PRECALCULUS MR. MILLER

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PRECALCULUS MR. MILLER I. COURSE DESCRIPTION This course requires students to use symbolic reasoning and analytical methods to represent mathematical situations, to express generalizations, and to study mathematical concepts and relationships among them. Students use functions, equations and limits as tools for expressing generalizations and as a means for analyzing and understanding a broad variety of mathematical relationships. Students will also use functions, as well as, symbolic reasoning to represent and connect ideas in geometry, probability, statistics, and trigonometry. Students use a variety of representations (concrete, numerical, algorithmic, graphical), tools, and techniques to model functions and equations and solve real life problems. TENTATIVE LESSON PLAN (by date) I. Functions and Their Graphs (Chapter 1) 8/25-8/27 1. Functions (Ch. 1.4) a. Objectives: 1) Determine whether relations between two variables are functions 2) Use function notation and evaluate functions 3) Find the domain of functions 4) Use functions to model and solve real-life problems 5) evaluate difference quotients. b. TEKS: P.1.B, P.3.A c. Assignment: p. 48-52 >> 10, 18, 22, 24, 28, 30, 32, 34, 36, 38, 50, 52, 56, 58-70 even, 80, 82, 84, 88, 100 8/28 8/29 2. Analyzing Graphs of Functions (Ch. 1.5) a. Objectives: 1) Use the Vertical Line Test for functions 2) Find the zeros of functions 3) Determine intervals on which a function is increasing or decreasing and determine relative maximum and relative minimum values of functions 4) Determine the average rate of change of a function 5) Identify even and odd functions. b. TEKS: P.1.B, P.1.C, P.1.D, P.3.B, P.3.D c. Assignment: p. 61-64 >> 2-24 even, 46, 48, 50, 52, 68, 70, 72, 74, 76, 78, 80, 88 9/2 9/3, 9/4 9/5, 9/8 3. A Library of Parent Functions (Ch. 1.6) a. Objectives: 1) Identify and graph linear, quadratic, cubic, square root, inverse, and piece-wise functions 2) Recognize graphs of parent functions. b. TEKS: P.1.A, P.1.B, P.1.D, P.3.B, P.3.D c. Assignment: p. 71-72 >> 2-60 eoe 4. Transformations of Functions (Ch. 1.7) a. Objective: Use transformations to sketch graphs of functions. b. TEKS: P.1.A, P.1.B, P.2.A c. Assignment: p. 79-83 >> 2-64 eoe 5. Combinations of Functions: Composite Functions (Ch. 1.8) a. Objectives: 1) Add, subtract, multiply, and divide functions 2) Find compositions of functions 3) Use combinations and compositions of functions to model and solve real-life problems. b. TEKS: P.1.B, P.2.A, P.2.B c. Assignment: p. 89-92 >> 2-64 eoe

9/9 9/10, 9/11 9/12 9/15 6. Inverse Functions (Ch. 1.9) a. Objectives: 1) Verify inverses 2) Use graphs of functions to determine whether functions have inverse functions 3) Determine if functions are one-to-one 4) Find inverse functions algebraically. b. TEKS: P.1.B, P.2.B c. Assignment: p. 99-102 >> 14-38 even, 72, 78 7. Mathematical Modeling and Variation (Ch. 1.10) a. Objective: Write and use mathematical models to approximate sets of data (direct, inverse, and joint variation, and direct variation as an nth power). b. TEKS: P.3.B, P.3.C, P.3D c. Assignment: p. 110-113 >> 8, 40-70 even 8. Chapter Review (p. 117-120 >> 71-165 eoo) 9. Chapter Test (p. 123 >> 1-25) 10. TEST (Ch. 1.6-10) II. Polynomial and Rational Functions (Chapter 2) 9/16, 9/17 1. Quadratic Functions and Models (Ch. 2.1) a. Objectives: 1) Analyze graphs of quadratic functions 2) Write quadratic functions in standard form and use the results to sketch graphs of functions 3) Use quadratic functions to model and solve real-world problems 4) Derive the x-value of vertex and the Quadratic Formula. b. TEKS: P.1.A, P.1.D, P.3.A, P.3.B, P.3.D c. Assignment: p. 134-137 >> 1-8, 34, 44, 46, 48, 56, 66, 68, 70, 74, 76, 78, 80, 86 9/18, 9/19 2. Polynomial Functions of Higher Degree (Ch. 2.2) a. Objectives: 1) Use transformations, end behavior, and zeros to sketch the graphs of polynomial functions 2) Use the Intermediate Value Thm. to locate zeros. b. TEKS: P.1.A, P.1.D, P.1.E, P.3.A, P.3.B, P.3.D c. Assignment: p. 148-149 >> 2-22 eoe, 28-42 eoe, 48-56 eoe, 64, 66, 68, 74, 80, 86, 90, 92, 98 9/22 3. Polynomial and Synthetic Division (Ch. 2.3) a. Objectives: 1) Use long and synthetic division to divide polynomials 2) Apply the Remainder and Factor Theorems. b. TEKS: Prerequisite skills and concepts for P.1.D c. Assignment: p. 159-161 >> 14-18 even, 26, 30, 36, 38, 40, 44, 70, 74, 84, 90, 96 9/23 4. Complex Numbers (Ch. 2.4) a. Objectives: 1) Write complex numbers 2) Add, subtract, and multiply complex numbers 3) Use complex conjugates to write the quotient of two complex numbers in standard form 4) Find the complex solutions of quadratic equations. b. TEKS: Prerequisite skills and concepts for P.1.D c. Assignment: p. 167-168 >> 6, 14, 16, 22-26 even, 30-44 even, 56, 58, 70-74 even, 83, 90

