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- Herausgeber: John Wiley & Sons
- Kategorie: Bildung
- Sprache: Englisch
- Veröffentlichungsjahr: 2023
Hone your math skills to score well on the SAT Digital SAT Math Prep For Dummies is a jam-packed study guide to the section of the SAT students struggle with most. This update covers major changes to the test as the SAT goes fully digital in spring 2024. With this book, you can improve your score with proven test-taking strategies and four practice exams. Drill down on the concepts you need help with the most, and prepare to breeze through all 44 questions on test day. * Learn exactly what will be on the new, all-digital SAT math section * Get tips for solving problems quicker and making good guesses when you need to * Practice, practice, practice, with 4 tests * Maximize your score--and your chances of getting into your top-choice colleges If you're a high school student preparing to take the SAT and you need to designate extra study time to developing your math skills, this book is for you.
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Table of Contents
Cover
Title Page
Copyright
Introduction
About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here
Part 1: Getting Started with SAT Math
Chapter 1: Welcome to SAT Math
Quick Overview of the New Online SAT Format
SAT Math Basics
Overview of SAT Math Topics
SAT Math Strategy
Three SAT Success Stories
Chapter 2: Review of Pre-Algebra
Looking at Sets of Numbers
Remembering Fractions, Ratios, Decimals, and Percentages
Evaluating an Absolute Value
Working with Radicals
Understanding Algebra Terminology
Graphing on the
xy
-Plane
Part 2: Algebra
Chapter 3: Algebra I Reboot Part 1: Expressions
Evaluating Expressions
Simplifying Expressions
Factoring Expressions
Chapter 4: Algebra I Reboot Part 2: Equations and Inequalities
Solving Simple and Intermediate Algebra Equations
Solving More Difficult Equations
Solving Inequalities
Chapter 5: Linear Functions
Interpreting Linear Functions as Words, Tables, Graphs, and Equations
Linear Function Basics
Using Two Formulas to Find the Slope
Solving Linear Function Problems
Solving Word Problems
Chapter 6: Systems of Equations
Looking at Systems of Linear Equations
Working with Problematic Systems of Equations
Solving Systems of Linear Inequalities
Solving Systems of Non-Linear Equations
Part 3: Problem Solving and Data Analysis
Chapter 7: Ratios, Proportions, and Percentages
Applying Ratios and Proportions
Using Ratios and Proportions to Solve SAT Word Problems
Using Percentages to Answer SAT Questions
Chapter 8: Statistics and Probability
Statistics
Probability
Chapter 9: Understanding Data and Information from Tables and Graphs
Reading Information from Tables
Understanding Bar Graphs, Histograms, and Dot Plots
Working with Line Graphs and Scatterplots
Part 4: Advanced Math
Chapter 10: Functions
Understanding Function Notation
Handling More Advanced Applications of Function Notation
Using the Vertical Line Test for Functions
Knowing Some Key Parent Functions
Transforming Functions
Chapter 11: Polynomials
Knowing Polynomial Basics
Identifying Odd and Even Polynomials
Finding the
x
-Intercepts of Polynomials
Sketching the Graph of a Polynomial
Equivalent Polynomials
Recalling Synthetic Division for Polynomials
Chapter 12: Quadratic Functions
The Quadratic Function in Standard Form
The Quadratic Function in Vertex Form
Connecting Standard and Vertex Forms
Finding the Roots of a Quadratic Function
Using Quadratic Equations to Solve Word Problems about Projectiles
Chapter 13: Exponential and Radical Equations
Solving Exponential Equations
Using Exponential Growth and Decay Functions
Graphing Exponential Functions
Solving and Graphing Radical Equations and Functions
Part 5: Geometry and Trigonometry
Chapter 14: Geometry
Using Geometric Formulas for Success
Knowing the Angles (and Triangles)
Looking at Circles on the
xy
-Plane
Chapter 15: Right Triangles and Trigonometry
Looking Closely at Right Triangles
Playing with Trigonometric Ratios
Looking at Radian Measure and Arc Length
Part 6: Practice Makes Perfect: SAT Math Section Practice Tests
Chapter 16: Practice SAT Math Test 1
Chapter 17: Answers and Explanations for Practice SAT Math Test 1
Section 3
Section 4
Chapter 18: Practice SAT Math Test 2
Section 3
Section 4
Chapter 19: Answers and Explanations for Practice SAT Math Test 2
Section 3
Section 4
Part 7: The Part of Tens
Chapter 20: Ten Things You Will Almost Definitely See on Your SAT Math Test
Representing Linear Functions
Solving Systems of Linear Equations
Tackling Quadratic Equations
Graphing Quadratic Functions
Working with Percentages
Answering Ratio/Proportion Problems
Finding the Mean and the Median
Working with Exponential Functions
Calculating Sines, Cosines, and Tangents
Plotting Circles on the
xy
-Graph
Chapter 21: Ten Tips to Improve Your SAT Math Score
Study Diligently in Your Math Classes
Get Good at Doing Basic Calculations in Your Head
Study SAT-Specific Math Skills
Study for the SAT with Friends
Get Comfortable Turning Words into Numbers
Take Timed Practice Tests
When Taking Practice Tests, Budget Your Time to Maximize Your Score
Study from Your Timed Practice Tests
Retake Your Timed Practice Tests
Take the SAT More Than Once
Index
About the Author
Advertisement Page
Connect with Dummies
End User License Agreement
List of Tables
Chapter 1
TABLE 1-1 Overview of the New SAT Format
TABLE 1-2 Easy, Medium, and Hard Questions
Chapter 2
TABLE 2-1 Squaring and Taking a Square Root (Radical) Are Inverse Operations.
