Advanced Algebra & Trigonometry
This course builds a strong foundation for precalculus and calculus. Topics include transformations of functions, absolute value, quadratics, circles, polynomial functions, inverses and root functions, exponential growth & decay, logarithms, trigonometry, combinations, permutations & probability.
Each book builds on the previous one with a self-paced structure, answer keys and optional videos. Start at Book 1 or use the placement test to find your starting point.
6
books
930+
pages
$14.95
per book
1
Function Analysis & Absolute Value
158 pages
2
Quadratics, Circles & Nonlinear Systems
144 pages
3
Polynomials, Inverse & Radical Functions
176 pages
4
Exponential & Logarithmic Equations & Functions
162 pages
5
Trigonometry, Unit Circle, Equations & Identities
154 pages
6
Trigonometric Functions & Counting Principles
144 pages
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Advanced Algebra & Trigonometry Videos
BOOK 1 | 158 pages
Unit 1 | Analyzing Functions & Transformations
Unit 2 | Absolute Value Functions, Equations & Inequalities
TOPICS COVERED:
Unit 1 • Types of Functions • Domain & Range • Increasing, Decreasing & Constant Intervals • Positive & Negative Intervals • Minima & Maxima • End behavior • Classifying Even & Odd Functions • Composition of Functions • Linear Regression & Average Rate of Change • Vertical & Horizontal Transformations of Functions Unit 2 • Graphing an Absolute Value Function • Writing an Absolute Value Function as a Piecewise Function • Algebraic & Graphical Methods for Solving Absolute Value Equations • Algebraic & Graphical Methods for Solving Absolute Value Inequalities
BOOK 2 | 144 pages
Unit 3 | Quadratic Functions, Equations & Inequalities
Unit 4 | Circles & Nonlinear Systems
TOPICS COVERED:
Unit 3 • Methods for Solving Quadratic Equations • Imaginary Numbers & Exponents of i • Completing the Square & The Quadratic Formula • The Discriminant • Operations with Complex Numbers • Rationalizing a Binomial Denominator • Applying Transformations to Parabolas • Graphing a Quadratic Function in Vertex Form • Writing a Quadratic Function in Vertex Form • Converting from Standard Form to Vertex Form • Maximum Revenue Quadratic Scenarios • Rectangular Area Optimization Scenarios • Quadratic Border Scenarios • Solving Quadratic Inequalities Unit 4 • The Equation of a Circle • Applying Transformations to Circles • Converting a Circle's Equation to Standard Form • Transforming a Circle to an Ellipse • Solving Nonlinear Systems of Equations • Scenarios Involving Nonlinear Systems
BOOK 3 | 176 pages
Unit 5 | Polynomial Functions & Roots
Unit 6 | Inverse, Square Root & Cube Root Functions
TOPICS COVERED:
Unit 5 • Introduction to Cubic Functions • Applying Transformations to Cubic Functions • Graphing Cubic Functions • Writing a Cubic Function • Graphing Polynomial Functions • The Roots of a Polynomial Function • The Shape of a Polynomial Function at its Roots • The Multiplicity of a Root • Using a Calculator to Find the Roots of Polynomial Function • Solving Cubic Inequalities • Finding Real Roots of Polynomials • Making Connections Between Roots & Factors • Synthetic Division • Imaginary Roots of Polynomials • Rational Root Theorem • Polynomials with Imaginary Roots • The Remainder Theorem Unit 6 • Notation for Inverse Functions • Graphing Inverse Functions • Inverses That are not Functions • Using Composition to Prove Two Functions are Inverses • The Square Root Function • Applying Transformations to Square Root Functions • Graphing Square Root Functions • Finding the Equation of a Square Root Function • The Domain & Range of a Square Root Function • The Cube Root Function • Applying Transformations to Cube Root Functions • Graphing Cube Root Functions • Finding the Equation of a Cube Root Function • Domains of Square Root Functions • Domains of Rational Functions • Combining Square Root & Rational Functions
BOOK 4 | 162 pages
Unit 7 | Exponential Equations & Functions
Unit 8 | Logarithmic Properties, Equations & Functions
TOPICS COVERED:
Unit 7 • Introduction to Rational Exponents • Converting Between Exponential & Radical Form • Solving Equations With Rational Exponents • Exponential Equations • Quadratic Exponential Equations • Exponential Scenarios • Half-Life Scenarios • Exponential Patterns • Writing an Exponential Function • Applying Transformations to Exponential Functions • Writing the Equation for an Exponential Function • Exponential Growth & Decay • Percent Scenarios • Simple Interest Rate Scenarios • Introduction to Compound Interest • Continuously Compounded Interest Unit 8 • Introduction to Logarithms • Switching Between Exponential & Logarithmic Form • Two Common Bases: 10 & e • Switching Forms to Solve Exponential & Logarithmic Equations • Switching Forms to Identify an Inverse Function • The Product Rule for Logarithms • The Quotient Rule for Logarithms • The Power Rule for Logarithms • Solving Logarithmic Equations • Applications of Exponential & Logarithmic Functions • The Graph of a Logarithmic Function • Positive, Negative & Undefined Intervals • Using Inverses to Simplify a Logarithm in an Exponent
BOOK 5 | 176 pages
Unit 9 | Radians, Degrees & Unit Circle Trigonometry
Unit 10 | Trigonometric Equations & Identities
TOPICS COVERED:
Unit 9 • Scenarios Involving Sine, Cosine & Tangent • Angles in Degrees & Radians • Negative, Coterminal & Reference Angles • Common Sine & Cosine Ratios • Building the Unit Circle • Common Tangent Ratios • Three Ways to Define the Tangent Ratio • Reciprocal Trig Ratios • Non-Unit Circle Ratios Unit 10 • Reviewing Common Unit Circle Ratios • Simple Trig Equations • Advanced Trig Equations • Simple Trig Equations: Non-Unit Circle Ratios • General Solutions of Trig Equations • Proving Trigonometric Identities • Reciprocal & Quotient Identities • Strategies for Proving Identities • The 9 Pythagorean Identities • Applying Strategies to Prove Identities
BOOK 6 | 162 pages
Unit 11 | Graphing Trigonometric Functions
Unit 12 | Permutations, Combinations & Probability
TOPICS COVERED:
Unit 11 • Graphing Sine & Cosine Functions • Vertical Shifts & Stretches • Horizontal Stretches & Shifts • Modeling Sinusoidal Patterns • The Cosecant & Secant Functions • The Tangent & Cotangent Functions Unit 12 • Counting Principles • Permutations & Factorials • Given N Items, Arrange R • Defining Combinations • Advanced Permutations & Combinations • Introduction to Probability • Using Permutations & Combinations to Calculate Probability • Binomial Expansion