AP Calculus AB
FRQ DATABASE:
Descriptions of the more common types of FRQs to show up on the AP exam as well as convient links to access the practice, scoring, average scores and help videos in one spreadsheet.FRQ DATABASE:
Frequently Asked Questions:
Do we get to use a calculator on the AP exam? There are 4 sections to the AP exam and 2 of them allow a calculator. There are actually many times where College Board expects you to use a calculator on a particular question. Even if it is possible to do it by hand, sometimes it only makes sense to use a calculator based on the amount of time you have for it. Anytime you need to find the derivative for a particular value or want to integrate and you have the limits of integration (and it is in a calculator part of the exam) then you should just let your calculator do the computation for you. In these types of questions they are not trying to see if you can take a derivative or if you are able to integrate, but rather just that you understand why they apply there. And using the calculator is faster and less prone to mistakes. For these reasons, I'd suggest you watch this video showing how to use the Derivative and Integrate Functions of your calculator. For similar reasons, you may want to let your calculator solve an equation for you. Watch this video demonstrating how to use the Equation Solver feature on your calculator.Frequently Asked Questions:
Frequently Used Resources:
What are some resources that I can use for extra practice? The Khan Academy's AP Cal AB course is probably the best single resource. Khan Academy partnered up with College Board to align their course to the expectations of the curriculum on the AP exam. The course is laid out in the same units as College Board suggests. Each unit has lesson videos, quizzes, and tests to check for understanding. I prefer to attempt the short quiz and if I can't answer all of them correctly and rather quickly, then I can click on the video to get a refresher on the topic. Also, Paul's Online Notes is great when you just need more questions to practice. This is really designed for a college level Calculus 1 and 2 course rather than an AP Calculus course but almost all of the content is still relevant. What I like about this as a resource is that it has very detailed notes, to explain topics. It also provides practice problems with solutions to check for understanding.Frequently Used Resources:
Unit 1 - Limits & Continuity
AP EXAM WEIGHT: 10% - 12%
Unit 1 - Limits & Continuity
AP EXAM WEIGHT: 10% - 12%
#1: Syllabus
#1: Syllabus
#2: Websites to sign up for
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#3: Unit Circle / Log Propeteries Notes
#3: Unit Circle / Log Propeteries Notes
#4: Notes: Evaluating Limits (graphically) and Properties of Limits
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Video of the notes
#4s: Suggested Practice for Evaluating Limits and Properties of Limits
KA: Limits IntroKA: Estimating limit values from graphsKA: One-sided limits from graphsKA Quiz: Connecting limits and graphical behavior#4s: Suggested Practice for Evaluating Limits and Properties of Limits
Evaluating Limits Practice (from graphs):Download a new copyCheck your answers with a completed copy.
#5: Unit Circle and Log Properties Review Mini-Quiz
#5: Unit Circle and Log Properties Review Mini-Quiz
#6: Notes: Evaluating Limits Practice Analytically (from a function)
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Video of the notes
Optional Extra Practice: Composite Limits Notes / Practice and its solutions.Optional Extra Practice: Evaluating Limits Practice (from functions)Download a new copyCheck your answers with a completed copy. Make notes of your mistakes to study later.
#7: Notes: Intermediate Value Theorem (IVT)
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Video of the notes
#8: IVT Khan Academy Practice (2 of them) - scratch paper
#8: IVT Khan Academy Practice (2 of them) - scratch paper
Optional Section 2.3 Book Assignment:
Pages 87-88 #s: 5, 15, 26, 33, 35, 37, 39, 41, 43, 51, 53, 55, 57, 59, 75, and 77.(Odd Solutions: https://bit.ly/2MmGkbg)
Extra Practice: #67
Textbook Pages: 87 and 88.