TABLE 2-2 Expressions with 1, 2, 3, and 4 Terms
TABLE 2-3 The Expression and Its Coefficients and Variables
TABLE 2-4 Polynomials of Degree 1, 2, 3, and 4
Chapter 3
TABLE 3-1 Difference of Squares Factoring
TABLE 3-2 Factoring Quadratic Trinomials
Chapter 4
TABLE 4-1 Flipping Inequality Signs
Chapter 5
TABLE 5-1 Tracking the Money in Your Bank Account
TABLE 5-2 Variety of Linear Functions and Three Coordinate Pairs for Each Functi...
TABLE 5-3 Pairs of Negative Reciprocals
Chapter 6
TABLE 6-1 Table for Solving a System of Equations Word Problem
TABLE 6-2 Systems of Equations with 0, 1, or Infinite Solutions
Chapter 7
TABLE 7-1 Finding the Multiplier to Calculate Percent Increase and Percent Decre...
Chapter 8
TABLE 8-1 A Two-Way Table for Probability Questions
Chapter 10
TABLE 10-1 Notation for Combining Functions
TABLE 10-2 Parent Functions for the First Four Polynomials
TABLE 10-3 Six Important Parent Functions
TABLE 10-4 Distinguishing Vertical and Horizontal Transformations
Chapter 11
TABLE 11-1 The Polynomials of Degrees 1 through 4
TABLE 11-2 End Behavior of Polynomial Functions as and as
Chapter 12
TABLE 12-1 Quadratic Trinomial Expressions as Equivalent Squares of Binomials
TABLE 12-2 Distinguishing
x
-Intercepts from Complex Roots
Chapter 13
TABLE 13-1 Identities for Simplifying Exponential Expressions
TABLE 13-2 Four Exponential Growth Functions
TABLE 13-3 Four Exponential Decay Functions
Chapter 15
TABLE 15-1 The 3–4–5 Triangle and Some Multiples
TABLE 15-2 Three Pythagorean Triples and Some Multiples
TABLE 15-3 Sine, Cosine, and Tangent of Three Common Angles
List of Illustrations
Chapter 1
FIGURE 1-1: The Reference list of formulas for the SAT.
Chapter 2
FIGURE 2-1: Radicals on the number line.
FIGURE 2-2: The
xy
-plane.
FIGURE 2-3: Plotting four points on the
xy
-plane: , , , and .
FIGURE 2-4: Plotting the graph of the equation .
Chapter 5
FIGURE 5-1: A graph of the function on the
xy
-plane.
Chapter 6
FIGURE 6-1: A system of linear equations with two intersecting lines has exactl...
FIGURE 6-2: A system of linear equations with two parallel lines has no solutio...
FIGURE 6-3: A system of linear equations with two overlapping lines has infinit...
Chapter 8
FIGURE 8-1: The set of scores for an SAT Math Test display a normal distributio...
Chapter 10
FIGURE 10-1: Parent functions for the four polynomials from degree 1 to degree ...
FIGURE 10-2: Graphs of six parent functions.
FIGURE 10-3: Vertical transformations of three functions.
FIGURE 10-4: Horizontal transformations of three functions.
FIGURE 10-5: Positive stretch and compress transformations of the function .
FIGURE 10-6: Negative stretch/compress/reflect transformations of the function
Chapter 11
FIGURE 11-1: Graphs of the parent functions of polynomials of degrees 1 through...
FIGURE 11-2: Comparing cross-through and bounce intercepts.
Chapter 12
FIGURE 12-1: Positive quadratic functions are concave up and have a minimum val...
FIGURE 12-2: The constant
c
term of a quadratic function tells you the
y
-interc...
FIGURE 12-3: Two vertical transformations of .
FIGURE 12-4: Two horizontal transformations of .
FIGURE 12-5: Two combinations of vertical and horizontal transformations of .
FIGURE 12-6: Two positive stretch-compress transformations of .
FIGURE 12-7: Two negative stretch-compress-reflect transformations of .
FIGURE 12-8: Quadratic functions with 2, 1, and no
x
-intercepts.
Chapter 13
FIGURE 13-1: Exponential growth and decay functions.
