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Precalculus
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Table of contents
1. Fundamental Concepts of Algebra
Worksheet
Algebraic Expressions, Mathematical Models, and Real Numbers
Exponents and Scientific Notation
Radicals and Rational Exponents
Polynomials
Factoring Polynomials
Rational Expressions
Equations
Models and Applications
Linear Inequalities and Absolute Value Inequalities
2. Functions and Graphs
Worksheet
Graphs and Graphing Utilities
Basics of Functions and Their Graphs
More on Functions and Their Graphs
Linear Functions and Slope
More on Slope
Transformations of Functions
Combinations of Functions, Composite Functions
Inverse Functions
Distance and Midpoint Formulas, Circles
Modeling with Functions
3. Polynomial and Rational Functions
Worksheet
Complex Numbers
Quadratic Functions
Polynomial Functions and Their Graphs
Dividing Polynomials, Remainder and Factor Theorems
Zeros of Polynomial Functions
Rational Functions and Their Graphs
Polynomial and Rational Inequalities
Modeling Using Variation
4. Exponential and Logarithmic Functions
Worksheet
Exponential Functions
Logarithmic Functions
Properties of Logarithms
Exponential and Logarithmic Equations
Exponential Growth and Decay, Modeling Data
5. Trigonometric Functions
Worksheet
Angles and Radian Measure
Trigonometric Functions: The Unit Circle
Right Triangle Trigonometry
Trigonometric Functions of Any Angle
Graphs of Sine and Cosine Functions
Graphs of Other Trigonometric Functions
Inverse Trigonometric Functions
Applications of Trigonometric Functions
6. Analytic Trigonometry
Worksheet
Verifying Trigonometric Identities
Sum and Difference Formulas
Double-Angle, Power-Reducing, and Half-Angle Formulas
Product-to-Sum and Sum-to-Product Formulas
Trigonometric Equations
7. Additional Topics in Trigonometry
Worksheet
The Law of Sines
The Law of Cosines
Polar Coordinates
Graphs of Polar Equations
Complex Numbers in Polar Form, DeMoivre's Theorem
Vectors
The Dot Product
8. Systems of Equations and Inequalities
Worksheet
Systems of Linear Equations in Two Variables
Systems of Linear Equations in Three Variables
Partial Fractions
Systems of Nonlinear Equations in Two Variables
Systems of Inequalities
Linear Programming
9. Matrices and Determinants
Worksheet
Matrix Solutions to Linear Systems
Inconsistent and Dependent Systems and Their Applications
Matrix Operations and Their Applications
Multiplicative Inverses of Matrices and Matrix Equations
Determinants and Cramer's Rule
10. Conic Sections and Analytic Geometry
Worksheet
The Ellipse
The Hyperbola
The Parabola
Rotation of Axes
Parametric Equations
Conic Sections in Polar Coordinates
11. Sequences, Induction, and Probability
Worksheet
Sequences and Summation Notation
Arithmetic Sequences
Geometric Sequences and Series
Mathematical Induction
The Binomial Theorem
Counting Principles, Permutations, and Combinations
Probability
12. Introduction to Calculus
Worksheet
Finding Limits Using Tables and Graphs
Finding Limits Using Properties of Limits
Limits and Continuity
Introduction to Derivatives
11. Sequences, Induction, and Probability
Arithmetic Sequences
11. Sequences, Induction, and Probability
Arithmetic Sequences
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Find the Common Difference for an Arithmetic Sequence
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Quick Intro to Arithmetic Sequences
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Write Terms of an Arithmetic Sequence
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11:06
Arithmetic Sequences: A Formula for the ' n - th ' Term
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Use the Formula for the General Term of an Arithmetic Sequence
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03:00
Arithmetic Sequences: Finding a General Formula Given Two Terms
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11:06
Arithmetic Sequences: A Formula for the ' n - th ' Term
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186
Use the Formula for the Sum of the First <i>n</i> Terms of an Arithmetic Sequence
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09:56
Finding the Sum of a Finite Arithmetic Series
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