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# PART I – About The SAT Math Test

I want to break down the whole SAT math test and show you what it’s composed of, what it tests, and how to ace to it. The first thing to realize is that the SAT math test has changed its focus to mainly test students on algebra and problem-solving using real-world scenarios. The majority of it covers Basic Algebra and Advance Algebra. Therefore, most of the concepts in these two divisions of math are fair game. And there are a lot of concepts. But, the good news is that you’ve already learned all or most of these concepts in school. The new SAT has really become aligned to your school curriculum. It basically covers most of Grade 11 Math and a tiny bit of Grade 12 Math. Take a look at this **TABLE 1** for the main sections on the SAT math test.

From this table, we can see that the additional topics only make up for 10.34% and the rest of the topics account for 89.66% of the total questions in the math section. This is very key for us to know, as it will guide our strategy for the math section.

## Calculator and No-Calculator Portions

The math test will be Section 3 and Section 4 of the whole SAT and will consist of portions where you will be allowed to use a calculator and portions where you will NOT be allowed to use a calculator. Don’t let this scare you, as most of the questions will be solvable without calculators. The calculator will mainly be for questions which give you ugly numbers with decimal places or things like the quadratic formula. In general though, the questions in the no-calculator portion will be solvable more faster than the questions in the calculator portions.

## Types of Questions

The majority of the questions in each section will be multiple-choice, accounting for 80% of all the questions. Each multiple-choice question will have four options to choose from, with only one correct or best answer. Remember, that there will be NO penalty for guessing wrong. So, make sure to answer each and every question.

The other type of question is the grid-in response question (20% of the total questions), which is basically a question without answer choices for you to choose from. For this type of question, you have to come up with the answer and write it in appropriately on the answer sheet. Again, NO penalty for getting wrong answers. *One major thing to note for this is that you must write your answer in the grid-in boxes provided and also fill-in the appropriate bubbles underneath – otherwise, you won’t get the credit!!*

## Heart of Algebra

The point of this category is to see if you can demonstrate both procedural skill and a thorough understanding of linear equations, linear functions, and linear equalities. This is accomplished by asking you to solve straightforward questions or challenging questions. Remember that a lot of these concepts can and will be asked in many different ways. So, it’s a good idea to practice with as many questions as you can to get an idea of how to solve the same concepts in different contexts.

Here, we have outlined these concept: **TABLE 2**

It is important to note that many Heart of Algebra questions will ask to solve for the following:

- Define one or more variables
- Determine the algebraic relationship between the variables
- Solve for the required variable
- Interpret the results to answer what the question is specifically asking

**There will be a total of 19 questions for this category – 11 for the Calculator portion and 8 for the No-Calculator portion.**

## Problem Solving and Data Analysis

This section tests your ability to understand and represent data. This means that you have to pay attention to things such as units, measurements, ratios, trends, and principles of statistics. Some questions may be as simple as reading a value off of a graph, whereas, other questions may ask you to calculate something, like the probability of occurrence of a particular event. You will definitely have to know how to read data from line graphs, bar graphs, histograms, box-and-whisker plots, scatterplots, and two-way tables (categorical data).

Here is a table of all the concepts covered in this section: **TABLE 3**

For some concepts, you simply have to understand them, rather, than calculate them. For example, you will not be expected to calculate standard deviation, but, will be expected to know that a large standard deviation means the data is more spread out from the mean. *You will NOT be asked to calculate standard deviation, margin of error, or confidence intervals. But, you must understand what these concepts mean. Another important thing to note here is that in statistics, confidence intervals other than 95% can be used, but the SAT questions will always use 95% confidence levels.)*

**There will be a total of 17 questions for this category – all for the Calculator portion.**

## Passport to Advanced Math

This category is all about understanding the structure of expressions and being able to manipulate them to solve for different variables. This also means that you have to understand what the variables represent. Basically, this section tests concepts that build on the concepts tested in the Heart of Algebra category. You are further expected to know the basics of equations, functions, and polynomial algebra. Yes, this means that all those things you hate – fractions, radicals, and exponents – are all tested!

Here is a table with all the concepts tested in this section: **TABLE 4**

The SAT Math test uses the following Cartesian plane assumptions for any graph on the xy-plane:

- The axes are perpendicular and the scales are linear.
- The values on the horizontal axis increase as you move to the right.
- The values on the vertical axis increase as you move up.

