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Welcome to the SHSATAcademy math course. These free lessons are designed to teach students various basic skills from the complete math course. If you enjoy what you learn, please consider subscribing to the complete course for as little as $25—a one-time payment for the year. If you want our help and prefer completing the program with small groups, we provide a service to plan and track your study schedule, and provide tutoring help as needed for as little as $50 monthly.

Introduction to Math

This course is designed to teach students the core SHSAT math subject material and how to execute related concepts to solve problems correctly. It is essential to gain a mastery of the broad array of subject material covered for the SHSAT math exam. In particular, it is important to develop a comfort level with geometry and algebra, which are big parts of the test. Unlike many guides, this course will provide background material and video tutorials for each math topic, provide skill exercises to test student knowledge of the lesson material, and then provide SHSAT level problems that include the lesson skills. Full-length SHSAT exams (and mini-exams for those with a busy schedule) are available to measure your progress.

Although essential, mastering the math does not guarantee a high score. The SHSAT is more than a typical math test. It is a series of problem-solving exercises. The SHSAT asks basic math questions in weird ways, chock full of details and these patterns repeat throughout the exam. In most cases, the cause for difficulty on the SHSAT exam boils down to time management and paying attention to details. Beyond learning the math subject material, this course will help teach students aspects of the test design including a process to follow that will help students avoid the common mistakes. Our answer walkthroughs are unique because most answer explanations do not do justice teaching students who do not already know the correct answer. Exam walkthroughs in this course will review the relevant math concepts covered in each problem, identify different methods to solve the problem, and highlight potential patterns and traps when applicable. Many of these rules and strategies apply equally to the SAT and PSAT, which is developed similarly. In other words, what you learn herein will be helpful down the road as you also look to succeed on college entrance exams. In fact, we like to think of the SHSATAcademy as the ultimate guide for 6th to 9th graders to not only prepare for the SHSAT but to get a head start and learn the necessary habits to succeed on the PSAT and SAT.

What is the new SHSAT exam and why should I prepare for it?

Any student hoping to gain admission to a specialized high school should prepare for the SHSAT. Perhaps more importantly, 6th to 9th graders everywhere can get a head start on the new SAT from this SHSAT course. This course might be the best way for middle school students to learn SAT design and strategy with age-appropriate material.


The SHSAT Math and English Language Arts (ELA) exam is a 3-hour standardized admission exam given each fall toward the end of October to nearly 30,000 8th and 9th-grade students in New York City seeking to gain admission to one of nine specialized high schools. Each of these specialized high schools offers a challenging curriculum and top-tier education tuition-free to motivated New York City students who do well on the exam. Similar education opportunities in private schools can frequently cost $20,000 or more annually.


The new SAT and new SHSAT are more alike than ever. As a result, even if you are from Nebraska and a specialized high school is not your goal, any future college-bound 6th to 9th grader has a lot to gain from this preparation course. The SHSAT exam changed for the calendar year 2017 to align the exam closer to skills taught in the classroom as part of the common core curriculum. One significant change included replacing the old 45 question verbal exam with the new 57 question ELA exam — only 47 questions are graded, and ten unmarked questions will be used to field-test future changes to the exam format. Old scrambled paragraph and logical reasoning sections were eliminated in favor of 20 revise-edit questions that align more closely with the writing and language common core – and also the SAT. Additionally, the number of reading questions increased to 37 questions and six passages with approximately six questions each. The non-fiction only passage topics cover history, anthropology/sociology, the arts, science, and biographies, but that may change in the future to include literary and other fictional topics. The total exam time was extended to 90 minutes, so students have approximately 90 seconds to answer each question, the same as before the changes. Reading, which was already the most significant part of the SHSAT verbal exam, is even a larger fraction of the new SHSAT as a result of the changes. In all, these changes make the SHSAT essentially the new SAT Junior – an extremely useful exam for learning about the SAT. The following course will start by focusing on the crucial SHSAT Reading exam section. Reading, unlike math and language(grammar), does not depend on various rules and theorems. It is less dependent on previously learned content and relies only on the ability to read and understand American English, so it is a great place to learn the rules of the standardized exam. The course continues with writing and language and finally math. The lessons in this course will directly translate to improved PSAT and SAT scores and develop a student’s understanding of the unique design and features of the SAT. For the first time, students at the middle school level can effectively learn the SAT through high-quality SHSAT preparation without being constrained by the lack of exposure to high school level subject material. The abbreviation SHSAT throughout also refers to SAT and PSAT unless otherwise stated.

