CLEP College Mathematics Review

A collection of key mathematical concepts and definitions for CLEP College Mathematics preparation.

Prime Number

Whole number that has only 2 factors (1 and itself).

Composite Number

Whole number that has factors in addition to 1 and itself.

Even Numbers

Composite numbers because they are all divisible by two.

Rational Number

Number that can be written as a ratio/fraction (e.g., 8 = 8/1).

Irrational Number

Number that can be written as a decimal but not a fraction (e.g., π = 3.141592…).

Absolute Value

Distance from 0 (|x|); never negative.

Factors

Numbers you multiply to get another number.

Domain

Set of all starting points (x) in a function.

Range

Set of all ending points (y) in a function.

Linear Function

A function of the form f(x) = x.

Quadratic Function

A function of the form f(x) = x^2.

Increasing Function

Function that goes up left to right.

Decreasing Function

Function that goes down left to right.

Odd Function

Function where replacing x with -x changes every sign of every term.

Greatest Integer Function

Greatest integer that is less than or equal to x (int(x)).

Union

All things that are members of either set A or set B.

Intersection

All things that are members of both sets A and B.

Cartesian Product

All ordered pairs of two sets A and B.

Truth Table

Tables used to compute truth values of logical expressions.

Conjunction

Combining of statements (P^Q = P and Q).

Disjunction

Including and/or to link two statements (P V Q).

Negation

Turns statement opposite (~P).

Independent Events

Outcome of one event doesn't affect the outcome of another event.

Standard Deviation

Measure of how spread out numbers are.

Logarithm

Inverse of exponentials, used to undo exponentials.

Pythagorean Theorem

a^2 + b^2 = c^2, relates legs of a right triangle to hypotenuse.

Area of Triangle

1/2 (b * h) or various other forms involving angles.

Volume of Sphere

Volume formula: (4/3)πR^3.

Complex Number

Form a + bi, where a and b are real numbers.

Adding Complex Numbers

Add real parts and imaginary parts separately.

Factor Theorem

Polynomial can be divided by a factor, yielding a remainder of 0.