FIGURE 13-2: The parent radical function .
Chapter 14
FIGURE 14-1: The SAT Reference Sheet.
FIGURE 14-2: Vertical angles are equal to each other; linear pairs add up to ....
FIGURE 14-3: Corresponding angles are equal to each other.
FIGURE 14-4: Two examples of circles on the
xy
-plane.
Chapter 15
FIGURE 15-1: Constructing the two special right triangles from a square and an ...
FIGURE 15-2: A right triangle with sides of 1, 1, and .
FIGURE 15-3: A right triangle with sides of 1, , and 2.
FIGURE 15-4: The opposite side, adjacent side, and hypotenuse side of a right t...
FIGURE 15-5: The 3–4–5 right triangle.
FIGURE 15-6: The and right triangles.
FIGURE 15-7: The unit circle.
Guide
Cover
Table of Contents
Title Page
Copyright
Begin Reading
Index
About the Author
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Digital SAT® Math Prep For Dummies®, 3rd Edition
Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com
Copyright © 2024 by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions.
Trademarks: Wiley, For Dummies, the Dummies Man logo, Dummies.com, Making Everything Easier, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc. and may not be used without written permission. SAT is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product. All other trademarks are the property of their respective owners. John Wiley & Sons, Inc. is not associated with any product or vendor mentioned in this book.
LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: WHILE THE PUBLISHER AND AUTHORS HAVE USED THEIR BEST EFFORTS IN PREPARING THIS WORK, THEY MAKE NO REPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETENESS OF THE CONTENTS OF THIS WORK AND SPECIFICALLY DISCLAIM ALL WARRANTIES, INCLUDING WITHOUT LIMITATION ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. NO WARRANTY MAY BE CREATED OR EXTENDED BY SALES REPRESENTATIVES, WRITTEN SALES MATERIALS OR PROMOTIONAL STATEMENTS FOR THIS WORK. THE FACT THAT AN ORGANIZATION, WEBSITE, OR PRODUCT IS REFERRED TO IN THIS WORK AS A CITATION AND/OR POTENTIAL SOURCE OF FURTHER INFORMATION DOES NOT MEAN THAT THE PUBLISHER AND AUTHORS ENDORSE THE INFORMATION OR SERVICES THE ORGANIZATION, WEBSITE, OR PRODUCT MAY PROVIDE OR RECOMMENDATIONS IT MAY MAKE. THIS WORK IS SOLD WITH THE UNDERSTANDING THAT THE PUBLISHER IS NOT ENGAGED IN RENDERING PROFESSIONAL SERVICES. THE ADVICE AND STRATEGIES CONTAINED HEREIN MAY NOT BE SUITABLE FOR YOUR SITUATION. YOU SHOULD CONSULT WITH A SPECIALIST WHERE APPROPRIATE. FURTHER, READERS SHOULD BE AWARE THAT WEBSITES LISTED IN THIS WORK MAY HAVE CHANGED OR DISAPPEARED BETWEEN WHEN THIS WORK WAS WRITTEN AND WHEN IT IS READ. NEITHER THE PUBLISHER NOR AUTHORS SHALL BE LIABLE FOR ANY LOSS OF PROFIT OR ANY OTHER COMMERCIAL DAMAGES, INCLUDING BUT NOT LIMITED TO SPECIAL, INCIDENTAL, CONSEQUENTIAL, OR OTHER DAMAGES.
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Wiley publishes in a variety of print and electronic formats and by print-on-demand. Some material included with standard print versions of this book may not be included in e-books or in print-on-demand. If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com. For more information about Wiley products, visit www.wiley.com.
Library of Congress Control Number: 2023945300
ISBN: 978-1-394-20738-1 (pbk); 978-1-394-20739-8 (ebk); 978-1-394-20740-4 (ebk)
Introduction
The first quarter of the 21st century is now history, but the SAT is still with us. And like most things that endure, the SAT has morphed more than once in order to stay current.
In its new format, the SAT is now almost exclusively an online test. This means that the days of carrying half a dozen well-sharpened yellow Number 2 pencils are something you’ll only hear about from older relatives.
What hasn’t changed (too much) is the math that you’ll need to know in order to get a good SAT math score. Math, for the most part, is still math. And that’s what this book is about.
About This Book
A lot of SAT prep books divide their attention between the Reading and Writing test and the Math test. This is fine as far as it goes, because you probably want to boost both scores. But in this book, I focus exclusively on math, math, and more math to help you achieve the best score you can on this — what can I say? — most often dreaded part of the test.
The SAT covers a variety of areas, including algebra, geometry, trigonometry, functions and graphs, and statistics and probability. This book focuses on those SAT topics and helps you get used to problem-solving so that you can turn facts and formulas into useful tools.
