mess around with stuff like this. 

Now, let's get serious.

When dealing with averages on the SAT Math, you will most likely NOT encounter a simple, "find the average of the following five terms: 5, 10, 15, 20, and 25." That's way too easy. Remember, to do well on the SAT Math, you need to know how to play around with basic math concepts. For solving SAT average problems, knowing how to manipulate the "average formula" will be paramount.

Notice how I multiplied each side of the equation by "Number of Terms" and got the formula above? You will need this to solve SAT average problems.

Try out the problem below.

The Squad

18.       Ash Ketchum has six Pokémon weighing an average of 45 pounds. He heads to the Pokémon Center, and drops off three Pokémon weighing a total of 90 pounds. He also picks up one Pokémon weighing 50 pounds. He heads to another Pokémon Center, picking up two more Pokémon, which weigh 30 and 40 pounds. What is the average weight in pounds, of the Pokémon that remain with Ash Ketchum?

(A) 45

(B) 47

(C) 50

(D) 55

(E) 60

Remember how I wrote "let's get serious"? I still stay true to that. Pokémon is just as serious as prepping for the SAT. (Sarcasm at its finest.) Obviously, the SAT won't be mentioning Pokémon in its problems. I just figured that using Pokémon would make the "average" SAT average problem less "average". If Pokémon is throwing you off (which it really shouldn't), then here's a "normal" average problem.

PWN the SAT

How to solve #18:

18.       Ash Ketchum has six Pokémon weighing an average of 45 pounds₁. He heads to the Pokémon Center, and drops off three Pokémon weighing a total of 90 pounds₂. He also picks up one Pokémon weighing 50 pounds₃. He heads to another Pokémon Center, picking up two more Pokémon, which weigh 30 and 40 pounds₄. What is the average weight in pounds, of the Pokémon that remain with Ash Ketchum?₅

(A) 45

(B) 47

(C) 50

(D) 55

(E) 60

Notice the subscripts 1, 2, 3, 4, and 5?
Those are there to indicate the chronology of the problem, i.e. the order of steps.

Step 1.

Ash has six Pokémon, and his Pokémon weigh an average of 45 pounds.

Plug in the numbers, and you will get the equation: 

45 pounds x 6 Pokémon  = 270 pounds of Pokémon 

Step 2.

Our hero drops off three Pokémon. And the total weight of the three dropped Pokémon is 90 pounds.

Since Ash initially had 270 pounds of Pokémon: 

270 pounds of Pokémon - 90 pounds of Pokémon  = 180 pounds of Pokémon 

Remember that Ash dropped off three Pokémon from his initial six, so he currently has three.

Step 3.

At the same Pokémon Center, Ash picks up a Pokémon that weighs 50 pounds. 

So: 180 pounds + 50 pounds = 230 pounds of Pokémon 

Don't forget that Ash added one more Pokémon to his team of three, which now makes four.

Step 4.

Our forever ten year old (get the reference?) continues his journey, and he stops by at another 

Pokémon Center, picking up two Pokémon that weigh 30 and 40 pounds.

Thus: 230 pounds + 30 pounds + 40 pounds = 300 pounds

Since Ash picked up two more Pokémon and added them to his team of four, he has a total of six Pokémon with him.

Step 5.

Now we use the "average formula": 

For this problem, the "sum of terms" is the total weight of Pokémon Ash Ketchum currently holds, which is 300 pounds. The "number of terms" is the number of Pokémon Ash Ketchum carries at the moment, which is 6. 

Plug in 300 in the "sum of terms" and 6 in the "number of terms", thus 300/6 = 50.

Therefore, the answer is 50 pounds. 

You can find the solution for #19 by clicking the link under the problem. It's basically the same idea, but the approach/setup is different (PWN the SAT uses tables). 

My Graphing Calculator Is Too Slow

I tried to avoid graphing functions on my graphing calculator when I took an SAT Math test. My TI-84 Plus C Silver Edition graphs functions SUPER SLOWLY, wasting my precious time. It gets worse when I insert an incorrect function. I have to wait until the incorrect function is finished, then I have to redo the process by typing in the correct function, and wait again for the function to graph.


Sadly, I just recently learned how to increase a graphing calculator's graphing speed.

Darn it. If only I knew about this trick before taking my last SAT, then I would have used the graphing calculator better. But seeing how I still scored an 800 on the Math Section, graphing functions on a graphing calculator isn't necessary. Of course, at times, it might be easier to graph out a function in a calculator if you don't fully understand the concept of functions.


Whatever the case, you'd probably want to use the graphing calculator because you're more comfortable letting the machine do the dirty work. That's perfectly fine. When taking the SAT, the ends justify the means. As long as you are comfortable and bound to answer the question correctly, then all is good.

Now, to boost up your graphing calculator's graphing speed:

First, type in the function of your choice. 


Second, hit the "WINDOWS" button next to the "Y=" button.

Third, increase the number for "Xres". (Plug in something like 3 or 5 or something.)

Last, punch "GRAPH" and tah-dah, Flash speed graphing at its finest.

Does the SAT Math Measure Your "Talent" in Math?

IDK. Easy school?

I know a lot of kids who get A's in math class, but can't do well on SAT Math.

