SAT Algebra

SAT Algebra questions appear throughout the math section of the digital SAT, testing your ability to manipulate equations, interpret expressions, and model real-world relationships. You’ll need to master linear, quadratic, and higher-order equations, as well as functions, exponents, and polynomials. Success comes from recognizing patterns, translating word problems into mathematical expressions, and solving efficiently through algebraic reasoning.

Let’s talk about how algebra shows up on the digital SAT, what kinds of problems you’ll face, and how to use the test’s new format to your advantage.

Here are the topics we’ll cover:

• The Digital SAT in a Nutshell
• The SAT Math Topics
• Two Types of SAT Math Questions
• Algebra Is “King” on the SAT
  • SAT Linear Equations and Inequalities
    • Example 1: Linear Equations
  • SAT Systems of Linear Equations
    • Example 2: SAT Linear Systems of Equations
  • Linear Functions and Graphs
    • Example 3: SAT Linear Graphs
  • Quadratic Equations
    • Example 4: Factoring Quadratic Equations
  • Exponential Growth and Decay
    • Example 5: Exponential Growth
  • Function Notation
    • Example 6: Function Notation
• How Algebra Mixes with Other Math Topics
• Smart Strategies for Algebra on the Digital SAT
  • Practice Like It’s the Real Thing
• Summary
• What’s Next?

Let’s start with a quick overview of the digital SAT.

The Digital SAT in a Nutshell

The digital SAT is shorter than the old paper version. It’s divided into 2 main sections: Reading & Writing and Math, and each section is further divided into 2 modules. For math, there are 2 35-minute modules containing a total of 44 questions.

A new feature of the digital version is that the SAT is now “adaptive.” This means your performance in the first math module affects how challenging the second module will be. If you crush the first module, the second one will have harder questions, but correctly answering these harder questions will lead to a higher score.

Another change, one that makes students relieved, is that you can use a calculator on every math question. The test includes a built-in Desmos graphing calculator, which is surprisingly powerful once you become familiar with it.

KEY FACT:

The math section of the SAT is subdivided into 2 modules of 22 questions each.

The SAT Math Topics

The Math section focuses on the 4 areas of math that play the biggest roles in college success. They are:

• Algebra (35%)
• Advanced Math (35%)
• Problem Solving and Data Analysis (15%)
• Geometry and Trigonometry (15%)

The percentages following each area indicate the approximate percentage of the 44 questions that you can expect to see for that area.

It is important to note that both topics — Algebra and Advanced Math — present you with questions you studied in Algebra class in high school. Here are the types of questions you can expect to encounter from these 2 SAT Algebra topics:

• Algebra: linear topics, such as linear equations in 1 or 2 variables; linear functions; systems of 2 linear equations in 2 variables; and linear inequalities in 1 or 2 variables.
• Advanced Math: nonlinear functions, including absolute value, quadratic, polynomial, exponential, and radical functions.

As a result, you can see that roughly 70% of the math questions on the SAT are algebra.

KEY FACT:

Roughly 30 of the 44 math questions are algebra-based.

Two Types of SAT Math Questions

The digital SAT Math section includes 2 types of math questions:

1. Multiple-choice questions — You choose 1 correct answer from 4 options.
2. Student-produced response (SPR) questions — You must enter your own answer (no answer choices are given).

Roughly 75% of the math questions are multiple-choice, and 25% of the questions are SPR questions.

It’s critical that you know the complete rules for entering your SPR answers. Let’s look at a summary of those rules:

For student-produced responses, you must format fractions as improper fractions; don’t use mixed numbers. Ensure that decimals are rounded or truncated to fit the grid if they are too long. Enter only 1 correct answer if multiple exist, and do not include symbols like percent signs or dollar signs. For repeating decimals, you must fill all the spaces provided with the most accurate value the grid will accommodate.

KEY FACT:

The 2 types of math questions on the SAT are 4-option multiple choice and fill-in student-produced response (SPR) questions.

Algebra Is “King” on the SAT

If you can confidently handle equations, inequalities, functions, and graphs, you’ll be prepared for a huge portion of the math section. Think of it like this: algebra is the language spoken on SAT math. If you’re fluent in it, you can “translate” almost any problem the test throws at you — even the ones that look complicated at first glance.

You might be used to thinking of algebra as just solving for x, but on the SAT, it’s much more than that. It’s about interpreting relationships, building models, and understanding how changes in one thing affect another.

KEY FACT:

SAT Algebra is much more than just solving for x.

Let’s now get some SAT Algebra practice and look at some straightforward sample questions representing those ideas.

SAT Linear Equations and Inequalities

Linear equations and inequalities are the bread and butter of SAT Algebra. You’ll solve for x, interpret slopes and intercepts, and work with SAT inequalities, all of which show up in real-world word problems. These problems will use the familiar linear equation y = mx + b.

 For instance, you might see something such as the following example.

For the above example, you’ll also need to know what the numbers mean — in this case, 0.5 is the rate per mile (the slope), and 4 is the fixed cost (the y-intercept).

SAT Systems of Linear Equations

The SAT tests you on your ability to solve a system of (2) linear equations. You might solve them by the substitution method, the elimination method, or even by graphing. Let’s look at an example.

Linear Functions and Graphs

Algebra and geometry interact in this topic. You’ll interpret graphs, find slopes, and describe how lines move when equations change. The SAT might show you a graph and ask what happens if a parameter increases or decreases, so it’s good to visualize how those changes affect the line. Let’s consider the following example.