I wrote this book to give you the best possible advantage at achieving a good score on the math portion of your SAT. There’s no shortcut, but most of what you need to work on comes down to four key factors:
Knowing the basics inside and out
Strengthening SAT-specific math skills
Practicing answering SAT questions
Timing yourself taking SAT practice tests
For that last point, almost every example and problem here is written in SAT format — either as a multiple-choice question or as a student-produced response question. Chapters 3 to 15 contain math skills that are essential to the SAT. And, to give you that test-day experience, this book also includes two practice tests, with access to two additional online practice tests. That’s hundreds and hundreds of questions designed to strengthen your “SAT muscle,” so to speak.
This book also has a few conventions to keep in mind:
New terms introduced in a chapter, as well as variables, are in
italics.
Keywords in lists and numbered steps are in
boldface.
Foolish Assumptions
This is an SAT prep book, so my first assumption is that you or someone you love (your son or daughter, mom or granddad, or perhaps your cat) is thinking about taking the SAT sometime in the future. If not, you’re still welcome to buy the book.
My second assumption is that you’re currently taking or have in your life at some point taken an algebra course — even if you feel like it’s all a blur. Now, I wish I could tell you that algebra isn’t very important on the SAT — oh, a mere trifle, hardly a thought. But this would be like saying you can play NFL football without getting rushed by a bunch of 250-pound guys trying to pulverize you. It just ain’t so.
But don’t worry — this book is all about the blur and, more importantly, what lies beyond it. Read on, walk through the examples, and then try out the practice problems at the end of each chapter. I can virtually guarantee that if you do this, the stuff will start to make sense.
Icons Used in This Book
In this book, I use these four icons to signal what’s most important along the way:
This icon points out important information that you need to focus on. Make sure you understand this information fully before moving on. You can skim through these icons when reading a chapter to make sure you remember the highlights.
Each example is a formal SAT-style question followed by a step-by-step solution. Work through these examples and then refer to them to help you solve the practice problems at the end of the chapter.
Tips are hints that can help speed you along when answering a question. See whether you find them useful when working on practice problems.
This icon flags common mistakes that students often make if they’re not careful. Take note and proceed with caution!
Beyond the Book
In addition to what you’re reading right now, this book comes with a free access-anywhere Cheat Sheet that includes tips to help you prepare for the math sections of the SAT. To get this Cheat Sheet, simply go to www.dummies.com and type SAT Math For Dummies Cheat Sheet in the Search box.
You also get access to three full-length online practice tests. To gain access to the online practice, all you have to do is register. Just follow these simple steps:
Register your book or ebook at Dummies.com to get your PIN (go to
www.dummies.com/go/getaccess
).
Select your product from the drop-down list on that page.
Follow the prompts to validate your product, and then check your email for a confirmation message that includes your PIN and instructions for logging in.
If you do not receive this email within two hours, please check your spam folder before contacting the Technical Support website at http://support.wiley.com or by phone at 877-762-2974.
Now you’re ready to go! You can come back to the practice material as often as you want — simply log on with the username and password you created during your initial login. No need to enter the access code a second time.
Your registration is good for one year from the day you activate your PIN.
Where to Go from Here
This book is organized so that you can safely jump around and dip into every chapter in whatever order you like. You can strengthen skills you feel confident in or work on those that need some attention.
If this is your first introduction to SAT math, I strongly recommend that you start out by reading Chapter 1. There, you find some simple but vital SAT-specific information that you need to know before you sit down in front of your computer to take the test.
If you’d like to start out by getting a sense of how ready you are for the SAT, skip forward to Chapter 16 and take a practice test. When you’re done, check out Chapter 17 to see how many questions you got correct, and to read through the answer explanation for every question you got wrong.
However, if it’s been a while since you’ve taken a math course, read Chapter 2, which covers the pre-algebra math skills you need to know before you proceed to the more difficult math later in the book. Chapters 3 and 4, which cover algebraic expressions and equations, can get your math brain moving again, and you may find that a lot of this stuff begins to look familiar as you go along.
Finally, if you read through a few chapters and feel that the book is moving more quickly than you’d like, go ahead and pick up my earlier book, Basic Math & Pre-Algebra For Dummies (John Wiley & Sons). There, I adopt a more leisurely pace and spend more time filling in any gaps in understanding you may find along the way.
Part 1
Getting Started with SAT Math
IN THIS PART …
Getting familiar with the new online SAT format
Reviewing important pre-algebra concepts you may have forgotten
Chapter 1
Welcome to SAT Math
IN THIS CHAPTER
Looking at the new SAT
Knowing how the SAT Math Test is organized
Getting familiar with the Reference tab
Using the Calculator tab
Understanding how to enter answers to student-produced response (fill-in-the-blank) questions
Identifying the math topics tested on the SAT
Knowing some basic strategies for attaining scores of 500, 600, or 700
Coming up with a basic plan of action for getting the SAT Math score you need
In this chapter, I give you a general overview of the new SAT. Then I provide you with a more thorough look at the SAT Math test, including the math topics you’re most likely to find there. I discuss the Reference and Calculator tabs you’ll have access to. I also help you avoid a few unnecessary errors you may encounter when entering answers to fill-in-the-blank questions.
