# Course IV Curriculum for Pre-Calculus

Textbook: Blitzer, Pre -Calculus, 3^{rd} edition,
Prentice-Hall, 2007.

**Chapter P: PREREQUISITES: FUNDMENTAL CONCEPTS OF
ALGEBRA
**Algebraic Expressions and Real Numbers; Exponents and Scientific Notation;
Radicals and Rational

Exponents; Polynomials; Factoring Polynomials; Rational Expressions; Equations; Modeling with

Equations; Linear Inequalities and Absolute Value Inequalities

**Chapter 1: FUNCTIONS AND GRAPHS**

Graphs and Graphing Utilities; Basics of Functions and Their Graphs; Linear Functions and Slope;

Transformations of Functions; Combinations of Functions ; Composite Functions; Inverse Functions;

Distance and Midpoint Formulas ; Circles; Modeling with Functions

**Chapter 2: POLYNOMIAL AND RATIONAL FUNCTIONS**

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

**Chapter 3: EXPONENTIAL AND LOGARITHMIC FUNCTIONS**

Exponential Functions; Logarithmic Functions; Properties of Logarithms; Exponential and Logarithmic

Equations; Exponential Growth and Decay; Modeling Data

**Chapter 4: TRIGONOMETRIC FUNCTIONS**

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

**Chapter 5: ANALYTIC TRIGONOMETRY**

Verifying Trigonometric Identities; Sum and Difference Formulas; Double-Angle, Power-Producing, and

Half-Angle Formulas; Product-to- Sum and Sum -to-Product Formulas; Trigonometric Equations

**Chapter 6: ADDITIONAL TOPICS IN TRIGONOMETRY**

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

**Chapter 7: SYSTEMS OF EQUATIONS AND INEQUALITIES**

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

**Chapter 8: MATRICES AND DETERMINANTS**

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

**Chapter 9: CONIC SECTIONS AND ANALYTIC GEOMETRY**

Parametric Equations; Conic Sections in Polar Coordinates

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