Semester 1ap Calculus

AP Calculus AB Semester 2 Volumes. 3/16/2016 0 Comments Volumes, our last big thing to deal with in AP Calculus AB! We are able to rotate a function about an axes. SEMESTER 1-2020/2021. Home; Modules; Assignments; AP CALCULUS AB. View Course Stream Coming Up View Calendar Nothing for the next week. This is the review for the semester 1 AP Calculus final. These are common problems that students missed or needed help with. Semester 1 is offered only during the fall term. Calculus is the mathematics of change. It is used to solve complex problems that are continuously evolving and would otherwise be unsolvable with only algebra and geometry. This online advanced placement course is designed to prepare students to become deep mathematical thinkers. Nothing for the next week.

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Date	Learning Targets/Agenda	Suggested Practice
8-18 (s)	Understand how distance, velocity, acceleration and speed relate to each other Books	AP Calculus SyllabusPARENTS and STUDENTS MUST SIGN AT THE BOTTOM OF THE SYLLABUS
8-21 (s)	Evaluate a limit numerically and algebraically Be able to explain if a function is continuous using limit notation Understand how limits relate to derivatives Be able to find a derivative by using the two limit forms Review Limits Notes	pg 131-133 #2, 4, 11, 12, 14, 17, 26, 31, 32, 51 Work on One Problem Summary (Due 8-29/30)
8-22/23	Understand properties of derivatives (graphing derivatives) Given a function, find it's derivative using the product rule, quotient rule and chain rule	pg 240-243 #9, 14-18, 20, 21, 41, 42, 53a-c,54, 62
8-24/25	Given a curve, find it's derivative using implicit differentiation Find the equation of a tangent and normal line Understand how derivative rules (product rule, quotient rule, chain rule) relate to implicit differentiation AP Practice Problems #2	pg 208 #5, 9, 10, 13, 18, 26, 29, 69 HSA #1 Accuracy Check Answers and Retake
8-28 (s)	Derivatives of Inverses Discovery WS Find derivatives of inverse functions Understand when an inverse can be found and when the Derivative of an Inverse Function Theorem should be used	pg 229 #7, 8, 15, 16, 26, 33, 47, 50, 52
8-29/30	Quiz #1 - Limits, Basic Derivatives, Tangent lines Find out how fast the water temp is changing using derivatives of logs and exponential functions Heat It-Cool It Activity (Due next class)	Heat It-Cool It Activity (Due next class)
8-31/9-1	Find the derivative of an exponential and log function Understand how logarithmic differentiation can make finding the derivative of a complex product, quotient, or composite function easier Use logarithmic differentiation to find the derivative of a function Notes	pg 219 #11-19 odd, 24, 26, 32, 40, 55, 61, 63, 65, 67
9-5/6	Understand how two or more rates relate to each other Translate verbal descriptions into equations in order to solve the related rate HSA #2 Due (pg 208, pg 229, pg 219) w/ Accuracy Check	pg 235 #5, 12, 18, 21, 25, 27, 34, 37, 44, 45, 50 Accuracy Check Make Up
9-7/8	Related Rates WS Understand how two or more rates relate to each other Translate verbal descriptions into equations in order to solve the related rate	Finish any Related Rates HW
9-11(s)	Sec. 4.1 Notes Understand the difference between a local max or min and absolute max or min Be able to find critical points on a function by taking the derivative and setting it equal to zero Be able to determine the absolute maximum or minimum by finding critical numbers and testing endpoints of a function	pg 253 #5, 8, 11, 13, 15, 18, 23, 26, 28, 33, 41, 46, 50, 51
9-12/13	Quiz #2 - Implicit DifferentiationDerivatives of Inverse Function, Logarithmic Differentiation, Related Rates Understand what do f ' and f ' tell us about f Locate maximums, minimums and intervals where f is increasing or decreasing from f '	pg 267 #3, 7, 11, 14, 17, 27, 30, 35, 40, 43, 57, 62, 69