After that, I give you a bit of essential SAT Math strategy that every student needs to know. I encourage you to think about your goal for the next SAT based on the level you’re currently working at.
Finally, I present three SAT success stories, in which three very different students who set and reached different SAT goals got into the colleges that they were aiming for.
Quick Overview of the New Online SAT Format
The SAT is a college readiness test and, in some U.S. states, is now being used as a skills test required for high school graduation.
It covers two main subjects in four sections: two Reading and Writing sections, followed by two Math sections. Each subject is scored on a 200-to-800 point scale, resulting in a composite SAT score from 400 to 1,600 points.
The big news is that starting in March of 2024, the SAT will be changing to an exclusively online format. In this section, I give you a basic overview of the SAT in its new online format.
Knowing how many questions you’ll face and how much time you’ll have to answer them
Starting in March of 2024, the wise elders of the SAT are changing its format from a paper-based to online format.
The new version will comprise 98 questions (down from 154), for which you’ll be given a total of 134 minutes (down from 180). I’ve summed up the information you’ll need most in Table 1-1.
TABLE 1-1 Overview of the New SAT Format
Section
Subject
Time in Minutes
Number of Questions
Minutes Per Question
Section 1
Reading and Writing
35
27
1:20
Section 2
Reading and Writing
35
27
1:20
Section 3
Math
32
22
1:30
Section 4
Math
32
22
1:30
This is all fairly good news for students. You’ll spend less time answering fewer questions, but you’ll have a little less time pressure, with tad more time to answer each question. To me, that looks like a win-win-win.
Understanding key changes found in the SAT online format
The new online SAT format provides a few important upgrades to the previous paper-based version of the SAT.
For starters, the SAT questions that you answer will be drawn from a large pool of SAT questions, rather than printed in booklets and distributed to students. This change means that the test you take will literally be different from the test that the person sitting next to you is taking — or that your best friend will take the following week.
One result of this change is that cheating becomes a lot more difficult. Students may (and probably will) still post SAT questions and answers online, and other students like yourself may still read them. But if you do, you’ll probably just end up figuring out how to answer a lot of questions that will never actually appear on your test. (Another word for this practice is studying, which virtually all teachers encourage, so please have at it!)
Furthermore, the SAT is now adaptive, which means that it adjusts its difficulty level depending upon how well you perform. So, after you complete your Section 1 Reading and Writing Test, an algorithm adjusts the type and difficulty levels of the questions that you’ll see on Section 2 just for you. Likewise, after you finish your Section 3 Math Test, a similar algorithm performs the same magic, adjusting the questions on Section 4.
The good news here is that this new feature makes it possible for the system to produce a reliable score using 56 fewer questions and using 41 fewer minutes of your valuable time compared with the paper-based test.
SAT Math Basics
In the new format, both SAT Math sections will include 22 questions.
That’s a total of 44 questions, each of which counts for 1 point on your raw score of correct answers (from 0 to 44). This raw score is converted to a scaled score (from 200 to 800), which becomes your SAT math score.
Using the Reference tab
The SAT math test includes a handy Reference list of formulas that you can use while taking the test, as shown in Figure 1-1. As you can see, this list includes a variety of geometric formulas for the area and circumference of a circle, the area of a rectangle and triangle, the Pythagorean Theorem, and other favorites.
FIGURE 1-1: The Reference list of formulas for the SAT.
To access this list at any time, click the Reference tab at the top right of the test page.
Before taking the SAT, be sure you’re familiar with this Reference information, so you’ll remember it’s there when you’re working under time pressure on the actual test.
Clicking the Calculator tab
On the new version of the SAT, you can use a calculator on every question! This marks a big change from the previous paper-based version of the test, which had a No Calculator section.
The test itself provides an online calculator. To open it, click the Calculator tab at the top right of the page. The calculator is relatively self-explanatory, with a variety of calculator functions available to you. It also includes a graphing component to help you answer more difficult questions.
You can also use an SAT approved calculator, such as the one that you’re using in your current math class. It should go without saying (but I’ll say it anyway) that you’re not allowed to use any non-approved calculator — especially the one on your phone! — while you’re taking the SAT.
Answering student produced response (fill-in-the-blank) questions
The SAT math test includes 44 questions:
33 multiple-choice questions (Answer A through D)
11 student-produced response questions (sometimes called open-ended questions or fill-in-the-blank questions)
From your online adventures as a math student, you’re almost certainly familiar with both of these types of test questions.
Multiple-choice questions are just about foolproof. What can I say to be helpful? Don’t click B when you meant to click C.
Fill-in-the-blank questions aren’t all that much more difficult to handle. The new online SAT has, fortunately for you test takers out there, done away with the confusing grid that it used to employ in its paper-based format. (And we don’t miss it one bit!) So, in most cases, entering positive or negative integer answers should be a no-brainer.
