SAT Math Mastery: The Origin Story of an SAT Math Textbook
This is a guest post by Christian Heath, author of SAT Math Mastery Volume 1 and Volume 2. Chris has been teaching SAT and ACT prep to high school students for 10 years and has perfect scores on both tests.
For 10 years, I’ve helped high school students improve their SAT Math scores. In that time, I’ve tried a huge variety of tactics and teaching styles. In this post, I’m going to explain what you need to improve your score on the SAT Math test - and why, with all the other materials already available for studying, I still felt driven to write SAT Math Mastery: a 1,000+ page, 2-volume textbook on SAT Math prep.
These are just the reflections of an SAT Math super-nerd who’s spent a lot of time working on, thinking about, and teaching SAT Math.
What follows will not be abstract theory, but hard fact - based on my own experiences taking the test and my 10 years of teaching over 1,000 high school students to improve their SAT Math scores. In fact, I actually enjoy taking the SAT Math test at this point.
Now, let’s get into the good stuff you need to know to achieve similar results…
How to Get a Great SAT Math Score: Strategies vs. Content
The question everyone wants to ask me is “How do I get a good SAT Math score?” And - frequently - they seem to think the answer lies in strategies and time management.
But I don’t think that’s true at all. The secret to the highest SAT Math scores lies in content mastery.
What’s the difference? Well, “strategies” are about finding an answer when you don’t know what to do. But “content mastery” is about knowing what is on the test and how to do it. And “time management” is applying a blend of content mastery and strategy to get the most questions correct within the time limit.
See, “content mastery” is like having the keys to the front door of the house. You just grab the right key, put it in the knob, and boom - you’re inside, easily and quickly.
In contrast, “strategy” is what you would do if you lost your house keys and were forced to find an alternate way of getting inside. You might try the windows, or the chimney, or you might just knock down part of the wall. But wouldn’t it be so much easier and faster to just have the right key for the lock?
As I go through the SAT Math test, I constantly have the right key for each lock that the questions give me. I don’t need - or want - to find sneaky ways of getting into my own house. The key to the front door of each math question is easily available in my pocket. That’s the power of content mastery.
So the answer to “How do I get a good SAT Math score” is to master the content of the test.
But how do we do that?
First, we need to know what’s on the test…
The Surprising Blend of Topics on the SAT Math Test
[Topics Appearing on the SAT Math Test, broken down by percentage of appearance]
When I was preparing to write my SAT Math textbook, I spent several weeks doing original research on the SAT Math test itself - before I wrote a single word. And even after 10 years of working on the SAT, what I found still surprised me.
The most astonishing thing I discovered was that the SAT Math test is 84% Algebra (this includes both Algebra 1 and Algebra 2). That is truly amazing. It means that on average, more than four out of five questions on the SAT are based on Algebra topics.
As I thought more about it, I realized that it did make sense. A huge amount of my time on the SAT had always been spent just working through basic Algebra setups and related topics. But I was still surprised.
See, this leaves just 16% of the SAT test for the other Math disciplines of Geometry and Statistics. Even if you add up every Geometry and Statistics topic and question on a typical SAT Math test, they will only represent about a fifth of the entire test. That is a tiny amount compared to the Algebra on the test.
Now, it’s true that “Algebra 1 and Algebra 2” includes a very broad range of sub-topics: there are many techniques and types of questions that fall under the umbrella of “Algebra.” Still, this is very encouraging. It means that we should focus the vast majority of our effort and study time into mastering the essential Algebra content tested on the SAT.
So, as I reviewed the surprising results of my research, I was already starting to make plans to create the perfect SAT Math textbook…
What I Wanted for Students (as their SAT Math Tutor)
Still planning my SAT Math textbook from the ground up, the next question presented itself: What do high school students need to get higher SAT Math scores?
You already know about my belief in the importance of content mastery - like having the key to the front door of the house on each math question.
The followup challenge is identifying what math topics a student doesn’t currently understand (because obviously, it’s not a very productive use of time to study topics you’ve already mastered.)
