AP Calculus BC Lesson Outlines Third Quarter: January 5 March 11, 2016

Transcription

1 Jan. 6 The Calculus of Integration CH 4.3 (Review from before the break) Riemann Sums, Definite Integrals CH 4.4 (Review from before the break) First Fundamental Theorem CH 4.4 Mean Value Theorem for Integrals CH 4.4 The Definite Integral as a Function CH 4.4 The Second Fundamental Theorem CH 4.6 Trapezoidal Rule - Apply Riemann Sums to estimate definite integrals - Evaluate a definite integral using the Fundamental Theorem - Appreciate and apply the Mean Value Theorem for Integrals - Find the average value of a function on a closed interval - Appreciate and apply the Second Fundamental Theorem - Apply the Trapezoidal Rule to estimate a definite integral - Apply error estimates to trapezoidal approximations HW Practice Due Tuesday, Jan. 12 A1 CH4.4 P291 (30pts) 5-41eoo, 43, 46, 47, 54, A2 CH4.4 P291 (11pts) 69, 74, 75-91o A3 CH4.6 P314 (10pts) 1-7o, 39, 52 (Trapezoidal. Rule only) Jan. 8 The Calculus of Integration CH 4.5 Integration by Substitution - Use pattern recognition to find an indefinite integral - Apply the substitution technique to find an indefinite integral - Apply pattern recognition / substitution to evaluate definite integrals - Evaluate definite integrals involving even and odd functions HW Practice Due Tuesday, Jan. 12 A4 CH4.5 P304 (16pts) 1-5o, 7-31eoo, 37, 49, 52, 61, 65, 87 Jan. 12 CH 5.1 Natural Log Function: Differentiation CH 5.2 Natural Log Function: Integration - - Develop and apply properties of the natural log function - Appreciate the definition of Euler's Number - Find derivatives involving the natural log function - Apply the Log Rule for integrating rational functions - Integrate trig functions HW Practice Due Thursday, Jan. 14 A5 CH5.1 P329 (24pts) 7-10, 20-22, 28, 31, 33, 41, 43, 49-59o, 69, 75, 78, 80, 93, 95 A6 CH5.2 P338 (26pts) 1-25o, 29-35o, 47, 51, 62-64, 66, 88, 91 Jan. 14 CH 5.3 Inverse Functions - Verify functions are inverses of each other - Determine if an inverse function exists - Find the derivative of an inverse function HW Practice Due Tuesday, Jan. 19 A7 CH5.3 P347 (14pts) 3-7o, 9-12, 22, 25, 27, 71, 73, 76, 93 Page 1 of 6

2 Jan. 19 CH 5.4 Exponential Functions: Differentiation & Integration CH 5.5 Bases Other Than e and Applications CH 5.6 Arctrig Functions and Differentiation - Differentiate & integrate exponential functions - Re-write exponential functions with any base - Differentiate and Integrate exponential functions with any base - Model exponential growth - Appreciate the properties of the arctrig functions - Differentiate an arctrig function HW Practice Due Thursday, Jan. 21 A8 CH5.4 P356 (22pts) 1, 3, 7, 9, 21-24, 26, 28, 33-35, 39, 44, 45, 57, 61, A8 continued. 65, 85, 95, 103 A9 CH5.5 P366 (19pts) 21, 27, 37-49o, 53, 55, 61-65o, 79, 80, 91, 92, 94 A10 CH5.6 P377 (23pts) 7-16, 17-19, 41-45o, 50, 55, 94abcef Jan. 21 Jan. 25 Jan. 27 Jan. 29 Test 3.1 CH 4.3 Through CH 5.6 CH 5.7 Arctrig Functions and Integration - Find anti-derivatives involving arctrig functions HW Practice Due Monday, Jan. 25 A11 CH5.7 P385 (18pts) 5, 11, 13, 21-25o, 29-35o, 40, 43, 45, 63, 67, Applications of Integration CH 7.1 Area of a Region Between Two Curves CH 7.2 Volumes of Rotation - Disk/Washer Method CH 7.2 Volumes of Known Cross-Section - Find the area of a region between two curves - Find the area of a region formed by intersecting curves - Find the volume of a rotational solid using the disk method - Find the volume of a solid of known cross-section HW Practice Due Tuesday, Feb. 2 A12 CH7.1 P452 (17pts) 1-5o, 13, 15, 21-27o, 35,39, 45-49o, 57, 71, 75 A13 CH7.2 P463 (12pts) 1-4, 7-9, 23, 25, 33, 49, 53 A14 CH7.2 P463 (14pts) 5, 11, 12, 21, 30, 61, 63 (2pts each) Applications of Integration CH 7.1 Area of a Region Between Two Curves CH 7.2 Volumes of Rotation - Disk/Washer Method CH 7.2 Volumes of Known Cross-Section - Find the area of a region between two curves - Find the area of a region formed by intersecting curves - Find the volume of a rotational solid using the disk method - Find the volume of a solid of known cross-section HW Practice Due Tuesday, Feb. 2 A12 CH7.1 P452 (17pts) 1-5o, 13, 15, 21-27o, 35,39, 45-49o, 57, 71, 75 A13 CH7.2 P463 (12pts) 1-4, 7-9, 23, 25, 33, 49, 53 A14 CH7.2 P463 (14pts) 5, 11, 12, 21, 30, 61, 63 (2pts each) Page 2 of 6

