Digital SAT Math Ultimate Guide – Crack the SAT Math
In this Digital SAT Math Ultimate Guide, we’ve listed what’s tested on SAT Math, how to prepare for a higher Digital SAT Math Score, different types of questions you may see on SAT exams, common mistakes students make, and all frequently asked questions by SAT exam students.
In this article
šĀ Hint:Ā Do not skip this article, you will findĀ FREE Digital SAT Math Prep resourcesĀ throughout the article.
SAT stands for Scholastic Aptitude Test. Every year, nearly two million students sit for the SAT exam. A high SAT score is vital to getting you to the college you dream of. After teaching thousands of students, we’ve experienced that most students falter in the SAT Math Prep. Therefore, we’ve prepared this Digital SAT Math Ultimate Guide. This guide will help you to reach your target scores.
What is the Digital SAT?
Recently, the SAT exam structure changed, and the new exam is called Digital SAT. The new format of the SAT is more studentfriendly, so no need to be afraid of the recent changes. The Digital SAT measures the knowledge and skills that students are learning in school and that matter most for college and career readiness. College Board, the administrator of the SAT exam, states that the Digital SAT exam will be easier to take, easier to give, more secure, and more relevant.
š”You might be interested in reading theĀ 7Step Digital SAT Math Study GuideĀ post!
The biggest change in the Digital SAT is adaptive testing.Ā In the previous paper format, all SAT exam questions were fixed when you started the test. However, in the digital SAT, the adaptive testing will show you mediumdifficulty questions first, if you answer them correctly, the next questions will be getting harder. Similarly, as you answer wrong, the next questions will get easier.
Digital SAT Adaptive Testing Model
SAT is divided into two equallength and separately timed stages, each composed of a module of questions. As illustrated in the figure below, students begin each test section by answering the set of questions in the first module. This module contains a broad mix of easy, medium, and hard questions that allow students to demonstrate their achievement before moving on to the second module. The questions in this second module are broadly targeted to the test takerās achievement level based on how they performed in the first module; questions are either (on average) higher difficulty or lower difficulty than questions in the first module. This means that the test āadaptsā to present questions that are more appropriate to a studentās performance level.
The following figure depicts the Digital SAT adaptive testing model.
Anna B. Scored 800 on SAT Math!
Anna B. is one of our thousands of successful SAT students. She scored 800 on SAT Math. You can watch her SAT story.
Digital SAT Math Modules
There are two Math modules in the Digital SAT exam. Digital SAT Math is a twostage adaptive test and one Math section administered via two separately timed modules. Module 1 and Module 2. Each module consists of 22 questions. 20 of these questions are operational and scored. 2 of the questions are for pretest and for testing purposes of College Board, and not scored. However, students will not know which questions are operational and which ones are for pretest. Therefore, answer each question carefully.
The total time allotted for each Math Module is 35 minutes. In total, you will be allowed 70 minutes to answer 44 SAT Math questions. The calculator is allowed in both Math modules and there will be two types of questions:
 Discrete; fouroption multiplechoice:Ā Approximately 75% of the questions will be this type. There will be four options and only one of the options will be true. Students should select the correct answer.
 Studentproduced response (SPR): Approximately 25% of the questions will be this type. The student will have to do the solution and type the answer.
Note that, there might be questions including science, social science, or realworld stimulus topics as well. For instance, the following is an example SAT Math question.
SAT Math Example Question Including a Stimulus Topic
A sample of oak has a density of 807 kilograms per cubic meter. The sample is in the shape of a cube, where each edge has a length of 0.90 meters. To the nearest whole number, what is the mass, in kilograms, of this sample?
A) 588
B) 726
C) 897
D) 1,107
For example, this question refers to density. To solve this question, the student must know that
Note: The answer and rationale for this question are at the end of the post in Appendix 1.
Free Digital SAT Math Prep Course
SFBS offers a Free Digital SAT Math Prep course. The course goes through a particular skill and knowledge testing point and improvesĀ your problemsolving skills and testtaking strategies.
