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 n^th 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)