#10: Notes: Continuity
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Video of the notes
#11: Khan Academy Practice (3 of them) - scratch paper
#11: Khan Academy Practice (3 of them) - scratch paper
#12: Limits Review
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Check your answers with a completed copy. Make notes of your mistakes to study later.Video Solutions: #2b, #3, #5, #12Unit 1 Limits Review Video from College Board
#13: (on your own paper) Past Unit 1 Test Questions
#13: (on your own paper) Past Unit 1 Test Questions
#14: Continuity and Intermediate Value Theorem (IVT) Practice
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Video Solutions: Front Page #4, Front Page #6, Back Page #7, Back Page #8,
#15: Khan Academy Practice (8 practice assignments)
#15: Khan Academy Practice (8 practice assignments)
#16: Unit Reflection (Limits)
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Unit 2 - Definition and Basic Derivative Rules
AP EXAM WEIGHT: 10% - 12%
Unit 2 - Definition and Basic Derivative Rules
AP EXAM WEIGHT: 10% - 12%
#17: Notes (and practice) - Definition of a Derivative
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#18: Khan Academy Assignment - Definition of a Derivative
Login to Khan Academy and the assignment should be assigned to you. If you don't see it, make sure you joined that class on the first day of school (look at handout #2). You should keep trying until you end up with a 100% on this assignment. There is no limit on the number of retries.#18: Khan Academy Assignment - Definition of a Derivative
#19: Notes - Basic Derivative Rules
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(Odd Solutions: https://bit.ly/2HQiujB) (Extra Practice: #26) (Paul's Online Notes and Practice: https://bit.ly/1EHaOUu)(Khan Academy's Derivatives Videos and Quizzes: https://bit.ly/2EWsd7P)
#21: Notes - Position vs Velocity vs Acceleration (AND SPEED!)
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(Optional) Extra Practice with Solutions Provided
(Odd Solutions: https://bit.ly/2YU26nU) Textbook Pages 146 -149(Khan Academy's Derivatives Videos and Quizzes: https://bit.ly/2EWsd7P)(Paul's Online Notes and Practice: https://bit.ly/2Wx0Ev9)
#23: Notes - Position vs Velocity vs Acceleration (AND SPEED!)
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(Optional) Extra Practice with Solutions Provided
#24: Circuit- Power Rule
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Video Solutions: #14, #15
#25: 2 Khan Academy Assignments (Product Rule and Quotient Rule)
#25: 2 Khan Academy Assignments (Product Rule and Quotient Rule)
#26: Circuit- Do you know your calculator?
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Video Solutions: #7
#28: Chain Rule Notes
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#30: Khan Academy Assignments (2 on chain rule)
#30: Khan Academy Assignments (2 on chain rule)
#32: Unit 2 Test Review
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Solutions
Video Solutions: #15, #16, #25, #26, #39, #40, #41, #42, #43, #51, #54, #55, #56
#34: Circuit: Chain Rule
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Solutions
Video Solutions: #5
#35: Unit 2 Exam
#35: Unit 2 Exam
Unit 3 - Differentiation: Composite(Chain Rule), Implicit, and Inverse Functions
AP EXAM WEIGHT: 9% - 13%
Unit 4 - Contextual Applications of Derivatives
AP EXAM WEIGHT: 10% - 15%
Unit 3 - Differentiation: Composite(Chain Rule), Implicit, and Inverse Functions
AP EXAM WEIGHT: 9% - 13%
Unit 4 - Contextual Applications of Derivatives
AP EXAM WEIGHT: 10% - 15%
#36: 3.5 Notes (Implicit Differentiation)
Download a new copyVideo of the Notes#36: 3.5 Notes (Implicit Differentiation)