Summary of Format and Delivery of the Digital SAT Math
We prepared the following table to summarize the format and delivery of the SAT Math sections.
Format  Question Types  Stimulus Topics  Test Length  Time Per Module  Number of Questions  
Module 1 
Twostage adaptive test design: one Math section administered via two separately timed modules

Discrete; fouroption multiplechoice (ā75%) and studentproduced response (SPR) (ā25%)

Science, social science, realworld topics

20 operational questions and 2 pretest questions  35 minutes  22 
Module 2  20 operational questions and 2 pretest questions  35 minutes  22  
Total  40 operational questions and 4 pretest questions  70 minutes  44 
Digital SAT Math Content Domains, Skills, and Knowledge Testing Points
College Board assesses the studentsā attainment of critical college and career readiness knowledge and skills in math in math sections of the Digital SAT.
SAT Mathematics covers four content domains.
 Algebra. In this domain, SAT measures the ability to analyze, fluently solve, and create linear equations and inequalities and analyze and fluently solve equations and systems of equations using multiple techniques. You might be interested in seeing our SAT Algebra post. It covers the hack points you should know and 31 SAT Algebra Practice Questions!
 Advanced Math. This domain measures skills and knowledge central for progression to more advanced math courses, including demonstrating an understanding of absolute value, quadratic, exponential, polynomial, rational, radical, and other nonlinear equations. You might be interested in seeing our SAT Advanced Math post. It covers the hack points you should know andĀ 27 SAT Advanced Math Practice Questions!
 Problemsolving and Data Analysis. In this domain, SAT measures the ability to apply quantitative reasoning about ratios, rates, and proportional relationships; understand and apply unit rates; and analyze and interpret one and twovariable data. You might be interested in seeing our SAT ProblemSolving and Data Analysis post. It covers the hack points you should know and 15 SAT ProblemSolving and Data Analysis Practice Questions!
 Geometry and Trigonometry. This fourth domain measures the ability to solve problems focusing on area and volume; angles, triangles, trigonometry; and circles. š”You might be interested in seeing our SAT Geometry and Trigonometry post. It covers the hack points you should know and SAT Geometry Practice Questions!
š”You can see our Free SAT Math Exercises which has 50 exercises on all SAT Math domains.Ā
Watch SAT Math Prep Online Course – Sample Lecture on YouTube
We have a sample 8minute video lecture from our SAT Math Prep Online Course on YouTube. You can watch below.
SAT Mathematics Content Domains, Skills, and Knowledge Testing Points
Under each content domain, there are several skills and knowledge testing domains with a total of 19 skill and knowledge testing points. The following table summarizes the Digital SAT Math contain domains, each skill and knowledge testing point under each content domain and approximately how many questions appear from each content domain.
Content Domains  Algebra  Advanced Math  Problemsolving and Data Analysis  Geometry and Trigonometry 
Skill and Knowledge Testing Points

Linear equations in one variable  Equivalent expressions  Ratios, rates, proportional relationships, and units  Area and volume 
Linear equations in two variables  Nonlinear equations in one variable and systems of equations in two variables  Percentages  Lines, angles, and triangles  
Linear functions  Nonlinear functions  Onevariable data: distributions and measures of center and spread  Right triangles and trigonometry  
Systems of two linear equations in two variables  Twovariable data: models and scatterplots  Circles  
Linear inequalities in one or two variables  Probability and conditional probability  
Inference from sample statistics and margin of error  
Evaluating statistical claims: observational studies and experiments  
Number of Questions  13 to 15 questions.  1315 Questions  57 Questions  57 Questions 
Once you grasp the details of how to approach each skill and knowledge testing point question, you will double your chances of reaching an 800 score on the SAT Math test.
š”You might be interested in seeing our Digital SAT Math Practice Test. It covers the hardest questions you may see on the SAT Math exam for each skill and knowledge testing point!
SFBS Digital SAT Math Prep Through Questions Program
San Francisco Business School offers a comprehensive Digital SAT Math Prep program taught by 99thpercentile SAT Instructors and exam experts. The program cracks down each content domain and 19 skills and knowledge testing points through 322 realistic Digital SAT Math questions. You will see all the different types of questions that may appear in Digital SAT.
