Mark Zegarelli - SAT Math For Dummies with Online Practice

The SAT is a college readiness test and, in some U.S. states, is now being used as a skills test for high school graduation. It covers two main subject areas: English and math. Each subject area is scored on a 200-to-800 point scale, resulting in a composite SAT score from 400 to 1,600 points. (If you have any older sisters or brothers who took the SAT before 2016, they may recall that the test used to be scored on a 600- to 2,400-point scale, but that’s all history now.)

Here’s an overview of the two math sections of the current SAT.

A 25-minute No Calculator section containing the following:15 multiple-choice questions, which require you to choose the right answer from among four choices, (A) through (D)5 gridded-response questions (also called student-produced response questions), which require you to record your answer in a special grid

A 55-minute Calculator section containing the following:30 multiple-choice questions8 gridded-response questions

That’s a total of 58 questions, each of which counts for 1 point on your raw score of correct answers (from 0 to 58). This raw score is converted to a scaled score (from 200 to 800), which becomes your SAT math score.

Every SAT math section (No Calculator and Calculator) includes a handy Reference list of formulas that you can use while taking the test, as shown in Figure 1-1. As you can see, this list includes a variety of geometric formulas for the area and circumference of a circle, the area of a rectangle and triangle, the Pythagorean Theorem, and other favorites.

FIGURE 1-1:The Reference list of formulas for the SAT.

Before taking the SAT, be sure you’re familiar with this Reference information, so you’ll remember it’s there when you’re working under time pressure on the actual test.

Thirteen of the 58 math questions you’ll answer when taking the SAT are gridded-response questions. These are Questions 16 to 20 of the No Calculator math test and Questions 31 to 38 of the Calculator math test. To answer them, you need to fill in the grid provided with your answer sheet.

Most students don’t find the grid too difficult to work with. The official SAT instructions for using the grid are provided on every test just before the gridded-response questions. Here are a few things to keep in mind as you work with the grid:

The grid has four columns, into each of which you can place a digit from 0 to 9, or in some columns a fraction slash (/) or a decimal point (.).

Be sure to fill in the appropriate bubble in each column so the computer can read your answer. If you don’t, your answer will be marked wrong.

Use the boxes at the top for recording your answer so you can read it easily and change it if necessary.

The grid contains no minus sign, so all answers are non-negative numbers. (This includes “0”.)

If your answer is a whole number, you can enter it into the grid using any consecutive boxes. For example, here are three equally valid ways to enter the answer “23”:232323

If your answer is a fraction, use the fraction slash to record your answer. For example, here are two equally valid ways to enter the answer “1/2”.1/21/2

Don’t attempt to enter a mixed number such as into the grid, because the computer will read this answer as and mark it wrong. Instead, convert mixed numbers to improper fractions or decimals () and use one of these formats to enter your answer.

If your answer is a decimal that’s less than 1, use the decimal point without a leading zero to record your answer. For example, you can enter the answer “.5” in any of following ways:.5.5.5

If your answer is a decimal with more decimal places than will fit in the grid, fill in as many decimal places as will fit, either truncating the last decimal place or rounding it up. For example, here are the two ways you can enter the decimal 3.479 into the grid:3.473.48

Although these rules may seem overly complicated, in most cases your actual SAT answers will be relatively straightforward.

The math that’s covered on the SAT is very closely tracked to the math that’s covered in most U.S. high school math classes. So if you’re a current or recent U.S. high school student, you’re probably familiar with most of this curriculum.

The SAT breaks this down into three general areas of study: Heart of Algebra, Problem Solving and Data Analysis, and Passport to Advanced Math (and Other Topics). In this section, I give you an overview of each of these topics.

Heart of Algebra centers on the linear function and other information covered in a typical high school Algebra I class. To answer SAT math questions in this area, you’ll need to feel comfortable working with the following:

Evaluating, simplifying, and factoring algebra expressions ( Chapter 3)

Solving algebra equations and inequalities ( Chapter 4)

Working with linear functions in four complementary ways: words, tables, graphs, and equations ( Chapter 5)

Solving systems of equations (both linear and non-linear), and identifying when such systems have either no solution or infinitely many solutions ( Chapter 6)

In Part 2, I cover all these topics in depth.

Problem Solving and Data Analysis focuses on a short list of problem-solving techniques:

Working with ratios, proportional equations, and percentages ( Chapter 7)

Relying on a basic understanding of statistics and probability ( Chapter 8)

Applying these techniques to information presented visually in tables and graphs ( Chapter 9)

Part 3focuses exclusively on these ideas.

Passport to Advanced Math (and Other Topics) requires you to understand a core of information covered in high school Algebra II:

Working with functions using notation, and knowing how to graph a core of basic functions and their most elementary transformations ( Chapter 10)

Understanding how to work with and graph polynomials, especially linear, quadratic, cubic, and quartic polynomials ( Chapter 11)

Graphing quadratic functions using standard, vertex, and factored forms ( Chapter 12)

Graphing exponential and radical equations ( Chapter 13)

Solving problems using basic geometry and trigonometry ( Chapter 14)

Working with complex numbers and circles on the xy -plane ( Chapter 15)

I provide this information in Part 4.

When it comes to doing well on the SAT, your test-taking strategy is a small but important piece of the puzzle. And this strategy also extends to knowing which questions to answer and which to skip, depending on the score you’re currently striving for.

In this section, I fill you in on this essential information.