9-14/15	Finish Sec. 4.2 Notes Understand what do f ' and f ' tell us about f Locate inflection points and intervals where f is concave up or concave down from f ' Use the second derivative test to prove local max or mins	Add #72, 77, 87, 90 to previous HW Link to Help Topics Link to Khan Academy Help Topics
9-18 (s)	Sec. 4.3-Curve Sketching Day 1 Notes Understand what f' tells us about the graph of f Given f' and/or other attributes of the graph of f', graph f Given a function f, graph the function using the first and second derivative tests Go over Quiz	Curve Sketching WS
9-19/20	Sec. 4.3-Curve Sketching Day 2 Notes Given a function f, graph the function using the first and second derivative tests Card Activity	pg 279 # 9, 13, 11, 16, 18, 22-25, 34
9-21/22	Start Optimization Day 1 Notes Understand how first and second derivative tests can verify if a problem has a maximum or minimum (optimization) Translate written descriptions into equations in order to optimize the given problem Sec. 4.1-4.3 Accuracy Check	pg 285-289: #3, 12, 14, 17, 24, 29, 37, 47, 54 Sec. 4.1-4.3 Accuracy Check Make Up
9-25(s)	Quiz Sec. 4.1-4.3 Optimization Day 2 Notes Translate written descriptions into equations in order to optimize the given problem Use the first and second derivative tests to verify if a problem has a maximum or minimum (optimization)	WS and finish book work
9-26/27	Optimization Day 3 Optimization Practice Problems Translate written descriptions into equations in order to optimize the given problem Use the first and second derivative tests to verify if a problem has a maximum or minimum (optimization)	MC/FR #2Due 10-3/4
9-28/29	Sec. 4.5 Notes Understand when/how to use a linear approximation Find a linear approximation for a value Calculate percent error for a linear approximation Sec. 4.4 Accuracy Check	p. 300: #13, 16, 18, 23, 27, 31, 33, 37, 38, 41, 47, 52, 55 Sec. 4.3-4.4 Accuracy Check Make Up More Optimization Practice
10-2(s)	Quiz 4.3-4.4	Chapter 4 Review
10-3/4	Sec 4.6-MVT Notes Understand how to use the Mean Value Theorem Find a point c on an interval that satisfies the MVT Sec. 4.7 Notes Use L'Hopitals Rule to evaluate limits of indeterminate form MC/FR #2 Due Chapter 4 Review (Move to Friday)	Sec. 4.6 p. 306-8: #3, 5, 7, 11, 16, 17, 22, 33, 35, 37, 41 Sec. 4.7 pg 319 #13, 17, 22-24, 33, 40, 45
10-5/6	Sec. 4.5-4.7 HSA Due Chapter 4 Review (CHANGE) NO TEST
10-9 (s)	Sec. 5.1-Antiderivatives Understand how antiderivatives relate to derivatives Understand that the f(x) can have a vertical shift given f'(x) Find the antiderivatives of indefinite integrals Solve the antiderivative given initial condition(s) Practice WS over Antiderivatives	p. 347: #12, 13,15, 17, 26, 28, 30, 37, 41, 55, 68, 88, 92, 99
10-10/12	Chapter 4 Test	Finish 5.1 HW
10-16(s)	Sec. 5.2 Part 1-Sigma Notation Sec. 5.2 Part 2-Approximating Areas Notes Use rectangular area approximations (Riemann Sums) to estimate area under a curve when geometric means don't apply. Determine whether our approximations are under- or overestimates to the actual area when possible. Convert expanded notation to sigma notation Convert sigma notation to expanded notation Evaluate sums in sigma notation	p. 359: #1, 6, 9, 12, 14, 17, 27, 35, 37, 39, 40, 41(a, c, e, g), 42(b, d, f, h) 55, 58
10-17/18	Finish Sec. 5.2 Sec. 5.3-The Definite Integral and its Properties WS and Notes Understand how Riemann Sums relate tot the definite integral Evaluate the definite integral using a Riemann Sum Evaluate the definite integral using geometry Understand properties of definite integrals	WS
10-19/20	Finish 5.3 Notes Evaluate the definite integral using geometry Understand properties of definite integrals Sec.5.1-5.2 HSA Due AP Practice over Riemann Sum and Definite Integrals	Finish WS from 5.3 Accuracy Check 5.1-5.2 Answers and Make-up
10-23(s)	Quiz 5.1-5.2 Start (If Time) Sec. 5.4-The Fundamental Theorem of Calculus Part ll Understand that area under a velocity curve is the same as the final position minus the initial position Use the fundamental theorem of calculus to evaluate definite integrals
