10/7/2021

2019ap Calculus

66

2011 answers to free response AP questions
The Mr. Calculus page can provide further resources for you to find assistance! Look further down the page or go to the links' pages.

As always, your corrections and suggestions are welcome-->e-mailyour corrections or suggestions by clicking here.


2019 ap calculus frq
Clickhere to see the solutions to the 2020 AP Released Free Response questions.As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[the questions are not included as they are copyrighted]
  1. (a) = 153.457690 To the nearest whole number, 153 fish enter the lake from midnight to 5 A.M. Dt = 6.059038 (b) 5-00 The average number of fish that leave the lake per hour from.
  2. AP Calculus AB Exam. This course is organized around the foundational concepts of calculus. This includes limits, derivatives, integrals, and the Fundamental Theorem of Calculus. The AP Calculus AB exam format is: Section I: Multiple Choice Part A (60 minutes, calculator not permitted) 30 Questions. Part B (45 minutes, graphing calculator required).
  3. AP Calculus AB 2017 Free Response Question 3. The function f is differentiable on the closed interval −6, 5 and satisfies f(−2) = 7. The graph of f', the derivative of f, consists of a semicircle and three line segments, as shown in the figure above.
  4. AP Calculus BC 2019 Free Response Question 3 3. The continuous function f is defined on the closed interval −6 ≤ x ≤ 5. The figure above shows a portion of the graph of f, consisting of two line segments and a quarter of a circle centered at the point (5, 3).

2019 AP Calculus AB Exam Free Response Question #5 Area of a region; integral by hand; Fundamental Theorem, FTC; volume with known cross sections; volume giv.

Clickhere to see the solutions to the 2019 AP Released Free Response questions. As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[the questions are not included as they are copyrighted]

Clickhere to see the solutions to the 2018 AP Released Free Response questions.As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[the questions are not included as they are copyrighted]

Clickhere to see the solutions to the 2017 AP Released Free Response questions.As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[thequestions are not included as they are copyrighted]

Clickhere to see the solutions to the 2016 AP Released Free Response questions.As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[thequestions are not included as they are copyrighted]

Clickhere to see the solutions to the 2015 AP Released Free Response questions. As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[thequestions are not included as they are copyrighted]


Clickhere to see the solutions to the 2014 AP Released Free Response questions.As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[thequestions are not included as they are copyrighted]


. As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[thequestions are not included as they are copyrighted]


. As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[thequestions are not included as they are copyrighted]



[including Form B]As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[the questions are not included as they are copyrighted]
Clickhere to see the solutions to the 2010 AP Free Response questions[including Form B]As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[the questions are not included as they are copyrighted]
Clickhere to see the solutions to the 2009 AP Free Response questions[including Form B]As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[thequestions are not included as they are copyrighted]
Clickhere to see the solutions to the 2008 AP Free Response questions[including Form B]As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[the questions are not included as they are copyrighted]
Clickhere to see the solutions to the 2007 AP Free Response questions[including Form B ]As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[the questions are not included as they are copyrighted]
Clickhere to see the solutions to the 2006 AP Free Response questions[including Form B ]As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[the questions are not included as they are copyrighted]
Clickhere to see the solutions to the 2005 AP Free Response questions[including Form B ]As always, your corrections and suggestions are welcome--> e-mailyour corrections or suggestions by clicking here.[the questions are not included as they are copyrighted]
AP 1998 Multiple Choice Exam Answers
Clickhere to see the solutions to the 1998 AP Multiple Choice questions[the questions are not included as they are copyrighted].As always, your corrections and suggestions are welcome-->e-mail your corrections or suggestions by clicking here.
Links to sites on Conic sections
Links to Mathematics Dictionaries and Encyclopedias
Famous Curves Index
Everything about those weird named curves you'd ever want to know
The Mr. Calculus page can provide further resources for you to find assistance! Look further down the page or go to the links pages.
Somehelpful tables
Derivatives Convergence Tests
Logarithms Exponents
Special Technique Simple Sequence Limits
A comprehensive reference to and list of mathematical constants
The proof pi, e, and log(2) are irrational
2001 AP FREE RESPONSE
AB and BC solutions
2000 AP FREE RESPONSE
AB and BC solutions
1999 AP FREE RESPONSE

Ap Classroom

AB and BC solutions
1998 AP FREE RESPONSE
AB and BC solutions
1997 AP FREE RESPONSE
AB and BC solutions
How to get the graph of the derivative or definite integral of a given function f(x) on your TI-83 or TI-84 calculator.