Quadratic Equations

Quadratics appear a little less frequently on the new SAT than before, but they’re still around — especially if you score well on the first module and are encountering tougher questions on the second. You should know how to factor, use the quadratic formula, and recognize a parabola’s vertex or direction on a graph.

A typical word question might describe a ball being thrown in the air, and you’re asked to find the maximum height. That’s just a parabola in disguise — the vertex gives you your answer.

Once you recognize the pattern, these problems become some of the easiest points on the test.

Let’s look at a more basic example of the kind of question about quadratics that you might encounter.

Exponential Growth and Decay

These are the problems that describe something “growing by 10% each year” or “losing half its value every month.” They use equations like y = a(1 + r)^t for exponential growth or y = a(1 – r)^t for exponential decay.

You don’t have to memorize every formula variation, but you do need to recognize what kind of relationship is being described. If something changes by a percentage repeatedly, it’s exponential, and if it changes by the same amount repeatedly, then it is linear.

Function Notation

At first glance, function notation like f(x) = 2x + 3 can look intimidating, but it’s just a fancy way of saying “the output when x goes in.” Function notation acts as a shorthand. Instead of asking “What is the answer when we plug in 4 for x?” we can simply ask: “What is f(4)?” In addition, the use of function notation allows us to easily differentiate between 2 functions f(x) and g(x).

Let’s consider a basic question about function notation.

How Algebra Mixes with Other Math Topics

In addition to “pure” algebra questions, such as the ones we’ve presented here, you’ll discover that you need to use your algebra skills in many of the math questions from the other 2 topics tested in SAT Math: Problem-Solving/Data Analysis and Geometry/Trigonometry. Algebra can pop up inside a data analysis problem, in a geometry question that involves coordinate planes, or as an integral part of a messy trigonometry problem. You might be asked to interpret a linear model from a scatter plot or find the slope of a line passing through 2 points on a circle. The better your algebra foundation, the easier all those cross-topic SAT Algebra questions become.

KEY FACT:

Algebra is a mathematical tool used in nearly every math topic or subtopic tested on the SAT.

Smart Strategies for Algebra on the Digital SAT

Because the digital SAT is adaptive, every early question matters. You want to be accurate and calm in that first math module — it sets the tone for what comes next.

Here are a few SAT Algebra tips to follow.

• First, get comfortable with your calculator. Many students prefer a TI-84 or a TI-Nspire CX, as they are powerful and can perform many useful operations. And don’t forget the Desmos calculator, which is built into your test. Even though any of these calculators can be useful, don’t lean on them too heavily. Think of them as tools, not crutches. In any case, practice using your calculator so that you are comfortable with it on test day.
• Second, keep your work neat and organized. Use your physical scratch paper to write out equations and calculations clearly. It’s too easy to make an error if you try to do everything in your head.
• Third, plug in numbers if needed. If a problem gives you variables like “x is 4 greater than twice y,” pick a simple number for y — say, 3 — and figure it out. It’ll help you see patterns more clearly.
• Fourth, use backsolving only as a last resort. Backsolving is when you plug the answer choices into the original question to discover which answer works. This is an inefficient technique that is recommended only if you are totally stumped. Do note that many SAT questions are constructed so that backsolving can’t even be used.
• And fifth, don’t panic if a question looks complex. Often, what seems hard is just wrapped in extra words. Take a deep breath, strip away the story, and you’ll find the same familiar algebra underneath.

TTP PRO TIP:

Use tips and strategies to enhance your performance on test day and to get the best score possible.

Practice Like It’s the Real Thing

Because the SAT is digital and adaptive, the best way to practice is to use the real tools. Download the Bluebook app, which simulates the exact test interface and includes digital SAT Algebra questions. Practice moving between questions, marking them for review, and using the calculator efficiently. Be completely comfortable with the digital platform and the nuances of the exam.

When you review your practice tests, don’t just note which ones you got wrong — figure out why. Did you make a careless error? Misread the question? Forget a rule or formula? The more specific your self-review, the faster you’ll improve.

And here’s a tip most students overlook: redo your missed problems a few days later. If you can solve them correctly the second time without looking at notes, you’ve actually learned the concept.

TTP PRO TIP:

Download and use the Bluebook app to get practice with the SAT testing platform while you are preparing for the SAT.

Summary

• The digital SAT has 2 sections: Math and Reading/Writing. Each section has 2 modules.
• Each module of the Math section asks 22 questions. You have 35 minutes to complete each module.
• About 30 of the math questions are SAT Algebra problems, encompassing linear and nonlinear topics.
• The 2 types of math questions are multiple choice with 4 options, and student-produced response (SPR) questions, where you must type your answer into an answer box.
• A knowledge of algebra is necessary for success on the SAT.
• It’s important to be very familiar with the calculator you choose to use on test day, whether it’s your own or the one built into the exam. 
• Be sure to download the Bluebook app to take practice exams and get familiar with the format and structure of the digital SAT.

What’s Next?

Doing well on SAT algebra questions has been our focus here. Read this article if you want to improve your overall SAT Math score.

You can get more math practice by reading our article that presents additional SAT Math practice problems.

Good luck!

You May Also Like...

Acing the New SAT Math (Digital SAT)

SAT Math Flashcards: Your Secret SAT Weapon

Digital SAT vs. Paper SAT: Key Differences