SAT Math Reference Sheet

The digital SAT (dSAT) is here, and many students and educators are lauding the changes from the previous non-digital version. There is one item on the dSAT that has not changed, and that is the SAT math reference sheet. Previously, with the paper-and-pencil SAT, you had to search for this useful sheet with SAT math formulas by flipping through your exam booklet until you found it. But with the digital SAT, it is as close as a single mouse click!

In this article, we’ll look at some of the recent changes to the SAT. But we’ll focus our attention on the SAT math formula sheet in detail, to help you ensure that you are using it efficiently and effectively.

Here are the topics we’ll cover:

• Overview of the Digital SAT
  • Length
  • Platform
  • Format
  • Section Adaptivity
  • Tools on the Digital SAT
  • Other Considerations
  • Scoring
  • Changes to the Math Section From the Paper-and-Pencil Version
  • What Shapes Are on the SAT Math Reference Sheet?
  • What Formulas Are on the SAT Math Reference Sheet?
    • Example 1: The Radius of a Cone’s Base
    • Example 2: Right Circular Cylinder
    • Example 3: Rectangular Prism

    Before we concentrate on the SAT math formula sheet, let’s get an overview of the changes brought on by the digital SAT.

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    Overview of the Digital SAT

    Let’s consider the major changes that the digital SAT includes.

    Length

    The dSAT is shorter than the paper-and-pencil version. The exam will take you 2 hours and 24 minutes to complete. The Reading and Writing section is 64 minutes long. It is followed by a 10-minute break. The Math section is 70 minutes long.

    Platform

    The dSAT is now digital instead of paper-and-pencil. You will be able to take the exam at school or a testing center. You’ll download Bluebook, the SAT application, to the computer (Mac or PC) before your exam. Note that when you are using Bluebook, the rest of the computer is “locked down,” preventing you from using any other application during the exam.

    Note that you can download Bluebook during your SAT prep. You can access four exams on Bluebook for free, giving you plenty of practice with the digital platform.

    Download the free Bluebook app to your computer during your SAT prep. You can take four free practice tests on Bluebook.

    Format

    You will discover that the dSAT has only two sections: Reading and Writing, and Math. The Reading and Writing section has two modules, each lasting 32 minutes and presenting you with 27 questions. The Math section also has two modules, each lasting 35 minutes and presenting you with 22 questions.

    Section Adaptivity

    Let’s look at what ”section adaptivity” means by using the Math section as an example.

    When you start Math Module 1, you will be presented with a mix of 22 easy, medium, and hard math questions. After you finish Module 1, your performance will determine the difficulty level of the questions you will encounter on Module 2. More difficult questions will award more points to your score. Thus, it is important that you do well on Math Module 1 so that you will be presented with harder (but score-enhancing) questions on Module 2.

    A similar situation occurs with the Reading and Writing section. It is to your benefit to do as well as you can on Module 1 so that Module 2 will present questions that allow you to maximize your score.

    Understand the mechanics of section adaptivity.

    Tools on the Digital SAT

    • You will have access to a countdown clock so that you can gauge your progress through each module.
    • You may skip questions within a module, marking them for later review. Just make sure you answer every question in the module before time is up.
    • You will have access to a Desmos graphing calculator during both math modules. It is imperative that you learn how to use it before exam day!
    • You will have access to the math reference sheet during both math modules.

    Other Considerations

    • All students will take the digital SAT in the same order: Reading and Writing Modules 1 and 2; 10-minute break; Math Modules 1 and 2.
    • Reading passages will be shorter, and each passage has only one question.
    • Each Reading and Writing module will first present you with reading passages and questions, followed by writing questions.
    • Math questions will be roughly 75% multiple choice and 25% “student-produced responses” (fill in the blank).
    • Fill-in-the-blank Math answers can now be negative.
    • You may have only 5 pieces of scratch paper for the entire exam.

    Know the format and structure of the digital SAT.

    Scoring

    The dSAT total score ranges from 400 to 1600. The Reading and Writing section score ranges from 200 to 800, as does the Math section. And good news! You won’t have to wait for weeks to get your score. You can expect it within a few days of testing.

    One limitation of the digital SAT is that you won’t be able to order the Question-and-Answer Service to review your test questions.

