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Course IV Curriculum for PreCalculus
Textbook: Blitzer, Pre Calculus, 3^{rd} edition, PrenticeHall, 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;
DoubleAngle, PowerProducing, and
HalfAngle Formulas; Productto 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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