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Welcome to the SHSATAcademy math course.


Standardized math exams like the SHSAT and SAT are not designed to force students into complicated calculations as they may normally see in honors or advanced classes. Most questions are designed to be answered in 30 seconds or less if the student identifies the right approach, which often combines relatively basic ideas from different topics. In other words, there are usually simple answers to strange, detailed questions. In short, the SHSAT is a simple, repetitive, strange, and detailed exam.


Simple (if you learn the material):

It is essential to learn the basic concepts covered for the math exam and gain familiarity with the application of those concepts. It can be a tall order, for example, to succeed on a test where more than half of the questions are word problems if test takers do not have a command of algebra. This course will cover the key math concepts in lessons and exercises to provide students the core knowledge they require. The good news is that there is a simple solution to most every problem if students know the core math concepts. At that point, success reverts to creativity, understanding the test design, and an ability to see the simplest solution all of which will be covered in our answer walkthroughs.



The playing field begins to level for students who know the subject material. The biggest factor for success or failure at that point is attentiveness to detail. We see it all the time. Two students have an equal mastery of the math concepts and their application, but one student misses a detail in the question prompt or doesn’t answer the right question. One student carefully follows a process discussed below to avoid errors, while the other student develops bad habits, and, at the range of cut-off scores for most specialized high schools, there is a narrow difference between students who gain admission and those who do not. Nearly half of admitted students — about 2,500 test takers — are statistically equivalent to the 2,500 students who narrowly miss the cut-off. Details are important.



One common problem and a key challenge for many students is to diagnose what the question prompt is asking for in the first place. Questions for the SHSAT are written in weird ways, and they often combine different math concepts, which is not typical for math exams in class. Armed with a process to follow below and continued practice, most students will gain greater levels of comfort throughout the course interpreting question prompts. Word problems are a typical cause for concern in many cases. The course will present some oddly phrased word problem exercises, so students can learn to interpret weird phrases and convert them into concrete algebra expressions and equations.



Last but not least the test design and types of questions and patterns tend to repeat throughout the exam. In other words, your commitment to practice and analyze your own mistakes will pay off. There will be several similar problems on exam day and many of the same traps and pitfalls. Some common traits among students who succeed on the SHSAT are a determination to work on their own and utilize many resources. If you have read this far into the course, chances are that you are among the students who share this determination to do well. Keep reading. This course is designed to provide not only practice but teach you how to get the most out of the test design and study efficiently.

Tips for Getting a Perfect Math Score

Every reasonably intelligent student can get a perfect score on the SHSAT math test. Of course, not everyone will, but know that more than anything else, your SHSAT score is a reflection of how hard you work and how smartly you study. Our goal is to provide both the practice material and to develop your understanding of the exam design and contents to help you succeed, not just for the SHSAT, but ultimately on the PSAT and SAT also. Hopefully, some of the following suggestions will get you started on the right path.

1. Do a LOT of Practice, and Understand Every Single Mistake

It goes without saying that the first step to success is to put in the hours of work — no pain no gain. That said, too many students who do several practice tests and solve hundreds of questions still find themselves nowhere near a perfect score. The reason why? Taking a practice exam is just one part of the process. Students forget that analyzing their results is even more important.

  • Review EVERY single question that you guessed on or missed.
  • Write down 1) the nature of the question, 2) why you missed it, and 3) what you can do to avoid that mistake in the future. Organize these results by separate subjects (algebra – solving equations, word problems, factors, etc.) It’s not enough to just think about a problem and move on. It’s not enough to just read the answer explanation. You have to think hard about why you specifically failed on each question.
  • Always dig a little deeper to understand why every mistake occurred:
    • Content Issues: I didn’t learn the math skill or knowledge needed to answer this question.
      One step further: What specific math skill do I need to learn, and how will I learn this skill?

Our Course: We have the largest repository of SHSAT lessons to help you. The lessons in this book are only the beginning. Join the online course for more instruction.

  • Incorrect Approach: I knew the content, but I didn’t know how to approach this question.
    One step further: How do I solve the question? How will I solve questions like this in the future?

Our Course: Learn different methods to solve math problems, diagnose strange wording, and find the fastest, most efficient solution.

  • Careless Error: I misread what the question was asking or solved the wrong thing.
    One step further: Why did I misread the question? What should I do in the future to avoid this? Get the idea? Expect to dig into understanding why you’re missing questions.

