Welcome back to our 6th tactic to score over a 600 on your math section of the SAT. If you have not seen our first 5, please take a look at them before diving into this new tactic. (1, 2, 3, 4, 5)
If you’ve been following us for a while, I hope you notice that we focus more on the underlying concepts and core abilities than how to correctly answer 1 specific question. The reason is that these skills and abilities help student be able to answer whatever questions are asked on the SAT. I hate to beat a dead horse, but there is no definitive list of questions that are going to be asked on the test! One of the most important concepts to master is what I like to call Equation Manipulation.
What is Equation Manipulation? Basically it is the ability to “shift” and “adjust” an equation to put it into a form that allows you to answer the question. It sounds so simple and is something that we have been doing in math classes for years, but as usual, the SAT has a way of complicating it. Let’s take a look at a simple example…
This can be “manipulated” in different directions such as…
There are obviously more forms of this equation, but I hope you understand where I am coming from. All of these are the same equation, but the student would be using different forms depending on what the question is asking us to do. The reason this is such an important skill is two fold.
1) There are questions on the SAT that ask us to specifically do this! (I use 3 examples taken from one section of the SAT in the blog “All questions are not created equal”)
2) There are many questions where you need this skill as a step to solve the problem. These problems are not the typical “Which one of the following are in an equivalent form?” Here are two examples from the 4th practice exam
The likelihood is that you are going to see at least one system of equations problem (as you can see above). If you don’t feel comfortable manipulating and changing the equation around, these problems are sure to give you issues. You’ll also see in the first example where they are asking for “possible” values. This is a HUGE hint that you should be looking to adjust the equation to fit for what they are asking.
One last thing to finish this up. I believe the most difficult part of the SAT is the time limit. Let’s call it what it is, answering 20 questions in 25 minutes in section 3 is tough. Answering 38 questions in section four in 55 minutes is difficult considering that there will likely be a “reading comprehension” type problem (at least 1). This is one of the biggest reasons that being able to manipulate an equation quickly and correctly is massively important. So, in your preparation to take the test, don’t forget to spend some extra time brushing up on your ability to shift an equation into the correct form!
I love this quote from Alice in Wonderland and I think it draws a lot of parallels to students who are starting to prepare for the SAT. One of the questions I hear a lot from students and families is, “What should I focus on and what should I be studying?” Unfortunately there is no one “right” answer to this question and is really dependent on the student's goals. It becomes even more difficult when you look at what is covered on the math section of the SAT. College Board states that the exam covers three areas of math, 1) Heart of Algebra 2) Problem solving and data analysis and 3) Passport to advanced math. Where do we even start?
In contrast to such broad topics that can cover pretty much anything that you have learned in math classes, we instead break the test down into specific subjects and skills that the student should focus on in order to increase their scores. We did this by going through and looking at hundreds of actual SAT math questions. What we found was pretty astounding…
While there is obviously more covered, I hope this gives you a good starting point on what to actually review when it comes to the SAT. When we first start working with a student on SAT prep, we have them take our Pre-Test. This short test is focused on these specific concepts and allows tutoring sessions to be laser focused on the areas where the student needs the most improvement. Not sure where to start? Take the test and get started improving your score now!!!
In tactic 3, you notice we said “worst case, get it down to 2 possible answers”. This leads us into our 4th tactic, which is learning how to guess. I know this may sound silly, but there is a “skill” in guessing! Everything we do is to stack the deck in our favor as much as possible. So when we “guess” we are really saying, “I feel confident that the answer is one of these two options”. There are two main tactics as far as guessing that we teach our students. The first, and most applicable, is to eliminate at least 2 answers that CANNOT be correct. By doing this alone, you have in effect doubled your chances to guess the correct answer.
Let's take a look at a problem to show how we use the first strategy. Remember, the goal is to ELIMINATE as many answers as we can.
Looking at this question, there are a couple of concepts that are being tested. For the sake of this example, let’s say that you don’t know ANY of the concepts. If you look at the 4 answers you will notice that each of them have two distinct “parts”. There is the coefficient, and then the part that is being raised to the power of t. Notice that there are really only 3 numbers that we are dealing with, 325, .87 and .13.
With this information we can begin to start eliminating answers, or at least narrowing down for our guess. As we read through the problem, there is a major hint in the question that can help us narrow down to 2 answers. The “hint” is in the last sentence, “the remaining amount”. So, knowing that the substance decays as 13% and they are looking for the REMAINING amount, we know that 87% or .87 MUST be represented in the equation. Without even understanding what the equations represent in the answers, we can feel confident that the answer must be either A or C. We can obviously take it further to logically come up with the answer, but this is a great example of how to eliminate answers without even fully understanding the question. Remember, our main focus is to get to the 600 score, so we are doing everything we can to get those 38-39 correct answers. By eliminating B and D, you have doubled your chances to get the right answer!