    Now that we have covered the length, format, and section adaptivity feature of the SAT, let’s focus on what math topics are tested.

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    What Math Is Needed for SAT?

    The College Board has categorized the math that is tested on the SAT into four main headings. They are listed here, with the major subtopics included for each category.

    1. Algebra (13-15 questions)
       Linear equations; linear functions; systems of linear equations (substitution and combination methods); linear inequalities
    2. Advanced Math (13-15 questions)
       Nonlinear equations in one variable (e.g. parabola); nonlinear systems of equations in two variables; nonlinear functions; equivalent expressions
    3. Problem-Solving and Data Analysis (5-7 questions)
       Percentages; ratios, rates, proportions; measures of center and spread; scatterplots; probability; margin of error; observational studies and experiments
    4. Geometry and Trigonometry (5-7 questions)
       Area, volume; lines, angles, triangles; right triangle trigonometry; circles

    There are four main categories of math concepts tested on the digital SAT.

    Changes to the Math Section from the Paper-and-Pencil Version

    The two math modules of the digital SAT have several differences from the previous paper-and-pencil version:

    • Figures are now drawn to scale.
    • Student-produced response (fill-in-the-blank) answers can now be negative.
    • There is an online calculator that can be accessed for any Math question.
    • imaginary and complex numbers are no longer tested.

    For student-produced response questions, there are very specific rules for entering answers into the answer box. You will want to read the rules and practice what is and is not allowed as to the format of your answer. The practice exams in the Bluebook app provide detailed guidance for correctly entering fractions and decimals.

    One item that has not changed from the paper-and-pencil version of the SAT is the Math Reference Sheet. Let’s take a look at it now.

    Make sure you are familiar with the many minor changes to the digital SAT.

    A Terrifying Scenario!

    Imagine this scenario: You are tooling along in the first SAT math module, confident and feeling great. So far, the questions have been solvable, and your timing is good. You read question 16, and you get a weight in the pit of your stomach. The question reads:

    “What is the radius of a sphere with a volume of 1200 cubic cm?”

    And you have no idea what to do. “A sphere?? Its radius. Are you kidding me? I studied that maybe 3 years ago in Geometry class. And I have no idea how to solve this problem!”

    The digital SAT is kind enough to provide students with a free, legal SAT math cheat sheet! And guess what? The formula for the volume of a sphere is there! So… go ahead and click on the icon for the reference sheet, and you are golden.

    “Oh, wait what do I click on? Where is the icon?”

    Fear not, weary pilgrim! On the Bluebook app, just click on the icon at the top right of the screen, the one that looks like “X^2,” and you’ll be transported to the entire Math Reference sheet. Hurrah!

    (And, by the way, the radius of that sphere is solved with the formula V = 4/3 (pi) r^3, so the answer is 30 / cuberoot (pi).)

    Access the Math Reference Sheet by clicking on the X^2 icon in the upper right hand of the Bluebook screen.

    The SAT Math Reference Sheet

    What Shapes Are on the SAT Math Reference Sheet?

    The shapes on the top row are a circle, a rectangle, a non-right triangle, a right triangle, and two special right triangles: the 30-60-90 right triangle and the 45-45-90 right triangle. You should have memorized the ratios of the sides of these two special right triangles in Geometry or Trigonometry class, but it is a relief to see that they are on the reference sheet, in case your mind goes blank during the exam.

    It’s important to know the names of the shapes on the second row. For example, a word problem might ask you a question about the height of a right circular cylinder; if you don’t know which shape to use, you’re up the creek without a paddle!

    From left to right, the shapes on the second row are: rectangular prism, right circular cylinder, sphere, right circular cone, and a square-based pyramid. Notice, too, that below each shape, the volume formula is provided.

    There are 11 shapes illustrated on the SAT Reference Sheet, including 6 2-dimensional shapes and 5 3-dimensional shapes.

    What Formulas Are on the SAT Math Reference Sheet?

    First and foremost, you see that the SAT reference sheet includes geometry formulas galore! From the circle formulas for area and circumference to the area of a triangle, this sheet is a treasure trove of long-forgotten geometry facts. The entire second row includes volume formulas for the 3-dimensional figures.

