Textbook: Finney, Demana, Waits, Kennedy. Calculus Graphical, Numerical, Algebraic. Pearson Education, Inc., 2007, Third Edition

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1 AP Calculus AB Syllabus Textbook: Finney, Demana, Waits, Kennedy. Calculus Graphical, Numerical, Algebraic. Pearson Education, Inc., 2007, Third Edition Unit 1: Limits and Continuity. Essential Questions: How high can you jump? How fast can you swim? I can evaluate limits from graphs, tables, and equations using different techniques. I can use the Intermediate Value Theorem and the Extreme Value Theorem to solve problems. I can use the definition of a limit to write a δ- ε proof. I can determine whether a function is continuous at a point, and if needed, find a value to make a function continuous at a point. 1: Thursday, August 07 Friday, August 08 Limits #1A Canvas + Textbook: 66/ 19, 22, 37, 39, 51, 67; 76/ 13, 19 2: Monday, August 11 Tuesday, August 12 The Definition of Limit, Intermediate Value Theorem, Extreme Value Theorem #1B Canvas + Textbook: 66/ 24, 28, 43, 53, 69; 77/ 61, 63; 575/5 3: Wednesday, August 13 Thursday, August 14 Continuity (Frayer Model for definition of continuity at a point) #1C Canvas + Textbook: 84/ 19, 21, 25, 41, 47, 49, 57, 59 4: Friday, August 15 Practicing Unit 1 (Canvas) Monday, August 18 5: Tuesday, August 19 Wednesday, August 20 Free Response: 82AB2, SI94M1, SI94M2 Mastering Unit 1 6: Thursday, August 21 Friday, August 22 Unit 1 Assessment (See Canvas for practice assessments) Free Response: Turn in 78AB3 and 97/54 next time Unit 1 Labs (at least one lab is required; all files on Canvas) Limit of sin x x One- sided Limits Epsilon- Delta Challenge Unit 2: Derivatives. EQs: An object is dropped. How long will it take to fall? How fast will it be going when it falls? I can use the definition of the derivative. I can evaluate derivatives from graphs, tables, and equations using different techniques. I can write the equations of tangent and normal lines at a point on a graph. I can solve related rates problems with a real- world context. 7: Monday, August 25 Tuesday, August 26 The Definition of Derivative & Derivative Trace #2A Canvas + Textbook: 92/ 1,29,37,39; 105/ 3,5,27,29 8: Wednesday, August 27 The Power Rule Thursday, August 28 #2B Canvas + Textbook: 114/ 3,39; 124/ 5,11,3,37,53,56; 136/13,19 9: Friday, August 29 The Product & Quotient Rules Tuesday, September 02 #2C Canvas + Textbook: 124/ 15,17,23; 135/1,9; 146/ 5,7,29,47,48 10: Wednesday, September 03 The Chain Rule Thursday, September 04 #2D Canvas + Textbook: 153/ 13,16,17,19,51,56,63,73; 162/ 35,43 11: Friday, September 05 Implicit Differentiation Monday, September 08 #2E Canvas + Textbook: 162/ 1,9,17,29,59,60,61,62,63,64 12: Tuesday, September 09 Related Rates Wednesday, September 10 #2F Canvas + Textbook: 251/ 11,13,14,15,17,19,23,27,38,39 13: Thursday, September 11 Related Rates, continued Friday, September 12 14: Monday, September 15 Practicing Unit 2 Tuesday, September 16 15: Wednesday, September 17 Mastering Unit 2 Thursday, September 18 16: Friday, September 19 Unit 2 Assessment Monday, September 22 Unit 2 Labs (three required; all files on Canvas) Derivative Function Local Linearity Maximums, Minimums, & Product & Quotient Rules Zeros Symmetric Secant Higher Order Derivatives Filling the Urn Falling Ladder Elevator Height and Velocity Position, Distance, and Velocity Unit 3, Part 1: Applications of Derivatives. EQ: What is the most efficient way to package my product? I can use the derivative to determine maxima and minima of a function. I can analyze functions from graphs, tables, and equations using different techniques. I can use the original function to deduce information about the first and second derivatives. I can use the derivative to deduce information about the second derivative and the original function. I can use the second derivative to deduce information about the first derivative and the original function.