10-24/25	Finish Sec. 5.4 - FTC Part l Notes part 1 and Notes part 2 Understand the difference between the FTC part 1 and part 2 Use the FTC part 2 to evaluate the derivative of an integral	pg 390 #23, 29, 32, 35, 39, 41, 45, 48, 58, 87, 93, 97 pg 390 #9, 11, 21, 61, 65, 69, 75, 83, 100-103, 105
10-26/27	Sec. 5.5-Average Value of a Function Notes MC/FR #3 in class MC/FR #4in class Khan Academy Links: Average Value Average Value Example Understand the mean value theorem for integrals Be able to find the average value of a function Use symmetry and even/odd properties of functions to evaluate integrals Sec.5.3-5.4 Accuracy Check	pg 398 #7, 9, 11, 12, 23, 26, 32, 35, 40, 47 Accuracy Check 5.3-5.4 Answers and Make up
10-30(s)	Sec. 5.6-Substitution Method Notes Understand when to use U-substitution to evaluate integrals Evaluate indefinite and definite integrals using U-substitution to 'undo' the chain rule	p. 408: #13, 15, 18, 20, 23, 47, 49, 51, 56, 60, 83, 95
10-31/11-1	Finish Sec. 5.6 Quiz 5.3-5.4 Start Chapter 5 Review	Chapter 5 Test Review
11-2/3	Chapter 5 Review Sec. 5.5-5.6 HSA Due
11-6(s)	Sec. 6.1-Velocity and Net Change Notes Extend our knowledge of the relationships between position, velocity and acceleration to include displacement and total distance traveled by using integrals. Use the FTC (evaluation part) to predict future positions or velocities. Use the FTC (evaluation part) to compute net change and predict future value of other quantities.	pg 440: #7, 9, 13, 18, 21, 24, 25, 38, 40, 54
11-7/8	Chapter 5 Test
11-9/10	Sec. 6.2-Area Between Curves Notes Understand how to find the area between curves Find the area between curves by integrating along the x-axis or the y-axis	p. 450: # 5, 7, 11, 16, 19, 23, 27, 29 (no calculator) 37, 47, 53 (calculator ok) Show all work for no calc allowed problems, set up and evaluate on the calculator for the rest.
11-13(s)	Sec. 6.3-Volume By Revolutions Notes Understand the difference between a disc and a washer Find the volume of a solid by rotating the area around a given axis	pages 465-6: #20, 27, 34, 38, 45 (no calculator) #25, 31, 40, 46, 48 (with calc)
11-14/15	Geometric Volume Formulas WS Volume of a Cup Activity Volume Practice WS MC/FR #5 Understand the difference between a disc and a washer Find the volume of a solid by rotating the area around a given axis	Finish WS
11-16/17	Finish WS from 11-15/16 Sec. 6.3 Part 2-Volume By Cross Sections Notes Understand how a solid is formed by taking a known 2D shape and moving it along a curve Find the volume of a solid given 2D shapes and an equation of a curve	p. 464: #5, 7-9, 11 plus worksheet
11-27 (s)	Accuracy Check 6.1-6.3 HSA Due Sec. 6.4-Volume By Shells Notes Understand how a shell can be used to calculate the volume of a solid Find the volume of a solid by rotating a shell around an axis of revolution parallel to the representative rectangle	Accuracy Check 6.1-6.3 Answers and Makeup p. 477: #5, 7, 15, 33 (no calculator) #29, 34-36 (calculator ok)
11-28/29	Quiz 6.1-6.3 AP Volume Problems	Chapter 6 Review
11-31/ 12-1	Sec. 6.5-Arc Length Notes Review for Test Understand how to find the length of a nonlinear function	p. 485: #3, 7, 11, 34 (No Calc) #18, 19, 25, 37 (Calc OK)
12-4(s)	Sec. 7.1-Basic Approaches to Integration Notes Understand there are more algebraic ways to integrate than just the substitution method Integrate by splitting up fractions, using long division, completing the square Sec. 6.4-6.5 HSA Due	p. 509: #11, 14, 23-25, 28, 30, 31, 33, 53
12-5/6	Chapter 6 Test
12-7/8	Finish 7.1 Notes on completing the square integration Sec. 7.2-Integration by Parts Notes Recognize patterns in integrands that allow students to pick which method of integration is appropriate Use Integration by Parts as another method to evaluate an integral	p. 514: #5, 7-9, 16, 23, 25, 27, 30, 35, 41
12-11(s)	Finish 7.1/7.2 Work on Extra Credit Problem
12-12/13	Quiz 7.1-7.2 Start Review
12-14/15	Semester Review Semester Review Answers	Extra Credit Problem Due
12-18/19	Semester 1 Final

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