Since the spring of 2024, the SAT has shifted to a digital format, forgoing the traditional pencil-and-paper format it’s used since it was first administered as an army IQ test, nearly a century ago. This means some important changes are taking place in the Digital SAT Math Test!

Although the Reading and Writing test has gotten the more obvious overhaul between the two SAT sections, the Math exam has also undergone some very important content changes. In this article, we’ll delve into the differences between the math tests on the old SAT versus the new, digital SAT format, including an exhaustive breakdown of content and skills tested in the math section of the Digital SAT.

**What has changed on the Digital SAT Math Test?**

Although the majority of this article is a deep-dive into the content covered by the new Digital SAT Math Test, it’s worth first considering the changes between the previous version of the test and this one, in order to contextualize the content on the exam.

**Calculators**

Get your TI-84s ready, because perhaps the most important change in the new Digital SAT Math Test is the elimination of the “no calculator” section! Never again will students have to face SAT math calculator-less.

Previously, the Math Test was divided into two sections: a no-calculator section and a calculator section. Now, the Digital SAT Math Test is divided into two even modules, during which students will have constant access to a calculator.

Desmos, a graphing calculator web application, will be available *within* Bluebook, College Board’s test taking software. Students who prefer to use their own personal devices should double check to make sure that their calculator is on College Board’s list of approved devices. If you want to see what the Bluebook Desmos calculator will look like, practice with it on the Desmos website!

**Test Length**

The other major change to the Digital SAT Math test is its length. Overall, College Board has managed to significantly decrease the amount of time students will spend taking the test (from about 4 hours to about 2 hours), while *increasing* the time per question by limiting the number of questions students will see.

Previously, students had 55 minutes to complete the calculator section of the test— at 38 questions, it gave them a little more than 86 seconds per question. This might not sound like a lot, (less than a minute and a half!), but the no-calculator section required an even faster pace: students had to answer 20 questions in 25 minutes, an average time of 75 seconds per question.

Despite being 10 minutes shorter overall than the previous math test, the Digital SAT Math test increases the time per question that students get: each of the two math modules consist of 22 questions that students have 35 minutes to answer. This gives students an average time of about *95 seconds per question *on the Math portion of the Digital SAT.

The new length is great news for students who experience test fatigue, or those who rely heavily on checking and circling back to answers. But remember, in this new test, each question is weighted more heavily than in previous tests—a few wrong answers might affect a student’s score much more than they could in the past!

**Types of Questions**

Largely, the content of the Digital SAT Math section has remained the same as it was on the paper-and-pencil test, with a few differences.

First, let’s discuss word problems. These questions, which include short paragraphs of text meant to contextualize the mathematical operations students are asked to perform, account for about 30% of all questions on the Digital SAT Math Test. This is fairly similar to the old SAT; however, the majority of these questions will now be capped at 50 words. On the old SAT math test, students commonly saw much longer questions.

Now let’s talk about actual content changes. Previously, the SAT was composed of four distinct topic sections: Heart of Algebra, Passport to Advanced Math, Problem Solving & Data Analysis, and Additional Topics in Mathematics. These have been modified slightly for the new Digital SAT Math Section, and are now labeled: Algebra, Advanced Math, Problem Solving & Data Analysis, and Geometry and Trigonometry.

Content-wise, the succinctly–named Algebra and Advanced Math topics are generally the same, though Advanced Math will now test on absolute value functions, a topic which was absent from the previous test. The Problem Solving & Data Analysis category has remained largely unchanged, in both title and content.

The greatest change is on the previous Additional Topics in Mathematics section, now labelled Geometry and Trigonometry. Functionally, this change does less to affect the content of the section than might first be thought—students will see more area and perimeter questions, and perhaps a few more angles questions than before, but largely the two categories test the same skills. That being said, students now won’t have to worry about complex numbers, which was a concept that used to be tested in this section.

**What does the Digital SAT Math Test cover?**

Now, to dive more deeply into what is covered on the Digital SAT Math Test. This section is organized by the four major question categories, with a breakdown of the skills and concepts tested in each and sample questions that students might encounter on the test.

Unlike the Reading and Writing Test, Digital SAT Math Test question categories don’t appear as distinct sections on the test; rather, questions that fall into each category are mixed up *throughout* the exam. The main organizing principle of the Digital SAT Math Test is a general move from easier questions to more difficult ones.

This means that as students work through the test, they should remember to bank time for the questions at the end—they’re likely to need it!

**Algebra**

Questions that fall within the Algebra category account for about 35% of the test, or about 13-15 questions across two modules. This makes it one of the most common question types on the test.

