SAT / ACT Prep Online Guides and Tips

What's Tested on the SAT Math Section? Topics and Practice

Posted by Rebecca Safier | Apr 29, 2015 11:43:00 PM

SAT General Info

 

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Your first step in preparing for the math section of the SAT should be familiarizing yourself with exactly what’s on it. This guide has been completely updated to tell you the format, topics, and skills tested on the math section of the redesigned SAT.

Whatever math class you’re taking in school, you should be able to conquer the SAT math topics with the right approach to test prep. Let’s start this guide by reviewing the overall format of the math section of the SAT.

  

SAT Math Format

Math will be your third and fourth sections on the SAT, right after Reading and Writing & Language. You’ll first get a 25-minute section, during which you can’t use a calculator. After a short break, you’ll move onto the 55-minute section. During this longer section, you’re allowed to use your calculator.

Both sections will begin with multiple choice questions, each of which will feature four answer choices. Then you’ll be asked for some student-produced responses, more commonly known as "grid-ins." On the calculator section, some of these grid-ins will relate to one another as part of an Extended Thinking question.

Here’s the breakdown of time, number of questions, and question types on the two SAT math sections.

Section Number of Questions Time

No calculator

15 multiple choice, 5 grid-ins


25 minutes

Calculator 30 multiple choice, 8 grid-ins (including one Extended Thinking question) 55 minutes
 Total 58 questions


80 minutes

 

While you can only use a calculator on the longer Math section, you’ll have access to the following reference information for geometry in both sections:

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Of course, you’d be better off having this information memorized than wasting time flipping back in your test booklet to these formulas. This material isn’t actually all that important on the math section, as geometry problems make up less than 10% of the questions. That being said, what skills and concepts are most prevalent in the math section?

 

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Content is king! Or, at least, it's very important to master before you take the SAT.

  

SAT Math Topics

While the math section doesn’t place a large emphasis on geometry problems, it does focus on algebra, solving equations, and data interpretation from tables and graphs. College Board sorts the question types into three main categories: Heart of Algebra, Passport to Advanced Math, and Problem Solving and Data Analysis (they apparently gave up on the creative naming once they reached the third category).

These three realms describe about 90% of the SAT math questions. The remaining 10% are simply called Additional Topics, and they mainly include geometry, basic trigonometry, and complex numbers.

Let’s take a closer look at each of these categories by going over the SAT math topics and skills they test. After a description of each one, you’ll see three official sample practice questions from College Board. To begin, let’s take a look at exactly what topics are included under the heading of Heart of Algebra.

 

Heart of Algebra

SAT math questions in the Heart of Algebra category have to do with linear equations, inequalities, functions, and graphs. Below are the official topics as defined by College Board, followed by a summary of tasks you’ll need to be prepared for to tackle these questions and some example problems.

Official Topics

  • Solving linear equations and linear inequalities (in these expressions, x is a constant or the product of a constant)
  • Interpreting linear functions
  • Linear inequality and equation word problems
  • Graphing linear equations
  • Linear function word problems
  • Systems of linear inequalities word problems
  • Solving systems of linear equations

 

Summary of Tasks

  • Use multiple steps to simplify an expression or equation or solve for a variable.
  • Solve for a variable within functions or systems of inequalities with two variables (usually x and y).
  • Determine whether a given point is in a solution set or what value would make an expression have no solution.
  • Select a graph that shows an algebraic equation, or, on the flip side, choose the equation that describes a graph.
  • Indicate how a graph would be affected by a given change in its equation.

 

Sample Questions

Solving systems of linear equations:

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Solving systems of linear inequalities: 

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Graphing a linear equation:

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Grab your passport - we're crossing the border into the land of advanced math. 

 

Passport to Advanced Math

While Heart of Algebra questions are focused on linear equations, Passport to Advanced Math questions have to do with nonlinear expressions, or expressions in which a variable is raised to an exponent that’s not zero or one. These questions will ask you to work with quadratic equations, exponential expressions, and word problems. Read on for the full list of topics that fall under Passport to Advanced Math, followed by a summary of tasks and three sample SAT questions.