Then, you have to learn those specific topics in a way that a student can understand and remember.
Next comes practice in weak areas.
I’m a classical pianist by training, so I have a religious belief in the power of practice to solve all problems - and other musicians, artists, and athletes will surely understand what I mean.
While you practice, you also must identify and correct your mistakes. It’s natural to make a lot of mistakes during practice, but the goal should always be to catch those mistakes and correct them - learning from each mistake so that it doesn’t happen again in the future.
And although you already know that I think “strategy” is similar to breaking into your own house because you’ve forgotten your key to the front door, it’s still useful to know a few key SAT math strategies that help in unexpected or confusing situations. In rare cases, the right strategy can be faster than actually solving the question the “correct” way.
Last but not least, I wanted some sort of final review to demonstrate to students (and to me, as their tutor) that they had actually mastered all of the content on the SAT Math test. If there were any weak topics remaining, they needed to be exposed and revealed before the day of the real test.
Building My SAT Math Book: Content Mastery and Practice
After I digested the results of my research on the makeup of the SAT Math test and my thoughts about what students needed for higher scores, an excellent structure for my own SAT Math textbook naturally presented itself.
I had identified 38 total topics that appeared across all SAT Math tests. 26 of these topics came directly from Algebra 1 and Algebra 2. Another 10 topics came from Geometry, and 2 more topics were based on Statistics.
So, I decided to separate the textbook into four major sections: Algebra 1, Algebra 2, Geometry, and Statistics.
Within each of these major sections, I divided into chapters that each focused on a single math topic. For example, Algebra 1 includes chapters on “Ratios & Proportions” and “Linear Equations.” Algebra 2 includes topics like “Parabolas” and “Imaginary and Complex Numbers.” The Geometry section covers topics such as “Angles” and “Soh Cah Toa,” while the Statistics section rounds things out with two chapters on topics like Median, Mode, and Standard Deviation.
Next, I ordered those chapters in such a way that the basics and fundamentals were covered first, leading into more intermediate topics, and ending with the more challenging or complex topics.
This Table of Contents that I had drafted was very satisfying to my SAT tutor side. It began with Algebra 1, building up from the basics into more advanced question types. Then it turned to Algebra 2, starting again with basic & intermediate topics and building into the more advanced questions. The end of the book covered the Geometry topics - again, starting more basic and becoming more advanced. And finally, the two Statistics chapters rounded things out with the final question types we expect to see on the SAT Math test.
There was only one problem, though - and it was big one…
The Fatal Flaw in My SAT Math Plan
After I set up this lesson plan, I realized that I had a problem. In its very essence, this SAT Math study plan was so complete that it was overwhelming. Surely, the finished textbook would be over 1,000 pages long. I simply couldn’t see a way that it would be any shorter.
Keep in mind that I’ve been working with high school students for 10 years. I know exactly what would happen if I gave them a 1,000 page SAT Math textbook and told them to work through the whole thing.
Even if a student had enough motivation to finish (and let’s be completely honest with each other - most high school students don’t), they still simply wouldn’t have enough time. Students have school homework, sports, and other clubs and activities every single day. No way they would finish my book.
And this wasn’t just a problem for the students - it was a problem for me! I didn’t want to commit my time and energy to writing a 1,000 page SAT Math textbook only to have it sit unused and unopened on a shelf.
What to do?
…And the Solution:
[The Start of a Diagnostic Pretest for the SAT Math Test]
The solution to my problem became obvious as I thought back to my previous textbook, SAT & ACT Grammar Mastery.
In that book, I had created a diagnostic “Pretest” at the beginning of that textbook that only took about 30 minutes. And when finished, this Pretest pinpointed the exact grammar topics that a student needed to study and practice.
