BC Calculus Semester 1AP Links: AP CREDIT POLICY-Colleges and Universities
HW Solutions: Block 1-HW Solutions Block 4-HW Solutions
Class Forms: HSA
Calculus Help: Link to Help Topics | 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
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| | 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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