Precalculus Spring 2008 Update 3 - For Instructor and Student clients March 25, 2008 Updates Precalculus Fall 2007 to the Spring 2008 Update 3 version (1.1.8) Version 1.1.8 corrects issues in the following lessons: 1.2a Properties of Exponents 1.5a Linear Equations in One Variable 10.8 Nonlinear Systems of Equations 3.1 Relations and Functions 3.2a Linear and Quadratic Functions 3.4 Variation and Multi-Variable Functions 3.6 Combining Functions 3.7 Inverses of Functions 4.2 Polynomial Division and the Division Algorithm 4.5 Rational Functions and Rational Inequalities 5.2 Applications of Exponential Functions 6.1 Radian and Degree Measure of Angles 6.2 Trigonometric Functions of Acute Angles 7.3 Product - Sum Identities 8.4b Operations with Complex Numbers Version 1.1.7 adds multiple choice questions to the following lessons: 3.4 Variation and Multi-Variable Functions 4.2 Polynomial Division and the Division Algorithm 6.1 Radian and Degree Measure of Angles 6.2 Trigonometric Functions of Acute Angles 7.3 Product - Sum Identities Version 1.1.6 corrects issues in the following lessons: 1.1b The Arithmetic of Algebraic Expressions 1.2a Properties of Exponents 2.1 The Cartesian Coordinate System 2.3 Forms of Linear Equations 2.6 Introduction to Circles 3.1 Relations and Functions 3.4 Variation and Multi-Variable Functions 4.2 Polynomial Division and the Division Algorithm 4.3 Locating Real Zeros of Polynomials 4.5 Rational Functions and Rational Inequalities 5.2 Applications of Exponential Functions 5.4 Properties and Applications of Logarithms 5.5 Exponential and Logarithmic Equations 6.1 Radian and Degree Measure of Angles 6.2 Trigonometric Functions of Acute Angles 6.3 Trigonometric Functions of Any Angle 6.4 Graphs of Trigonometric Functions 6.5 Inverse Trigonometric Functions 7.1 Fundamental Identities and their Uses 7.2 Sum and Difference Identities 7.3 Product - Sum Identities 7.4 Trigonometric Equations 8.1a The Law of Sines and the Law of Cosines 8.1b Area of Triangles 8.2 Polar Coordinates and Polar Equations 8.3a Parametric Equations - Graphing and Applications 8.3b Parametric Equations - Eliminating the Parameter 8.3c Parametric Equations - Constructing Equations 8.4a Trigonometric Form of Complex Numbers 8.4b Operations with Complex Numbers 8.5 Vectors in the Cartesian Plane 8.6 The Dot Product and Its Uses 9.4 Rotation of Conics 9.5 Polar Form of Conic Sections 10.1 Solving Systems by Substitution and Elimination 10.6 Partial Fraction Decomposition 10.7 Linear Programming version 1.1.5 corrects issues in the following lessons: 4.5 Rational Functions and Rational Inequalities 5.1 Exponential Functions and their Graphs 5.5 Exponential and Logarithmic Equations 6.1 Radian and Degree Measure of Angles 6.2 Trigonometric Functions of Acute Angles 6.3 Trigonometric Functions of Any Angle 6.4 Graphs of Trigonometric Functions 6.5 Inverse Trigonometric Functions 7.1 Fundamental Identities and their Uses 7.2 Sum and Difference Identities 7.3 Product - Sum Identities 8.1a The Law of Sines and the Law of Cosines 8.2 Polar Coordinates and Polar Equations 8.4a Trigonometric Form of Complex Numbers 8.4b Operations with Complex Numbers 8.5 Vectors in the Cartesian Plane 9.4 Rotation of Conics v1.1.4 corrects issues in the following lessons: 2.3 Forms of Linear Equations 2.6 Introduction to Circles 3.1 Relations and Functions 3.6 Combining Functions 4.3 Locating Real Zeros of Polynomials 4.4 The Fundamental Theorem of Algebra 4.5 Rational Functions and Rational Inequalities 5.2 Applications of Exponential Functions 5.4 Properties and Applications of Logarithms 5.5 Exponential and Logarithmic Equations 6.4 Graphs of Trigonometric Functions 8.4b Operations with Complex Numbers 9.2 The Parabola 10.4 The Algebra of Matrices 10.6 Partial Fraction Decomposition 10.7 