Math 119 Pre-Calculus

Fall 2019, The Citadel




Syllabus  Schedule  Homework videos Exams  

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-