Course Outline

Algebra II / Trigonometry Honors (5330)

Text:

 Algebra 2 McDougal Littell Series

(Larson, Boswell, Kanold, Stiff)

 

Equations and Inequalities: Chapter 1

(This Chapter is a review from Algebra 1 and should be completed in about 4 class meetings)

         1.1 Real Number and Number Operations

         1.2 Algebraic Expressions and Models

         1.3 Solving Linear Equations

         1.4 Rewriting Equations and Formulas

         1.5 Problem Solving Using Algebraic Models

         1.6 Solving Linear Inequalities

         1.7 Solving Absolute Value Equations and Inequalities

Linear Relations and Functions: Chapter 2

         2.1 Functions and their graphs (relations, mapping, domain, range, vertical line test, graphing and evaluating functions))

         Introduce Polynomial Function Notation: A polynomial function is a function of the form:  where , the exponents are all whole numbers, and the coefficients are all real numbers. Discuss polynomial function in standard form, the degree of a polynomial function, define is the leading coefficient is the constant term and is the degree of each term

         Constant Function is a polynomial function of degree 0.  Takes the form

          Linear Functions are polynomial functions of degree 1.  Take the form

         2.2 Slope and Rate of Change

         2.3 Sketching Graphs of Linear Equations

         2.4 Writing Equations of Lines: (point-slope, slope-intercept and standard form)

         2.5 Finding lines of Best Fit/Linear regression/Scatter Plots/Using calculator for lines of Best Fit

         2.6 Linear Inequalities in Two Variables

         2.7 Piecewise Functions defined /graphing piecewise defined functions (cover with honors)

         2.8 Absolute Value Functions (cover only with honors)

Systems of Linear Equations and Inequalities: Chapter 3

         3.1 Solving Linear Systems by Graphing

         3.2 Solving Linear Systems Algebraically (substitution method, elimination or linear combination method

         3.3 Graphing and Solving Systems of Linear Inequalities

Quadratic Functions: (Polynomial Function of Degree 2): Chapter 5

         Define quadratic expression, quadratic function, quadratic equation and quadratic formula

         5.1 Graphs of Quadratic Functions (5 key parts of the parabola: graphic)

         5.2 Solving Quadratic Equations by Factoring and the Zero Product Property (will need to review factoring from Algebra I)

         5.3 Solving Quadratic Equations by Finding Square Roots: (will need to review radicals: simplifying; addition/subtraction/multiplication/division of radicals, rationalizing denominators)

         5.4 Complex Numbers

         5.5 Solving Quadratic Equations by Completing the Square (you can use completing the square to write the quadratic function in vertex form, )

         5.6 The Quadratic Formula and the Discriminant (solving quadratic equations with the quadratic formula; derive the quadratic formula and now find the 5 key parts of the parabola the algebraic way)

         5.7 Graphing and Solving Quadratic Inequalities (determine the domain of a quadratic that makes the function positive, negative or zero) (honors only)

         5.8 Modeling Quadratic Functions:  (Word Problems building functions to solve real world problems. Writing Quadratic Functions given the x- intercept form or the vertex form) (honors only)

Polynomial Functions of Degree 3 and Higher: Chapter 6

         6.1 Properties of Exponents

         6.2 Evaluating and Graphing Polynomial Functions of Degree 3 and Higher (Evaluating through Direct and Synthetic Substitution

         Graphs of Polynomial Functions (Investigating End Behavior)

         6.3 Adding Subtracting and Multiplying Polynomials (Skills needed to factor higher degree polynomials)

         6.4 Factoring and Solving Polynomial Equations

         6.5 Remainder and Factor Theorems (Long And Synthetic Division)

         6.6 Finding Rational Zeros:  Rational Zero Theorem

         6.7 Using the Fundamental Theorem of Algebra

         6.8 Analyzing Graphs of Polynomial Functions (Turning Points: local maximum and local minimum (honors only)

Powers Roots and Radicals:  Chapter 7

         7.1 nth Roots and Rational Exponents

         7.2 Properties of Rational Exponents

         7.3 Power Functions and Function Operations (Arithmetic of Functions and Composite Functions) (honors only)

         7.4 Inverse Functions

         7.5 Graphing Square Root and cube Root Functions (honors only)

         7.6 Solving Radical Equations

Exponential and Logarithmic Functions:  Chapter 8

         8.1 Exponential Growth

         8.2 Exponential Decay

         8.3 Natural base e (honors only)

         8.4 Logarithmic Functions (using inverse properties and finding inverses)

         8.5 Properties of Logarithms

         8.6 Solving Exponential and Logarithmic Equations

Circles: Chapter 10

         10.1 The Distance and Midpoint Formulas

         10.3 Circles Graphing and Writing Equations of Circles

Trigonometric Functions: Chapter 13

         13.1 Right Triangle Trigonometry

         13.2 General Angles and Radian Measure

         13.3 Trigonometric Functions of Any Angle

         13.4 Inverse Trigonometric Functions (honors only if time permits)

Trigonometric Graphs: Chapter 14

         14.1 Graphing the Sine, Cosine and Tangent Functions (honors only if time permits)

         14.2 Translations and Reflections of Trigonometric Graphs (honors only if time permits)