# How to Solve Digital SAT® Math Problems Tricks and Strategies

The Digital SAT® Math Section tests a wide range of topics, spanning multiple years of math education. The breadth of the exam can make studying for it seem daunting. Thankfully, you can simplify this task by familiarizing yourself with the categorizations that the College Board® uses to group Digital SAT math question types. This grouping method is especially helpful for advanced math students, allowing them to focus their studies on unfamiliar domains. By tackling one subject at a time, they can learn Math Section strategies more effectively, rather than trying to tackle everything all at once.

Below, we've broken down the Digital SAT Math Section into its four official domains: Algebra, Problem Solving and Data Analysis, Advanced Math, and Geometry and Trigonometry. Read on for examples, questions, strategies, and tricks for each domain.

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## Algebra

Digital SAT's "Algebra" domain, formerly known as "Heart of Algebra," emphasizes linear functions, equations, and inequalities. Questions within this domain also involve systems of equations without any exponents or word problems related to rates (growth in size, price per unit, or speed).

Approximately 13-15 questions (35%) of all math questions on the Digital SAT are derived from this domain.

### Tricks and strategies to ace Algebra questions

The key to approaching linear functions correctly is understanding what they represent. Begin by drawing a graph or annotating an existing one. Graphs of linear equations help visualize slopes and intercepts, and the intersection of two such graphs provides the solution to a system of linear equations. If you’re unsure how to plot a graph for a given Algebra question, rewrite the equation in slope-intercept form.

• Slow Down for Complicated or Multi-Step Problems:

If you encounter an algebra question with many steps, it is vital to slow down. Take your time. Spend extra effort on complex problems to avoid making silly mistakes or missing a step.

• Practice Complicated Problems:

If you encounter a problem on test day that requires more steps than you expect or are accustomed to, it is easy to become overwhelmed. In your practice work, build up your confidence with these questions. Show your work and proceed slowly to avoid silly mistakes.

Specifically, learn your formulas! This is crucial. Memorizing the formulas is necessary for questions focusing on linear equations, absolute values, and graphs.

You can check your work on multiple-choice questions by testing your answer choices using the relevant formula. Testing the options in the answer choices is an excellent strategy for solving tricky equations and inequalities.

### Algebra examples

The solutions to which inequality are represented by the shaded region of the graph?

 A. y ≤ −2x − 4 B. y ≤ −4x − 2 C. y ≥ 2x − 4 D. y ≥ 4x − 2
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Hint:
The graph of a linear inequality of the form ymx + b has shading above a boundary line.
The graph of a linear inequality of the form ymx + b has shading below a boundary line.

Ryan used yarn to knit rows of a scarf.  The function w(r) = −4r + 840 approximates the length, in feet, of yarn Ryan had remaining after knitting r rows.  Which statement is the best interpretation of the y-intercept of the graph of y = w(r) in the xy-plane in this context?

 A. Ryan used approximately 4 feet of yarn for each row. B. Ryan had approximately 4 feet of yarn when he began to knit the scarf. C. Ryan had approximately 840 feet of yarn when he began to knit the scarf. D. Ryan used approximately 840 feet of yarn for each row.
Submit

Hint:
The linear function is in slope-intercept form y = mx + b, where m is the rate of change in quantity y per quantity x and b is the initial value.

p(−2x − 1) + x = 9x − 4

The equation above has no solutions.  If p is a constant, then what is the value of p ?

 A. − 9 / 2 B. −4 C. 0 D. 4
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Hint:
To find the value of p for which the given equation p(−2x − 1) + x = 9x − 4 has no solution, first rewrite the left side so that the equation is in the form ax + b = cx + d.

## Problem-Solving and Data Analysis

While all Digital SAT Math problems require problem-solving, this category refers to solving problems that rely on ratios, percentages, and the collection and use of one or two variables. You can recognize these questions by their reference to statistical terms like mean, median, and mode; their use of scatter plots and lines of best fit; their description of experiments and data collection or sampling methods; and their inclusion of percent or ratio relationships. Also, although only present on some exams, box-and-whiskers plot questions on the Digital SAT belong to this section.

