# SAT Math Exam Syllabus

Given the importance of math on the SAT, it’s helpful to have a road map of what SAT math you’ll have to learn from beginning to end in your test prep. So, this article will provide an SAT exam math syllabus and walk through the types of questions you can expect to see in the SAT mathematics section and the topics on which those questions will be based. Even if you are already familiar with the math concepts tested on the SAT, you will be better positioned to determine how much time you will need to learn SAT math fully.

## The Basics of the SAT Math Section

The SAT has four sections, two of which are math sections, sections 3 and 4. Section 3 is a “no calculator” section containing 15 multiple-choice and 5 grid-in questions. Section 4 is calculator-based and contains 30 multiple-choice and 8 grid-in questions. You are given 25 minutes to complete section 3 and 55 minutes to complete section 4.

There are two SAT math question types:

1. multiple-choice questions, which present answer choices
2. grid-in questions, which require you to enter in an answer.

An important feature of SAT math is that you can use a hand-held calculator in section 4. As long as you are familiar with your calculator and know when and how to use it, it can be very useful for test day! With that in mind, be sure that you read up on the SAT math calculator policies before test day. Also, if you are unsure of which calculator to use, speak to some past SAT students to get some calculator recommendations.

KEY FACT:

You will see two types of questions in SAT math: multiple-choice and grid-in.

Let’s discuss the first major question type: multiple-choice.

### Multiple-Choice SAT Math Questions

I have some very good news! Multiple-choice questions make up 45 of the 58 math questions you’ll see on the SAT. Now, why is this good news? It’s good news because you are already familiar with multiple-choice questions! So, although there are some SAT math problem-solving strategies you must learn, having familiarity with this question type will be one less thing to worry about during your test preparation.

If you need a refresher, multiple-choice questions on the SAT have four answer choices (A, B, C, D) and one correct answer.

KEY FACT:

There are 45 multiple-choice questions on the SAT.

Let’s practice with an example.

#### Multiple-Choice Example

On a multiplication quiz, students answered as many questions as they could in three minutes. Selma answered 24 more questions than Farrah. Together, they answered 66 questions. How many questions did Selma answer?

• 21
• 24
• 42
• 45
• 52
##### Solution:

We can create two equations, and then use the substitution method to answer this question.

We can let the number of questions that Selma answered = s and the number of questions that Farrah answered = f. Now we can create two equations:

Together, the two students answered 66 questions. So, we have:

Equation 1:

s + f = 66

Selma answered 24 more questions than Farrah. So, we have:

Equation 2:

s = f + 24

We can substitute f + 24 for s in Equation 1, and we have:

f + 24 + f = 66

2f = 42

f = 21

We see that Farrah answered 21 questions. However, we are asked the number of questions that Selma answered. So, we substitute f = 21 into Equation 2:

s = f + 24

s = 21 + 24

s = 45

KEY FACT:

The majority of SAT math questions will come in the form of multiple-choice.

Next, let’s discuss grid-in questions.

### Grid-In Questions

Although grid-in questions may look scary, they are quite similar to multiple-choice questions. Instead of selecting a correct answer from four choices, you actually “grid in” the numerical answer.

One small wrinkle to this question type is that some questions can have multiple correct answers. But as long as you grid one of those possible answers, you will answer the question correctly. For example, if you solve a grid-in question and your answer is 4 < x < 7, then you could grid in any value between 4 and 7, including 5 or 6, or even 5.73 or 4.02.

Remember, too, that grid-in questions test the same concepts as multiple-choice questions. For example, just as multiple-choice questions test linear equations and inequalities, so do grid-in questions!

KEY FACT:

You will see a total of 13 grid-in questions on the SAT.

Let’s look at what the grid actually looks like:

Since filling in the grid may be new to you, let’s review some rules you must follow.

#### Grid-In Rules

There are four main rules to be aware of when dealing with grid-in questions.