 

Official Topics

  • Solving quadratic equations
  • Interpreting nonlinear expressions
  • Quadratic and exponential word problems
  • Radicals and rational exponents
  • Operations with rational expressions and polynomials
  • Polynomial factors and graphs
  • Nonlinear equation graphs
  • Linear and quadratic systems
  • Structure in expressions
  • Isolating quantities
  • Functions

 

Summary of Tasks

  • Solve equations by factoring or using other methods to rewrite them in another form.
  • Add, subtract, multiply, or divide two rational expressions or divide two polynomial expressions and simplify your results.
  • Select a graph that matches a nonlinear equation or an equation that corresponds to a graph.
  • Determine the equation of a curve from a description of a graph.
  • Figure out how a graph would change if its equation changed.

 

Sample Questions

Functions:

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Nonlinear expressions:

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Nonlinear equation graphs:

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The next category's all about Data.

 

Problem Solving and Data Analysis

This third and final major category includes questions that ask you to work with rates, ratios, percentages, and data from graphs and tables. Read on for the official topics, a summary of tasks, and three sample questions.

 

Official Topics

  • Ratios, rates, and proportions
  • Percents
  • Units
  • Table data
  • Scatterplots
  • Key features of graphs
  • Linear and exponential growth
  • Data inferences
  • Center, spread, and shape of distributions
  • Data collection and conclusions

 

Summary of Tasks

  • Solve multi-step problems to calculate ratio, rate, percentage, unit rate, or density.
  • Use a given ratio, rate, percentage, unit rate, or density to solve a multistep problem.
  • Select an equation that best fits a scatterplot.
  • Use tables to summarize data, such as probabilities.
  • Estimate populations based on sample data.
  • Use statistics to determine mean, median, mode, range, and/or standard deviation.
  • Evaluate tables, graphs, or text summaries.
  • Determine the accuracy of a data collection method.

 

Sample Questions

Calculating data based on rate:

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Scatterplot and calculating rate:

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Calculating percentage based on table data: 

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These next few categories don't quite fit anywhere else.

 

Additional Topics in Math

While 90% of your questions will fall into the Heart of Algebra, Passport to Advanced Math, or Problem Solving and Data Analysis categories, the remaining 10% will simply be classified as Additional Topics. These topics include geometry, trigonometry, and problems with complex numbers.

 

Official Topics

  • Volume word problems
  • Right triangle word problems
  • Congruence and similarity
  • Right triangle geometry
  • Angles, arc lengths, and trig functions
  • Circle theorems
  • Circle equations
  • Complex numbers

 

Summary of Tasks

  • Determine volume of a shape.
  • Apply properties of triangles to determine side length or angle measure.
  • Apply properties of circles to measure arc length and area.
  • Solve problems with sine, cosine, and tangent.



Sample Questions

Right triangle problem with trigonometric functions:

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Congruence and similarity:

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Angles and parallel lines:

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To truly prepare for the math section of the SAT, you should make sure to review all of the above mentioned topics. Some problems, furthermore, will integrate topics and require you to apply multiple skills and concepts as you work toward a solution. Multi-step problems are prevalent throughout the math section. Let’s take a closer look at multi-step problems, along with the other main features you need to be aware of as you prep for SAT Math.

 

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Grab your snacks and turn off your cell phone - it's time for the main feature(s)!

 

What Are the Key Features of SAT Math?

In addition to understanding content and format of the SAT Math section, there are some key features you should know about. As you study, keep an eye out for these features. By familiarizing yourself with them, you may even be able to use practice materials for the old SAT effectively to prepare for the redesigned SAT.

 

Multi-Step Problems

You may notice that several of the above problem types state that they require multiple steps to solve. While wording of math questions should be straightforward, the thinking and calculations required will be relatively involved. To prepare, you'll especially want to focus on time management and working quickly and efficiently.

You may have to combine skills from one more than one content area or use several steps to get to your answer. Word problems may present a long scenario, and you’ll need to figure out what data to use and what concepts to apply to get to your answer. Speaking of word problems...

 

Emphasis on “Real World” Applications

According to College Board, much of its purpose behind redesigning the SAT was to make the test more closely aligned with classroom learning and real world skills. As a result, the math section won’t feature too many abstract reasoning questions.

Instead, the word problems will be grounded in realistic situations. Some may ask you to calculate gas left in a car’s gas tank or the conversion of money from one country’s currency to another. Most word problems will present scenarios that you might encounter in your life.