#37: Khan Academy (1 assignment; Implicit Differentiation)
#37: Khan Academy (1 assignment; Implicit Differentiation)
#38: 3.5 Book Assignment (Implicit Differentiation)
Pages 171-172 #s: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 45, 47, 71, and 73.(Odd Solutions: https://bit.ly/2JOlJKA) Extra Practice (optional):(Paul's Online Implicit Differentiation Notes and Practice: https://bit.ly/2Ycool5)#38: 3.5 Book Assignment (Implicit Differentiation)
#39: Implicit Differentiation (AP Practice Questions)
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Video Solutions: 2000 FRQ #5, 2004 FRQ #4
#40: Related Rates Notes and Examples
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#41: Basic Related Rates Practice Worksheet
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Video Solutions (front page): #2, #3, #5, #6b
Video Solutions (other pages): #1, #2, #3, #5, #6, #7, #8, #9, #10, #11,
(Optional) Related Rates Circuit: Download a new copy / Solutions
#42: Geometry Formulas that you need to know
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#44: Related Rates (Khan Academy - Pythagorean Type)
#44: Related Rates (Khan Academy - Pythagorean Type)
#48: Unit 3 Assessment
#48: Unit 3 Assessment
Unit 5 - Analytical Applications of Differentiation
AP EXAM WEIGHT: 15% - 18%
Unit 5 - Analytical Applications of Differentiation
AP EXAM WEIGHT: 15% - 18%
Unit 5 Part 2 - Analytical Applications of Differentiation (Curve Sketching)
Unit 5 Part 2 - Analytical Applications of Differentiation (Curve Sketching)
#49: Notes over the 1st derivative test (section 4.3)
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Textbook Pages 223 - 224(Odd Solutions: https://bit.ly/2FgxTrG) (Khan Academy's Videos and Quizzes: https://bit.ly/2Kq3mfy)
#51: Notes for EVT and MVT
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#52: 5 Khan Academy Assignments (1: Inc./Dec. Intervals 2: MVT Justification 3: MVT Finding "c" 4: EVT 5: Relative min/maxs)
#52: 5 Khan Academy Assignments (1: Inc./Dec. Intervals 2: MVT Justification 3: MVT Finding "c" 4: EVT 5: Relative min/maxs)
#53: Notes over the 2nd derivative test (section 4.4)
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#54: Circuit: What f' and f'' tell you about f
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Video Solutions: #1, #2, #3, #4, #5, #6, #7, #8, #9, #10, #11, #12, #13, #14, #15, #16
#55: Organizing Information from the 1st and 2nd derivatives
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#56: Unit 4 Practice FRQs
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Solutions / Scoring Guides
Video Solutions: FRQ#1, FRQ #2, FRQ #3, FRQ #4, FRQ #5
#57: 4.1-4.4 Review
Download a new copySolutionsVideo Solutions: #4, #5, #6, #9, #12, #13, #15, #16, #18, #21, #26, #27, #28, #29#57: 4.1-4.4 Review
4.1-4.4 Suggested (Optional) Practice: Download a new copy
MVT Circuit (Download a new copy / Solutions / Video Solutions: #5, #6, #8, #10, #11, #13, #14, #15)
#58: 4.1-4.4 Assessment
#58: 4.1-4.4 Assessment
#60: Curve Sketching f and f'' given f'
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#61: f to f' to f'' Card Sort Activity
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#62: 4.6 - 4.7 Review / Practice Quiz
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Video Solutions: #1, #7
#63: Curve Sketching Quiz
#63: Curve Sketching Quiz
Unit 6 - Integration and the Accumulation of Change
AP EXAM WEIGHT: 17% - 20%
Unit 6 - Integration and the Accumulation of Change
AP EXAM WEIGHT: 17% - 20%
#64: Riemann Sums (introduction) & Practice FRQ
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#65: Trapezoidal Rule.