1. You are required to bubble in your response. It is not sufficient to just write your response in the boxes at the top of each column.
2. Only numbers with a positive value can be bubbled. Therefore, if you get a negative number as an answer, you know you’ve made a mistake in your calculations.
3. For a decimal answer, ensure you use one position for the decimal point and be sure to bubble it in. Thus, a decimal number like 2.368 would require rounding before bubbling in as 2.37. Also note that it is not necessary to enter a leading 0 for decimal numbers between 0 and 1.
4. You do not have to reduce fractions. They can be entered conventionally, with the “slash” mark bubbled in to indicate the division between the numerator and the denominator. You can also express the result of your fractional calculation as a decimal.

Let’s practice with an example.

##### Grid-In Example

For an Easter egg hunt, Zelda hid 186 eggs. The neighborhood children found 150 of the eggs during the egg hunt. What fraction of the eggs were not found?

###### Solution:

The problem gives us these two pieces of information:

Number of eggs found = 150

Total number of hidden eggs = 186

We also know that 186 – 150 = 36 eggs were not found.

Thus, we know that the fraction of eggs that were not found is 36/186.

Because this is a grid-in question, we cannot directly grid in the value 36/186 because there are not enough positions in the grid to accommodate this fraction. Thus, we have two options: (1) reduce the fraction or (2) convert the fraction to a decimal number.

(1) Reduce the fraction:

Since both 36 and 186 are divisible by 6, we can divide the numerator and denominator by 6:

36/186 = 6/31

(2) We can convert the fraction 36/186 to a decimal value:

36/186 = 0.194

We could bubble 6/31 or .194 (no leading zero) or 0.19 (with a leading zero) into the grid.

KEY FACT:

The grid-in question type on the SAT requires that you bubble in an answer into the grid. There are no answer choices from which to choose.

Now that we are familiar with SAT math question types, let’s discuss the major SAT math subjects you must know in order to score well on the exam.

## The Major SAT Math Topics

College Board, the makers of the SAT, have broken down SAT math into four SAT math content areas. These areas cover all the math topics on the SAT test.

1. Heart of Algebra
2. Problem Solving and Data Analysis

However, since those categories are pretty general, we have a more specific SAT math curriculum overview. Our SAT exam syllabus is as follows:

• Basic Arithmetic
• Linear Equations
• Exponents and Roots
• Inequalities
• Absolute Value
• SAT Math Word Problems
• Rates
• Unit Conversions
• Ratios
• Percents
• Statistics
• Probability
• Geometry
• Coordinate Geometry
• Functions
• Data Analysis
• Graphic Analysis
• Trigonometry

The list above covers every major SAT math topic. However, because there are just 58 questions on the SAT, there is no guarantee of what you’ll encounter on test day. Thus, following a linear and structured approach to your studying will be the key to mastering SAT math. Because there are so many SAT math test-taking strategies you must learn, you want to focus on just one topic at a time. This way of studying will serve you well when you start taking SAT math practice tests as well as on the actual SAT.

KEY FACT:

There are 19 major math topics on the SAT.

While understanding the major SAT math topics is important, the real key to success is knowing all the subtopics within each major topic. Remember, each subtopic has its own set of SAT math tips and tricks, so be sure to learn those for each subtopic. Those subtopics will make up your math syllabus for the SAT, so let’s look at them now.

### Basic Arithmetic Subtopics

You can look at basic arithmetic as the foundation, or building block, for much of what you will focus on during your SAT math preparation. So, even if you are on a tight deadline, remember that you need to walk before you run! Learning foundational material is essential.

Here are some key arithmetic subtopics:

• fraction rules
• decimal rules
• basics of percents
• basics of squares and square roots
• estimation shortcuts
• PEMDAS

Now, let’s review linear equations.

### Linear Equations Subtopics

Mastering algebra on the SAT exam is key because algebra plays an important role in almost all SAT math questions. For example, you’ll have to deal with algebra and equations in topics such as word problems, percents, functions, and coordinate geometry.

Here are some subtopics from linear equations:

• solving equations with one variable
• solving a system of equations for two variables
• the substitution method
• the combination method
• expressing one variable in terms of another variable
• cross-multiplication of equations
• factoring out common fractions
• when an equation produces no solution, one solution, or infinite solutions

Quadratic equations share some common properties with linear equations regarding your thought process. However, solving them requires more knowledge and skill. Once again, they can be present in various math topics, such as functions, coordinate geometry, and geometry.

