# GIFTED MATH PROGRAM

## Course IV Curriculum

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 3: EXPONENTIAL AND LOGARITHMIC FUNCTIONS**

Exponential Functions; Logarithmic Functions; Properties of Logarithms;
Exponential and Logarithmic Equations; Exponential Growth and Decay; Modeling
Data

**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