Although students will see some Algebra questions in the harder second half of each module, these are largely considered a little easier than Advanced Math questions. Algebra questions will largely be testing skills covered in mostly Pre-Algebra and Algebra I courses.

#### What skills are tested in Algebra questions on the Digital SAT Math Test? This is College Board’s official list of Algebra question topics:

- Linear equations in one variable
- Linear equations in two variables
- Linear functions
- Systems of two linear equations in two variables
- Linear inequalities in one or two variables.

The main concepts tested here are linear equations. Many questions focus on modeling equations, identifying the role of variables and other elements within the equation, and solving simple equations and simple systems of equations. (Note that “simple” in this context denotes the lack of terms with exponents, not the difficulty of the questions, since some of these can be difficult!)

**Sample Algebra Questions on the Digital SAT Math Test**

This is one of the easier Algebra questions students will encounter. Here, they are provided a linear equation and asked which option has the same solution.

Although this might typically be done by checking each equation in each answer option, that’s not necessary here. Instead, the only thing that needs to be done is to subtract 6 from each side of the given equation. This reveals an equation 4*x* = 12, that is the same as option C.

Remember, even with more time per question provided for the Digital SAT Math Test, one of the most important things to think about as students are testing is conserving time. Always try to minimize the actual calculations that must be done in order to reach the correct answer!

Now, let’s look at two examples of questions where students are given different kinds of information and asked to develop a linear equation from it:

In this example question, students see a word problem and have to extrapolate the necessary data in order to turn it into a mathematical representation. This is a skill called *modeling*, that is, modeling an equation based on real-world scenarios.

In this case, students must know that the rate at which Juan cycles must be multiplied by the number of miles he cycles, in order to get the total number of minutes his bike ride takes, meaning option D is correct.

The next example above provides students with a graph of a line and asks them to select the equation for the line. In the same way the previous question tested students on understanding on how real-world details relate to the elements of a linear equation, this asks them to do the same thing with details from a graph, including intercepts and slope.

In order to properly answer this question, students must be familiar with the slope-intercept form of linear equations, *y* = *mx* + *b*. Using the *y*-intercept (-8) and the slope (-2), students can determine that the correct answer is A.

Before we move on to the next section, let’s consider one more example of a difficult Algebra question. This one is the third-to-last question in a module, meaning that it is a comparatively more difficult question, and one that will likely take longer to answer.

Here, students must combine skills that previous, easier Algebra questions may have tested discretely, including modeling equations and solving systems of linear equations.

To answer this question, students will have to use the real-world information provided to model two equations, *x* + *y* = 21 and 60*x* + 80*y* = 1440, and solve for *x* (the number of children in the group), resulting in the answer 12, which is C.

**Advanced Math**

The next category of question on the Digital SAT Math Test is Advanced Math, which, as the title suggests, tends to be a little more challenging than the Algebra questions. About 35% of questions students encounter will fall into this category, which accounts for about 13-15 individual questions across two modules.

What skills are tested in Advanced Math questions on the Digital SAT Math Test? This is College Board’s official list of Advanced Math question topics:

- Equivalent expressions
- Nonlinear equations in one variable and systems of equations in two variables
- Nonlinear functions

Now, these are very broad testing points, so Piqosity has broken down these concepts further so students have a better understanding of what specifically they can expect to see on the test:

- Radical, rational, and absolute value equations
- Rearranging equations
- Quadratic functions and their graphs
- Exponential functions and their graphs
- Polynomials and their graphs
- Factoring expressions
- Nonlinear functions and their graphs
- Linear and quadratic systems of equations

Based on this breakdown, it should be clear that Advanced Math is pulling largely from Algebra I and II courses. Although students will encounter easy, medium, and hard questions in this category, overall they’ll skew a little more toward the middle and second half of each testing module than the Algebra questions did.

**Sample Advanced Math Questions on the Digital SAT Math Test**

Let’s begin by looking at a simple quadratic equation question. Quadratics are one of the most common questions students will see in this category. Here, students are presented with a quadratic equation and asked to determine the *x* value of the resulting parabola’s vertex (i.e. its minimum). If students use the vertex formula, they will get 7, which is the correct answer.

This is the first grid-in (or “fill-in”) question that we’ve encountered. When students encounter such problems, they should follow the SAT’s guidelines for writing out the answers. Typically, they shouldn’t use any symbols (except for a negative sign), should simplify fractions, and not use mixed numbers. Students can access the rules for fill-in responses throughout the test.