*Note that this means that you CANNOT assume that the size of the units or measurements on the two axes is the same (unless the question specifically states that they are).*

When you begin your prep for the SAT math section, make sure you master Heart of Algebra before moving on to this section.

**There will be a total of 16 questions for this category – 7 for the Calculator portion and 9 for the No-Calculator portion.**

## Additional Topics

This section covers topics in geometry and trigonometry. It also covers complex numbers. The good thing here is that a lot of the geometry formulas are provided for you, so, you don’t have to memorize a lot. *Remember, that this section only makes up about 10% of the total Math test (6 questions out of 58). So, don’t go spending more time prepping on this section than the other sections!*

Here are the concepts: **TABLE 5**

*One important thing to note in this section is that figures ARE drawn to scale unless explicitly stated otherwise (which is totally opposite from the Old SAT).*

**There will be a total 6 questions for this category – 3 for the Calculator portion and 3 for the No-Calculator portion.**

# PART II – Most Commonly Tested Concepts

In this part, I want to delve into what this SAT Math test really focuses on. If we can find which concepts are commonly tested and which aren’t, we can make our studying and prep work that much more efficient and productive.

Here’s what we did:

- We went through the Math Sections of all 4 released tests from CollegeBoard and wrote down which concept was being tested for each and every question.
- We came up with a total of 26 concepts that showed up repeatedly across the 4 tests, which totaled to 232 questions.
- We tallied up all the questions according to the concept they tested.
- We calculated the frequency by dividing the number of times a concept showed up across the 4 tests by the total number of questions we looked at (232).

Here are the results: **TABLE 6**

This table gives us some interesting stats to think about.

### ** Caveat **

But first, I just want to mention that all of this should be taken with a grain of salt for the following reasons:

- This data is only based off of 4 College Board tests – so the sample isn’t really that large, which makes our results less accurate.
- Just because I say “68% of the tested concepts will be from the first 11 concepts” doesn’t mean that that is exactly what you will see on the real thing. It is simply an analysis of what we found to be the case with the 4 released tests from College Board.
- All the percentages are from these 4 released College Board Tests and we are assuming that College Board will test in a similar manner on the real administered tests. So, we are trying to make predictions based off of these stats – nothing stated here is a 100% for sure thing.
- There were a few questions for which it seemed like they were testing a combination of concepts, rather than just one concept explicitly. For this type of question, we used our judgement to decide which concept it was ‘most importantly’ testing.

## Analysis

The first 11 concepts: **TABLE 7**

- The first 11 concepts make up 68% of the questions – which means that for any given math test of 58 questions, 40 of those questions would test these concepts.
- The last 15 concepts only make up 31% of the questions – which means that for any given math test of 58 questions, 18 of those questions would test these concepts.
- Out of the first 11 concepts, 6 of the concepts are Heart of Algebra concepts (blue), accounting for 32% or about 1/3 of all tested concepts.
- Out of the first 11 concepts, 3 of the concepts are Problem Solving and Data Analysis concepts (green), accounting for 22% of all tested concepts.
- Out of the first 11 concepts, 2 of the concepts are Passport to Advanced Math concepts (yellow), accounting for 14% of all tested concepts.

The next 7 concepts: **TABLE 8**

I didn’t want to include Function Notation, however, I felt that this concept is sooooo easy, compared to the last 8 concepts, that I might as well include it with this group. So, this next chunk of concepts comprises 20% of tested concepts.

- Questions about circles, part of the Additional Topics category, appear to be the most tested of the Additional Topics concepts.
- 5 of these concepts are from Passport to Advanced Math (yellow), accounting for 14% of all tested concepts.
- Statistics only makes up 3% of all tested concepts.

The last 8 concepts: **TABLE 9**

- 5 of the concepts are from the Additional Topics (red) category.
- 3 of the concepts are from Problem Solving and Data Analysis (green).