How Hard Are the Actual Digital SAT Math Questions?
In your actual Digital SAT test, there will be two Math sections and in each, there will be 22 questions. You will be allowed to use a calculator in each module. The Digital SAT is an adaptive exam. It starts with easy questions, and as you answer each question correctly, the difficulty of the questions will get harder. Since it is a computeradaptive test, it is crucial to respond to the first questions in the exam correctly.
College Board categorizes the Digital SAT Math questions into three difficulty levels: easy, medium, and hard.Ā Ā Typically, the Digital SAT exam starts with mediumdifficulty questions, and depending on the correct or wrong answers of the testtaker, the rest of the questions appear.
Below, we shared three easy, medium, and hard questions respectively. To provide consistency, we used all questions from the same content domain, Algebra, and the same skill and knowledge testing point, linear equations in one variable.
SAT Math EASY Question Example š¢
What is the solution to the equation
A. 1
B. 3
C. 5
D. 15
Note: The answer and rationale for this question are at the end of the post in Appendix 2.
SAT Math MEDIUM Difficulty Question Example š”
How many solutions does the given equation have?
A. Exactly one
B. Exactly two
C. Infinitely many
D. Zero
Note: The answer and rationale for this question are at the end of the post in Appendix 3.
SAT Math HARD Question Example š“
The equation 9x + 5 =a(x+b), where a and b are constants, has no solutions. Which of the following must be true?
I. a = 9
II. b = 5
III. b ā
A. None
B. I only
C. I and II only
D. I and III only
Note: The answer and rationale for this question are at the end of the post in Appendix 4.
š”You might be interested in seeing our Digital SAT Math Practice Test. It covers the hardest questions you may see on the SAT Math exam for each skill and knowledge testing point!
Frequently Asked Questions About the Digital SAT
We’ve listed some common frequently asked questions of SAT students below.
What changed from the Paper version of the SAT to the Digital SAT?
The topics and content of the SAT exam did not change. However, the questions and their structure have changed. Most sections now ask fewer questions and take less time. In the paper SAT, there were 500+ words long passages asking ~10 questions for each passage. In the Digital SAT, passages are around 100 words and they ask only one question per passage.
The Digital SAT is “module adaptive,” meaning that how you perform on the first module determines the difficulty of the 2nd module. For example, if you do well in Digital SAT Math Module 1, you’ll see harder questions in Math Module 2.
In the paper SAT, Reading and Writing used to be separate sections. In the Digital SAT, they are now combined.
The paper SAT had a “no calculator” math section. In the Digital SAT, a calculator can be used on any math question.
š San Francisco Business School offers a vast amount of FREE Digital SAT Prep Online materials. See it on the Free Digital SAT Prep Online Library.
Is the Digital SAT easier than the old version paper SAT?
Yes, the digital SAT is easier than the paperandpencil version according to students who have taken the exam and experts at College Board. As mentioned by Priscilla Rodriguez, College Readiness Assessments at College Board: āThe digital SAT will be easier to take, easier to give, and more relevantā.
How much should I score on the Digital SAT?
The maximum score a student can get on the SAT is 1600, and the minimum score is 400. While the average SAT score is around 1060, the SAT score you need depends on the school you dream of. If you are dreaming of an Ivy League university or college, you need to score over 1400.
Weāve listed some of the colleges’ SAT score percentiles below. You can look for otherĀ Collegesā SAT Score Percentiles and Acceptance rates in our post.
College  SAT Score Percentiles 
Cal Tech  1530 ā 1580 
Harvard  1460 ā 1580 
MIT  1510 ā 1580 
Yale  1460 ā 1580 
Stanford  1420 ā 1570 
University of Michigan  13401560 
Boston College  1330 ā 1500 
U.S. Military Academy  1210 ā 1440 
Purdue  1190 ā 1430 
Penn State U.Univ. Park  1150 ā 1340 
Univ. of Miami  1250 ā 1420 
For instance, if you are planning to apply to Boston College, you should be scoring around 1330 and 1500. Note that, that is the average of all college applications.Ā If you are planning to apply for a popular department of a college, you need to score more than these averages.Ā For instance,Ā Economics, Finance, and Computer Science are popular departments at Boston College. Therefore, the score percentiles of the accepted students in these departments are expected to be above the 1330 ā 1500 range.
