Sidebar Menu
GIFTED MATH PROGRAM
Course IV Curriculum
Textbook: Blitzer, Pre-Calculus, 3rd 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