Some quadratic equations subtopics are as follows:

• The Zero Product Property
• the difference of squares
• the discriminant
• higher order polynomials

Our next topic is exponents and roots.

### Exponents and Roots Subtopics

Exponents and roots may seem like a large topic (especially in the TTP SAT math course), but if you know a select number of exponent and root rules, you’ll see that much of what you learn builds on itself. So for such a topic, make sure that you get your rules on flashcards and get them memorized!

Here are some subtopics:

• combining exponential expressions — multiplication and division
• the power to a power rule
• equivalent exponents
• scientific notation
• perfect squares
• simplifying non-perfect roots
• conjugate pairs
• fractional exponents
• complex numbers

Next, let’s look at inequalities and absolute value.

### Inequalities and Absolute Value Subtopics

Inequalities and absolute value questions share some similarities with what you learn in linear equations, with some tweaks. For example, you can add or subtract inequalities, like equations, but you cannot divide by a variable unless you know the sign of that variable. Absolute value also follows these rules, but there are also specific absolute value rules you must learn and follow.

Some subtopics of inequalities and absolute value are below:

• equations and inequalities
• multiplying an inequality by a negative number
• compound inequalities
• linear inequalities
• systems of inequalities
• absolute value equations
• solving absolute value inequalities
• solving absolute value equations

Let’s move on to general word problems.

### General Word Problems Subtopics

General word problems consist of a vast array of problem types. To master general word problems, you must become skilled at translating words into equations. If you can master that skill, there is no word problem you cannot solve correctly!

Here are some of the general word problems subtopics:

• translating words into equations
• profit and loss
• determining the possible number of items
• consecutive integers
• fraction word problems
• price and salary problems
• inequality word problems
• complicated word problem formulas

Next, let’s discuss unit conversions and rates.

### Unit Conversions and Rates Subtopics

Although I would not consider unit conversions and rates a huge topic, you could see a few of these questions on your SAT. For unit conversions, you may see a basic conversion, or the unit conversion may be a part of a rate problem involving time and distance, or even another type of rate question involving time and work. Either way, having an efficient way of performing unit conversions will go a long way for you on test day.

Some of the subtopics of unit conversions and rates are as follows:

• rate-time-distance problems
• average rate questions
• elementary rate questions
• rate questions not involving distance
• single-step unit conversions
• conversions involving two sets of units
• rate-time-distance questions involving unit conversions

Let’s move on to percents and ratios.

### Percents and Ratios Subtopics

What people forget about ratios and percents is that they are related! In other words, a ratio can be converted to a percent, and a percent can be converted to a ratio. I’m sure you’ve learned about ratios and percents in your high school math classes, so hopefully they won’t seem so bad on the SAT.

Here are some of the subtopics:

• equivalent ratios
• the ratio multiplier
• proportions
• direct variation
• percent of problems
• “what percent” problems
• percent greater and percent less problems
• percent change

### Statistics

Statistics and data analysis on the SAT cover not only the basics, like mean, median, and range, but also many graphical topics. Graphs are covered along with statistics because, in many cases, graphs are the vehicle to ask questions based on concepts learned in statistics. Note that if you have not taken a statistics course in high school, you can learn the SAT statistics material in our TTP SAT self-study course.

Here are the subtopics that you will encounter:

• average (arithmetic mean), median, and mode
• weighted average
• range and standard deviation
• relationship between range and standard deviation
• grouped data and frequency tables
• charts and graphs
• bar graph
• dot plot
• margin of error
• statistical sampling

Let’s move on to geometry.

### Geometry Subtopics

If you have ever taken the SAT, you likely encountered several geometry questions. It’s a very large SAT math topic. It’s so large that most of the SAT math formulas and equations on the provided equation sheet are dedicated to geometry formulas. That said, don’t rely on the equation sheet provided for you on test day. Get your formulas on flashcards and memorize them!