2 I can solve optimization problems with a real- world context. 17: Tuesday, September 23 Extrema & the Mean Value Theorem Wednesday, September 24 #3A Canvas + Textbook: 194/ 17,21,27,41,47,48; 202/ 9,13,53,56 18: Thursday, September 25 The First Derivative: Derivative Analysis & Derivative Grapher Friday, September 26 #3B Canvas + Textbook: 202/ 17,21,25; 215/ 3,7,11,17,21,25,29 19: Monday, September 29 Tuesday, September 30 The Second Derivative: Derivative Analysis & Derivative Grapher #3C Canvas + Textbook: 216/ 33,39,41,45,47,49,51,55,57,59 20: Wednesday, October 01 Thursday, October 02 Limits at infinity & L Hopital s Rule #3D Canvas + Textbook: 76; 41,42,43,53,64; 451/ 29,33,64 21: Friday, October 03 Wednesday, October 08 Summary of Curve Sketching Free Response: Turn in 85AB1 and 92AB4 next time + Textbook: 218/ 1,2,3,4; 226/ QR/ 1,2 22: Thursday, October 09 Friday, October 10 More Curve Sketching Textbook: 260/ 70 23: Monday, October 13 Practicing Unit 3, Part 1 Tuesday, October 14 24: Wednesday, October 15 Mastering Unit 3, Part 1 Thursday, October 16 25: Friday, October 17 Monday, October 20 Unit 3, Part 1 Assessment Free Response: Turn in 90AB4 and 86AB2 next time Unit 3, Part 1 Labs (two required; all files on Canvas) MeanValueTheorem Critical Points Curve Sketching First Derivative Distance- Time- Velocity MVT First Derivative Test Derivative Time Derivatives Concavity_CAS Unit 3, Part 2: Applications of Derivatives. 26: Tuesday, October 21 Wednesday, October 22 Local Linearity & Newton s Method #3A _2 Canvas + Textbook: 242/ 1,3,5,7,11,15,17,27 27: Thursday, October 23 Friday, October 24 Differentials & The Box Problem #3B_2 Canvas + Textbook: 244/ 45,61,71; 255/ QQ/ 1,4 28: Monday, October 27 Tuesday, October 28 3C_2 Optimization #3C_2 Canvas + Textbook: 243/ 7,9,35,41,51,53,55,56 29: Wednesday, October 29 Mastering Unit 3, Part 2 Thursday, October 30 30: Friday, October 31 Monday, November 03 Unit 3, Part 2 Assessment Free Response: Turn in 92AB1 and 80BC7 next time Unit 3, Part 2 Labs (two required; all files on Canvas) Optimization Lab Optimization Beach Race Chicken Run Distance from a Point to a Line Rectangle in Parabola Basketball Key Random Rectangles Unit 4: Integration. EQs: What is the area of the rotor in a Wankel engine? How fast will a wound heal? When will the medication start working? How long will the medication work? I can approximate the area under a curve using Riemann Sums. I can approximate the area under a curve using the Trapezoidal Rule. I can set up and calculate the exact area under a curve using the limit of the sum of the areas of an infinite number of rectangles. I can use the Fundamental Theorem of Calculus. I can antidifferentiate using various techniques, including substitution of variables. 31: Tuesday, November 04 Approximating Area Under a Curve Wednesday, November 05 #4A Canvas + Textbook: 270/ 5,9,15,17,33,35; 312/ 3,5,7,33,34,35 32: Thursday, November 06 Antidifferentiation Exploration Friday, November 07 #4B Canvas + Textbook: 203/ 29,30,31,32,35,36,38,55 33: Monday, November 10 Tuesday, November 11 34: Wednesday, November 12 Thursday, November 13 The Definite Integral, part 1 Card Matching: Area under the Curve & Definite Integrals #4C Canvas + Textbook: 290/ 1,3,5,47; 282/ 7,13,17,33,47,49 The Definite Integral, part 2 Calculating the Limit of a Riemann Sum #4D Canvas + Textbook: 282/ 1,2,23,41,43,45,51,53 Fundamental Theorem of Calculus #4E Canvas + Textbook: 291/ 19,23,25,31,33,35,46,47,49,51 The Second Fundamental Theorem of Calculus #4F Canvas + Textbook: 302/ 1,3,5,9,13,21,29,39,41,43 Integration by Substitution, part 1 #4G Canvas + Textbook: 337/ 1,3,5,17,20,25,27,31 35: Friday, November 14 Monday, November 17 36: Tuesday, November 18 Wednesday, November 19 37: Thursday, November 20 Friday, November 21 38: Monday, December 01 Integration by Substitution, part 2