    Don’t overlook the three geometry facts/trigonometry formulas presented in the sentences below the 3-D shapes. These facts remind us that a circle has 360 degrees, and that a triangle’s angles sum to 180 degrees. Of note is the fact that there are 2π radians in a circle, a useful trig formula that is overlooked by many students.

    There are formulas for area, circumference, and volume on the SAT reference sheet.

    Let’s see how to use the SAT math formula sheet to solve a few tough questions.

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    Example 1: The Radius of a Cone’s Base

    What is the radius of the circular base of a right circular cone with a volume of 300 cubic feet and a height of 9 feet?

    Solution:

    What a relief! Right there on the SAT equation sheet is a diagram of a cone with the formula for its volume! All we need to do is plug in the numbers and solve for the value of the radius:

    Answer: B

    Example 2: Right Circular Cylinder

    A farmer stores grain in two right cylindrical silos, one large and one small. Both silos are 40 feet tall, and the larger silo has twice the diameter of the smaller one. How much greater is the storage capacity of the larger silo than the smaller silo?

    • The storage capacity of the larger silo is twice the capacity of the smaller one.
    • The storage capacity of the larger silo is four times the capacity of the smaller one.
    • The storage capacity of the larger silo is eight times the capacity of the smaller one.
    • The storage capacity of the larger silo is sixteen times the capacity of the smaller one.
    • Because we don’t know both the volume and the radius of the two silos, we cannot determine how much greater the capacity of the larger silo is.

    Solution:

    The SAT reference sheet is again a lifesaver! We easily find the formula for the volume of a right circular cylinder, V = π r^2 h, which will be used to determine the storage capacity of the two silos.

    We see that we must calculate the volume of each silo to determine its storage capacity. Because the diameter of the larger silo is twice the diameter of the smaller one, we know that the radius of the larger silo is also twice the radius of the smaller one. Thus, we will let r = the radius of the smaller silo and (2r) = the radius of the larger silo.

    Let’s calculate the volume of each silo.

    Let’s let V₁ = the volume of the larger silo.

    Now, let’s let V₂ = the volume of the smaller silo.

    Now, looking at the two volumes, we see that the larger silo has a volume that is 160 / 40 = 4 times greater than the volume of the smaller silo.

    Answer: B

    Example 3: Rectangular Prism

    Tara has installed a swimming pool with a square base with each side of 16 feet, and she wants to fill it with water so that it is filled up to the 5-foot level. Her water hose can fill the pool at a constant rate of 60 cubic feet per hour. To the nearest hour, how many hours will it take Tara to fill her pool?

    Solution:

    To solve this student-produced response question, we first see that the SAT reference sheet has the formula for a rectangular prism, which is the shape of the swimming pool. So we will use the formula for the volume: V = l x w x h, and we note that the length and width of the swimming pool are equal. Thus, the formula simplifies to V = s x s x h, where s = the length of the side.

    We know that s = 16 feet and h = 5 feet. Thus, the volume of the pool that is to be filled with water is:

    V = 16 x 16 x 5 = 1280 cubic feet

    The hose fills the pool at the rate of 60 cubic feet per hour. Thus, the time needed to fill the pool is:

    1280 cubic feet / 60 cubic feet / hour = 21.333 hour, which rounds to 21 hours.

    Answer: 21

    Summary

    In this article, we have summarized the changes brought about by the adoption of the digital SAT. Among them are the length, the format, and section adaptivity. The digital SAT requires the use of the Bluebook application, which you are advised to download and use during your SAT preparation.

    The SAT math topics tested have not significantly changed. But we have seen that fill-in-the-blank questions can now have negative answers and that the on-screen calculator can be used for any math questions.

    One aspect of the SAT that has not changed at all is the SAT reference sheet. This invaluable tool can be easily accessed at any time during the math portion of the exam. It illustrates common geometric shapes and area formulas, including circles and special triangles. It provides illustrations and formulas for volumes of common three-dimensional shapes, such as cylinders, cones, spheres, and pyramids.

    It’s important to be familiar with the SAT reference sheet. You might not need to use it at all during the exam, but it is nice to know that it is available, in case you forget a formula or want to verify that you are using the correct one.

    What’s Next?

    We have given you some great tips for the digital SAT math section in this article. But you don’t want to skimp on your Verbal prep! Read our article about the digital SAT reading and writing section to ensure that you are well-rounded in your preparation for the digital SAT.