## Results

- Just 6 Heart of Algebra concepts account for 32% of all tested concepts.
- Combined from above, just 4 Problem Solving and Data Analysis concepts make up 25% of all tested concepts.
- Combined from above, just 7 Passport to Advanced Math concepts make up 28% of all tested concepts.
- 18 concepts make up 88% of all tested concepts. This is equal to about 51 questions out of 58. This gives a raw score of about 690 according to the raw score conversion tables made available by College Board.
- 17 of these concepts make up 85% of all tested concepts. This is equal to about 49 questions out of 58. This gives a raw score of about 710 according to the raw score conversion tables made available by College Board.
- The 11 most common concepts make up 68% of all tested concepts. This is equal to about 40 questions out of 58. This gives a raw score of about 610 according to the raw score conversion tables made available by College Board.

## Discussion

So, what does all of this mean? How can it help you? Well, it really depends on what your specific situation and goals are. If you are in a time crunch, for example, then it might be wise to study the 11 most commonly tested concepts, so, that you can still get a score around 600. And if you have a bit more time, then study the first 18 concepts so that you have a chance at a 700. However, if you do have a lot of time on your hands, then it would be wise to begin with the concepts outlined in this analysis of the 4 released CollegeBoard tests. This would allow you to start doing really well on your practice tests, early in your prep, giving you a huge confidence and motivation boost. Then, you can focus on the rarer concepts, common mistakes, and harder material to go from 700 to 800.

Another thing to point out is that out of all of the Additional Topics concepts, it seems that concepts related to circles are the most important. So, if you really hate geometry and don’t want to bother with triangles and such, at the very least, you should study up circles.

In Heart of Algebra, we were quite surprised to see some topics so heavily tested. For example, systems of linear equations. Each of the 4 tests from CollegeBoard had anywhere between 2 to 6 questions on just this concept. Most of the time they gave you both equations, but rarely they asked you to come up with the equations also. Writing linear algebraic equations from word problems is also a big one. The next few heavily tested concepts were ratios & proportions, polynomials, quadratics, and being able to read graphs and tables for things such as trends, max/min points, and specific values. So, without a doubt, do not go into the test without being comfortable with these things.

In terms of difficulty of questions, it seemed that, generally, the difficulty increased as you got further along in the math section. Section 4 (the calculator portion) had more difficult questions than Section 3. However, a lot of the questions in Section 4 could easily be solved without using a calculator. So, depending on how much you rely on your calculator, you may or may not use it much for section 4.

Overall, I believe that the SAT Math test is fair and maybe even easier than the old SAT math. There are no tricks and strangely worded questions. You’ve learned the majority of these concepts in school – mainly Grade 11 Functions. And the questions are exactly as you’ve seen them in school also. I think this familiarity of these questions will help decrease anxiety for many students. If you have done well in math at school, then you will definitely do well on this SAT Math test. If you haven’t, then you’ll have to work a little harder to review all the concepts that your weak in and show colleges that you have improved in math by doing well on the SAT Math test.

I hope that these tables and analysis have given you a little more insight into the SAT Math test, making it a little more predictable and less scary. If you find that you are lacking in certain skills, then there are great resources like Khan Academy to help with your review. Our main goal is to use these findings to create the best practice tests we can for students. As CollegeBoard releases more tests and we can glean more information from student experiences, our tests will get better and better going into the future. We are going to release our first book of practice tests in early August.

# PART III – Strategy

## General Strategies For The SAT Math Test

**Process of Elimination:** This strategy is golden when you’re a bit stuck. If you weren’t able to solve the question and find the right answer right away, then start by eliminating the most wrong choices right away – and there are usually one or two of them for every question. Since, you only have four choices to begin with; this really helps narrow it down. After eliminating two choices, even if you have to totally guess, you’re chances to guess correctly are 50%.

**Plug-in Answer Choices:** This is another thing to try when you’re stuck. Pick one of the answer choices (usually the middle one is the best one to go with) and plug it in to the question. You can usually get the answer this way within two guesses, because the first guess will give you a good idea of what answer choice to try next.

**Substitute Numbers for Variables:**** **Sometimes, when you’re given a formula and asked to manipulate it, you substitute easy numbers into it to make sure you did it right.

**Target Easy Questions First:** This strategy works for those that are very nervous and need a confidence boost early on. You can quickly flip through the section and find which questions you think are easy and do them first. What constitutes an easy question? Well, it’s whatever topic you think you’re most comfortable with and whether you can get the answer under 30 seconds. That seems like a very short amount of time, but it’s not. 30 seconds is a long time. Try counting to 30 seconds right now and you’ll see. If you can’t get the answer in 30 seconds, then it’s not an easy question. Try to notice this during your practice and while you are doing the practice tests in this book. You will notice that you get the easy questions almost immediately. After you’re certain you’ve got all the easy questions, move on to the harder ones.