Linear Programming V1.1.3 corrects issues in the following lessons: 1.1a The Real Number System 1.1b The Arithmetic of Algebraic Expressions 1.2a Properties of Exponents 1.2b Scientific Notation and Geometric Problems Using Exponents 1.2c Properties of Radicals 1.2d Rational Number Exponents 1.3 Polynomials and Factoring 1.4 The Complex Number System 1.5a Linear Equations in One Variable 1.5b Applications of Linear Equations in One Variable 1.6 Linear Inequalities in One Variable 1.7a Quadratic Equations in One Variable 1.7b Higher Degree Polynomial Equations 1.8a Rational Expressions and Equations 1.8b Radical Equations 2.1 The Cartesian Coordinate System 2.2 Linear Equations in Two Variables 2.3 Forms of Linear Equations 2.4 Parallel and Perpendicular Lines 2.5 Linear Inequalities in Two Variables 2.6 Introduction to Circles 3.1 Relations and Functions 3.2a Linear and Quadratic Functions 3.2b Max/Min Applications of Quadratic Functions 3.3 Other Common Functions 3.4 Variation and Multi-Variable Functions 3.5 Transformations of Functions 3.6 Combining Functions 3.7 Inverses of Functions 4.1 Introduction to Polynomial Equations and Graphs 4.2 Polynomial Division and the Division Algorithm 4.3 Locating Real Zeros of Polynomials 4.4 The Fundamental Theorem of Algebra 4.5 Rational Functions and Rational Inequalities 5.1 Exponential Functions and their Graphs 5.2 Applications of Exponential Functions 5.3 Logarithmic Functions and their Graphs 5.4 Properties and Applications of Logarithms 5.5 Exponential and Logarithmic Equations 6.5 Inverse Trigonometric Functions 7.1 Fundamental Identities and their Uses 7.2 Sum and Difference Identities 9.1 The Ellipse 9.2 The Parabola 9.3 The Hyperbola 10.1 Solving Systems by Substitution and Elimination 10.2 Matrix Notation and Gaussian Elimination 10.3 Determinants and Cramer's Rule 10.4 The Algebra of Matrices 10.5 Inverses of Matrices 10.7 Linear Programming 10.8 Nonlinear Systems of Equations 11.2 Arithmetic Sequences and Series 11.3 Geometric Sequences and Series 11.4 Mathematical Induction 11.5a An Introduction to Combinatorics - Counting, Permutations, and Combinations v1.1.2 corrects issues in the following lessons: 1.1b The Arithmetic of Algebraic Expressions 1.8b Radical Equations 2.2 Linear Equations in Two Variables 2.3 Forms of Linear Equations 2.4 Parallel and Perpendicular Lines 2.5 Linear Inequalities in Two Variables 2.6 Introduction to Circles v1.1.1 corrects issues in the following lessons: 1.1a The Real Number System 1.1b The Arithmetic of Algebraic Expressions 1.2a Properties of Exponents 1.2b Scientific Notation and Geometric Problems Using Exponents 1.2c Properties of Radicals 1.2d Rational Number Exponents 1.3 Polynomials and Factoring 1.4 The Complex Number System 1.5a Linear Equations in One Variable 1.5b Applications of Linear Equations in One Variable 1.6 Linear Inequalities in One Variable 1.7a Quadratic Equations in One Variable 1.7b Higher Degree Polynomial Equations 1.8b Radical Equations 1.8a Rational Expressions and Equations 2.1 The Cartesian Coordinate System 2.3 Forms of Linear Equations 2.4 Parallel and Perpendicular Lines 2.5 Linear Inequalities in Two Variables 2.6 Introduction to Circles 3.1 Relations and Functions 3.2a Linear and Quadratic Functions 3.2b Max/Min Applications of Quadratic Functions 3.3 Other Common Functions 3.5 Transformations of Functions 3.6 Combining Functions 3.7 Inverses of Functions 4.1 Introduction to Polynomial Equations and Graphs 4.2 Polynomial Division and the Division Algorithm 4.3 Locating Real Zeros of Polynomials 4.4 The Fundamental Theorem of Algebra 4.5 Rational Functions and Rational Inequalities 6.5 Inverse Trigonometric Functions 7.1 Fundamental Identities and Their Uses 7.2 Sum and Difference Identities 10.8 Nonlinear Systems of Equations