2019 Ap Calculus Bc Frq

Want to try a selected problem for practice?
Try it --> then look at solution
Maximum length of a ladder able to go around a corner in a hallway
Largest trapezoid that can be inscribed in a semi-circle
Circular piece of paper with wedge cut out->maximum cone volume
f ' (x) = f(x) - g(x) & g ' (x) = g(x) - f(x) & f(0) = 5 & g(0) = 1 -->Show f(x) + g(x) = 6
A trough of given length with isosceles triangle cross section has water flowing in-->How fast is the surface rising
Maximum volume of a cone inscribed in a shpere
Inscribe maximum volume cylinder in a given sphere
Find the maximum volume of a closed can that can be made form given amount of material
Find the points where haseither horizontal or vertical tangents
Look around--Lots of help here!
Mathematics Resources[annotated]

Mr. Calculus is a College Board endorsed AP* Calculus AB and AP* Calculus BC consultant and teaches at DiamondBar High School in DiamondBar, California. Mr. Calculus taught at WalnutHigh School in Walnut and La Puente High School in La Puenteall in California. He received his BA and MA in mathematics at CaliforniaState University at Fullerton. Mr. Calculus went to high school at Mayfair High School in Lakewood, California. Besides teaching and mathematics, he enjoys the outdoors, travel, music, going to concerts, Bruce Springsteen, and surfingthe net. If you wish to share thoughts on any of these topics with him,e-mail by clicking here.

Mr. Calculus is on Twitter, he is http://twitter.com/MrCalculus and on Facebook, he is http://facebook.com/MrCalculus. Feelto visit the sites or to contact him.

Mr. Calculus must apologize for having to remove the free response questions. If you read the e-mail sent by the College Board, you will see that they will not permit this kind of posting. You may see this particular e-mail by clicking here.

Links to what your AP Calculus score will grant you in credit at universities and colleges
Site maintained by AP(the CollegeBoard)
On-line Encyclopedia of Integer Sequences--put in sequence, get lots of data if this sequence is known
An interesting look at Fibonacci Numbers
If you just wish to find an INTEGRAL, link up to the INTEGRATOR-sponsored by Mathematica!
Instructions are online and it's hot!
A table of derivatives including proofs of many of them
A table of differentiation and partial differentiation identities with some proofs


Mathematics is beautiful!
Copyright1995-2015CASand HMA as Mr. Calculus and Ask Mr. Calculus
AP Calculus AB - 1st Semester
Unit 1 - Limits and Continuity
Week 0

Zoom Meetings on 8/12, 8/13, and 8/14 at 10:45 AM
Meeting ID: 315 776 7806 Password: mryaton
Video on Introduction to Limits (Due on 8/12)
Introduction to Limits Self-Assessment (Due on 8/12)
Video on Finding Limits Graphically (Due on 8/13)
Finding Limits Graphically Self-Assessment (Due on 8/13)

Week 1
Video on Estimating Limits from Tables (Due on 8/16)
Estimating Limits from Tables Self-Assessment
(Due 8/16)
Video on Finding Limits Algebraically(Due on 8/17)
Finding Limits Algebraically Self-Assessment(Due 8/17)
Associating Limits w/ Graphical Behavior (8/19 in class)
Kuta - Limits at Removable Discontinuities (8/19 in class)
Selecting Procedures for Evaluating Limits (8/20 in class)
Kuta - Limits at Jump Discontinuities (8/20 in class)

Week 1 - Unit 1 Limits Quiz (8/21)
Week 2
Video on Types of Discontinuities(Due on 8/23)
Types of Discontinuities Self-Assessment (Due on 8/23)
Video on Defining Continuity at a Point(Due on 8/24)
Defining Continuity at a Point Self-Assessment(Due 8/24)
Video on Continuity over an Interval(Due on 8/25)
Continuity over an Interval Self-Assessment(Due 8/25)
Continuity Practice Set (8/26 in class)
Establishing Continuity for EVT and IVT (8/27 in class)

Week 2 - Unit 1 - Limits Quiz (8/28)
Week 3
Limits at Infinity of Graphs Video (Due on 8/30)
Limits at Infinity of Graphs Self-Assessment (Due on 8/30)
Limits at Infinity of Quotients Video (Due on 8/31)
Limits at Infinity of Quotients Self-Assessment (Due 8/31)
Limits Practice Set 1 (9/1 in class)

Intermediate Value Theorem Video (Due on 9/1)
Intermediate Value Theorem Self-Assessment (Due 9/1)

Unit 1 - Limits Test (9/4)
Unit 2 - Differentiation: Definition and Basic Derivative Rules
Week 4
Average Rate of Change Video (Due on 9/7)
Average Rate of Change Self-Assessment
(Due on 9/7)
Estimating the Rate of Change Video (Due on 9/8)
Estimating the Rate of Change Self-Assessment (Due 9/8)
Instantaneous RoC Using Limits Video (Due 9/9)
Instant. RoC Using Limits Self-Assessment (Due 9/9)
Week 4 - Unit 2 - Differentiation Quiz (9/11)
Week 5
Defining the Derivative of a Function Video (Due on 9/13)
Defining the Derivative Self-Assessment (Due on 9/13)
Differentiability & Continuity Video (Due on 9/13)
Differentiability & Continuity Self-Assessment (Due 9/13)
Derivatives & the Power Rule Video (Due on 9/13)
Derivatives & the Power Rule Self-Assessment (Due 9/13)
Derivatives at a Point Video (Due on 9/14)
Derivatives at a Point Self-Assessment
(Due on 9/14)
Manipulating Before Differentiating Video (Due on 9/15)
Manip Before Differentiating Self-Assessment
(Due 9/15)
Derivatives of sin x, cos x, e^x, ln x Video (Due on 9/16)
Deriv of sin x, cos x, e^x, ln x Self-Assessment (Due 9/16)
Week 5 - Unit 2 - Differentiation Quiz (9/18)
Week 6
The Product Rule Video (Due on 9/20)
The Product Rule Self-Assessment
(Due on 9/20)
The Quotient Rule Video (Due on 9/21)
The Quotient Rule Self-Assessment(Due on 9/21)
Differentiation Rules with Tables (9/23 in class)
Going Off on a Tangent (9/24 in class)