The key benefit of the Pretest? With one diagnostic test, you could immediately skip huge portions of the textbook that you already understood. If you proved from the very beginning that you could already correctly answer questions about topics like “Subject-Verb Agreement” and “Parallelism”, then it was unnecessary to invest further time in studying these chapters. On the other hand, if you missed a Pretest question about “Conjunctions and Transitions,” then you knew it was essential to study and practice that topic in detail.
And voila! I decided to do exactly the same thing for my SAT Math textbook. I would condense all 38 math topics into a diagnostic Pretest. And, I decided to make the Pretest questions pretty tough. That way, they would expose any potential weaknesses. But if you could answer a Pretest question correctly, then you were assured that you had that specific topic well-mastered and could skip the entire chapter on it - saving hours of study time.
The Time-Saving Power of SAT Math Diagnostics
Now I had a way for students to save a huge amount of time while massively increasing their SAT Math scores.
Students take the short Pretests, which quickly identify their problem areas for further study.
Then, they develop content mastery on their weak topics by only focusing on specific chapters - including extensive practice sets for each chapter.
Once they finish studying their weak topics, they move on to the final diagnostic Posttests. And these extra-difficult Posttests once again expose any remaining weak areas.
Then they do one final review of any chapters they missed from the Posttest, and at that point they’re ready for massive score improvements on their next SAT Math Test.
This setup also works perfectly whether a student is studying on their own, or with an SAT tutor like me. Either way, there’s a quick and efficient way to highlight specific SAT Math weaknesses, study and practice them, and then review with a final exam.
But even then, the SAT Math test isn’t like any other math test. There’s something really dangerous about the way the SAT Math test is written… read on, because you definitely need to know about this!
The Most Dangerous Thing About the SAT Math Test
So, what’s so dangerous about the SAT Math test?
It’s not the difficulty of the math itself. Instead, it’s one of the most important issues that hurts every student’s SAT Math score: careless mistakes.
I’ve actually written entire articles and taught whole lessons just about careless mistakes on the SAT Math test. This isn’t the time for me to explore it in detail, because this article is already pretty long.
I’ll just say a few words: there are four main careless math mistakes that absolutely ruin SAT Math scores. Here’s just a quick list of those mistakes:
- Negative Signs & Subtraction
- Order of Operations
- The Switcheroo
These mistakes are extremely common and every student makes them - from the weakest to the strongest test-takers. Heck, I still make these mistakes on a daily basis.
Even worse, the SAT test-writers know about these mistakes, and they specifically design the SAT Math questions to take advantage of these careless errors.
A lot of students find this cruel and evil, but personally I enjoy it. It’s fun knowing that there are so many careless mistakes waiting around every turn. It makes the whole test so much more exciting! Well, you may not agree…
Mastering Careless SAT Math Mistakes
But regardless of how we feel about the SAT Math test’s ruthless exploitation of our careless mistakes, it’s still something we have to deal with.
So, I wanted to make sure my math textbook readers really mastered their careless math mistakes. And, after seeing thousands of SAT Math questions done by hundreds of students, I knew exactly how to bait my traps and catch you with the same types of errors.
Armed with my understanding of careless mistakes on the SAT Math test, I designed the questions in my textbook to lure these careless mistakes to the surface.
This was one of the most challenging and fun phases of the project. There are more than 600 practice questions in my textbook - and I worked every single question at least four different ways. As I did so, I deliberately made some of the common careless mistakes that students are famous for. And then I designed the answer choices to match to these careless mistakes.
In other words, I made sure my own SAT Math textbook is constantly tempting you to make the same careless mistakes that happen on the SAT Math test.
The Kindness of SAT Math Cruelty
Does this approach seem cruel and calculating? Well, calculating it is - but cruel it is not.
If you make a mistake in my textbook, you can quickly learn from it and prevent it in the future - like on a real SAT test, for example.
Listen - if you’re going to make careless math mistakes - and you will - then we’d both prefer for you to make them in practice, instead of on the actual test.
So I made my practice questions very “tricky” - but only with the best of intentions. I promise. And after you’ve fallen for the same trap a few times, you’ll learn your lesson. Then on SAT test day, you’ll notice the same traps in advance, and carefully step around them.