The main reason for mistakes on the SHSAT, PSAT, and SAT

SHSAT mistakes very often result from reasons other than lack of prior knowledge in the subject matter, and that is perhaps more prevalent for reading where prior subject knowledge is not critical in the same way it is on the math exam. Most students think good grades in algebra, geometry, or English class will necessarily translate to a high SHSAT math or ELA score. That is not necessarily true. While subject knowledge is an essential requirement, it is not sufficient. Prior exposure to courses like algebra and geometry are a huge plus in math, for example. Both topics comprise a large part of the math test, and there is a chasm between students who have seen these courses early enough to gain familiarity and those who have not seen the material or are currently taking such courses when the SHSAT exam is given in late October in the 8th grade. If this is an issue for you, consider planning and preparing early for the SHSAT. That said, even among students with excellent grades and top-level state math and ELA exams scores, only about half the test takers will gain admission.


The SHSAT — and SAT and PSAT for that matter — ask questions in strange ways. Questions often repeat topics and phrase their wording in ways students are not used to seeing in their classroom setting. Accurately diagnosing what the question prompt is asking is a large part of the battle. Moreover, questions are written in ways that require test takers pay extra careful attention to detail. Every word is important, and a loss of focus will result in mistakes that often separate two students who both have a strong grasp of the subject matter. The following typical reasons for mistakes on the SHSAT explain why student results do not always correlate with school grades. One or two reasons may come as a surprise. In either case, this course will teach each student how to evaluate their results and weaknesses to improve their score on the SHSAT.




  1. Subject-Matter Knowledge – does not know the subject matter or lacks confidence in the procedures to solve
  2. Time pressure – student runs out of time before finishing
  3. Confused by Question Prompt – cannot identify what the question is about
  4. Misses Details – did not pay attention to a particular word or detail in the prompt or answer choice
  5. Calculation Errors – student made an execution error while solving

What tests are best for practice?

In the case of the SHSAT and SAT alike, questions are written according to specific rules and patterns, and the ability to excel on the exam depends on learning to take advantage of these rules and procedures. Many of the difficulties students have on the SHSAT result from poor test-taking skills, not poor subject-matter knowledge. Any material that breaks the rules of the real test will encourage bad habits or prevent good habits from developing. Even “harder” questions will not help unless they are guaranteed to follow the same rules, so don’t assume harder questions will better prepare you for the actual test. Official sources are the best, and anyone who states otherwise is probably trying to sell you something you probably should not buy.

How to Begin

You have already taken your most effective first step: you have begun our SHSATAcademy course for free. We hope you enjoy it. Whether you are new or experienced, chances are the free version will teach you some basic skills or strategies you had not previously considered. Start with a real SHSAT practice exam. Follow the lessons in order or focus only on certain topics. We want you to learn. Follow up with another practice exam. If you like what you see, we welcome you to subscribe to complete the course for only $25.

President’s Letter

Photo: Richard Baxter Foster

This course is dedicated to that modern, handsome, well shaven gentleman in the picture. No, that is not our President – not really. Richard Baxter Foster is a late relative and, much to my chagrin, I could never sport a beard and mustache with quite the same demeanor nor muster the same energy as he did. Richard Baxter Foster was abolitionist, soldier, teacher, Ivy League graduate, minister, frontiersman and the inspiration for this course. As a volunteer in the 62nd U.S. Colored Infantry Regiment since its formation in 1863, he spent many days and evenings teaching soldiers in his unit who typically did not have access to education before the war nor likely would afterward. The troops believed in Richard, and they valued education highly enough to pitch in $5,000 of their hard earned savings (a fortune to the men at the time) to help Richard Baxter Foster start Lincoln Institute – the first African American college in the United States today known as Lincoln University. We too started with $5,000 provided from students or their parents in this case – our early adopters. Richard Baxter Foster made it his mission to provide equal education opportunities to all and, in a small way, we hope to continue his mission today in NYC. 

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