Depending on your initial result, if there is a huge gap from the target score, you should be studying harder.
Where can I take the Digital SAT?
You can take the digital SAT at a school or test center. A proctor will be present during the test. You cannot take the digital SAT at home.
How long is the Digital SAT?
Digital SAT lasts 2 hours and 15 minutes without the essay. The test has four sections:
 Reading & Writing Module I
 Reading and Writing Module II
 Math Module I
 Math Module II.
With the digital SAT, a calculator is allowed in both of the Math modules.
Can I use scratch paper when I am taking the digital SAT?
Yes, scratch paper will be provided to you on test day.
What Kind of Devices Can I Use to Take the Digital SAT?
Students can take the digital SAT Suite tests on a wide range of devices, including their own laptops (Windows or MacOS), iPads, schoolowned desktops and laptops, and schoolmanaged Chromebooks. Students will take the digital SAT Suite using a custombuilt digital testing application that theyāll download in advance of test day.
Make sure you bring your device fully charged on the exam as there may not be enough power outlets in your testing room.Ā The SAT exam application works even if internet connectivity drops. Therefore, your exam progress won’t be affected by internet outages.
If you do not have your own device, students taking the SAT on a weekend who do not have access to a device can request to borrow one from the College Board. College Board will provide one for use on test day. You must request a device when you are registering for the SAT.
What Are the Tools Provided in the SAT Exam?
The digital testing application will include many test tools for students. Examples include:
 Mark for review: Students can flag and return to any question within a given test module they want to come back to later.
 Testing timer: A clock counts down the time remaining in each module. Students can hide the timer, and they get an alert when 5 minutes remain in the module.
 Calculator: A builtin graphing calculator is available in the entire Math section. (Students can also bring their own approved calculator.)
 Reference sheet: In the Math section, students have access to a list of common formulas.
 Annotation: Students can highlight any part of a question and leave themselves a note.
How many times can I take the Digital SAT?
We recommend taking the PSAT or a practice test your sophomore year. You can plan to take the SAT in the spring or winter of your junior year. This will leave you some time to get ready and take it again if you are unhappy with your first results.
What is the validity of the Digital SAT?
Once you get SAT scores, your scores are good for 5 years. If you took the SAT more than 5 years ago, you need to retake the SAT.
Appendix 1: Answer & Rationale for SAT Math Example Question Including a Stimulus Topic
Answer: A
Rationale: It’s given that the shape of the oak is a cube and each edge has a length of 0.90 meters. The volume of a cube formula is as follows:
Appendix 2: Answer & Rationale for SAT Math š¢ EASY Question Example
Answer C.
If we subtract 5 from both sides of the given equation;
Appendix 3: Answer & Rationale for SAT Math š” MEDIUM Difficulty Question Example
Answer C.
If two sides of a linear equation are equivalent, then the equation is true for any value. If an equation is true for any value, it has infinitely many solutions.
Since the two sides of the given linear equation
Appendix 4: Answer & Rationale for SAT Math š“ HARD Question Example
Answer D.
Rationale: If we expand the right side of the equation;
9x + 5 = ax + ab.
For a linear equation in the form of ax + b = cx + d, if the coefficients of x are the same and if the remaining terms are not equal, there are no solutions. Therefore;
If a = 9; and ab ā 5, there are no solutions. ā I is true.
If a is 9, ab = 9b ā 5Ā ā b ā
š”You can see our SAT Math Exercises which has 50 exercises on all SAT Math domains. It’s for FREE!
Disclaimer: SATĀ® is a registered trademark of the College Board, which is not affiliated with San Francisco Business School and was not involved in the production of, and does not endorse this product or website.