College Algebra, Pre-Calculus, & Trigonometry Explained

Master College Level Algebra with our Step by Step Video Tutorials. Over 4500 Practice Questions! Ace your Algebra Exam!

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Math

What you will learn

Review of Basic Concepts: Real Numbers, Order of Operations, Number Line, Absolute Value

Review of Polynomials: Adding, Subtracting, Multiplying, Dividing, Synthetic Division, Factoring

Review of Rational Expressions: Lowest Terms, Undefined, Addition, Subtraction, Multiplication, Division, Complex Fractions

Review of Radical Expressions: Radical Notation, Simplifying a Radical, Operations with Radicals, Rationalizing Denominators

Solving Linear Equations and Inequalities

Solving Application of Linear Equations Problems (Word Problems)

Solving Absolute Value Equations and Inequalities

Working with Complex Numbers

Solving Quadratic Equations and Inequalities

Solving Applications of Quadratic Equations (Word Problems)

Solving Rational Equations and Inequalities

Solving Radical Equations and Inequalities

The Rectangular Coordinate Plane

The Complex Coordinate Plane

Distance and Midpoint Formulas

Relations and Functions

Domain and Range

Function Notation, Function Composition, Operations on Functions

Graphing Linear Equations

Linear Equations, Finding the Slope of a Line and Equations of Lines

Graphing Circles

Graphing Elementary Functions

Graphing Transformations

Solving Systems of Linear Equations in Two Variables

Solving Systems of Linear Equations in Three Variables

Solving Word Problems with Linear Systems

Using Curve Fitting to Find an Equation Through Three Points

Partial Fraction Decomposition

Solving Linear Systems using Gaussian Elimination and Gauss-Jordan Elimination

Matrix Algebra

Adding and Subtracting Matrices

Solving Matrix Equations

Multiplying a Matrix by a Scalar

Multiplying Matrices

Finding the Inverse of a Matrix

Solving Linear Systems using Matrix Inverses

Determine if functions are one-to-one using the horizontal line test

Determine if functions are one-to-one algebraically

Find the Inverse of a One-to-One Function

Find the Inverse of a Domain Restricted One-to-One Function

Graphing the Inverse of a Function

Graphing an Exponential Function

Solving Exponential Equations with Like Bases

Solving Compound Interest Word Problems

Graphing Logarithmic Functions

Properties of Logarithms | Condensing Logarithms | Expanding Logarithms

Change of Base Rule for Logarithms

Solving Exponential and Logarthimic Equations

Solving Exponential and Logarithmic Inequalities

Applications of Exponential and Logarithmic Functions

Finding the Vertex Form of a Parabola

How to Graph a Parabola

Remainder Theorem

Using the Remainder Theorem to Test Zeros for a Polynomial Function

The Factor Theorem

Using the Factor Theorem to Factor a Polynomial Function Given One Zero

The Rational Zeros Theorem

The Fundamental Theorem of Algebra

The Number of Zeros Theorem

Writing Polynomial Equations Given Zeros and a Point

Conjugate Zeros Theorem

Descartes' Rule of Signs

Intermediate Value Theorem

Boundedness Theorem

Finding the upper and lower bounds for the real zeros of a polynomial function

Solving NonLinear Systems of Equations

Conic Sections: Parabolas - Focus and Directrix

Conic Sections: Ellipses - Finding the Foci and Graphing

Sequences

Arithmetic Sequences

Geometric Sequences

Arithmetic Series

Geometric Series

Finding the Common Difference in an Arithmetic Sequence

Evaluating an Arithmetic Series

The Binomial Theorem

Working with sets, roster method, subsets, Venn diagrams

Combinations

Permutations

Counting Theory

Probability

Angles in Trigonometry

Complementary Angles

Supplementary Angles

Determine if two angles are coterminal angles

Finding Angle measures for similar triangles

Finding side lengths for similar triangles

Finding the Trigonometric Function Values of an Angle

Finding Trigonometric Function Values Given One Value and the Quadrant

Finding Trigonometric Function Values Based on Reciprocal Identities

Finding Trigonometric Function Values Based on Pythagorean Identities

Finding Trigonometric Function Values Based on Quotient Identities

Finding Trigonometric Function Values of Acute Angles

Writing a Trigonometric Function in terms of its Cofunction

Solving Trigonometric Equations Using Cofunction Identities

Finding Reference Angles

Special Angles as Reference Angles

Finding Angle Measures with Special Angles

Finding Trigonometric Function Values of Non-Acute Angles

Finding Trigonometric Function Values Using a Calculator

Finding Unknown Angle Measures Using Inverse Trigonometric Functions: arcsin, arccos, arctan

Solving Right Triangles

Solving Word Problems that involve angles of elevation

Solving Word Problems that involve angles of depression

Radian Measure

Converting Between Degrees and Radians

How to Find the Arc Length on a Circle

How to Find the Area of a Sector of a Circle

Defining the Six Trigonometric Functions Using the Unit Circle

Working with Circular Functions

Solving Trigonometry Word Problems that Involve Linear Speed

Solving Trigonometry Word Problems that Involve Angular Speed

Graphing Sine and Cosine

Function Transformations with Sine and Cosine

Finding the Period, Amplitude, and Phase Shift

Using the Fundamental Trigonometric Identities to Find Missing Trigonometric Ratios

Using the Fundamental Trigonometric Identities to rewrite Trigonometric Expressions

How to Verify Trigonometric Identities

Sum and Difference Identities for Sine, Cosine, and Tangent

Finding sin(A + B)

Finding cos(A + B)

Finding tan(A + B)

Double-Angle Identities

Product-to-Sum Identities

Sum-to-Product Identities

Half-Angle Identities

Evaluating Inverse Trigonometric Functions

Graphing the Inverse Trigonometric Functions

Finding the Composition of the Inverse Trigonometric Functions

Solving Trigonometric Equations Using Linear Methods

Solving Trigonometric Equations by Factoring

Solving Trigonometric Equations by Squaring/Square Roots

Solving Trigonometric Equations Using Identities

Solving Trigonometric Equations Using the Quadratic Formula

Solving Trigonometric Equations with Half-Angles

Solving Trigonometric Equations with Multiple Angles

Solving Trigonometric Equations Involving Inverse Trigonometric Functions

Law of Sines

Law of Sines (Ambiguous Case)

Area of a Triangle using Sine (SAS) and (ASA)

Law of Cosines

Area of a Triangle using Heron's Formula

Finding the Component Form of a Vector

Finding the Magnitude of a Vector

Finding the Direction Angle of a Vector

Finding the sum (resultant) of two vectors

Multiplying a vector by a scalar

Finding the Unit Vector

Writing a Linear Combination of Unit Vectors

Find the Dot Product of Two Vectors

Find the Angle Between Two Vectors

Determine if Two Vectors are Orthogonal

Adding Two Complex Numbers Graphically

Finding the Trigonometric (Polar) Form of a Complex Number

Converting a Complex Number between Rectangular and Polar Forms

Multiplying Complex Numbers in Polar Form

Dividing Complex Numbers in Polar Form

Product and Quotient Theorems

De Moivre's Theorem

Powers of Complex Numbers in Polar Form

Solving Equations Using Roots of Complex Numbers

Plotting Points on the Polar Coordinate Grid

Converting Points Between Rectangular and Polar Forms

Writing Polar Coordinates in Alternative Forms

Finding the Distance Between Two Polar Points

Converting a Line Between Polar and Rectangular Forms

Graphing a Line on the Polar Grid

Finding the Inclination of a Line

Finding the Angle Between Two Lines

Finding the Shortest Distance Between a Line and a Point

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