SAT Math For Dummies Cheat Sheet

You have a much better chance of getting a good SAT math score if you know what to expect. Focusing your study time on what will be included in the math sections of the SAT (without wasting your time with things that definitely won’t) is key to your success.

The SAT covers math usually taught in U.S. high school Algebra I, Geometry, and Algebra II classes. Occasionally, some Pre-Calculus course material may be included, but no Calculus course work is required.

Here’s how the College Board — the team of exalted creators of the SAT — describes the breakdown of the test:

Heart of Algebra centers on the linear function y = mx + b 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
• Solving algebra equations and inequalities
• Working with linear functions in four complementary ways: words, tables, graphs, and equations
• Solving systems of equations (both linear and non-linear), and identifying when such systems have either no solution or infinitely many solutions

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

• Working with ratios, proportional equations, and percentages
• Relying on a basic understanding of statistics and probability
• Applying these techniques to information presented visually in tables and graphs

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 f (x) notation, and knowing how to graph a core of basic functions and their most elementary transformations
• Understanding how to work with and graph polynomials, especially linear, quadratic, cubic, and quartic polynomials
• Graphing quadratic functions using standard, vertex, and factored forms
• Graphing exponential and radical equations
• Solving problems using basic geometry and trigonometry
• Working with complex numbers and circles on the xy-graph

Almost as important as knowing which math topics are covered on the SAT is knowing the topics you can safely avoid. Here’s a list of the math skills that you don’t need for the SAT:

• Doing big number-crunching — large numbers or endless calculations, such as standard deviations
• Writing geometry proofs
• The base e
• Logarithms and the natural log ln
• The complex plane
• Limits, derivatives, and integrals
• Summations using sigma notation Σ

Students often ask how to budget their time on the SAT. You have only a certain amount of time to complete each SAT math section, and you need to make the best use of that time to optimize your score. Here are a few tips for pacing yourself:

• Don’t sacrifice accuracy for speed. This rule is all-important. Although speed makes a difference, don’t rush so fast that you start making mistakes on questions you know how to answer.
• Be aware of the time. Remember that the two math sections of the SAT are timed as follows:

No Calculator: 25 minutes for 20 questions (75 seconds per question)

• • 15 multiple-choice questions
  • 5 gridded-response questions

Calculator: 55 minutes for 38 questions (about 87 seconds per question)

• • 30 multiple-choice questions
  • 8 gridded-response questions
• Plan to skip hard questions. You don’t have to answer all 58 SAT math questions to get a good score. In fact, many students do better when they actively plan to skip hard questions to give themselves more time to focus on the easier ones. The following table gives the approximate difficulty level of every SAT math question. Unless your SAT math score is already 700, you should probably plan to guess rather than answer most of the hard questions.

• Skip over questions that don’t make sense to you. If you find a question to be confusing or difficult, skip to the next question.
• When the going gets tough, circle back to answer the questions you skipped over. If you’re skipping over more questions than you’re answering, circle back to work on the early questions you skipped. You may find that some of them are not as bad as you thought, and even the tricky easy and medium questions are probably easier than the hard ones.

Although you obviously can’t use a calculator in the No Calculator section of the SAT, many questions in the Calculator section would be much harder to solve without one. A calculator can save a lot of time on the SAT, especially when you can’t quickly and easily do a calculation in your head.

But remember, the more complicated a single calculation is, the more likely you are to enter it incorrectly. So if possible, break down complicated calculations into several steps before keying them in.

Make sure you know how to use your calculator to do the following (check out your calculator’s manual or reference card if you’re having trouble):

• Perform basic numerical operations. Make sure you feel very comfortable doing basic addition, subtraction, multiplication, and division on your specific calculator.
• Work with decimals. Locate the decimal point key and make sure you know how to use it.
• Make numbers negative. On many calculators, the key for negating a number is distinct from the key for subtraction.
• Find a square root. Locate the square root key and make sure you can find square roots.
• Square a number. Your calculator probably has a key that looks something like x², used for squaring a number.
• Raise a number to the power of another number. Your calculator may have a key that looks something like ^ or x^y, which allows you to raise a number to the power of another number.