At least in my area, getting a high grade in a class isn't impossible. If you do your work and study moderately (or hard), getting an A or an A- is doable. Especially in math classes. With the exceptions of AP Calculus AB, AP Calculus BC, and AP Statistics, math courses in my school tests on questions that are IDENTICAL with the questions gone over in class. Of course the numbers and words are changed, but the type of questions are the same. Simply put, my school's math tests check on how you memorized the choreography. The SAT, however, doesn't care if you picked up a routine at school, it wants to see if you know how to play around with math.

Many students know basic math concepts like the Pythagorean theorem, functions, exponents, all of that stuff taught in math class. If you show a high school student " a² + b² = c² ", chances are that he/she will recognize it. It's great that many high school students are familiar with some basic math, but that doesn't mean they know how to use it.

Source: PWN the SAT

If you can calculate the value of x by your hand (or your head), then you know your exponent rules well. The answer is 998, if you wanted to know.

As mentioned in previous posts, knowing advanced math concepts won't do you many favors on the SAT. Take the question above for example. Exponents aren't advanced math, although this exponent problem is difficult.

Unmistakably, the SAT Math obscures basic math concepts so students like you (and I) have trouble solving the problem.

But does that mean the SAT Math measures your ability in math? After all, it does require you to see through the veil placed over the problem.

Not with those glasses though

Answer is: yeah... kind of... sort of...?


Certainly, it takes some thinking to do well on the SAT Math. You can't stroll through the problems like it's a predictable rehearsal. At all times, you have to be alert and observant. And definitely, you need to know how to play around with basic math concepts. So the SAT certainly does measure your math capabilities to some degree.

However, the SAT Math can't determine your math capabilities perfectly. The test is worded in an overly complicated way, so it takes some reading comprehension to understand the problem. (I thought this was a math test!?!?) Practicing the SAT Math a LOT can make even the SAT problems look like a routine, because the test reuses similar questions. Also, the SAT Math tests on SOME math concepts, NOT all of them. You can be really good at trigonometry, but struggle with arithmetic word problems.

Here's my case. I've scored an 800 (hence my blog) on the SAT Math. By no means I am a math genius. I have yet to score a hundred on Pre-Calculus tests and I am finding AP Calculus AB quite a challenge (at this moment). And I am certain that you can tell that I, despite scoring perfectly on the SAT Math, is NOT, by any means, a math genius.

By the end of the day, it doesn't matter whether or not the SAT Math measures your "talent" in math. What matters is that you achieve the score that you wish to get.


TLDR: The SAT measures a part of your math ability, and don't sweat it.

Straight A's Mean NOTHING In Front of the SAT

NOTE: Meme isn't relevant to post.

Let's say you're a great soccer player (if you really are, that's awesome). Since you are brilliant at soccer, you compete in state level competitions and become state champ. Now, I ask you: can you do just as well at basketball? If the answer is yes, then great for you, but the answer is likely no. Not that you can't be good at two sports, however, it's not easy to transfer to one sport from another.

Shout out to my school's State Champion Soccer Players (picture is NOT any of them).

High school math and SAT Math are sort of like that. You (should) know trigonometry, so you know how to do some fancy math. Guess what? You don't need ANY trig on the SAT. (If you are taking the SAT in 2016, then you DO need to know trig.) When I took the SAT for the first time, I scored a 640 on the Math, yet I scored perfectly on a standardized Trigonometry Exam. See the score discrepancy? I'm pretty sure the disconnect is clear.

As you have read already, acing a math test based on the material taught at school doesn't mean you will naturally ace the SAT Math. The SAT Math is like the Joker. You can't beat him to submission nor reason with him. You can learn AP Calculus, (often) the highest high school math course, and score less than a 600 on the SAT Math. You can argue with the "questionable" SAT Math problems and get nothing accomplished.

The SAT vs You (see the analogy?)

Having high level math concepts in your arsenal is certainly a good thing, and in fact, essential for college readiness. However, your proud Calculus can't do you many favors when taking the SAT. If you have seen my previous post here, you would have figured that calc isn't the best way to solve things. Heck, I tried to use some trig on my first SAT, and I wasted so much time. I have more, I know a Junior that is taking AP Calculus BC, and can't land a high SAT Math score.

Some of you (and hopefully many) are good at math. Math in high school is so easy, you don't have to study much to ace tests and quizzes. So math is something that you take for granted. You understand everything, so if a math question doesn't make sense, you might find yourself doubting the validity of the problem. I sure remember I did. It was hard for me to accept how I could do well on an advanced topic, i.e. trigonometry, and fail to achieve just as high marks on a test with less advanced topics, the SAT Math. I couldn't help but blame questions for being worded poorly or just being plain wrong (which they were not).

So if you are a student who earns A's in math classes in high school, but struggles to score well on the SAT Math, you'll need to accept these facts:



1. Getting A's in math classes doesn't mean you'll do well on the SAT Math. 

2.  The SAT Math is nasty. It's worded in a bizarre way, confusing many strong math students. And sadly, you need to deal with it.

3. If you can't score well on the SAT Math, you need to do a LOT of practice, probably more work than you do in school. I know, it sucks.

4. Know and UNDERSTAND all of the math concepts covered on the SAT. Despite how impossible the SAT may seem, knowing how to PLAY around with basic math topics is how to ace the SAT Math.

5. Getting used to SAT Math might take some time. It took me months to see through the tricks and traps the SAT had in store.



I know studying for the SAT is a pain, and you may choose not to prepare for it because the SAT is not important in your plans. That's awesome. But for those who need to do well on the SAT, then you will need to do as much work as necessary to obtain whatever goal you have.

Good luck on your SAT prep.