Algebra and Precalculus Resources

Getting Started

This Algebra and Precalculus Resource is meant to aid you as you "brush up" on the content that you will need to be successfull in a Calculus 1 course. You may use the tutorials and examples gathered below to help you on your diagnostic test. This resource will, however, be available to you thoughout the term. Please take advantage of it.

 

Please use the navagation from the Conents page to jump to any topic that you would like to learn or review. You may return to this page whenever you would like by clicking on "Conents" at the top left of the screen or "toc" at the bottom left of any page.

 

Disclaimer:

The tutorials and other online resources are not controlled by the faculty at Gannon University. If any of the links do not seem to be taking you to the correct place, please let your instructor know so the problem can be resolved.

 

Algebra - Exponents and Simplifying

Order of operations

PEMDAS

"Please Excuse My Dear Aunt Sally."

YouTube Tutorial for PEMDAS

Examples:

 

The 5 main properties of exponents

Khan Academy Tutorial for the 5 main properties of exponents

 

Negative exponents and an exponent of zero

 Khan Academy Tutorial for Zero and Negative Exponents

 

Rational exponents

 

Khan Academy Tutorial for Rational Exponents 

 

How to simplify expressions involving square roots

YouTube Tutorial for Simplyfing Expressions Involving Square Roots

 

How to simplify expressions with exponents

 

Simplifying rational expressions

Khan Academy Tutorial for Simplifying Expressions with Rational Exponents

 

 

Adding and subtracting rational expressions

Khan Academy Tutorial for Adding and Subtracting Rational Expressions

 

Multiply by conjugate

YouTube Tutorial for Conjugates

 

Common mistakes

Adding Fractions

YouTube Tutorial for Adding Fractions

 

Square Roots

YouTube Tutorial for Working with Square Roots

 

Algebra - Binomials and Factoring

The basics

From Stewart's Essential Calculus 2nd Edition

 

How to add, subtract, and multiply polynomials

Khan Academy Tutorial on Polynomials

 

Multiplying binomials and the FOIL method

From Stewart's Essential Calculus 2nd Edition

Khan Academy Tutorial for FOIL

 

Binomials raised to the third power

 

 

How to factor quadratic expressions

Khan Academy Tutorial for Factoring

Khan Academy Tutorial for Factoring Quadratics

 

How to factor cubic or "like-quadratic" expressions

YouTube Tutorial for Factoring "like-quadradic" Expressions

 

How to complete the square

Khan Academy Tutorial for Completing the Square

 

Algebra - Solving Equations and Inequalities

 

Solving quadratic equations through factoring

Khan Academy Tutorial for Solving through Factoring

 

Solving quadratic equations using the quadratic formula

Khan Academy Tutorial for Solving using the Quadratic Equation

 

Solving equations involving square roots

YouTube Tutorial for Solving Equations Involving Square Roots

 

Solving equations involving absolute values

Khan Academy Tutorial for Solving Equations Involving Absolute Values

 

Inequalities

Khan Academy Tutorial for Introduction to Inequalities

 

Solving inequalities and interval (or set) notation

You Tube Tutorial for Set Notation

 

Solving inequalities

Khan Academy Tutorial for Solving Inequalities

 

Solving inequalities involving absolute values

Khan Academy Tutorial for Inequalities Involving Absolute Values

 

Analytic Geometry

Linear equations

Khan Academy Tutorial for Linear Equations

 

Graphing linear equations: intercepts, slope, and y=mx+b form.

Khan Academy Tutorial for Graphing Linear Equations

 

Graphing a line using point/slope form

Khan Academy Tutorial for Graphing using Point/Slope Formula

 

Vertical and horizontal lines

You Tube Tutorial for Vertical and Horizontal Lines

 

Equation of a circle

YouTube Tutorial on the Equation of a Circle

 

How to complete the square

Khan Academy Tutorial for Completing the Square

YouTube Tutorial for Completing the Square

  

Midpoint formula

YouTube Tutorial for the Midpoint Formula

 

Finding the distance between two points

Khan Academy Tutorial for the Distance between Two Points

 

Perpendicular bisector

YouTube Tutorial for the Perpendicular Bisector

 

How to graph inequalities

Education Portal Tutorial for Graphing Inequalities

 

Graphing inequalities involving the absolute value

Khan Academy Tutorial for Inequalities Involving Absolute Values

 

Sketching nonlinear inequalities

YouTube Tutorial for Sketching Nonlinear Inequalities 

 

Functions

Basics of functions

Khan Academy Tutorial for the Basics of Functions

 

Domain and range of a function

Khan Academy Tutorial for Domain and Range

 

Difference quotient

YouTube Tutorial for the Difference Quotient

 

Transformations of functions

Khan Academy Tutorial for the Transformation of Functions

 

Basic functions:

, ,

,

YouTube Tutorial on Basic Functions

 

Piecewise-defined functions

YouTube Tutorial on Piecewise-Defined Functions

 

Function composition

Khan Academy Tutorial on Function Composition

 

Trigonometry

Conversion from degrees to radians

YouTube Tutorial on Converting from Degrees to Radians

 

Conversion from radians to degrees

YouTube Tutorial on Converting from Radians to Degrees

 

Arc length

YouTube Tutorial on Arc Length

 

Sine and cosine

Khan Academy Tutorial on Sine and Cosine

 

Soh-Cah-Toa

Khan Academy Tutorial on the Trigonometry and the Pythagorean Theorem

 

Trigonometric Identities

Reciprocal

 

 

 

 

Ratio

 

 

Pythagorean

 

 

 

Sum and Difference

 

 

 

 

Double-Angle

 

                     

                     

 

OR

 

 

Half-Angle

 

 

Product to Sum

 

Sum to Product

 

 

 

 

Solving trigonometric equations

YouTube Tutorial on Sovling Trigonometric Equations

Sources

Much of the content from this resource has been gained from the following sources:

Stewart's Essential Calculus, Second Edition,
the Khan Academy, and YouTube.