Just a couple of words on entering rational numbers — that is, fractions and decimals:
Enter rational numbers that are greater than 1 (or less than –1) either as decimals or as improper fractions — never try to enter them as mixed numbers.
For example, suppose you want to enter the number 4.5. This decimal format works fine, or if you like, you can enter it as 9/2, which will appear as . But don’t try to enter it as 4 1/2, because this will show up incorrectly as .
Enter rational numbers that are repeating decimals either as fractions or by filling out the entire space available — don’t truncate them to save space.
For example, suppose you want to enter the number 2/3. This fractional format will show up correctly as , or if you like you can enter it as a decimal in any of the following ways:
Right:
.6666
.6667
0.666
0.667
When entering a repeating decimal like this one, just make sure to fill in as many numbers as possible to fit in the space given — that is, four numbers and a decimal point. Don’t truncate (cut short) your answer in any of the following ways:
Wrong:
.666
.667
0.66
0.67
Doable, right?
Overview of SAT Math Topics
The math that’s covered on the SAT is very closely tracked to the math that’s covered in most U.S. high school math classes. So if you’re a current or recent U.S. high school student, you’re probably familiar with most of this curriculum.
The SAT breaks this down into four general areas of study: Algebra, Problem Solving and Data Analysis, Advanced Math, and Geometry and Trigonometry. In this section, I give you an overview of each of these topics.
Algebra
Algebra centers on the linear function and other information covered in a typical high school Algebra I class. To answer SAT Math questions in this area, you’ll need to feel comfortable working with the following:
Evaluating, simplifying, and factoring algebraic expressions (
Chapter 3
)
Solving algebraic equations and inequalities (
Chapter 4
)
Working with linear functions in four complementary ways: words, tables, graphs, and equations (
Chapter 5
)
Solving systems of equations (both linear and non-linear), and identifying when linear systems have either no solution or infinitely many solutions (
Chapter 6
)
In Part 2, I cover all of these topics in depth.
Problem Solving and Data Analysis
Problem Solving and Data Analysis focuses on a relatively short list of problem-solving techniques:
Working with ratios, proportional equations, and percentages (
Chapter 7
)
Relying on a basic understanding of statistics and probability (
Chapter 8
)
Applying these techniques to information presented visually in tables and graphs (
Chapter 9
)
Part 3 focuses exclusively on these ideas.
Advanced Math
Advanced Math requires you to understand a core of information covered in high school Algebra II:
Working with functions using notation, and knowing how to graph a core of basic functions and their most elementary transformations (
Chapter 10
)
Understanding how to work with and graph polynomials, especially linear, quadratic, cubic, and quartic polynomials (
Chapter 11
)
Graphing quadratic functions using standard, vertex, and factored forms (
Chapter 12
)
Graphing exponential and radical equations (
Chapter 13
)
Part 4 covers these Advanced Math topics.
Geometry and Trigonometry
Geometry and Trigonometry covers math that focuses on shapes and solids in two and three dimensions:
Solving problems using basic geometry and circles on the
xy
-plane (
Chapter 14
)
Working in-depth with right triangles, the Pythagorean theorem, and trigonometric ratios such as sine, cosine, and tangent (
Chapter 15
)
I provide this information in Part 5.
SAT Math Strategy
When it comes to doing well on the SAT, your test-taking strategy is a small but important piece of the puzzle. And this strategy also extends to knowing which questions to answer and which to skip, depending on the score you’re currently striving for.
In this section, I fill you in on this essential information.
Isn’t there some way to get a good SAT Math score without actually knowing math?
No.
I’d love to tell you otherwise, but no.
If the key to getting a great score were, say, choosing Answer C on every question, the name of this book would be Answer C Math For Dummies and it would be a lot shorter.
While you fully absorb that difficult truth, I will add that there’s a reasonable amount of strategy you should absolutely know before taking your first SAT. And while you may think that lots of students already know this stuff, plenty of others don’t — yet.
I don’t want you to be one of them.
So read on.
Is there a penalty for guessing?
If you have an older brother or sister who took the SAT before 2016, they may remember the old format, which had a penalty for filling in a wrong answer.
So please take note: The SAT in its current form has no penalty for filling in a wrong answer. This goes for all four sections, the Reading and Writing as well as the Math sections.
Obviously, then, you want to make sure that you fill in at least some answer for each multiple-choice question on the two Math sections. That’s 33 questions, so by pure chance, you can expect to get about 8 of these questions right just by making wild guesses.
Let’s take that thinking a step further: If you don’t fill in guesses for all the questions you don’t have time to think about, you’ll be competing against a ton of other students who are guessing. So, bottom line, you can’t afford not to guess every multiple-choice question you don’t know the answer to.
What about the fill-in-the-blank questions? Well, because these questions are entirely open ended, you don’t have much chance of answering them correctly with a wild guess. But if you have any idea what the answer might be, go ahead and enter it. Worst case, doing this won’t lose you any points.