3 Tuesday, December 02 #4H Canvas + Textbook: 338/ 23,35,37,53,55,59,71,75 39: Wednesday, December 03 Thursday, December 04 Particle Motion (AP Curriculum Module: Motion, 2008) FTOC applications #4I Canvas + Textbook: 303/ 45,55,57,59,60,63,69,70; 304/ 58 40: Friday, December 05 Monday, December 08 Practicing Unit 4 #4J Textbook: 386/ 1,3,5,9,11,16,19,27,31,33 41: Tuesday, December 09 Mastering Unit 4 Wednesday, December 10 42: Thursday, December 11 Friday, December 12 Unit 4 Assessment Free Response: Turn in AC93/94-1 and 88AB2 next time Unit 4 Labs (two required; all files on Canvas) Area Accumulation Riemann Sums Acceleration- Velocity- Applied FTOC Position Velocity, Position, Distance Piecewise Linear Integral Riemann Rectangle Errors Average Value of Fun Elevator Height as Integral of Velocity 43: Monday, December 15 Tuesday, December 16 44: Wednesday, December 17 Thursday, December 18 45: Friday, December 19 Semester Exams Semester Exam Practice Oral exam: Make an appointment to come in for minutes sometime next week Free Response: Turn in 94AB1 and 84AB4 next time Calculus I Final Semester Exams Free response presentations #1: 91AB4, #2: SI94M3, #4: 81AB5, #5: SI94R2, #6: 88AB1, #7: 89AB4, #8: 94AB3, #9: 80AB6, #10: 95AB3, #11: 85AB5, #12: 87AB5, #13: 91AB5, #14: 90AB5, #15: 86AB1, #16: 93AB1, #17: AC95/96-1, #18: 77AB2, #19: 81AB3, #20: 90AB6, #21: 85AB6, #22: 89AB5 Unit 5: Exponential Functions. EQs: How fast will the plastic cool? How long ago was the victim murdered? I can calculate and use derivatives of exponential and logarithmic functions. I can calculate and use antiderivatives of exponential functions. I can calculate and use antiderivaties involving logarithmic functions I can calculate and use slopes for inverse functions. I can calculate and use derivatives of inverse trigonometric functions. I can calculate and use antiderivatives involving inverse trigonometric functions. 1: Monday, January 05 Differentiation of Natural Logarithmic Functions A New Function Exploration Tuesday, January 06 #5A Canvas + Textbook: 178/ 15,17,19,21,23,25,27,31,37,39,43,45,47 2: Wednesday, January 07 Integration of Natural Logarithmic Functions Thursday, January 08 #5B Canvas + Textbook: 291/ 29; 338/ 25,39,41,73,61,63,65 3: Friday, January 09 Differentiation and Integration of Exponential Functions Exponential Function Exploration Monday, January 12 #5C Canvas + Textbook: 178/ 3,5,7,9,11,13,29; 291/ 1; 339/66,74; 386/ 21,36 4: Tuesday, January 13 Differentiating Inverse Functions Wednesday, January 14 #5D Canvas + Textbook: 170/ 28,29; 178/ 33,41,49,55,57,60,61,62 5: Thursday, January 15 Differentiating and Integrating Inverse Trigonometric Functions Friday, January 16 #5E Canvas + Textbook: 170/ 1,3,5,9,25,27,31; 291/ 27; 338/ 21,42 6: Tuesday, January 20 Mastering Unit 5 Wednesday, January 21 7: Thursday, January 22 Unit 5 Assessment Friday, January 23 Free Response: Turn in 90AB1 and 88AB4 next time Unit 5 Labs (one required; all files on Canvas) Natural Logarithm Exponential Functions Unit 6: Applications of Definite Integrals. EQs: How do I construct an arch dam? What is the volume of a fuel tank? I can calculate and use the area between two curves. I can use the disc and washer methods to calculate and use the volume of a solid. I can use the shell method to calculate and use the volume of a solid. I can calculate and use volumes of solids created by known cross sections. 8: Monday, January 26 Area between Curves Tuesday, January 27 #6A Canvas + Textbook: 395/ 3,5,9,13,19,25,51,52,53,55 9: Wednesday, January 28 The Disc and Washer Methods Thursday, January 29 #6B Canvas + Textbook: 407/ 7,11,13,17,31 10: Friday, January 30 Cross Sections

