A Review of Concepts on the SAT Math Test

by Amy Harris Google

The math section of the SAT tests concepts of arithmetic, geometry, elementary algebra and basic intermediate algebra. It includes includes 54 question, 10 of which are free response and 44 of which are multiple choice. The questions are divided into three timed sections totaling 70 minutes. All problems can be solved without a calculator, but using one can save time and reduce the chance for arithmetic errors. Students needn't memorize complicated formulas for the exam; common necessary formulas -- such as those for the area of a triangle and circumference of a circle -- are provided in the exam booklet.

Number Sense and Operations

In the realm of arithmetic, students need to be able to perform addition, subtraction, multiplication and division on all sort of real numbers, including negatives and fractions. Some of these questions may be in the form of word problems and may also involve percentages, proportions and ratios. Students should be familiar with number classifications, such as rational, integer, whole and prime. Other concepts that could appear on the test include divisibility, sequences, series, exponential growth, union and intersection of sets.

Algebra and Functions

In terms of algebra, students need to know how to solve linear, quadratic, rational and radical equations and inequalities, including systems of equations and inequalities in two variables. This could entail processes such as applying the distributive property, factoring and substitution, or it could require you to convert written words into algebraic expressions. The SAT will contain questions involving properties of exponents; students must know the rules for multiplying, dividing and raising powers of variables with exponents. Students also should understand the concept of absolute value, know the difference between direct and inverse variation and be able to state the domain of a function.

Geometry and Measurement

Geometric concepts that may appear on the SAT include transformations, similarity, congruence and parallel and perpendicular lines. Students ought to be able to calculate areas and perimeters of two-dimensional shapes and volumes of simple three-dimensional shapes, namely rectangular prisms and cylinders. Graphing in the coordinate plane -- including calculating slope -- is another important concept. Students will likely encounter questions necessitating use of the Pythagorean theorem and knowledge of right, isosceles and equilateral triangles. Additionally, they should be familiar with the different types of angles, including acute, obtuse, right, vertical and interior.

Statistics, Probability and Data Analysis

The SAT also tests students’ understanding of concepts of probability and statistics. Most probability problems revolve around determining chance, or number of ways in which a specific outcome will occur. Students should be prepared to find measures of central tendency, namely the mean, or average, median and mode. Students will also be asked to interpret data stemming from tables, charts and graphs, such as pie charts, bar graphs or line graphs.

About the Author

Based in western New York, Amy Harris began writing for Demand Media and Great Lakes Brewing News in 2010. Harris holds a Bachelor of Science in Mathematics from Penn State University; she taught high school math for several years and has also worked in the field of instructional design.

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