Let’s look at another example of an Advanced Math question:

Here, students are asked to determine which function best models the real-world example. Since the function is *increasing*, we can eliminate the first two options. Since it’s increasing by a percent of its previous value, the amount it’s increasing by is getting bigger and bigger each year. This means that the function must be exponential. The correct answer is, thus, C.

Now, let’s look at a rearranging equations question:

Here, students will have to rely on their knowledge of order of operations in order to rearrange the equation and isolate a specific quantity, in this case, *j*. This is a fairly easy example of such a question, where both sides of the equation simply need to be divided by 8, resulting in the correct answer D.

Finally, let’s consider a nonlinear function question:

In this question, students are presented with a graph of a nonlinear function and are asked to identify the value of *y* when *x* is equal to 0. This is a fairly easy question to answer, since students just need to refer to the provided graph to see that *y* = 3 when *x* = 0, which means D is the correct answer.

That brings us to the end of our Advanced Math sample questions. It’s important to reiterate that this is a broad category, and we can’t cover all the different question types students might encounter with only these four examples. Furthermore, for the sake of this article, we’ve highlighted some easy-medium questions, but these questions can get quite tricky.

Given the wide-ranging content that students are likely to encounter in this category of question, its difficulty, and the amount of Advanced Math questions that appear across the test, it is likely that most students should focus much of their studying efforts here.

**Problem-Solving & Data Analysis**

The third category that questions on the Digital SAT Math Test might fall into is Problem-Solving & Data Analysis. This is a wide-ranging category, into which most charts, graphs (ones not in the *xy*-plane, at least), and tables will fall into.

Percentage-wise, these questions account for a smaller portion of the total questions than the previous two categories we’ve considered. Only about 15% of the questions on the Digital SAT Math Test fall into this category, which equates to about 5-7 questions across two modules. These questions are pretty well spread out across the test.

#### What skills are tested in Problem-Solving & Data Analysis questions on the Digital SAT Math Test? This is College Board’s official list of Problem-Solving & Data Analysis question topics:

- Ratios, rates, proportional relationships, and units
- Percentages
- One-variable data: distributions and measures of center and spread
- Two-variable data: models and scatterplots
- Probability and conditional probability
- Inference from sample statistics and margin of error
- Evaluating statistical claims: observational studies and experiments

As should be clear from that list, this category is largely about data: reading data representations, calculating different statistical values like percent, probability, and ratios, understanding statistical concepts like margin of error, etc.

Students will also encounter questions that require them to understand how to perform unit conversions, and understand measures of center and spread (mean, medium, and mode).

**Sample Problem-Solving and Data Analysis Questions on the Digital SAT Math Test**

Here’s a very basic example of a data representation question, where students must analyze a bar graph. Here, they must identify how many students chose a certain option. The bar inquisition is a little below the 40 tick mark, meaning the correct answer must be between 35 and 40. The only answer that reflects this is 39, or B.

Let’s look at another type of data representation that students might encounter on the test:

Here, students have to understand how box plots represent data: that the line in the center of the box in box plots represents the *median* of the data. That means that in this case, answer C presents a true statement, since the median of group 1 is about 25 while the median of group 2 is about 24.

Now, let’s look at a very specific type of Data Analysis question on the test:

This is called a *data inference* question, where students must make an inference about a large data set, based on information sampled from a subset of that data set. Here, they’re asked to make an inference about the proportion of people that have a certain trait, based on the conclusions of a certain study with an accompanying margin of error.

These questions require students to understand that margin of error affects the *range* of likely values of a certain situation or outcome, in this case, the proportion of the population that has the trait. Since the study suggested that 0.49 of people have the trait, with a margin of error of 0.04, it means that that the *real* value could reasonably be anywhere from 0.45 – 0.53, or answer option A.

Beyond the examples shown here, students can also expect to encounter percentage, probability, rate, and ratio questions in this category, in addition to unit conversations. Like the last example, many of these questions won’t necessarily contain a visual data representation.

**Geometry & Trigonometry**

This brings us to the final question category in our deep-dive into the content of the Digital SAT Math Test. This category used to be called “Other Topics in Mathematics,” though now it has been narrowed to simply “Geometry & Trigonometry.”

Like Problem-Solving and Data Analysis, Geometry & Trigonometry questions account for 15% of all math questions, about 5-7 across two modules. Let’s dive into the content covered in this category.

