Instructional Calendar Accelerated Integrated Precalculus. Chapter 1 Sections and 1.6. Section 1.4. Section 1.5

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1 1 st Semester 32. Compare and contrast properties of functions within and across a variety of functions. -Tabular, Graphical, and Algebraic Representations of Functions -Domain and Range of Functions -Increasing, Decreasing, and Constant Functions -Relative Minima and Maxima -Even and Odd Functions - Inverse Functions 33. Investigate transformations of functions. 6 days 3 days Chapter 1 Sections and 1.6 Exploring Precalculus with The Geometer s Sketchpad Inverses of Functions Pages Section 1.4 Exploring Precalculus with The Geometer s Sketchpad Function Transformations Pages Investigate characteristics of functions built through sum, difference, product, quotient and composition. 3 days Section 1.5 Exploring Precalculus with The Geometer s Sketchpad Composition of Functions Pages Page 1 of 18

2 20. Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior. 21. Find inverses of rational functions, discussing domain and range, symmetry, and function composition. 22. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology. 32. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise days 3 4 days for Rational, 3 4 days for Radical, 2 3 days for the appendices, 1 or 2 days for assessment. Chapter 2, Appendix B3, Appendix B4. Radical Functions NUMB3RS Activity: Energy Episode: Burn Rate Radical Equations (attached pdf file) Rational Functions Introduction to Rational Functions (attached Word Doc and necessary installation file) Students should load and run the program. This will install the necessary graph databases (GDBs) for the activity. Instructions for doing this are included in the activity. s will benefit from the information file detailing the specifics of the program and the activity. Geometer s Sketchpad for Precalculus (I don t have the book yet, but, I ve heard that the labs are great especially those introducing trig functions and transformations.) This entire Unit (Chapter 2 and Appendices B3 & B4) should be completed within the first 2 weeks. The students should already be familiar with rational and radical functions, as well as polynomials. Perhaps a pretest can be given to assess the level of the students. s can load this program on the calculators prior to using them, using a link this will save some time. Page 2 of 18

3 33. Investigate transformations of functions. 34. Investigate characteristics of functions built through sum, difference, product, quotient, and composition. 1. Use appropriate technology to solve problems Communicate mathematical thinking coherently to peers, teachers, and others. 14. Recognize and use connections among mathematical ideas. 19. Use representations to model and interpret physical, social, and mathematical phenomena. Page 3 of 18

4 23. Convert between angles measured in degrees and radians, including but not limited to 0,30,45,60,90 their multiples and equivalences. 24. Apply the six trigonometric functions as functions of general angles in standard position. 25. Find values of trigonometric functions using points on the terminal sides of angles in the standard position. 26. Apply the six trigonometric functions as functions of arc length on the unit circle. 25 days 1 day Section days Section day Section day Section 4-1 Chapter 4 Trigonometric Functions For graphic organizers: For Activity/Task idea: Find values of trigonometric functions using the unit circle. 28. Apply the six basic trigonometric functions as functions of real numbers. 29. Determine characteristics of the graphs of the six basic trigonometric functions. 4 days Section 4-2 and day Section 4-2 Sections 4.5 and 4.6 For sections 4.5 and 4.6: Page 4 of 18

5 30. Graph transformations of trigonometric functions including changing period, amplitude, phase shift and vertical shift. Sections 4.5 and 4.6 Exploring PreCalculus with the Geometer s Sketchpad by Key Curriculum Press p Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena. 32. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise. 33. Investigate transformations of functions. 34. Investigate characteristics of functions built through sum, difference, product, quotient and composition. 37. Use the coordinates of a point on the terminal side of an angle to express x as r cos and y as rsin. Sections 4.5, 4.6, and 4.8 Sections 4.5, 4.6, and supplement to compare and contrast all Sections 4.5 and days Sections 4-3 and day Section 4-4 Exploring PreCalculus with the Geometer s Sketchpad by Key Curriculum Press p.38 and 42 Page 5 of 18

6 40. Find values of the inverse sine, inverse cosine and inverse tangent functions using technology as appropriate. Section Determine characteristics of the inverse sine, inverse cosine and inverse tangent functions and their graphs. Section 4.7 Page 6 of 18

7 35. Establish and utilize trigonometric identities to simplify expressions and verify equivalence statements. 1-2 days CHAPTER 5 SEC 5.1 USING FUNDAMENTAL IDENTITIES 35. Establish and utilize trigonometric identities to simplify expressions and verify equivalence statements. 1-2 days SEC 5.2 VERIFYING TRIG. IDENTITIES 36. Solve trigonometric equations both graphically and algebraically over a variety of domains, using technology as appropriate. 2-3 days SEC 5.3 SOLVING TRIG. EQUATIONS A mid-chapter assessment is suggested following Sec. 5.3 to assess students mastery of the content. 40. Find values of the inverse sine, inverse cosine, and inverse tangent functions using technology as appropriate. 34. Investigate characteristics of functions built through sum, difference, product, quotient and composition. 40. Find values of the inverse sine, inverse cosine, and inverse tangent functions using technology as appropriate. 2-3 days SEC 5.4 SUM AND DIFFERENCE FORMULAS Page 7 of 18