4 Monday, February 02 #6C Canvas + Textbook: 406/ 1,3,5,29 11: Tuesday, February 03 Wednesday, February 04 The Shell Method #6D Textbook: 407/ 33,35,37,39 12: Thursday, February 05 Friday, February 06 Free Response Practice Area & Volume #6E Textbook: 409/ 64,65,66,67,68; 411/ QQ/ 1,2,3,4 13: Monday, February 09 Tuesday, February 10 Mastering Unit 6 Free Response: Turn in 81AB2 and 96AB2 next time 14: Wednesday, February 11 Thursday, February 12 Unit 6 Assessment MSMS Calculus Contest Practice Unit 6 Labs (one required; all files on Canvas) Area Between Solid_Disk_CN VolumeChallenge VolumeMCCrossSection Unit 7: Differential Equations. EQs: How do the noise levels in a stadium compare when the roof is open and when the roof is closed? EQs: How do I create a map that shows curved lines as straight lines? I can graph and use slope fields. I can calculate and use differential equations. 15: Friday, February 13 Slope Fields & Euler s Method Tuesday, February 17 #7A Canvas + Textbook: 327/ 1,3,5,11,15,26-28,29,30,31 16: Wednesday, February 18 Introduction to Differential Equations: DE Match Thursday, February 19 #7B Canvas + Textbook: 357/ 1,3,5,9,11,13 17: Friday, February 20 Applications of Differential Equations: Infestation Monday, February 23 #7C Canvas + Textbook: 357/ 21,23,25,39,47,49,50,51 18: Tuesday, February 24 Basic Integration Rules Wednesday, February 25 #7D Canvas + Textbook: 349/ QQ/ 1,4; 372/ QQ/ 1,2 19: Thursday, February 26 Free Response Practice Differential Equations Friday, February 27 #7E Canvas + Textbook: 319/ 58,59,60; 376/ 69 20: Monday, March 02 Mastering Unit 7 Tuesday, March 03 21: Wednesday, March 04 Unit 7 Assessment Thursday, March 05 Free Response: Turn in SI94E1 and 93AB2 next time Units 7 Labs (one required; all files on Canvas) Integrating Logs Integration by Parts The questions that encompass the whole course are the following. 1. What is the slope of the tangent line? 2. What is the area under the curve? 22: Friday, March 06 Targeted Free Response Analyzing f(x) Monday, March 16 C_Unit 1 Canvas: Limits & Continuity 23: Tuesday, March 17 Released Exam 1: Free Response Wednesday, March 18 C_Unit 2 Canvas: Derivatives 24: Thursday, March 19 Released Exam 1: Multiple Choice, No Calculator Friday, March 20 C_Unit 3_1 Canvas: Applications of Derivatives 25: Monday, March 23 Released Exam 1: Multiple Choice, Calculator Active Tuesday, March 24 C_Unit 3_2 Canvas: Applications of Derivatives 26: Wednesday, March 25 Mastering Released Exam 1 Thursday, March 26 C_Unit 4 Canvas: Antidifferentiation 27: Friday, March 27 Free Response Practice Accumulation Monday, March 30 C_Unit 5 Canvas: Transcendental Functions 28: Tuesday, March 31 Multiple Choice Practice No Calculator Wednesday, April 01 C_Unit 6 Canvas: Applications of Definite Integrals 29: Thursday, April 02 Free Response Practice Analyzing f(x) Tuesday, April 07 C_Unit 7 Canvas: Differential Equations 29: Wednesday, April 08 Multiple Choice Practice Calculator Active Thursday, April 09 C_AP1 Canvas: Released Exam 30: Friday, April 10 Free Response Practice Tabular Data Monday, April 13 C_AP2 Canvas: Released Exam 31: Tuesday, April 14 Multiple Choice Practice No Calculator Wednesday, April 15 C_AP3 Canvas: Released Exam 32: Thursday, April 16 Multiple Choice Practice Calculator Active Friday, April 17 C_AP4 Canvas: Released Exam 33: Monday, April 20 Tuesday, April 21 Released Exam 2: Free Response C_AP5 Canvas: Released Exam

5 34: Wednesday, April 22 Thursday, April 23 35: Friday, April 24 Monday, April 27 36: Tuesday, April 28 Wednesday, April 29 37: Thursday, April 30 Friday, May 01 Tuesday, May 05 Released Exam 2: Multiple Choice, No Calculator C_AP6 Canvas: Released Exam Released Exam 2: Multiple Choice, Calculator Active C_AP7 Canvas: Released Exam Mastering Released Exam 2 C_AP8 Canvas: Released Exam Stuff You Must Know Cold AP Jeopardy C_AP9 Canvas: Released Exam AP Calculus Exam