The short guide to preparing for SAT Math

Step one:  Know your situation

First and foremost- Do you need to take the SAT?  If you’re certain of your potential college destinations, and none require the test, there’s no reason to put yourself through the stress of it.  

If you need to take it- How well do you need to do?  If you’re scoring higher on your practice tests than you need for the schools you’re applying to, you probably only need a little practice.

I would never take this “do as little as possible” attitude into the classroom, or the workplace, but the SAT is a hurdle that comes at a very stressful time of life.  College is a major life change. Let’s keep our kids as happy and healthy as possible. If we’re going to stress something, let’s take a second and make sure it’s really important.

Step two:  Know the test

If you’ve taken pre-calculus, you’ve seen all the material you need to score an 800.  But, the SAT is full of curve balls. They will ask questions you’re totally capable of answering, just in ways you haven’t seen before.

Start by taking practice tests.  Pay careful attention to what you get wrong.  Sometimes you’ll get things wrong because you just forgot things that you were taught in school, like systems of equations or rules for exponents.  Other times you’ll get things wrong because the problem seems completely unfamiliar, like it’s something you’ve never even seen in school.

If it’s a concept that you’ve forgotten, it’s easy enough to study the traditional way:  Look it up in a text book (borrow one if you have to), or use youtube, Khan Academy etc… and you should be good.  Remember watching or reading problems isn’t enough, you have to actually do some problems to really retain the material.

Tackling the type of problem that feels completely unfamiliar can separate the good scores from the mediocre.  When first tackling these problems, forget about timing and just explore the problem. Read through the explanation.  Try filling in intermediate steps in the explanation; Show the algebra of how to get from one step to the next. Try doing smaller steps your own way.  Try answering the question in a different way. Once you’ve gone through all that- see if you can make your own question that is like it. (Yes I just asked you to make a question.)

After all that seek out other problems like that one, and attempt to get them without peeking at the answer, or the last question.  Most people have never done this sort of studying before (seeking out questions rather than seeking out information), and that’s because studying for the SAT is different than studying for a typical academic test.  

You’ll probably have to look through a lot of material to find similar questions, just because of the format of most books.  It’s useful to have a lot resources for this, especially since you still want to have full practice sections later on to keep studying.  

The process can involve a lot of doubt and second guessing.  It’s easy to slip into all the negative self talk at this point- “I’ll never get this!” and “OMG I’m gonna fail this test!”   Remember to keep a growth mindset about intelligence. The struggle makes you smarter. You’re doing the hard stuff that the other students just aren’t.  

That’s the meat and potatoes of knowing the test.  The rest is probably what you expected to hear: Know how the test is administered, what materials you can bring or access, how long you have etc… so that you don’t have any surprises on the day of the test.  But if you’re reading this I think you already knew that. So on to step three!

Step three:  Plan smart

Plan on having to take the test more than once.  The end of the junior year is a good time for the first test.  Students lose a lot over the summer, as a result a lot of students score lower at the beginning of their senior year, in September and October, than they do at the end of their junior year.  

Hopefully you can take it once and be done.  If not, try not to stress out. The absolute best scores actually come around November and later in senior year.  You will have had more schooling, you’re out of your summer funk, and you’re simply more mature biologically. (Which matters more than you might think, you’re not a full-on adult yet, sorry!)

The other reason to take it at the end of junior year is you can gauge how much work you need to put in over the summer.  If you don’t put in any work, expect to go backwards. It’s just easier to put in the work when you have the time, trust me.

If you wait until school starts back up you’ll have to keep your grades up, send out college and scholarship applications, and study for the test, all on top of whatever extracurricular activities you do.  Say goodbye to your social life.

Plan for the score you need.  If you’re scoring 500 now, and need a 700, you’ve got a long way to go.  You’re not getting there overnight, and if you wait too long to start studying, you’re not getting there at all.

Another thing to keep in mind, if possible, is the time of day you’re taking the test.  The science says a senior in high school has a later circadian rhythm than most other people.  It’s a biological thing, not a willpower thing.  Go ahead and show that sentence to your parents if you need to.  I’ll send them the research if they’re not convinced.

You’re not going to do as well on six hours of sleep as you would on nine.   A full night of sleep is a powerful thing. If you can take the test during the school day that is an excellent option, so long as you are getting a full night’s sleep on typical school days.

Plan on eating a fairly big breakfast.  Protein and fat are important, we don’t want your blood sugar crashing mid-test.  You should also be packing a snack for that reason as well.

Step four:  Study smart

First, consider what we talked about in “Know the Test.”  This test is different, and in some ways requires a different strategy than studying for a typical test.  Beyond that, the ideas here apply to studying in general.

To start, use short, intense study sessions broken up by breaks.  For 25 minutes don’t let your mind wander to other things, don’t get up for a drink, don’t change the song, don’t reply to texts.  Put your phone on silent. Don’t do anything that’s not studying. Then for 5-10 minutes do something completely unrelated. Put a load of laundry in.  Watch a cat video. Then do another 25 minutes of studying.

This technique is called the Pomodoro technique.  I’m using it right now to write this article. I think of it as a mental “sprint.”  What you’re practicing is bringing 100% of your focus onto just one thing. You’re not getting your best score if you can’t bring 100% to the table.  

To start, your first sprint should just be taking a practice section.  Once you’ve taken a section, you’ll have an idea of what topics you should be studying.  Then you can do another sprint on one topic you might need help in.

Make Pomodoros at least 1/2 of your studying time.  It’s Ok to spend some time sipping a coffee with your favorite music on while studying.  It’s just not nearly as efficient. It’s also Ok to tailor your studying to your mental energy level.  If it’s the end of a long day, and you just really have no energy, go ahead and read from your test prep book.  (Don’t watch videos though- the light will keep you up and interfere with your sleep!)