2. Identify at a high level whether you have content or time management issues or both.

Time your exam and mark where you are when time runs out, so you can score the timed version. Then complete the exam using as much time as needed. Compare the extra time score to the timed score. This procedure should apply to every exam and exercise. If you are scoring below the target cut-off scores (close to 70% for the specialized high schools or as high as 85%+ for a school like Stuyvesant) on the extra time result, then you have significant content issues that need to be addressed. You may lack coverage of a broad array of math topics or have deeper issues in a few core areas. If you scored above the target on the extra time version, but below on the timed version, then you probably have a good background in the math topics, but need to address time management issues. There are several lessons herein to address time management including the answer walkthroughs which, unlike typical answer explanations, review multiple methods to solve each exam problem. If both timed and extra time scores are above your targets, then you are already on your way to a potential perfect score.

3. If you have math content issues, then you must be rigorous about resolving them.

There are a lot of math concepts to master for the SHSAT — more than in any other section of the exam. Further, mistakes in one topic area for math multiply to other math topics on the SHSAT where problems tend to combine different topic skills into one question. Don’t just focus on understanding the one question you missed. Take the opportunity to research that subject and get more practice in it. You need to find a way to get lesson material to teach yourself the main ideas — including memorization of all related formulas. The lessons in this book will get you started and include follow up practice questions in each skill, and the online course will supplement that with the deepest repository of topic lessons and practice questions — over 100 topic lessons in math alone.

4. If you missed a question, try it again before reading the explanation.

It is too easy to look at an explanation and gain a cursory sense of how to solve the problem and move on. Almost every student takes this approach, and it is not very helpful to learn new ideas. Instead, take note of the correct answer option and try to solve the problem again for up to 10 minutes with the goal of arriving at the correct answer. The investment in the effort, even if you still have to resort to the explanation, will cause the ideas to sink in and take hold more firmly. i.e., it is a good way to learn ideas you have not yet mastered.

5. Master even the more esoteric math concepts and skills.

Once you have a strong foundation in the core math concepts and achieve better scores, the goal of attaining a perfect score becomes increasingly difficult. Small sources of errors become a big percentage of the troubled questions remaining. Some topics or problems types may appear less frequently, but you must be ready when they do if your goal is a perfect score. For example, most students will remember the area of a triangle isBase x Height. Do you, however, know the area of an equilateral triangle is?

6. Check your answers after you complete the exam.

SHSAT questions are designed to be answered in 30 seconds or less if the student identifies an efficient approach. At the end of all the work in this book, you will hopefully have extra time to check your work. Don’t take this casually as too many students do. It is human nature to think, “I got it!” the first time. However, the greatest source for errors after lack of subject matter knowledge is careless mistakes. Attention to detail differentiates many equally talented students. Read the question again.

  • If the question asks for a specific variable, make sure you’re solving for that variable! Underline the question prompt if you like. Before circling your answer check one last time. “What is the question asking? “ Did you answer the specific prompt?
  • Question your assumption about what the prompt is asking. Can you identify the essence of the problem? For example, a question that asks for the probability may really be asking if you understand the concepts underlying the set count going into the probability calculation. In this case, students who do the correct probability calculation often fail to think deeply about the conditions and set count underlying the calculation.
  • Try to solve the question a different Our answer walkthroughs will address various approaches and methods in each exam problem. The ability to employ alternative methods will help check mistakes from the first method without the bias of taking the same approach. In the simplest case perhaps, if you resolve a question algebraically, you might check the answer by plugging the result back into the original equation.
  • Last, but not least, if you follow the bubbling answer approach in a later chapter, rapidly double check that you bubbled the answers correctly.

7. Keep calm during the test.

Too often students have an expectation developed in practice, and they get to the actual test, find a question they cannot resolve at first, and panic. Of course, the panic doesn’t result in screams or hysteria — we hope. Instead, test-takers tend to freeze. Don’t! Do something. Take an active approach to solve the problem. Remember your training. Follow your process. If necessary, before investing too much time, skip the question and return to the question again later. Chances are you will get it after you continue at a good pace on the rest of the exam assuring an overall good score in most cases. In the end, you may not be perfect, but you will be positively surprised how well you perform if you rely on your training.

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