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Course IV Curriculum for Pre-Calculus

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 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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