 

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There will be a few questions that test your understanding of sines. Also, cosines and tangents.

 

A Few Geometry and Trigonometry Questions

About 10% of the questions will feature geometry and/or trigonometry. Since not everyone has studied trigonometry in school by the time they take the SAT, these questions may call for separate, SAT-specific preparation.

You should acquaint yourself with the relevant concepts and formulas, but focus most of your energies on preparing for algebra, functions, inequalities, graphs, and word problems.

 

A No-Calculator and Calculator Section

For 25 minutes, you won’t be able to bring out your calculator to answer any of the math questions. There’s no need to worry! The problems in the 25-minute section won’t require a calculator; in fact, using one on those problems would probably just slow you down.

Calculator fluency, or knowing how and when to use your calculator effectively, is an important skill on the SAT math. College Board says, “Calculators are important tools, and...you’ll need to know how - and when - to use them...The calculator is, like any tool, only as smart as the person using it. The Math Test includes some questions where it’s better not to use a calculator, even though you’re allowed to.”

So you definitely won’t need one on the shorter “no calculator” section, and you may not even need one on many of the problems in the longer “calculator” section. Answering lots of practice questions can help you get better at deciding when a calculator would be helpful and when it would just slow you down.

 

An Extended Thinking Problem

A few of your questions will be part of an Extended Thinking problem. Typically, this Extended Thinking problem will be part of the grid-in questions near the end of your 55-minute section.

Basically, you’ll get a graph, table, or word problem scenario and then have to answer multiple questions about it. The following is one example of a word problem-based Extended Thinking question. Notice the bent toward “real world” application!

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Grid-in Math Questions

Speaking of grid-ins, you'll have thirteen of these student-produced responses that you'll answer in a special part of the bubble sheet at the bottom. While you can write your answer in the spaces provided, you'll have to fill in the corresponding bubbles for credit. There are bubbles for digits between 0 and 9, as well as for decimal point (a period) and fraction line (a slash). To practice gridding in your responses, you can practice on College Board's SAT practice test answer sheet.  

As long as you're familiar with the key features and directions of the SAT math, you can hit the ground running and not waste time figuring out logistics. So whether you're prepping with PrepScholar, online practice questions, official College Board tests, or a combination of all of these, how should you approach prepping for the SAT math?

 

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Unleash the power of prep.

  

How You Should Study SAT Math

Many of the concepts on the SAT math you'll learn in your math classes in school. This doesn't mean that classwork will prepare you enough to perform well on the SAT, though. SAT math questions test the above concepts in a unique, SAT-specific way. In order to prepare and learn to be speedy in your time management, you'll want to practice and get familiar with the wording with high quality practice questions.

Official practice tests will also help you uncover and diagnose your strengths and weaknesses. If you find yourself consistently stumped by function questions, for example, you'll know to focus your energy and studying there. Even if you haven't taken an advanced algebra or trigonometry class yet in school, you can still prep for these questions by studying SAT concepts and questions.

Since there aren't a ton of practice materials for the redesigned SAT yet, you might benefit from using ACT math questions. They feature the straightforward wording and realistic scenarios present on the new SAT, and they incorporate some trigonometry as well. Additionally, you could use math questions for the old SAT to practice, while eliminating obsolete questions, such as those that ask for abstract reasoning. 

If you're strong in math and looking to achieve a top score, you want to approach the math section in a strategic way. This perfect scorer shares the techniques he used and how they can help you score at or near 800 on your SAT math.

 

What's Next? 

Are you scoring on the low side on math and hoping to break 600? Here are the steps you need to take to score a 600 or more on the SAT math.

Looking for book recommendations specific to the math section? Here are our suggestions for the best prep books for SAT Math, along with a few pointers on how to use them most effectively.

For a complete summary of the key features and question types on all sections, check out our complete guide to the new SAT. Once you've learned about the changes, head on over to this guide to read about how to study for the new SAT. 

 

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Rebecca Safier
About the Author

Rebecca graduated with her Master's in Adolescent Counseling from the Harvard Graduate School of Education. She has years of teaching and college counseling experience and is passionate about helping students achieve their goals and improve their well-being. She graduated magna cum laude from Tufts University and scored in the 99th percentile on the SAT.



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