College Algebra & Trigonometry Explained by John Greene, M.A.

Description

That sounds like a comprehensive course that covers both college-level algebra and trigonometry concepts. By completing this course and practicing with the provided test questions, students can develop a strong understanding of these fundamental concepts and increase their chances of success in higher-level math classes like Calculus and Linear Algebra.

What will you learn:

• Basic Concepts: Real Numbers, Order of Operations, Number Line, Absolute Value
• Polynomials: Adding, Subtracting, Multiplying, Dividing, Synthetic Division, Factoring
• Rational Expressions: Lowest Terms, Undefined, Addition, Subtraction, Multiplication, Division, Complex Fractions
• Radical Expressions: Radical Notation, Simplifying a Radical, Operations with Radicals, Rationalizing Denominators
• Linear Equations and Inequalities
• Application of Linear Equations Problems (Word Problems)
• Absolute Value Equations and Inequalities
• Complex Numbers
• Quadratic Equations and Inequalities
• Applications of Quadratic Equations (Word Problems)
• Rational Equations and Inequalities
• 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
• Systems of Linear Equations in Two and Three Variables
• Word Problems with Linear Systems
• Curve Fitting to Find an Equation Through Three Points
• Partial Fraction Decomposition
• 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
• Compound Interest Word Problems
• Graphing Logarithmic Functions
• Properties of Logarithms, Condensing Logarithms, Expanding Logarithms
• Change of Base Rule for Logarithms
• Solving Exponential and Logarithmic Equations
• Finding the Vertex Form of a Parabola
• Graphing 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
• 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
• Sets, roster method, subsets, Venn diagrams
• Combinations
• Permutations
• Counting Theory
• Probability
• Angles in Trigonometry
• Complementary Angles

Requirements

• Basic Arithmetic (Addition, Subtraction, Multiplication, Division)
• Pre-Algebra (Must Have)
• Basic Algebra (Algebra 1) (Highly Suggested)
• Intermediate Algebra (Algebra 2) (Highly Suggested)