The second tactic when guessing is to find one part of the problem that you feel confident answering and matching answers to your feeling. That may sound complex, but it actually can be used to take a complex problem and make it “easy”. Let’s look at another example…
While this may not be the most complex problem asked on the SAT, there are many pitfalls that a student could make that will sway their answer. Between distributing the negative sign to the 2nd part of the equation, properly completing the square, to simple addition and subtractions errors, you can see where many students would miss this problem. Let’s take the approach of putting together the best guess we can.
So, after we have read the problem, we want to take a look at the answers given. One thing that immediately jumps out to me is the similarity between A and B, and conversely between C and D. If you notice, the first term in the two sets (A and B or C and D) are the same. So immediately I know that if I can get that first term correct, then I’ve got a 50/50 shot at answering the question. The next thing is that the LAST term in each answer is different. Because the last terms do not contain a variable (x), the math is much easier for many students and cuts down on the number of careless mistakes that can be made.
Without doing any of the math actually out, let me walk you through the thought process. Starting with the portion to the left… I know 2.4 is going to be squared and that when I multiply two negative numbers together I am going to get a positive. When I look at the 2nd part of the problem, I notice that I am going to have to distribute a negative (-) to the already negative -6.4. This means that I am going to be adding two positive numbers together. So very simply, I know that 2 squared is 4 and 3 squared is 9, so that first term is going to be somewhere between 4 and 9, closer to 4 because 2.4 is closer to 2 than 4. Next, I’ll add 6.4 from the second part of the equation. So, without actually doing any specific math, I know that the last term in the answer has to be between 10.4 and 15.4 (4+6.4 or 9+6.4). With that little bit of work, I can confidently eliminate answers A and D from the possible list. Now I’m working with a 50/50 shot again!
Now that we have determined that the majority of our focus should be on the Multiple Choice sections, how do we approach these questions? Fortunately for us, the brains behind the SAT stack the questions so that the “easiest” questions are at the beginning, followed by “medium” and finally a few “hard” questions at the end of each section. So while our main focus is to get as many of the multiple choice questions correct as possible, we can break that down as well.
Let’s take a look at the different difficulties of questions so we can identify which ones would be classified as easy/medium/hard. If you haven’t found them already, College Board has 8 practice tests that are actually old SATs. There isn’t much better practice than to look at actual test from the past.
If we take a look at the practice exam #7, here are three different questions. They all test the same ability, but it should be pretty easy to see how the difficulty changes.
All of these questions have similar instructions, “Which of the following is an equivalent...”. Hopefully you can see the varying difficulty and we can now use this to our advantage.
In the first math section(section 3), there are 15 multiple choice questions. For this tactic, we are going to focus on the first 12 questions asked. These should encompass all of the “easy” and “medium” level questions. Once you get to question 12 and beyond, start asking yourself,
“Do I know what they are asking for in this problem?”
If you have no idea, that is a good sign that you are at the “hard” section of questions. Don’t get discouraged if you don’t know how to do the questions moving forward in this section. It is much more important that we focus on nailing those first 12. If you can answer questions like #13, then that is just gravy!
***One item to point out here, many students have issues with timing in section 3. The obvious reason is that we only have 25 minutes to answer 20 questions. Don’t focus on that. Remember, our big goal here is to get those first 12 questions right. Focus on knocking the first 7-12 out as quickly as possible with as much certainty as possible. From there we should work through the last 5-8 questions, but not get so focused on one question that we don’t get to finish the exam. In this last 5-8 question portion we should read the question, if it is something we know how to do GREAT, but if not, try to get it down to 2 possible answers . For questions where you don’t even know where to start, just skip it and make sure that you leave yourself enough time to come back and make an educated guess.
You want to do the same thing on the second section(section 4), just understanding that there are 30 multiple choice and 8 fill in the blank. Using the same logic as we did on section 3, we really want to focus our time on the first 24 questions. Again, this should be all of the “easy and medium” difficulty level questions. If we follow this strategy, then we should be sitting with 36 total correct questions (12 from section 3 and 24 from section 4). This means that to reach our goal of 600, all we have to do is get 2-3 correct answers out of the following 22 questions! Considering that the first 2 questions of each of the fill in the blank sections are “easy”, I hope you can see how we’ve set ourselves up to win!
One big note before we finish up, what is “easy” for some will be “hard” for others. The great news is that an "easy" question gives you the same number of points as a "hard" question. I’ll talk about this a little later on, but please understand that you should be focusing on answering whatever questions YOU find easiest!