3 Feb. 2 Applications of Integration CH 7.3 Volumes of Rotation - The Shell Method CH 7.4 Arc Length & Surfaces of Revolution - Find the volume of a rotational solid using the shell method - Find the arc length of a smooth curve - Find the area of a surface of revolution HW Practice Due Thursday, Feb. 4 A15 CH7.3 P472 (12pts) 4, 7, 11, 21, 23, 27 (2pts each) A16 CH7.4 P483 (13pts) 3, 5, 6, 15, 16, 21, 25, 26, 33, 34, 39, 41, 43 Feb. 4 Feb. 8 Feb. 10 Feb. 12 Test 3.2 CH 5.7, and 7.1 through CH 7.4 Differential Equations CH 6.1 Slope Fields & Euler's Method CH 6.2 Differential Equations: Growth & Decay CH 6.3 The Logistic Equation - Use Euler's Method to approximate differential equation solutions - Use Separation of variables to solve differential equations - Solve and analyze logistic differential equations HW Practice Due Friday, Feb. 12 A17 CH6.1 P409 (21pts) 1-17eoo, 20, 25, 26, 33-45eoo, 49, 53-56, 71-77o A18 CH6.2 P418 (14pts) 5-7, 11-17o, 25, 27, 33, 35, 42, 69, 71 A19 CH6.3 P429 (27pts) 1-21eoo, 45-48, 55-58, 67-70, 71, 73, 77, 79 Differential Equations CH 6.1 Slope Fields & Euler's Method CH 6.2 Differential Equations: Growth & Decay CH 6.3 The Logistic Equation - Use Euler's Method to approximate differential equation solutions - Use Separation of variables to solve differential equations - Solve and analyze logistic differential equations HW Practice Due Friday, Feb. 12 A17 CH6.1 P409 (21pts) 1-17eoo, 20, 25, 26, 33-45eoo, 49, 53-56, 71-77o A18 CH6.2 P418 (14pts) 5-7, 11-17o, 25, 27, 33, 35, 42, 69, 71 A19 CH6.3 P429 (27pts) 1-21eoo, 45-48, 55-58, 67-70, 71, 73, 77, 79 Integration Techniques CH 8.1 Basic Integration Rules (Reading Assignment) CH 8.2 Integration by Parts Technique CH 8.5 Integration by Partial Fractions - Find an antiderivative using integration by parts - Apply integration by parts repetitively to find an antiderivative - Apply the partial fractions technique to find an antiderivative HW Practice Due Tuesday, Feb. 16 A20 CH8.1 P522 (16pts) 1-4, 5-49eoo (these are fun, meet the challenge) A21 CH8.2 P531 (18pts) 9-17o, 23-33o, 53, A22 CH8.5 P539 (13pts) 7-27o, 41, 43, 47 Page 3 of 6

4 Feb. 16 Integration Techniques CH 8.7 Indeterminate Forms & L'Hopital's Rule CH 8.8 Improper Integrals - Recognize limits that produce indeterminate forms - Apply L'Hopital's Rule to evaluate the limit of an indeterminate form - Evaluate an improper integral that has an infinite limit of integration - Evaluate an improper integral that has an infinite discontinuity HW Practice Due Thursday, Feb. 18 A47 CH8.7 P574 (13pts) 2, 3, 5, 9, 13, 16, 19, 27, 31, 33, 43, 49, 54 A48 CH8.8 P585 (9pts) 20, 28-32e, 38, 40, 67, 74, 76 Feb. 18 Parametric & Polar Equations CH 10.2 Plane Curves and Parametric Equations CH 10.3 Parametric Equations and Calculus - Appreciate the parametric definition of a plane curve - Eliminate the parameter in a set of parametric equations - Find a set of parametric equations to represent a curve - Find the slope of a tangent to a parametrically defined curve - Find arc length & surface area in parametric form HW Practice Due Monday, Feb. 22 A49 CH10.2 P716 (9pts) 3, 7, 19, 23, 27, 40, 42, 53, 66 A50 CH10.3 P725 (7pts) 5, 9, 14, 19, 49, 51, 81 Feb. 22 Parametric & Polar Equations CH 10.4 Polar Coordinates and Polar Graphs CH 10.5 Area and Arc Length in Polar Coordinates - Understand the Polar Coordinate System - Write rectangular coordinates in polar form and vice versa - Sketch the graph of an equation given in polar form - Find the slope of a tangent line to a polar graph - Appreciate several special types of polar graphs - Find the area of a region bounded by a polar graph - Find points of intersection of 2 polar graphs - Find the arc length of a polar graph - Find the area of a surface of revolution in polar form HW Practice Due Wednesday, Feb. 24 A51 CH10.4 P736 (17pts) 1, 3, 12, 13, 35, 37, 43-46, 49-51, A52 CH10.5 P745 (6pts) 7, 9, 12, 31, 47, 50 Feb. 24 Test 3.3 Chapters 7.3, 7.4, , 8.1, 8.2, 8.5, , Page 4 of 6