Doing something is better than doing nothing, but doing a Pomodoro is better than doing some easy going studying, which is better than passively reading a book.

In my personal experience, the length of the sprint and the length of the rest can stretch and shrink a little depending on the task.  My sprint could be as little as 15 minutes, or up to 45 minutes. If you try to push beyond 25 minutes and your attention starts wavering, it’s time to take a break.  We want to practice accessing that state of mind that is 100% focused on the task at hand. The more often you do it, the better you’ll get at it.

You should also be summarizing or reviewing at the end of each study session.  Put everything away except a blank piece of paper and answer the question “What did I just learn?”  This might be a struggle. That’s Ok, the struggle makes you smarter. Write anything. It can be sentences, diagrams, formulas, or whatever!  It could be an example of a type of problem you learned to solve today. Write in full sentences. I know this isn’t English, but a full sentence is a full thought. You should be putting a lot onto the paper, so use every abbreviation you know, and feel free to make some new ones up.

Once you’ve gone through everything you can think of, go back through your notes, or pages of the book, or tabs and fill in all the blanks.  This should be about a five minute process, and by no means has to encapsulate every single thing you did. But you should touch on anything that was new, and anything that was challenging that you now understand.  Write about the things that are teetering on the edge between what you understand and don’t understand.

You should also take a full test or two in preparation, all 3.5 hours of it.  You only need to do a couple. Taking the test itself your junior year counts, and is actually superior in many ways to taking full practice tests.  I’ve seen some tutors and teachers go overboard with this, doing a full test almost every week. That’s counterproductive, as students quickly adapt unintentionally, and end up just taking the whole thing in an easy going fashion, instead of going hard the whole time.

Step five:  Test smart

There are a handful of types of questions where using some simple techniques can help significantly.  They’re not something that’s going to boost your score significantly, but they might help you get a few more points.

First- let’s address the process of elimination.  It doesn’t work 99% of the time, at least in the math section.  The other 1% of the time the question looks like this:

12.  Which of the following ordered pairs (x,y) satisfies the inequality

2x < y+4

  1. (1,4)

  2. (3,-2)

  3. (-2,8)

A. I only

B. II only

C. I and II only

D. I and III only

Since we can eliminate option II, we can eliminate answers B and C.

In most other situations elimination isn’t useful.  There have been countless times that students have, without me even hinting at elimination, been like “Well it can’t be… because…”, and eliminated the correct answer right off the bat.  So at best elimination can save a little time on questions like the one above.

The next technique is called substituting answers.  

25. What is the set of all solutions to the equation sqrt(-x+6)=x ?

A. {2,-3}

B. {2}

C. {-3}

D. No solution

Put the number 2 in the equation.  -(2)+6=(2)  Does it work?  

Put -3 in.  Does it work?

Bam! You’ve got your answer.  

These opportunities tend to come up with square roots and absolute value.  This is a technique even advanced test takers can use. Solving the above question the conventional way (squaring both sides etc…) involves checking your answers by substitution anyway!

Our last technique is called substituting numbers.  If you’re very good with your algebra this technique shouldn’t be necessary.  But sometimes it’s nice to have a backup plan.

We’re going to pick a number to put in instead of dealing with a variable that they’re giving us.  Never pick zero or one. Consider the following problem:

42.  A candy maker is making 45 special candies for a birthday party.  It takes 7 minutes to make 1 candy. If c candies have already been made, which of the following expressions represents the number of additional minutes needed to finish making all the candies?

A. 45(c-7)

B.  7(c-45)

C.  45(7-c)

D.  7(45-c)

Let’s say 15 candies have been made, so the value of c is 15.  How did I pick 15?  Out of a hat. Ok, not literally out of a hat, but the process works the same with whatever number you pick.  

Make sure the number makes sense in the context of the problem, so don’t pick 50 because the candy maker would be done, and don’t pick -3 because what does -3 candies even mean?   Don’t use numbers that are already in the problem, in this case don’t use 7 or 45. Lastly, don’t pick zero or one.

So our candy maker has 30 candies left to make.  At 7 minutes per candy, it should take 210 minutes to finish.  We now take substitute 15 in for c in each of our answers and see which gives 210 as a result.  Stop, take a second, and actually do that please.

This method typically works when there’s a variable in the question and in the answer.  There are other instances where it’s applicable as well:

6.  A linear function intercepts the y axis at (0,a) and the x axis at (b,0).  If a=-b, and a is not zero, what is true of the slope of the line?

A. It is undefined

B. It is zero

C. It is positive

D. It is negative

Pick numbers for a and b.  Just make sure a=-b. Try a few different values just to convince yourself.  Here’s another example that straddles the line between substituting numbers and substituting answers:

10.  Two points on a number line are 5 units from point P.  If point P is located at -2, which equation could be used to find the two points?

A. |x-2|=5

B. |x-5|=2

C. |x+2|=5

D. |x+5|=2

There’s a lot of fluff here.  What two numbers are 5 units away from the number -2 on a number line?  Draw it if you have to, I’m not giving you the answer. Now that you have those, put them into each equation for x.  Both answers will work in the correct equation.

So that’s it for our short guide to the SAT math section.  I hope you’ve taken some things from here that can help with the test, and I hope you’ve taken something that can help outside the test!  (Hint- I mean the Pomodoro method and summarizing your study session.) It’s been real.  It’s been cool.  It’s been real cool…  Oh, and don’t forget to take five minutes to summarize what you’ve just read!

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