This domain accounts for only 5-7 questions (15%) of the total Digital SAT math questions.

### Tricks and strategies to ace Problem-Solving and Data Analysis questions

As you prepare for this section, keep track of definitions for technical terms and, when referring to values or sets of values, learn how to calculate them. Digital SAT math questions frequently include wrong answers based on common errors or misconceptions. For example, if a question asks about the mean of a dataset, the answer choices will likely include the median. Once you've mastered the relevant vocabulary, you'll approach this domain more confidently and answer the questions with less distraction.

Another common challenge in this section is that the data points in these questions may appear randomly rather than in numerical order. When calculating statistical values like the median, numerical order is critical.  Therefore, reordering any values is always worth taking a few seconds.

### Problem-Solving and Data Analysis examples

The bar graph shows the number of points scored by a football team in each of four games. For these four games, how much greater is the median number of points scored than the mean number of points scored?

Hint:
The mean of a data set is the sum of the values divided by the number of values.
The median is the middle of a data set when all values are ordered numerically.

A small company classifies its employees according to how long they have been employed. Eight employees have worked at the company for less than 6 months and are classified in Group A. Nine employees have worked at the company for at least 6 months but no more than 12 months and are classified in Group B. Ten employees have worked at the company for more than 12 months and are classified in Group C. Which of the following could be the median amount of time, in months, that these 27 employees have worked at the company?

 A. 5.5 B. 7 C. 12.5 D. 16
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Hint:
The median of a data set is the middle of the set when all values are ordered numerically.

The scatterplot shows the relationship between two variables, x and y.  Of the following, which equation best represents the line of best fit shown?

 A. y = −11.7 − 0.6x B. y = −11.7 + 0.6x C. y = 11.7 − 0.6x D. y = 11.7 + 0.6x
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Hint:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

This domain covers a wide range of topics that go beyond the “Algebra” section and delve into Algebra II. Depending on the structure of your classes, it may also potentially touch on precalculus. Specifically, this category includes any nonlinear functions, expressions, or equations, such as quadratics, exponential and square root functions, and systems of equations with at least two variables. You can recognize these questions by their references to quadratics in any form, expressions with exponents or roots, and function notation— mainly composite functions (e.g., g(f(x))).

This domain accounts for 13-15 questions (35%) on the Digital SAT math exam.

### Tricks and strategies to ace Advanced Math questions

This category primarily focuses on higher-order functions and expressions, so familiarize yourself with the manipulation of different types of expressions you will encounter. For instance, solving or rewriting quadratic functions using techniques such as factoring, completing the square, and the quadratic formula will significantly enhance your comfort and consistency with these types of questions. Similarly, it's beneficial to understand how to rewrite exponents and roots in terms of each other, as this can simplify and make many equivalent expression questions easier.

Data sets X and Y are shown in the graphs above. Each data set consists of 18 integers. Which of the following statements must be true?

 A. Data sets X and Y have the same mean, but the standard deviation of data set X is greater than the standard deviation of data set Y. B. Data sets X and Y have the same mean, but the standard deviation of data set Y is greater than the standard deviation of data set X. C. Data sets X and Y have the same standard deviation, but the mean of data set X is greater than the mean of data set Y. D. Data sets X and Y have the same standard deviation, but the mean of data set Y is greater than the mean of data set X.
Submit

Hint:
The standard deviation of a data set is a measure of how spread out the data points are from the mean.

y = x2 + bx + c

In the equation above, b and c are constants.  The graph of the equation in the xy-plane has x-intercepts at x = −4 and x = 11.  What is the value of b ?

The complete graph of the function g is shown in the xy-plane above.  What is the y-intercept of the graph of y = g(x − 3) ?

 A. (0, 0) B. (0, 2) C. (0, 3) D. (0, 4)
Submit

Hint:
The y-intercept of a graph is the point where the graph crosses the y-axis.
Transform the given graph of g to get the graph of g(x − 3), and then find the y-intercept of the transformed graph.

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## Geometry and Trigonometry

This section asks a total of 5-7 questions (15%) on area, volume, parameters of lines, angles, circles, right triangles, and right triangle trigonometry.