Heck, you might even start to enjoy the traps as much as I do (feel free to disagree)!
Now my new SAT Math textbook was nearing completion, but there was one completely-unexpected problem that threatened to derail the entire project…
A Final Challenge
After writing all 38 SAT math lessons, all my best strategies, over 600 practice questions, detailed explanations for every single problem, and a total of eight diagnostic tests, I ended up with exactly what I predicted from the start - an SAT Math textbook that was over 1,000 pages.
“No problem!” I thought to myself. “I planned for this - and made sure that students could skip anything they don’t need to study.”
Well, there was one thing I hadn’t planned for: the book printer physically could not print a 1,000 page book.
That’s right - at the tail-end of the entire project, I discovered that my SAT Math textbook was literally too big to print.
And there was no way to shorten it. Everything I had written was essential. Nothing could be cut. Even if it could, the maximum page limit was less than 600 pages. There was just no way to fit everything into the book.
Can you imagine how discouraging that feels? Of all the obstacles I expected to face, that was the one I never saw coming.
I’ll admit, I felt pretty down for a few days. And then I perked up, realizing the solution was easy.
A Happy Ending
The answer to my problem was so obvious that I felt embarrassed for taking so long to think of it. I would just split the single original book into two separate volumes!
And that’s what I did. It took a bit of careful planning, but I eventually found the perfect place to divide my new book into two separate halves. In fact, it cut almost exactly down the middle, with 19 math topics in the first volume and another 19 in the second.
The first volume would focus on “Essential Algebra 1 and Algebra 2.” The second volume would dive into “Advanced Algebra, Geometry and Statistics.”
With a little more time spent reformatting and re-arranging the original manuscript, the final volumes were ready to go. And those are the two volumes that make up SAT Math Mastery as I published it.
That’s also why I say you should be sure to get both volumes if you want to study from my SAT Math textbook. It’s really one giant book - just split into two separate half-textbooks - simply because the printer literally could not print the massive original project!
Now Write the Next Chapters of Your SAT Math Score!
So here, dear reader, I will leave you.
You’ve stuck with me as I explained the original thoughts that lead me to design my ideal SAT Math textbook. We’ve walked through the necessary requirements for a great SAT Math score, and how I decided to deliver all of them in textbook form. Everything from content mastery to careless mistakes is cooked into the glorious stew of SAT Math Mastery.
You’ve also learned how I decided to structure this 1,000 page textbook for maximum efficiency and the fastest math score improvements in the shortest time, knowing that most high school students definitely don’t have enough time (or motivation) to work through every page of the book - and luckily, they don’t need to!
And finally, you followed my trials as I discovered that my book was too big to print, and the happy resolution of this story into two separate volumes.
There’s so much more I could say about what comes next. My SAT Math textbooks are useful, but not the only weapon in your arsenal - a diligent student must also practice with The Official SAT Study Guide and take as many timed, full-length practice tests as possible.
But perhaps that’s a story for a different day.
For now, I’ll just invite you to get your own copies of SAT Math Mastery Volume 1 and Volume 2. I know they’ll help you get higher SAT Math scores.
Final Thoughts & Encouragement
I deeply believe in your ability to get much higher SAT Math scores. It’s not even hard - I promise. You just have to know what’s on the test, find your weak spots, and then study and practice hard.
None of the individual concepts are difficult. Most SAT Math topics just come from the basics of Algebra 1 and 2. You can do this! Just watch out for those evil careless mistakes…
And always keep your eyes on the big picture: stronger college and scholarship applications, access to fun and satisfying careers, and in the long-term, a great life that excites you and motivates you every day.
May your SAT Math studies be fast, painless, and productive. Best of luck (not that you need it!)
This was a guest post by Christian Heath, founder of Love the SAT Test Prep and author of SAT Math Mastery Volume 1 and Volume 2. Chris has been teaching SAT and ACT prep to high school students for 10 years and has perfect scores on both tests.