9/24, 9/25 9/26, 9/29 9/30, 10/1 10/2 10/3 5. Zeros of Polynomial Functions (Ch. 2.5) a. Objectives: 1) Use Fundamental Theorem of Algebra 2) Find rational zeros 3) Find conjugate pairs of complex zeros 4) Find all zeros of a polynomial function 5) Apply Descartes s Rule of Signs. b. TEKS: P.1.D, P.3.A, P.3.B, P.3.D c. Assignment: p. 179-183 >> 12, 14, 16, 34, 40, 42, 58, 60, 62, 68, 70, 99-102, 106, 108 6. Rational Functions (Ch. 2.6) a. Objectives: 1) Find the domain of rational functions 2) Find the horizontal, vertical, and slant asymptotes of the graphs of rational functions 3) Sketch the graph of rational functions 4) Use rational functions to model real-world problems. b. TEKS: P.1.A, P.1.B, P.1.D, P.1.E, P.3.B, P.3.D c. Assignment: p. 194-195 >> 28-46 even, 74, 76, 81-84 all, 92 7. Nonlinear Inequalities (Ch. 2.7) a. Objectives: 1) Solve polynomial and rational inequalities 2) Use iequalities to solve real-life problems. b. TEKS: extension c. Assignment: p. 204-205 >> 1-46 eoe, 68-72 even 6. Chapter Review (p. 208-210 >> 1-153 odd) 7. Chapter Test (p. 212 >> 1-18) 8. TEST (Ch. 2.1-7) III. Exponential and Logarithmic Functions (Chapter 3) 10/6, 10/7 1. Exponential Functions and Their Graphs (Ch. 3.1) a. Objectives: 1) Recognize and evaluate exponential functions with base a and base e 2) Graph exponential functions 3) Use exponential models. b. TEKS: P.1.A, P.1.B, P.1.E, P.3.B, P.3.D c. Assignment: p. 226-227 >> 7-10, 12-68 eoe 10/8, 10/9 2. Logarithmic Functions and Their Graphs (Ch. 3.2) a. Objectives: 1) Recognize and evaluate logarithmic functions with base a and base e 2) Graph logarithmic functions 3) Use logarithmic models. b. TEKS: P.1.A, P.1.B, P.1.E, P.2.C, P.3.B, P.3.D c. Assignment: p. 236-238 >> 2-78 eoe, 88, 90 10/10, 10/13 3. Properties of Logarithms (Ch. 3.3) a. Objective: Use the properties of logarithms to evaluate or rewrite logarithmic expressions. b. TEKS: P.2.C, P.3.B, P.3.D c. Assignment: p. 243-244 >> 24-78 eoe, 84

10/14, 10/17 10/20, 10/21 10/22 10/23, 10/24 4. Exponential and Logarithmic Equations (Ch. 3.4) a. Objective: Solve exponential and logarithmic equations. b. TEKS: P.2.C, P.3.B, P.3.D c. Assignment: p. 253-256 >> 22-102 eoe, 112, 119-122 all 5. Exponential and Logarithmic Models (Ch. 3.5) a. Objectives: 1) Recognize the five most common types of exponential and logarithmic functions 2) Use each of these functions to model real-life problems. b. TEKS: P.2.C, P.3.B, P.3.D c. Assignment: p. 264-269 >> 1-6 all, 38-64 eoe, 67-71 all 6. Chapter Review (p. 271-274 >> 1-155 eoo) 7. Chapter Test (p. 275 >> 1-29) 8. TEST (Ch. 3.1-5) IV. Trigonometry (Chapter 4) 10/27-10/29 1. Radian and Degree Measure (Ch. 4.1) a. Objectives: 1) Describe angles 2) Use radian and degree measure 3) Use angles to model and solve real-life problems. b. TEKS: P.1.A, P.2.A c. Assignment: p. 290-293 >> 7-70 eoe, 72, 74, 76, 78, 98, 100, 102, 104, 106, 108, 114, 116 10/30, 10/31 2. The Unit Circle (Ch. 4.2) a. Objectives: 1) Identify the unit circle and describe its relationship to the real numbers 2) Evaluate trigonometric functions using the unit circle 3) Use the domain and period of the sine and cosine functions 4) Use the calculator to evaluate trig. functions. b. TEKS: P.1.B, P.1.C, P.3.A, P.3.B, P.3.D, P.3.E c. Assignment: p. 299-300 >> 2-52 eoe 11/3 3. Right Triangle Trigonometry (Ch. 4.3) a. Objectives: 1) Evaluate trig. functions of acute angles 2) Use the fundamental trig. identities 3) Use the calculator to evaluate trig. functions 4) Use trig. functions to model problems. b. TEKS: P.2.C, P.3.A, P.3.B, P.3.D, P.3.E c. Assignment: p. 308-311 >> 6-70 eoe, 80 11/4-11/6 4. Trigonometric Functions of Any Angle (Ch. 4.4) a. Objectives: 1) Evaluate trig. functions of any angle 2) Use reference angles 3) Evaluate trig. functions of real numbers. b. TEKS: P.3.A, P.3.B, P.3.D, P.3.E c. Assignment: p. 318-319 >> 2-84 eoe