8 36. Solve trigonometric equations both graphically and algebraically over a variety of domains, using technology as appropriate. 40. Find values of the inverse sine, inverse cosine, and inverse tangent functions using technology as appropriate. 2 3 days SEC 5.5 MULTIPLE ANGLE & SUM- PRODUCT FORMULAS An assessment is suggested following Sec. 5.5 to assess students mastery of the content. Review of concepts Assessment 1-3 days 3 days TOTAL DAYS: days Page 8 of 18

9 2nd Semester 32. Compare and contrast properties of functions within and across a variety of functions. Verbally NAG Verbally Numeric Algebraically Graphically -Domain and Range of Functions -Increasing, Decreasing Functions -Relative Extrema -Odd and Even Functions -Inverse Functions -Asymptotes and End Behavior days 1 Day Chapter 3 Section 3.1 x x -Graphs of a and e, stressing domain ; range; intercepts; increasing/ decreasing; end behavior; asymptotes -Transformation of graphs without a calculator Applications: - e - Compound interest - Radioactive Decay - Population growth Activity: Have students find e x 1 fx ( ) 1 ; end behavior x The students should already be familiar with exponential and logarithmic functions. A pretest can be given to assess the level of the students. Include trigonometric functions from Chapter 5 that include exponential and logarithmic functions. Assignments: Use guide in text. If students do well on pretest, give every other odd/even. Calculus reference: Limits and the value of e Differential equations refer back to compound interest, decay and growth formulas Page 9 of 18

10 33. Investigate transformations of functions 34. Investigate characteristics of functions built through sum, difference, product, quotient and composition 28. Apply the six basic trigonometric functions as functions of real numbers 2 Days Section 3.2: -Review inverses and 1-1 functions -Define logarithm in terms of the inverse of an exponential function -Graph f( x) log a x and f( x) lnx stressing domain ; range; intercepts; increasing/ decreasing; end behavior; asymptotes -Transformation of graphs without a calculator - Inverse Property -One-to-One Property Group Activity: Have students teach a review class for these topics. Compare and Contrast exponential and logarithmic graphs Group Activity: Page 213 Synthesis problems Make sure to assign word problems. 2 Days Section 3.3: -Change of base -Logarithm Properties Product Quotient Power Students should be able to explain what the answer means; what the asymptotes mean in the context of the problem. Pages : Page 295: Students should be able to manipulate logarithmic expressions without the use of a calculator. See Examples 2 and 3 on page 208 Page 10 of 18

11 3 Days Section 3.4: -Students should be able to solve exponential and logarithmic equations with and without a calculator. -Stress Inverse and One-to-One properties -Students should be able to solve Exponential Equations in Quadratic form ( Example 5 page 216) -Students should be able to approximate solutions of equations that contain a combination of functions ( Example 11 page 219) Bring trig identities back: Section 5.1 page 359: Section 5.2 page 366: Calculus reference: AP multiple choice exams will use log and exponential properties to simplify a solution. Page 212: Include trig problems from Chapter 5 Students must use log properties for logarithmic differentiation. Page 212: (Choose odds or evens) Pretest this section some students will need to do most of the problems in this section. Word Problems: Page days Sections 3.5 and 3.6 -Exponential and Logarithmic Models Students need to be able to use a calculator so solve each type of model using exponential and logarithmic models. Section 3.5 has students solving real world problems. Students could find their own sets of data to model the nonlinear models. Page 11 of 18

12 Section 3.6 From a scatter plot students should be able to determine the appropriate model and then use the regression capabilities of their calculator to find an equation that models the given data. Assessments: 1.Pretest to see what they remember 2. Short Formative Quizzes that include non-calculator and calculator sections for graphs and properties 3. Quiz - Solving Equations using Exponential and Logarithms Include both calculator and noncalculator problems 4. Test - Include work problems that have students explain their answers in the context of the problem. Section 3.6 gives students data sets to fit the appropriate function to the given data. Calculus reference: Differential equations will refer to exponential growth, half-life, and logistic models. Page 12 of 18