Are some questions harder than others?
Generally speaking, SAT Math questions fall into three categories of difficulty: easy, medium, and hard. Both sections of the new SAT are identical in this regard. Table 1-2 shows the rough breakdown of questions by difficulty levels.
TABLE 1-2 Easy, Medium, and Hard Questions
Difficulty Level
Question Number
Easy
1-7
Medium
8-16
Hard
16-22
Remember that every question counts for one point toward your raw score, which directly affects your scaled score (200–800). So, unlike the tests you take in school, the easiest and hardest questions on the SAT both have the same value.
Do I have to answer every question?
The short answer is, no, you don’t have to answer every SAT Math question to get a good score.
In fact, depending on your current performance level on practice tests, it may very well be to your benefit not to answer all of the questions.
This piece of strategy definitely goes against a lot of your training as a high school student. After all, in most of your classes, you can’t get an A or even a B on a test without answering just about all of the questions. If you only answer 75 percent and skip the rest, even if you answer perfectly, probably the best you can hope for is a C.
However, the situation with the SAT is entirely different.
On the SAT, you can get a 500 Math score by answering only about 60% of the questions on the test correctly. Think about it — a respectable score on the SAT would be a failing grade on a math test at school!
I dive more deeply into this aspect of strategy later in this section, when I ask you to consider your own personal starting point, path, and goal for the SAT.
For now — and this goes double if you’re a perfectionist — simply let go of the compulsive need to answer all 44 math questions on the SAT. Until you’re already scoring 740+ on your practice tests, answering all of the questions would likely be a poor allocation of your time. If you’re answering all of the questions, you’re probably rushing through questions that are within your reach, getting them wrong, and losing points you should be gaining.
So, how many questions should I answer?
The answer to this question depends on your current score, which I break down into three basic scenarios.
Clearing 500
Most colleges and universities prefer to enroll students who have an SAT composite score of at least 1,000, which is approximately 500 on both the Reading and Writing and the Math tests.
If you're Reading and Writing score is 550 or higher, you may be able to get away with a Math score that’s slightly less than 500. Even so, a good first goal would be to break 500 on the Math test.
To get this score, you need to answer about 26 of the 44 SAT math questions correctly. To this end, refer to Table 1-1, and then plan to do the following:
Attempt to answer
all
14 easy questions correctly.
Choose 12 out of 16 medium questions to attempt to answer and guess the rest.
Guess on the 14 hard questions.
I know it seems weird to guess so many questions. But the SAT is different from the tests you take in school, where you need to get at least 80 percent right to get a decent grade.
Choosing 26 easy and medium questions to focus on gives you almost two and a half minutes per question, which increases your chances of answering more questions correctly. And remember that you have a 25 percent chance of guessing each hard multiple-choice question correctly, which will give you some wiggle room to make a few mistakes along the way with the easier questions.
Believe me, in my experience working with hundreds of students, if you’re simply trying to break 500, you probably need to give yourself more time by answering fewer questions.
Breaking solidly beyond 600
At the next level are students applying for colleges that strongly encourage a composite SAT score of 1,200 or more. That means aiming for at least a 600 score in Math, which requires approximately 33 correct answers, which is 75% of the questions.
Here’s what I recommend (again, referring to Table 1-1 for question difficulty):
Attempt to answer
all
14 easy questions correctly.
Attempt to answer
all
16 medium questions correctly.
Choose 3 of the 14 hard questions to attempt to answer, and guess the rest.
As when breaking 500, you still have a 25% shot at answering each hard multiple-choice question.
Reaching 700 and beyond
If you’re striving to break 1,400 or even 1,500 on your SAT composite score, you know that there’s no easy answer. You’ll want to get a Math score of 700 or more, with a little wiggle room if you’re confident of scoring 750 or more on the Reading and Writing test. This means answering about 38 out of 44 math questions correctly, which is just enough questions to clear 85%.
Attempt to answer
all
14 easy questions correctly.
Attempt to answer
all
16 medium questions correctly.
Choose 8 of the 14 hard questions to attempt to answer and guess the rest.
OK, we both know that if you’re aiming to break 700, you may not feel comfortable strictly “guessing” 8 hard questions. But please, please, please don’t feel you have to answer every question! With limited time to allocate, almost every student will do better to focus on a subset of the hard questions and get them right rather than waste time on the two or three hardest questions they'll probably get wrong anyway.
The good news is that you’re obviously a strong student with a well-practiced set of study skills. I recommend getting a private tutor if you don’t already have one (but you already have one, don’t you?) Take as many practice tests as you can, and then comb through your incorrect answers and do your best to figure out where you went wrong. If your math teacher is supportive, bring especially hard SAT problems to them — they’ll almost certainly be willing to help!
When’s the latest I can take the SAT and still get into school?
Most students take the SAT with their class in May or June of their junior year. They may try it out before that, but somehow, it doesn’t feel real until their whole class is doing it, too.
