# Math Concepts

## Algebra and Functions

Next Tests:
12/5 , 1/23

### 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
• 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) =  , 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) = = = 4.

Note: the symbol represents the positive, or principal, square root. For example, = 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:

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

Also, . For example,  .

Note: For any nonzero number x, it is true that .

### 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  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

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