**Save Data Tables For The End:** These questions usually want you to analyze the data and that can take you 30 seconds to a minute at least. Then they want you to do something with that data, which will take you another 30 seconds to a minute at least. So, although not hard, these questions are time consuming. Save them for the end. Time management is key to doing well on this test. Do the same for any complicated graph question. Sometimes, though, the question will be very simple – they may just want you to read a value off the graph, which you can do very quickly.

**Remember that you can mark-up and write all over your test booklet** – so make sure to actually cross things out that you want to eliminate, put a star besides ones that you think are hard, write down things that you’ve memorized, and whatever else you feel will help you.

**Read each and every question carefully** and try to come up with the answer before looking at the answers. Then look at every answer before picking the right one.

**Memorize common formulas and facts:** This will naturally help you do questions quicker. This includes memorizing all the formulas provided to you on the reference sheet. This prevents wasting time by flipping back and forth between your question and the reference sheet.

**Try not to depend on your calculator too much:** Most questions on the SAT math test can be done without using a calculator. We recommend using the calculator for mainly questions with really ugly numbers that make it hard to do mental math.

## How To Get A 500+ Score

Getting a score of 500 should be very easy on this test. You just have to know all the basic concepts.

Number of Correct Questions: 22 – 26

Percentage: 38% – 45%

Study Plan

- 1 hour a day to review concepts for 2 months
- 30 minutes a day to do practice questions
- At least 4 timed math practice tests

Main focus of studying:

- Heart of Algebra
- Top 11 concepts from our analysis

## How To Get A 600+ Score

Getting a score of 600 will require a little more effort but will also be relatively easy to accomplish.

Number of Correct Questions: 32 – 38

Percentage: 55% – 66%

Study Plan

- 1 – 2 hours a day to review concepts for 2 months
- 30 minutes a day to do practice questions
- At least 6 timed math practice tests

Main focus of studying:

- Heart of Algebra
- Passport to Advanced Math
- Top 18 concepts from our analysis

## How To Get A 700+ Score

Getting a score of 700 will be harder to accomplish and will require a good amount of effort. We really recommend you start prep early and leave about 4 months to get to this score and above (unless you’re very good at math already). From our analysis, we recommend that you study and be comfortable with all 26 of the most commonly tested concepts. You should also thoroughly review Basic Algebra and Advanced Algebra, which covers things such as quadratics, polynomials, rational expressions, radicals, exponents, graphs, functions, and more. This will prepare you very well for the math test and you should be able to get almost all the questions. You can get the hardest questions wrong. Even if you miss a handful of questions, you can still end up with a 700+ score.

Number of Correct Questions: 43 – 50

Percentage: 74% – 86%

Study Plan

- 2 – 3 hours a day to review concepts for 2 – 4 months
- 30 minutes – 1 hour a day to do practice questions
- At least 8 timed math practice tests

Main focus of studying:

- Heart of Algebra
- Passport to Advanced Math
- Problem Solving and Data Analysis
- All 26 commonly tested concepts from our analysis

## How To Get A Perfect 800 Score

Getting a perfect 800 score will be a challenge and will require a tremendous effort. BUT, it’s totally doable. You don’t have to be a genius to get a perfect 800; you just have to be a hard and disciplined worker. We really recommend you start prep early and leave about 4 months to get to this score. From our analysis, we recommend that you study and be comfortable with all 26 of the most commonly tested concepts, everything outlined for the ‘How To Get A 700+ Score’ section and also all the Additional Topics concepts tested on the SAT. That means that you should definitely be comfortable with trigonometry, geometry, and complex numbers. Three out of four of the practice tests, released by CollegeBoard, show that you need to get all 58 questions correct in order to get 800 – even missing one can drop you down to a 790. The key to this is going to be time management, targeting your weaknesses with practice tests, eliminating careless mistakes, and doing as many timed SAT math practice tests as possible.