5 Feb. 26 CH 9.1 Sequences CH 9.2 Series and Convergence - List the terms of a sequence - Determine whether a sequence converges or diverges - Write an expression for the n'th term of a sequence - Use the properties of monotonic and bounded sequences - Understand the definition of a convergent infinite series - Use the properties of infinite geometric series - Use the n'th Term Test for Divergence of an infinite series HW Practice Due Tuesday, Mar. 1 A53 CH9.1 P602 (16pts) 1-3, 32-36e, 70-80e, 83, 87, 93, 109 A54 CH9.2 P612 (12pts) 5, 7, 11, 13, 25, 27, 57-67o Mar. 1 CH 9.3 Integral Test and p-series CH 9.4 Comparisons of Series / Comparison Tests CH 9.5 Alternating Series - Use the integral test to determine convergence or divergence - Use the properties of p-series and the harmonic series - Use the Direct Comparison Test to determine convergence or not - Use the Limit Comparison Test to determine convergence or not - Use the Alternating Series Test to determine convergence - Use the Alternating Series Remainder to approximate the sum - Classify a series as absolutely or conditionally convergent - Rearrange an infinite series to obtain a different sum HW Practice Due Monday, Mar. 7 A55 CH9.3 P620 (9pts) 1-7o, 25, 29-35o A56 CH9.4 P628 (15pts) 3-27eoo, A57 CH9.5 P637 (11pts) 11-27eoo, 43, 45, 47-59eoo Mar. 3 CH 9.3 Integral Test and p-series CH 9.4 Comparisons of Series / Comparison Tests CH 9.5 Alternating Series - Use the integral test to determine convergence or divergence - Use the properties of p-series and the harmonic series - Use the Direct Comparison Test to determine convergence or not - Use the Limit Comparison Test to determine convergence or not - Use the Alternating Series Test to determine convergence - Use the Alternating Series Remainder to approximate the sum - Classify a series as absolutely or conditionally convergent - Rearrange an infinite series to obtain a different sum HW Practice Due Monday, Mar. 7 A55 CH9.3 P620 (9pts) 1-7o, 25, 29-35o A56 CH9.4 P628 (15pts) 3-27eoo, A57 CH9.5 P637 (11pts) 11-27eoo, 43, 45, 47-59eoo Page 5 of 6

6 Mar. 7 CH 9.6 Ratio and Root Tests CH 9.7 Taylor Polynomials and Approximations - Apply the Ratio Test to determine if a series converges - Apply the Root Test to determine if a series converges - Find Taylor and Maclaurin approximations of functions - Use the remainder of a Taylor Polynomial HW Practice Due Wednesday, Mar. 9 A58 CH9.6 P645 (23pts) 13-29o, 35, 37, 41, 43, 49, 51-67o A59 CH9.7 P656 (9pts) 13, 17, 20, 21, 25, 29, 41, 42, 46 Mar. 9 CH 9.8 Power Series CH 9.9 Representing Functions by Power Series - Understand the definition of a Power Series - Find the radius and interval of convergence of a Power Series - Determine the end-point convergence of a Power Series - Differentiate and Integrate a Power Series - Find a geometric power series that represents a function - Construct a power series using series operations HW Practice Due Friday, Mar. 11 A60 CH9.8 P666 (9pts) 5-17o, 45, 47 A61 CH9.9 P674 (12pts) 1-4, 5-13o, 17-21o Mar. 11 CH 9.10 Infinite Taylor and Maclaurin Series - Understand the definition of a Power Series - Find the radius and interval of convergence of a Power Series - Determine the end-point convergence of a Power Series - Differentiate and Integrate a Power Series - Find a geometric power series that represents a function - Construct a power series using series operations HW Practice Due Monday, Mar. 21 A62 CH9.10 P685 (10pts) 3, 9, 15, 18, 21-25o. 31, 37, 41 Have a Great Spring Break Page 6 of 6