But if that’s the beginning, it doesn’t have to be the end.
Usually, December of your senior year is your last shot at the SAT if you want to start college the following fall. Unless you’re applying for early acceptance, most colleges don’t make their final decisions until after the December SAT scores have been posted.
Hey, wait — do I even have to take the SAT to go to college?
I've saved this question for last because if you've read this far, you're clearly an engaged student who's looking for a quality answer to this question rather than an easy one. But in these obviously changing times in education — both in the U.S. and throughout the world — this is a valid question that's worth thinking about.
The short answer is “Definitely maybe.”
Even before the Covid-19 pandemic began, a significant number of U.S. colleges and universities had started de-emphasizing the SAT in their entrance requirements and, in some cases, dropping the requirement altogether. And most of them had already begun accepting the ACT in place of the SAT to fulfill this requirement.
The pandemic mostly accelerated this trend.
So a slightly longer answer to the above question would be, “Check the current requirements for the college(s) you're applying to.” These requirements may be in flux for the next few years, so stay attuned to any changes as they may be announced.
But here’s the thing. Since the end of the pandemic, even though a lot of colleges and universities are still SAT optional, many students applying to these schools are opting to take the test. And in most cases, that decision should give them an advantage over students who choose not to take it.
As for my own humble opinion, I would say that a good SAT (or ACT) score is still likely to open the ivy-draped gates you seek to enter for the foreseeable future. Entrance exams such as these have been around for a long, long time. Arguably, they aren't the best statistical indicator of future college success. (That, by the way, would be past success in high school — so keep those grades up!) But large educational institutions — and the institution of education as a whole — tend to be about as responsive and quick to change course as aircraft carriers.
Furthermore, even as colleges weigh the pros and cons of their SAT/ACT requirements, some state school systems have begun requiring the SAT as part of their high-school graduation requirements. And this trend appears to be growing in popularity, at least for the time being.
So to sum up, while your grandchildren may not end up having to take the SAT, if you want to keep your educational options open, you probably won't have the same luxury.
Three SAT Success Stories
Finally, here are three SAT success stories from my recent years of teaching and tutoring. Each of them is a composite of several similar students, with the names changed and all that. But I’m very proud of them all!
Jay’s story — clearing 500
When Jay started studying with me, his goal was very straightforward. A gifted lacrosse player, he was already being recruited by a coach at a college where several of his former teammates were already going. They loved it, and he wanted to join them.
So his high school plan was simple: play hard on the lacrosse field, keep his grades up, and break 1,000 on the SAT.
Jay and I worked together for two or three months, and when he took the test for the first time, he got a 520 in English and a 510 in Math. With a 1,030 composite SAT score to work with, the coach advocated for him, and Jay received an early acceptance letter a few weeks later.
As much as he enjoyed working with me on SAT Math, he was done. As I write this, he’s the captain of his college lacrosse team.
Shaun’s story — breaking solidly beyond 600
I met Shaun when he was a sophomore, in an SAT class full of all juniors and seniors. He was likeable, quirky, and smart, definitely holding his own in a class full of kids one and two years older than him. His real interest was engineering, and he had a garage full of cool projects in various states of completion.
After the SAT class was done, I started working with him one-on-one over the summer between his sophomore and junior years. He did well on the practice tests, but missed math questions he should have gotten, mostly because he misread the question or made a minor calculation error.
He and I worked together to solidify his skills in the areas of math that most SAT questions focus on: linear functions, linear systems of equations, and quadratic functions. I also encouraged him to spend more time answering the easy-to-medium questions and skipping over the difficult, time-consuming ones.
Shaun thought he was ready to take the SAT for real at the beginning of his junior year. His father thought he needed more practice. I recommended that he take it, if only to resolve their difference of opinion with an actual score. On his first try, he got a 1,340 — 680 in English, 660 in Math.
“If you’d like to break 1,400,” I suggested, “we can keep on going.”
But instead, Shaun just kept his grades up, applied to a good engineering program, and got early acceptance. Case closed.
Amy’s story — reaching 700 and beyond
Amy was a bright student, at the top of her class at a very competitive private school. She was already just about killing her SAT practice tests when I began to tutor with her.
We worked together for three or four months, and then she took the SAT with the rest of her class in May of her junior year. On her first try, she got a 750 in English and a 730 in Math.
For any other student, that would have been the ballgame. For Amy, getting a 1,480 just about drove her crazy. “Twenty more points! That’s all I need!”
We continued through the summer, and she worked tirelessly. For a day or two, just a couple weeks before the August test, I thought she might crack. “You don’t have to do this,” I explained, “You already have an amazing score. But if you’re going to the SAT Olympics, I’m going to coach you at that level.”
She pressed on, took the test — and got a 1,530 composite, with a 770 in English and a 760 in Math. With her grades, extra-curricular activities, and a tremendous common app essay, she was accepted to her first-choice Ivy League school. I bet you’ve heard of it!