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#66: 2 Khan Academy Assignments: - Left/Right Riemann Sums and Midpoint/Trapezoidal Sums
#66: 2 Khan Academy Assignments: - Left/Right Riemann Sums and Midpoint/Trapezoidal Sums
#68: Notes: L'Hospital's Rule
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#69: Fall Semester Exam Review Topics and Practice
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Solutions with work shown. FRQ Solutions/Justifications
Video Solutions: #3, #5, #8, #9, #10, #11-12, #15, #16, #19, #20, #21, #23, #25, #26, #27, #28, #29, #30, #31, #33, #34, #35, #36, #39, #40, #41, #42, #43, #44, #46, #48, #50-51
#69: Fall Semester Exam Review Topics and Practice
Download a new copy: Part 1 (Topics and FRQ Practice), Part 2 (Multiple Choice Practice with solutions at the end)
Solutions with work shown. FRQ Solutions/Justifications
Video Solutions: #3, #5, #8, #9, #10, #11-12, #15, #16, #19, #20, #21, #23, #25, #26, #27, #28, #29, #30, #31, #33, #34, #35, #36, #39, #40, #41, #42, #43, #44, #46, #48, #50-51
#70: Definite Integral to Limit of a Riemann Sum
Download a new copy with solutions providedSolutions with some work shown#70: Definite Integral to Limit of a Riemann Sum
#74: 5.1 - 5.4 Practice FRQs
Download a new copy2001 FRQ #3 Video / 1997 FRQ #1 Video / 2002 FRQ #3 Video / 1999 FRQ #1 Video#74: 5.1 - 5.4 Practice FRQs
#75: Circuit- Definite Integrals
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#81: 5.1 - 5.4 Quiz Review
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Solutions
Video Solutions: #1, #2, #3, #4, #5, #6, #7, #8, #9, #10, #11, #12, #1(back page), #2(back page), #3(back page), #4-7 (back page), #8(back page), #9(back page), #10(back page), #12(back page), #13 (back page), #14 (back page), #15 (back page)
#81: 5.1 - 5.4 Quiz Review
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Solutions
Video Solutions: #1, #2, #3, #4, #5, #6, #7, #8, #9, #10, #11, #12, #1(back page), #2(back page), #3(back page), #4-7 (back page), #8(back page), #9(back page), #10(back page), #12(back page), #13 (back page), #14 (back page), #15 (back page)
#83: 5.1 - 5.4 Quiz
#83: 5.1 - 5.4 Quiz
(OPTIONAL) #82a: Picking U and the form for U Substitution. Download a new copy with solutions provided.
(OPTIONAL) #82b: Tons of USUB practice. Download a new copy. Solutions with steps shown.
#86: Khan Academy; 3 assignments- (practice identifying "u", practice u sub with definite intergrals, practice u sub with indefinite intergrals)
#86: Khan Academy; 3 assignments- (practice identifying "u", practice u sub with definite intergrals, practice u sub with indefinite intergrals)
#94: U-SUB Worksheet 2
#94: U-SUB Worksheet 2
#95: 2022 FRQs (ALL 6 in handout but we did frq 1 and frq 3 at this time)
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Solutions / Scoring Guides / Help Videos are are linked in the document
#95: 2022 FRQs (ALL 6 in handout but we did frq 1 and frq 3 at this time)
Download a new copy
Solutions / Scoring Guides / Help Videos are are linked in the document
#96: Chapter 5 Exam
#96: Chapter 5 Exam
Unit 7 - Differential Equations
AP EXAM WEIGHT: 6% - 12%
Unit 7 - Differential Equations
AP EXAM WEIGHT: 6% - 12%
#97: Slope Fields Worksheet
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Solutions(Khan Academy's Slope Fields Videos and Quizzes: http://bit.ly/2VK8iAN)
#98: Separation of Variables Notes
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Video Solutions: #7, #11,
#99: Exponential Growth / Decay
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Solutions
#100: How to deal with absolute values signs in solving differential equations
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Textbook Page: 405
(Odd Solutions: http://bit.ly/2wHQpI6)
#102: MORE with Separation of Variables WorksheetDownload a new copy
Solutions
Video Solutions: #5
#103: Chapter 6 Quiz Review
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Video Solutions: #4, #6, Suggested Extra Practice: Separable differential equations: find the error, Separable Differential Equations, Particular solutions to differential equations, Particular solutions to separable differential equations. Released AP FRQS: Download a new copy with scoring guide attached. Video solution of 2004 FRQ #6, video solution of 2008 FRQ #5.