11/7 11/10, 11/11 5. Chapter Review (p. 365-368 >> 1-87 eoo) 6. Chapter Test (p. 369 >> 1-11) 7. TEST (Ch. 4.1-4) 11/12, 11/13 8. Graphs of the Sine and Cosine Functions (Ch. 4.5) a. Objective: Sketch the graphs of the basic sine and cosine functions. b. TEKS: P.1.A, P.1.B, P.1.C, P.1.D, P.1.E, P.3.A, P.3.B, P.3.D, P.3.E c. Assignment: p. 328-319 >> 2-26 even, 36-56 even, 64-70 even, 74, 76, 78, 81-83, 85 11/14, 11/17 9. Graphs of Other Trigonometric Functions (Ch. 4.6) a. Objective: Sketch the graphs of the tangent, secant, cosecant, and cotangent functions. b. TEKS: P.1.A, P.1.B, P.1.D, P.1.E, P.3.A, P.3.B, P.3.D, P.3.E c. Assignment: p. 339 >> 8-40 eoe 11/18 10. Inverse Trigonometric Functions (Ch. 4.7) a. Objective: Evaluate and graph the sine, cosine, and tangent functions. b. TEKS: P.1.A, P.1.B, P.1.E, P.3.A c. Assignment: p. 349-350 >> 2-74 eoe 11/19, 11/20 11. Applications and Models (Ch. 4.8) a. Objective: Solve real-life problems involving trigonometry. b. TEKS: P.3.B, P.3.D, P.3.E c. Assignment: Pg. 359-362 >> 16-60 even 11/21 12. Chapter Review (p. 365-368 >> 89-149 eoo) 13. Chapter Test (p. 369 >> 12-20) 11/24, 11/25 14. TEST (Ch. 4.1-8) V. Analytic Trigonometry (Chapter 5) 12/1, 12/2 1. Fundamental Trigonometric Identities (Ch. 5.1) a. Objective: Use the fundamental trig. identities to evaluate trig. functions, simplify trig. expressions and rewrite trig. expressions. b. TEKS: P.2.C, P.3.E c. Assignment: Pg. 379-381 >> 2-100 eoe, 111-114 all

12/3, 12/4 12/5, 12/8 2. Verifying Trigonometric Identities (Ch. 5.2) a. Objective: Verify trig. identities. b. TEKS: P.2.C, P.3.E c. Assignment: Pg. 387 >> 2-38 even 3. Solving Trigonometric Equations (Ch. 5.3) a. Objectives: 1) Solve trigonometric equations with algebraic techniques 2) Solve equations of the quadratic type and involving multiple angles 3) Use inverse trig. functions to solve trig. equations. b. TEKS: P.2.C c. Assignment: Pg. 396-398 >> 2-74 eoe VI. Additional Topics in Trigonometry (Chapter 6) 12/9, 12/10 4. Law of Sines (Ch. 6.1) a. Objectives: 1) Use the Law of Sines to solve oblique triangles (AAS, ASA, and SSA) 2) Find areas of oblique triangles 3) Use the Law of Sines to model and solve real-life problems. b. TEKS: P.3.E c. Assignment: Pg. 436-438 >> 2-40 even 12/11, 12/12 5. Law of Cosines (Ch. 6.2) a. Objectives: 1) Use the Law of Cosines to solve oblique triangles (SSS or SAS) 2) Use the Law of Cosines to model and solve real-life problems. b. TEKS: P.3.E c. Assignment: Pg. 436-438 >> 2-46 even 12/15 6. Chapter Review (p. 420 >> 1-49 eoo) Bonus on the test (5 pt.) Chapter Test (p. 423 >> 1-12, 17-20) Chapter Review (p. 482-485 >> 1-33 eoo) Bonus on the test (5 pt.) 12/16 Chapter Test (p. 486 >> 1-6, 8) 10. TEST (Ch. 5.1-3, Ch. 6.1-2)

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