Pre-Calculus

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How to Use the Roots of a Polynomial to Find Its Factors

The factor theorem states that you can go back and forth between the roots of a polynomial and the factors of a polynomial. In other words, if you know one, you know the other. At times, your teacher or [more…]

How to Graph Polynomials When the Roots Are Imaginary Numbers — An Overview

In pre-calculus and in calculus, certain polynomial functions have non-real roots in addition to real roots (and some of the more complicated functions have [more…]

Understanding the Binomial Theorem

A binomial is a polynomial with exactly two terms. Multiplying out a binomial raised to a power is called binomial expansion. Your pre-calculus teacher may ask you to use the binomial theorem to find the [more…]

Frequently Used Pre-Calculus Formulas

Mathematical formulas are equations that are always true. You can use them in algebra, geometry, trigonometry, and many other mathematical applications, including pre-calculus. Refer to these formulas [more…]

Counting Techniques for Pre-Calculus

Counting the number of ways to perform a task is fairly simple — until the number of choices gets too large. Here are three counting techniques used in pre-calculus: [more…]

Completing the Square for Pre-Calculus

Quadratic equations are written in many different formats, depending on what the current application is. Completing the square is helpful when you’re writing conics in their standard form, and you can [more…]

1,001 Pre-Calculus Practice Problems For Dummies Cheat Sheet

Pre-calculus draws from algebra, geometry, and trigonometry and combines these topics to prepare you for the techniques you need to succeed in calculus. This cheat sheet provides the most frequently used [more…]

Limits and Continuity in Pre-Calculus

In mathematics, a limit suggests that you’re approaching some value. Some functions, such as a rational function with a horizontal asymptote, have a limit as the [more…]

Solving Equations and Inequalities

The object of solving equations and inequalities is to discover which number or numbers will create a true statement in the given expression. The main techniques you use to find such solutions include [more…]

Function Basics for Pre-Calculus

A function is a special type of rule or relationship. The difference between a function and a relation is that a function has exactly one output value [more…]

Graphing and Transforming Functions

You can graph functions fairly handily using a graphing calculator, but you’ll be frustrated using this technology if you don’t have a good idea of what you’ll find and where you’ll find it. You need to [more…]

Polynomials and Pre-Calculus

Polynomial functions have graphs that are smooth curves. They go from negative infinity to positive infinity in a nice, flowing fashion with no abrupt changes of direction. Pieces of polynomial functions [more…]

Exponential and Logarithmic Functions Used in Pre-Calculus

Exponential and logarithmic functions go together. You wouldn’t think so at first glance, because exponential functions can look like f(x) = 2e3x, and logarithmic [more…]

Trigonometry Basics Needed for Pre-Calculus

Trigonometric functions are special in several ways. The first characteristic that separates them from all the other types of functions is that input values are always angle measures. You input an angle [more…]

Graphing Trig Functions in Pre-Calculus

The graphs of trigonometric functions are usually easily recognizable — after you become familiar with the basic graph for each function and the possibilities for transformations of the basic graphs. [more…]

Getting Started with Trig Identities

You need to become more familiar with the possibilities for rewriting trigonometric expressions. A trig identity is really an equivalent expression or form of a function that you can use in place of the [more…]

Beyond the Basics with Trig Identities

The basic trig identities will get you through most problems and applications involving trigonometry. But if you’re going to broaden your horizons and study more and more mathematics, you’ll find some [more…]

Complex Numbers in Pre-Calculus

Complex numbers are unreal. Yes, that’s the truth. A complex number has a term with a multiple of i, and iis the imaginary number equal to the square root of –1. Many of the algebraic rules that apply [more…]

Polar Coordinates for Graphing Complex Numbers

You’ll work on graphing complex numbers. Polar coordinates are quite different from the usual (x, y) points on the Cartesian coordinate system. Polar coordinates bring together both angle measures and [more…]

Conic Sections in Pre-Calculus

Conic sections can be described or illustrated with exactly what their name suggests: cones. Imagine an orange cone in the street, steering you in the right direction. Then picture some clever highway [more…]

Systems of Equations Used in Pre-Calculus

A system of equations is a collection of two or more equations involving two or more variables. If the number of equations is equal to the number of different variables, then you may be able to find a [more…]

Systems of Inequalities in Pre-Calculus

A system of inequalities has an infinite number of solutions (unless it has none at all). You solve these systems using graphs of the separate statements. [more…]

What You Need to Know About Sequences in Pre-Calculus

A sequence is a list of items; in mathematics, a sequence usually consists of numbers such as 1, 2, 4, 8, . . . or 1, 1, 2, 3, 5, 8, 13, . . . See the patterns in these two sequences? You need to know [more…]

What You Need to Know About Series in Pre-Calculus

A series is the sum of a list of numbers, such as 1 + 2 + 4 + 8. Many times, you can find a formula to help you add up the numbers in a series. Formulas are especially helpful when you have a lot of numbers [more…]

Algebra Basics Needed for Pre-Calculus

The basics of pre-calculus consist of reviewing number systems, properties of the number systems, order of operations, notation, and some essential formulas used in coordinate graphs. Vocabulary is important [more…]

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