#104: 2013 FRQ 6 and 2014 FRQ 6
Download a new copy of 2013 FRQ6. Solution Links and Help video is provided on the handout.Download a new copy of 2014 FRQ6. Solution Links and Help video is provided on the handout.#104: 2013 FRQ 6 and 2014 FRQ 6
#104a: 2023 FRQ 3 (MILK)
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CORRECT Scoring Guide
#105: Chapter 6 Quiz
#105: Chapter 6 Quiz
Unit 8 - Applications of Integraiton
AP EXAM WEIGHT: 10% - 15%
Unit 8 - Applications of Integraiton
AP EXAM WEIGHT: 10% - 15%
#106: Circuit: L'Hopital's Rule
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Video Solutions: #4, #10, #11, #12, #16, #17, #22
#107: Circuit: Area between two curves
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Video Solutions: #1, #2, #3, #4, #5, #6, #7, #8, #9, #10, #11, #12, #13, #14, #15, #16.
#108: Notes: Volumes of Revolutions Part 1 (disc method)
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#109: 1 Khan Academy Assignment over Volumes of Revolutions Part 1
#109: 1 Khan Academy Assignment over Volumes of Revolutions Part 1
#110: Notes: Volumes of Revolutions Part 2 (washer method)
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#111: 1 Khan Academy Assignment over Volumes of Revolutions Part 2
#111: 1 Khan Academy Assignment over Volumes of Revolutions Part 2
#112: Mini-Quiz: 2nd Fundamental Theorem of Calculus
#112: Mini-Quiz: 2nd Fundamental Theorem of Calculus
#113: Notes: Volumes from Revolutions around lines other than the x-axis or y-axis
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#114: Circuit: Volume from Rotations
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Video Solutions: #1, #2, #3, #4, #5, #6, #7, #8, #9, #10, #11, #12, #13, #14, #15, #16, #17, #18.
(Optional, Extra Practice) Volumes of Revolutions Practice Worksheet. Download a new copy / Answers are provided on the bottom of each page.
#115: Mini-Quiz: U-Sub
#115: Mini-Quiz: U-Sub
#116: Volumes of Solids with known cross sections PART 1
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Interactive Tool to help you visualize the volume from cross-sections.
#117: Mini-Quiz: Speeding Up vs Slowing Down
#117: Mini-Quiz: Speeding Up vs Slowing Down
#118: Inverse Trig Derivatives (to memorize)
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#119: Volumes of Solids with known cross sections PART 2
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Interactive Tool to help you visualize the volume from cross-sections.
#120: Mini-Quiz: Inverse Trig Derivatives
#120: Mini-Quiz: Inverse Trig Derivatives
#121: 2019 FRQ 5 and 2017 FRQ 4 (Potatoe)
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#123: Mini-Quiz: Area Formulas in terms of the BASE
#123: Mini-Quiz: Area Formulas in terms of the BASE
#124: 2014 FRQ 2
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#125: Circuit: Limits
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Video Solutions: #1, #3, #8, #12, #13, #15, #16, #17, #18, #19, #20, #21, #22, #23, #24
#126: Circuit: Average Everything (Calculus!)
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Video Solutions: #5, #8, #12, #13, #15, #16
#127: 2017 FRQ 5
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#128: 2017 FRQ 2
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#129: Circuit: Limit Definition of the Derivative
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#130: Circuit: Product, Quotient, and Chain Rules
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Video Solutions: #7
#131: When you see... This is what you do....
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#132: Circuit: Tangent Line Approximation
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Video of the Notes / Examples
Video Solutions: #7, #8, #9, #10, #14
#133: Miniquiz - Over page 1 of handout #131.
#133: Miniquiz - Over page 1 of handout #131.
#134: 10 Points Closer Part 1
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#135: 10 Points Closer Part 2
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#136: Miniquiz - Over page 2 of handout #131.
#136: Miniquiz - Over page 2 of handout #131.
#137: Circuit: Writing and Interpreting Riemann Sums
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#138: 10 Points Closer Part 3
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#139: Miniquiz - Over handout #134.
#139: Miniquiz - Over handout #134.
#140: Circuit: Riemann Sums
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#141: 10 Points Closer Part 4
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#142: Miniquiz - Over handout #135.
#142: Miniquiz - Over handout #135.
#143: 10 Points Closer Part 5
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#144: AP CALCULUS AB EXAM SURVIVAL GUIDE
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