#### What skills are tested in Geometry & Trigonometry questions on the Digital SAT Math Test? This is College Board’s official list of Geometry & Trigonometry question topics:

- Area and volume
- Lines, angles, and triangles
- Right triangles and trigonometry
- Circles

Unsurprisingly, this category mainly focuses on information covered in Geometry courses. There are also elements of trigonometry in this category, which is often taught in Pre-Calculus classes, though the level of difficulty of these questions remains largely at a geometry level (the two main trigonometric concepts that students should know are the right triangle trigonometric functions–sine, cosine, and tangent–as well as how to convert radians to degrees in a circle).

**Sample Geometry & Trigonometry Questions on the Digital SAT Math Test**

To begin, let’s take a closer look at this simple volume question. Although students will likely see questions that ask about perimeter, area, and volume formulas that they remember off the top of their heads (about squares, triangles, cubes, etc.), there will be a few that ask about shapes that students might not remember the formula for.

Don’t worry, though—unlike the ACT, the SAT is not interested in testing a student’s ability to remember specific formulas, but rather on their ability to *apply* those formulas. In light of this, students taking the Digital SAT Math Test will be provided a reference sheet that they can refer to as they work through the test:

Students should be familiar with the reference page, so they can quickly assess questions where it’s needed. Although this sheet will be *most* helpful when answering Geometry & Trigonometry questions, it can be used across the Math Test.

Using the formula listed for the volume of a cylinder, we know that the answer for the question will be π4^{2}(12). Or, 192π, which is option C.

Now, let’s look at an example of an angle question:

This is a very common type of question that students might encounter, and will depend on them using their knowledge of supplementary angles. Since supplementary angles must add to 180°, we can tell that the correct answer is 47°.

Remember, with fill-in answers, you don’t need to put in any symbols, so “47” is all that needs to be written.

Finally, let’s look at a harder question that deals with right triangle trigonometry:

Here, students will have to use their knowledge of similarity, trigonometric functions, and even ratios, in order to answer this question. Since trigonometric functions are ratios, it means that they will remain the same between similar triangles, even if the triangles aren’t congruent. This means that tan *W* will be equivalent to tan *T*. Since we know that tangent is the side opposite the angle over the side adjacent to the angle, we know that tan *T* is 440/384, which simplifies to 55/48, or option D.

**What is a Good Score on the Digital SAT Math Test?**

Like the old SAT, the digital SAT scores students on a 1600-point scale, with a student able to get a maximum score of 800 on the Math Test and a maximum score of 800 on the Reading and Writing Test.

What constitutes a good score on the SAT is highly dependent on what colleges a student is interested in applying to. Most schools will post the average range of scores that accepted students achieved on the SAT. Schools that have more selective admission processes will likely have higher ranges of SAT scores.

For example, many of the Ivy Leagues accept students with average scores in the 740-800 range for the Math Test, while a large state school, like the University of Texas, accepts students in the 610-770 range, with average score of accepted students being about 690. It’s important to remember that these are just average ranges, meaning that it is still possible for a student to be accepted at a school even if their scores are below this range, but having scores within or exceeding the range always makes an application stronger.

If a student is looking to break into the 600+ range of scores for the Digital SAT Math Test, they will have to reach the hard second module. If they receive the easy second module, they will have a difficult time scoring beyond 590. In order to reach the hard second module, students must answer approximately 60% of the questions in the first module correctly. This translates to about 12-14 questions out of 22.

Although the hard module has slightly harder questions, a student will almost certainly see an improvement in score by getting to this module, even if they answer the same number or slightly fewer questions correctly than they would in the easy second module. Although students should remain focused and attentive throughout the entire test, it’s very important they try their hardest during the first module so that they receive the score boost from reaching the hard second module.

**How to Improve Your Score on the Digital SAT Math Test**

There are a number of strategies that can be utilized quickly in order to improve standardized test scores, but ultimately, the best route is giving yourself enough time to properly prepare for the test.

The Digital SAT Math Test covers a wide variety of topics–since study time is limited, it’s important for students to focus their attention on 1) areas where they need the most improvement and 2) areas that show up the most frequently on the test.

This is where Piqosity can help—we offer a 26-question mini-diagnostic Digital SAT test that only takes about half an hour to complete. This is a great way to begin studying, as it gives students an estimated score and helps them determine which specific areas they might need improvement in.

In addition to our ACT test prep, ELA, and Math courses, Piqosity’s full Digital SAT course includes 12 full-length Digital SAT practice tests, 2 full PSAT practice tests, 1,000+ personalized practice Digital SAT Math questions, in-depth tutorial lessons with video explanations, and much more.

All of Piqosity’s Digital SAT content will be free to students until **August 24, 2024.** *Plus, by October 2024, Piqosity will offer 2 full-length PSAT 8/9 practice tests!*

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