13 38. Apply the law of sines and the law of cosines (GPS) 39. Verify and apply the trigonometric formula to find the area of a triangle (GPS) 2-3 days CHAPTER 6 SEC 6.1 LAW OF SINES 38. Apply the law of sines and the law of cosines (GPS) 1-2 days SEC 6.2 LAW OF COSINES 49. Represent vectors algebraically and geometrically. 50. Convert between vectors expressed using rectangular coordinates and vectors expressed using magnitude and direction. 51. Add and subtract vectors and compute scalar multiples of vectors. 52. Use vectors to solve realistic problems. 52. Use vectors to solve realistic problems. 2-3 days 1-2 days SEC 6.3 VECTORS IN THE PLANE SEC 6.4 VECTORS & DOT PRODUCTS Page 13 of 18

14 53. Represent complex numbers in rectangular and trigonometric form. 54. Find products, quotients, powers and roots of complex numbers in rectangular and trigonometric form. 3 4 days SEC 6.5 TRIGONOMETRIC FORM OF A COMPLEX NUMBER Suggested HW problems: Pgs (3 81)multiples of 3, (91 109)Odd, ( )Odd 42. Find and use recursive and explicit formulae for the terms of sequences (GPS) 43. Analyze and use simple arithmetic and geometric sequences (GPS) 44. Investigate and analyze limits of sequences (GPS) 45. Use mathematical induction to find and prove formulae for sums of finite series (GPS) 46. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series (GPS) 47. Use summation notation to express series (GPS) 48. Determine geometric series and their limits (GPS) 1 2 days 1 2 days 1 2 days 1 2 days Section 8.1 Sequences and Series Section 8.2 Arithmetic Sequences and Partial Sums Section 8.3 Geometric Sequences and Series Section 8.4 Mathematical Induction 1 2 days Review and Assessment Page 14 of 18

15 Parametric Equations: 55. Describe parametric representations of plane curves. 56. Convert between Cartesian and parametric form. 57. Graph equations in parametric form showing direction and endpoints where appropriate. 2 days Chapter 9 Section 9.5 pgs Smartboard, TI-Smartview, TI- Interactive Suggested HW problems: Pgs : 1 6, 9, 10, (11 33)odd, 35 42, Polar Coordinates: 58. Express coordinates of points in rectangular and polar form. 2 days Section 9.6 pgs Smartboard resources are really useful for plotting polar coordinates and graphing polar equations, TI- Smartview, TI-Interactive Suggested HW problems: Pgs : (2 42)Even, (43 85)Odd Graphs of Polar Equations: 59. Graph and identify characteristics of simple polar equations including lines, circles, cardioids, limaςons and roses. 3 days Section 9.7 pgs Smartboard resources are really useful for plotting polar coordinates and graphing polar equations, TI- Smartview, TI-Interactive Suggested HW problems: Pgs , (23 61)Odd Page 15 of 18

16 19. Use representations to model and interpret physical, social, and mathematical phenomena. 1 day (if desired) CHAPTER 10 SEC 10.1-THE THREE DIMENSIONAL COORDINATE SYSTEM 49. Represent vectors algebraically and geometrically. 50. Convert between vectors expressed using rectangular coordinates and vectors expressed using magnitude and direction. 51. Add and subtract vectors and compute scalar multiples of vectors. 52. Use vectors to solve realistic problems. 1-2 days SEC 10.2-VECTORS IN SPACE 52. Use vectors to solve realistic problems (GPS) 56. Convert between Cartesian and parametric form (GPS) Review of concepts Assessment 1-2 days 1-2 days 3 days 2 days TOTAL DAYS: days SEC 10.3-THE CROSS PRODUCT OF TWO VECTORS SEC 10.4-LINES AND PLANES IN SPACE Page 16 of 18

17 Statistics 60. Organize, represent, investigate, interpret and make inferences from data using the central limit theorem and the standard normal distribution. 3 days Statistics: The Art & Science of Learning from Data (Agresti & Franklin) Sections 6.2 & Apply the central limit theorem to calculate confidence intervals for a population mean using data from large samples. 3 days Statistics: The Art & Science of Learning from Data (Agresti & Franklin) Sections 6.5, 7.1 & 7.3. This can be done using a manual method or using the TI-83 or TI- 84 graphing calculator. 62. Use sample data and confidence intervals to draw conclusions about populations. 2 days Statistics: The Art & Science of Learning from Data (Agresti & Franklin) Sections 7.2 & Use simulation to develop the idea of the central limit theorem. 64. Use student-generated data from random samples of 30 or more members to determine the margin of error and confidence interval for a specified level of significance. 3 days 2 days Statistics: The Art & Science of Learning from Data (Agresti & Franklin) Sections 6.5 & 7.5. Statistics: The Art & Science of Learning from Data (Agresti & Franklin) Sections 7.1, 7.2 & Use confidence intervals and margins of error to make inferences from data about populations. 2 days Statistics: The Art & Science of Learning from Data (Agresti & Franklin) Sections 7.1, 7.2 & 7.3. Page 17 of 18

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