Fall 2019, The Citadel

Lessons & Objectives

■ 1.1 Real Numbers Properties: Addition, Subtraction, Multiplication, and Division. The Real Line, Sets and Intervals, Absolute Value and Distance.

■ 1.2 Integer Exponents, Rules for Working with Exponents, Scientific Notation, Radicals, Rational Exponents, Rationalizing the Denominator (standard form).

■ 1.3 Adding, Subtracting, and Multiplying Polynomials/Algebraic Expressions, Special Product Formulas, Factoring: Common Factors, Trinomials, and by Grouping Terms, Special Factoring Formulas.

■ 1.4 The Domain of an Algebraic Expression. Simplifying, Multiplying, Dividing, Adding, and Subtracting Rational Expressions, Compound Fractions. Rationalizing the Denominator or the Numerator, Avoiding Common Errors.

■ 1.5 Solving Linear, Quadratic, and other types of Equations.

■ 1.6 Arithmetic Operations on Complex Numbers, Square Roots of Negative Numbers, Complex Solutions of Quadratic Equations.

■ 1.7 Making and Using Models, Problems that involve Interest, Area or Length, Mixtures, Time Needed to Do a Job, and Distance, Rate, & Time.

■ 1.8 Solving Linear, Nonlinear, Absolute Value Inequalities, Modeling with Inequalities.

■ 1.9 The Coordinate Plane, Distance and Midpoint Formulas, Graphs of Equations in Two Variables, Intercepts, Circles, Symmetry.

■ 1.10 The Slope of a Line, Point-Slope Form & Slope-Intercept Form of the Equation of a Line, Vertical and Horizontal Lines, General Equation of a Line, Parallel and Perpendicular Lines.

■ 1.11 Solving Equations & Inequalities Graphically.

■ 2.1 Definition of Function, Evaluating a Function, the Domain, Ways to Represent a Function.

■ 2.2 Graphing Functions by Plotting Points, with a Graphing Calculator, Piecewise Defined Functions, The Vertical Line Test: Which Graphs or Equations Represent Functions?

■ 2.3 Values of a Function; Domain & Range, Comparing Function Values: Solving Equations & Inequalities Graphically, Increasing & Decreasing Functions, Local Maximum & Minimum Values.

■ 2.4 Average Rate of Change, Linear Functions Have Constant Rate of Change.

■ 2.5 Linear Functions, Slope and Rate of Change, Making and Using Linear Models.

■ 2.6 Transformations: Vertical & Horizontal Shifting, Reflecting Graphs, Vertical & Horizontal Stretching and Shrinking, Even and Odd Functions.

■ 2.7 Sums, Differences, Products, and Quotients. Composition of Functions.

■ 2.8 One-to-One Functions, Inverse of a Function, Finding & Graphing the Inverse of a Function.

■ 3.1 Graphing Quadratic Functions Using the Standard Form, Maximum and Minimum Values of Quadratic Functions, Modeling with Quadratic Functions.

■ 3.2 Polynomial Functions, Graphing Polynomial Functions, End Behavior, Using Zeros to Graph,

Shape of the Graph Near a Zero, Local Maxima and Minima of Polynomials.

■ 3.3 Long Division of Polynomials, Synthetic Division, the Remainder and Factor Theorems.

■ 3.4 Rational Zeros of Polynomials, Descartes’ Rule of Signs, Upper and Lower Bounds Theorem,

Using Algebra and Graphing Devices to Solve Polynomial Equations.

■ 3.5 The Fundamental Theorem of Algebra and Complete Factorization, Zeros and Their Multiplicities, Complex Zeros Come in Conjugate Pairs, Linear and Quadratic Factors.

■ 3.6 Rational Functions and Asymptotes, Transformations of y = 1/x, Graphing Rational Functions, Common Factors in Numerator and Denominator, Slant Asymptotes and End Behavior.

■ 3.7 Polynomial and Rational Inequalities.

■ 4.1 Exponential Functions, Graphs of Exponential Functions, Compound Interest.

■ 4.2 The Number e, The Natural Exponential Function, Continuously Compounded Interest.

■ 4.3 Logarithmic Functions, Graphs of Logarithmic Functions, Common & Natural Logarithms.

■ 4.4 Laws of Logarithms, Expanding & Combining Logarithmic Expressions, Change of Base Formula.

■ 4.5 Exponential Equations, Logarithmic Equations, Compound Interest.

■ 4.6 Exponential Growth (Doubling Time), Exponential Growth (Relative Growth Rate), Radioactive Decay, Newton’s Law of Cooling.

■ 5.1 The Unit Circle, Terminal Points on the Unit Circle, the Reference Number.

■ 5.2 The Trigonometric Functions, Values of the Trigonometric Functions, Fundamental Identities.

■ 5.3 Graphs of Sine and Cosine, Transformations, Using Calculator to Graph Trig. Functions.

■ 5.4 Graphs of Tangent, Cotangent, Secant, and Cosecant and Transformations of each.

■ 5.5 The Inverse Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent Functions.

■ 6.1 Angle Measure, Angles in Standard Position, Length of a Circular Arc, Area of a Circular Sector, Circular Motion.

■ 6.2 Trigonometric Ratios, Special Triangles; Calculators, Applications of Right Triangle Trig.

■ 6.3 Trigonometric Functions of Angles, Evaluating Trigonometric Functions at Any Angle, Trigonometric Identities, Areas of Triangles.

■ 6.4 The Inverse Sine, Inverse Cosine, and Inverse Tangent Functions, Solving for Angles in Right Triangles, Evaluating Expressions Involving Inverse Trigonometric Functions.

■ 6.5 The Law of Sines & the Ambiguous Case.

■ 6.6 The Law of Cosines, Navigation: Heading and Bearing, the Area of a Triangle.

■ 7.1 Simplifying Trigonometric Expressions & Proving Trigonometric Identities.

■ 7.2 Addition and Subtraction Formulas, Evaluating Expressions Involving Inverse Trigonometric Functions, Expressions of the form A sin x + B cos x.

■ 7.3 Double-Angle Formulas, Half-Angle Formulas, Evaluating Expressions Involving Inverse Trigonometric Functions, Product-Sum Formulas.

■ 7.4 Basic Trigonometric Equations, solving Trigonometric Equations by Factoring.

■ 7.5 Solving Trig. Equations by Using Identities, Eqns. w/ Trig. Functions of Multiples of Angles.

-Final Exam Review-

*FINAL EXAM*