Math Concepts

Algebra and Functions

Register Next Tests:
10/11 , 11/8

The following concepts are covered on the test:

  • Substitution and simplifying algebraic expressions
  • Properties of exponents
  • Algebraic word problems
  • Solutions of linear equations and inequalities
  • Systems of equations and inequalities
  • Quadratic equations
  • Rational and radical equations
  • Equations of lines
  • Absolute value
  • Direct and inverse variation
  • Concepts of algebraic functions
  • Newly defined symbols based on commonly used operations

Factoring

You may need to apply these types of factoring:

x2 + 2x = x (x + 2)

x2 – 1 = (x + 1) (x – 1)

x2 + 2x + 1 = (x + 1) (x + 1) = (x + 1)2

2x2 + 5x – 3 = (2x – 1) (x + 3)

Functions

A function is a relation in which each element of the domain is paired with exactly one element of the range. On the SAT, unless otherwise specified, the domain of any function ƒ is assumed to be the set of all real numbers x for which ƒ(x) is a real number. 

For example, if ƒ(x) =  square root (x + 2), the domain of ƒ is all real numbers greater than or equal to –2. For this function, 14 is paired with 4, since ƒ(14) = square root (14 + 2) = square root 16 = 4.

Note: the square rootsymbol represents the positive, or principal, square root. For example, square root 16 = 4, not ±4.

Exponents

You should be familiar with the following rules for exponents on the SAT.

For all values of a, b, x, y:

(x^a) times (x^b) = x^(a + b)    (x^a)^b = x^(a times b)    (x times y)^a = (x^a) times (y^a)

For all values of a, b, x > 0, y > 0:

x^a over x^b = x^(a minus b)    (x over y)^a = x^a over y^a    x^negative a = 1 over (x^a)

Also, x^(a over b) = b root (x^a) . For example,  x^(2 over 3) = cube root (x^2).

Note: For any nonzero number x, it is true that x^0 = 1.

Variation

Direct Variation: The variable y is directly proportional to the variable x if there exists a nonzero constant k such that y = kx.

Inverse Variation: The variable y is inversely proportional to the variable x if there exists a nonzero constant k such that y = k over x or xy = k.

Absolute Value

The absolute value of x is defined as the distance from x to zero on the number line. The absolute value of x is written as |x|. For all real numbers x

absolute value = x comma if x is greater than or equal to 0 or negative x comma if x is less than 0

for example colon absolute value 2 = 2 comma since 2 is greater than 0 and absolute value negative 2 = negative (negative 2) = 2 comma since negative 2 is less than 0 and absolute value 0 = 0

Official SAT Study Guide

Official SAT Study Guide

When it comes to getting answers, go to the source. This is the only guide with actual practice tests from the creators of the SAT. Review concepts and test-taking approaches, take 10 practice tests, and receive estimated scores.

 

The Official SAT Online Course™

Official SAT Online Course

The Official SAT Online Course features interactive lessons, auto essay scoring, and much more. It's personalized, comprehensive, easy to use, and available anytime and anywhere. Sign up, and you get 10 online tests, interactive lessons, and essay scoring.