Here are the subtopics you’ll need to know:

• lines and line segments
• perpendicular and parallel lines
• angles
• polygons
• triangles
• the Pythagorean theorem
• interior and exterior angles
• right triangles
• rectangles, squares, and trapezoids
• circles
• inscribed and circumscribed shapes
• solid geometry (cubes, rectangular prisms, and right circular cylinders)
• areas and volumes of geometric objects

Our next topic is coordinate geometry.

### Coordinate Geometry Subtopics

Some students consider coordinate geometry a topic that tests mostly on graphing. However, what many forget is that algebra plays a large role in this topic as well, and that’s good news! In other words, many skills that you learn from linear equations carry over to coordinate geometry.

Here is a breakdown of the coordinate geometry subtopics:

• the axes and the quadrants
• the coordinate plane
• slope and slope-intercept form of a line
• parallel and perpendicular lines
• determining the points of intersection
• the distance formula
• the midpoint formula
• circles in the coordinate plane
• graphing inequalities
• linear growth
• linear functions
• equation of a circle in the coordinate plane

Another large SAT math topic is functions. Let’s discuss that now.

### Functions Subtopics

Functions is another SAT math topic that involves both equations and graphing. Like coordinate geometry, the topic of functions deals with equations. Instead of linear equations, though, it deals mainly with quadratic equations. Although function notation can be intimidating, with a bit of practice, dealing with functions will be just as easy as dealing with more basic algebraic equations.

The topic of functions includes the following subtopics:

• function notation
• compound functions
• graphs of functions
• word problems with functions
• shifting function graphs
• determining the intercepts of a polynomial function
• parabolas
• axis of symmetry
• the vertex form of the equation of a parabola

Our final major math topic is trigonometry.

### Trigonometry Subtopics

In our experience, most students are initially scared of trigonometry in SAT math because they feel it’s one of the more advanced math concepts on the SAT. However, the nice thing about trig is that it is based on much of what you learn in geometry. So, with a solid foundation of special right triangles and a few other geometry concepts, learning trigonometry does not have to be too challenging.

Here are some trigonometry subtopics:

• trigonometric functions
• trigonometric functions of special right triangles
• complementary angles
• the unit circle
• sine and cosine values for common angles
• the tangent function for any angle

## SAT Math Exam Syllabus: In Summary

• There are two math sections on the SAT: calculator and no-calculator.
• There are two question types that you will encounter in the two math sections: multiple-choice and grid-in.
• There are roughly 19 major math topics on the SAT. Each has about 5-8 subtopics, which we have listed and discussed in this article.

Know the exam. Know the question types. Know which topics to study. Memorize needed formulas. Study smartly. Stay motivated. Be confident!

Let’s answer some common questions about SAT math and the SAT syllabus.

### Is There an SAT Exam Syllabus for Engineering?

Prior to 2021, students were able to take SAT Subject exams to show mastery in particular subjects pertaining to engineering, medicine, or other disciplines. Administration of the subject exams was discontinued in 2021.

### Is There an SAT Exam Syllabus for Medical Students?

No. Administration of the SAT Subject exams was discontinued in 2021.

### What Topics Are in the SAT Math Section?

There are 19 major math topics, from arithmetic to statistics to trigonometry. Each major topic includes 5-8 subtopics, so there is no shortage of material you need to study in order to earn a great SAT math score.

### Is the SAT Math Harder Than Other Exams?

SAT math is no harder than the math on any other standardized college entrance exam. No exam is difficult if you are well-prepared.

### Can You Use a Calculator in the SAT Math Section?

Yes. You may bring your own calculator to the exam. You should check College Board’s list of acceptable calculators. Be sure that you are completely comfortable with the capabilities of the calculator you use on your SAT, so that it is an asset instead of a liability.

## What’s Next?

Knowing the SAT math subjects is a great start. Now it’s time to start reviewing and learning these topics. So, check out our article on how to prepare for SAT math.

Studying all the SAT math topics might seem a daunting task, and keeping your focus and your motivation can be difficult. So, read our article about how to motivate yourself while you study for the SAT.

You can do this!