Number of Correct Questions: 57 – 58

Percentage: 98% – 100%

Study Plan

- 2 – 3 hours a day to review concepts for 2 – 4 months
- 30 minutes – 1 hour a day to do practice questions
- At least 10 timed math practice tests

Main focus of studying:

- Heart of Algebra
- Passport to Advanced Math
- Problem Solving and Data Analysis
- Additional Topics
- Al 26 commonly tested concepts from our analysis

# How To Use Practice Tests

- Always do the practice test under real conditions. Go to a quiet room, time yourself, and complete the whole test without any breaks. Also, it’s a good idea to do the practice test at the same time as when you will give your SAT – usually that’s around 8 am. This will make sure that you get used to having to think this early on in the day.
- Practice tests (and any practice questions you do) can let you know what your major and minor weaknesses are. Always analyze your results to find the reason why you got any question wrong (this includes questions you had to guess on). Categorize your weaknesses based on concept or question type. Then review those concepts, starting from the ones you get wrong the most and working your way down. And, of course, make sure to go back and re-do the questions you couldn’t do to make sure that you can do them.
- Practice tests can let you know whether or not your weakness is time management. The way you do this is to start noticing if you are always rushing near the end of a section. If you feel like you’re rushing the last 5 or so questions, then you have a time management issue. You can also check this by doing a practice test where you time yourself, but don’t stop a section once the time has run out. Keep going and finish the section, but make a note of all the questions that you had to do once the allotted time passed. Then when you score your test, break it up into two scores: one for the questions you finished within the allotted time and one score that includes the questions that you needed extra time for. Then compare the two scores. If you see that there is a difference of 50 or more points, then you definitely have a time management issue. And if there is almost no difference, then your timing is excellent and you should focus more on the concepts.
- Everyone makes careless mistakes. Practice tests give us a great glimpse at what these mistakes are. Go through each practice test and find the careless mistakes you made. Then write down on a piece of paper what that careless mistake was and make sure to read that piece of paper every day. The whole premise behind careless mistakes is that you simply don’t notice them when you make them. So, being more aware of them should help eliminate them.
- Take one practice test at the beginning of your prep to see where you stand and what you already know really well. This could tell you where to start your prep. For example, if you got most of the algebra questions right, but a lot of the quadratic questions wrong, then you would start your prep by reviewing quadratics concepts. After this first practice test, you should not take any more practice tests for 2 – 4 weeks, while you are reviewing concepts. Give yourself some time to learn a chunk of concepts and practice them on questions. Then, start doing 1 practice test every weekend. Remember to analyze the results of each practice test you do and target those weaknesses for the following week, before you do the next practice test. That way you will definitely see improvements every week and it will give you a big confidence and motivation boost.

# About Us and Our SAT Math Book

I’m a tutor and founder of Exam Masters Tutoring Service. We’ve been helping many students in the GTA ace the SAT, amongst other exams and subjects, for years. I’ve also been pretty active and helpful to students on reddit’s SAT subreddit page. I’ve personally been writing educational content and questions, as well as, tutoring for the SAT for over 10 years. I don’t want to bore you with my autobiography; you can read more about me on my **Amazon Author** page and my **website** if you like.

Since the SAT has been redesigned, we have analyzed all tests released by College Board to death and created an awesome math practice test book. Our team of math specialists and SAT experts researched all covered subject matter. This book is primarily created to give students a realistic experience for the SAT Math test. There are 6 full math practice tests, which are organized as section 3 and section 4 for each test.

Each test in this book contains the most commonly tested concepts based on our analysis of the materials released by College Board, as well as, concepts that we feel have the potential to be tested. We really spent a lot of time going over every question to make sure that it would help you [the student] prepare well for this test and made sure that there were many questions on the most commonly tested concepts.

There are a few questions which may seem really difficult, but for the student who aims for an 800, these types of questions should be expected. For example, most students learn analytic geometry, but have never come across the scenario of how to find the shortest distance between a point and a perpendicular line. Concepts like this have the potential to be tested, so we made sure to include them in our tests. We also delved into rarely tested concepts. For example, in statistics, every student has heard of the quartile, but few have heard of the decile! We even have questions on box-and-whisper plots – when was the last time, anyone has seen one of those?! Yet, these are testable concepts and must-know material for the student that aims for the **perfect 800**.

You can get our book on amazon (available worldwide): **Get Book Here!**

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