### Tricks and strategies to ace Geometry and Trigonometry

As geometry and trigonometry make up the core of this domain, familiarity with geometric rules, theorems, and trigonometry is vital. In particular, be sure you can recognize how angle values relate to each other within sets of parallel lines or triangles, noting which angles must be congruent (equivalent) or supplementary (adding up  to 180 degrees). Circle theorems comprise a small portion of this section, so they do not appear on every exam. Still, many students need to familiarize themselves with how to arrive at the size and angles of a given circle, so once you're confident in the other categories, take time to memorize these applications.

### Geometry and Trigonometry in Math examples

In the figure above, line m is parallel to line n.  If y = 75 and z = 50, what is the value of x ?

 A. 50 B. 55 C. 60 D. 65
Submit

Hint:
When parallel lines are intersected by a transversal, they form pairs of corresponding angles that are congruent.

Two lines intersect as shown in the figure above.  What is the value of x ?

Hint:
When two lines intersect, they form pairs of vertical angles that are equal in measure.

In the figure above, angles PSQ and PSR are right angles.  What is the length of SR

Hint:
First use the Pythagorean theorem with right triangle PQS to find the length of segment PS.

## How To Fill Student-Produced Responses on Digital SAT Math

Most Digital SAT Math test questions come in the form of multiple-choice questions. However, some questions do not provide answer choices and require you to come up with an answer on your own. These types of questions are known as student-produced responses (SPRs), and students fill in their answers directly into the exam system. These questions evaluate your capacity to solve math problems independently with less guidance and structure than the multiple-choice format. SPR questions may offer multiple correct responses, but you must provide only one answer.

## Key Takeaways

Studying for the Digital SAT Math Section can feel intimidating due to a lack of familiarity with the various question types. However, you can tackle these questions more easily by dividing them into the exam's four domains. As you practice each Digital SAT math category, study one domain at a time until you're comfortable and consistently answer related questions correctly. By arranging your study plan this way, you can master the subject one step at a time as the topics within a domain progressively build upon each other. This approach prevents you from overwhelming yourself by tackling the subject simultaneously.

Unfamiliar with the content for each domain, don't want to waste valuable practice time classifying the questions on your own, or simply prefer a more organized way to study the section? UWorld's Digital SAT Math QBank does this grouping for you. This invaluable tool allows you to easily build a test with rigorous questions and comprehensive answer explanations for each domain, one subsection at a time.

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Algebra and Advanced Math domain questions constitute 13–15 questions, respectively. Consequently, the exam’s most prevalent SAT math question types are linear functions, inequalities, nonlinear equations, and nonlinear functions. Together these topics comprise 70% of the Digital SAT math section.

Most Digital SAT Math mistakes, including those deemed “silly mistakes,” occur due to stress, unfamiliarity with how to approach a problem type or time mismanagement. The most effective approach to preventing these common errors is to practice with realistic practice questions of varying difficulty levels. Take the time to identify potential traps in the questions and possible answers, then write out your step-by-step process for each problem. As you become more familiar with a particular question type, you will naturally refrain from misreading parts of the question or falling into common miscalculation traps.

Remember that each question carries equal weight in your score, so focus on answering the questions you feel more confident about first. Due to the limited time allocated for each Digital SAT math question (approximately a minute and a half, on average), don’t be afraid to skip questions if you don’t know where to begin or feel you’d only be able to answer after a lengthy multi-step process. Once you finish the questions you’re more comfortable with, you can return to the challenging questions with less pressure.

If you encounter a challenging question while practicing, study its explanation and note it for later review (if you’re practicing with UWorld) or discuss it with peers, a tutor, or your math teacher. When possible, follow up with this process by answering similar questions; in doing so, you’ll apply the lessons you learned from the first explanation and cement those methods into your memory.

While not all math question types have shortcuts, there are strategies and formulas that can help reach solutions quickly. Many of these techniques are question-type-specific, so check out the explanations in our Digital SAT Math QBank for myriad examples of strategies and when to apply them. Additionally, engage in regular practice with your calculator or the integrated digital calculator to become adept at determining when to utilize it and mastering its specific functions.