Week 6 - Unit 2 - Differentiation Quiz (9/25)
Week 7
Finding Derivatives of tan, cot, sec, cot Video (Due 9/27)
Finding Deriv of tan, cot, sec, cot Self-Assess (Due 9/27)

Unit 2 - Differentiation Test (10/2)
Unit 3 - Differentiation: Composite, Implicit, and Inverse Functions
Week 8
The Chain Rule Video (Due 10/4)
The Chain Rule Self-Assessment
(Due 10/4)
The Chain Rule with Tables Video (Due 10/5)
The Chain Rule with Tables Self-Assessment (Due 10/5)
Implicit Differentiation Video (Due 10/6)
Implicit Differentiation Self-Assessment(Due 10/6)
Kuta Chain Rule Practice (10/6 in class)
Kuta Chain Rule with Trig Practice (10/6 in class)

Week 9
Differentiating Inverse Functions Video (Due on 10/11)
Differentiating Inverse Funct Self-Assessment (Due 10/11)
Differentiating Inverse Trig Functions Video (Due 10/12)
Differentiating Inverse Trig Self-Assessment (Due 10/12)
Calculating Higher-Order Deriv Video (Due on 10/13)
Calculating Higher-Order Deriv Self-Assess (Due 10/13)
Implicit Differentiation Practice (10/13 in class)

Unit 3 - Differentiation Test (10/16)
Unit 4 - Contextual Applications of Differentiation
Week 10
Contextual Meaning of Derivatives Video (Due on 10/18)
Contextual Meaning of Deriv Self-Assess (Due on 10/18)
Straight-Line Motion Video (Due on 10/19)
Straight-Line Motion Self-Assessment (Due on 10/19)

Related Rates Video (Due on 10/20)
Related Rates Self-Assessment (Due on 10/20)
Week 11
Local Linearity and Linearization Video (Due on 10/25)
Local Linearity & Linearization Self-Assess (Due on 10/25)
L'Hospital's Rule Video (Due on 10/26)
L'Hospital's Rule Self-Assessment (Due on 10/26)
Unit 4 - Contextual Applications Test (10/30)
Unit 5 - Analytical Applications of Differentiation
Week 12
Mean Value Theorem Video (Due on 11/1)
Mean Value Theorem Self-Assessment (Due on 11/1)
Extreme Value Theorem Video (Due on 11/1)
Extreme Value Theorem Self-Assessment (Due on 11/1)
First Derivative Test Video (Due on 11/2)
First Derivative Test Self-Assessment (Due on 11/2)

Unit 5 - Analytical Applications Quiz (11/6)
Week 13
Second Derivative Test Video (Due on 11/8)
Second Derivative Test Self-Assessment (Due on 11/8)
Sketching Graphs and Their Derivatives Video (Due on 11/9)
Sketching Graphs and Their Derivatives Self-Assessment (Due on 11/9)

Week 14
Optimization Problems Video (Due on 11/15)
Optimization Problems Self-Assessment (Due on 11/15)
Unit 5 - Analytical Applications Test (11/19)
Thanksgiving Break
Week 15
Week 15 HW - 2018 AP Calculus AB MC (Due on 12/3)
Week 16

Week 16 HW - 2019 AP Calculus AB MC (Due on 12/10)
Week 17
AP Calculus AB Midterm
Christmas Break
Lifesize AP Calculus AB Meeting Code: 4918470
AP Calculus AB Cheat Sheet

AP Calculus AB - 2nd Semester
Unit 6 - Integration and the Accumulation of Change
Week 18

Accumulation of Change Video (Due on 1/4)
Accumulation of Change Self-Assessment (Due on 1/4)
Left & Right Riemann Sums Video (Due on 1/4)
Left & Right Riemann Sums Self-Assessment (Due on 1/4)
Midpoint & Trapezoidal Riemann Sums Video (Due on 1/5)

Midpoint & Trapezoidal Sums Self-Assess (Due on 1/5)
Unit 6 Integration Quiz (1/8)
Week 19
Integration Rules Video (Due on 1/10)
Integration Rules Self-Assessment (Due on 1/10)
Integration of Trig (& Other Functions) Video (Due 1/11)
Int of Trig (& Other Funct) Self-Assessment (Due 1/11)
Fundamental Theorem of Calculus Video (Due on 1/12)
Fundamental Theorem Calc Self-Assessment (Due 1/12)
Week 20
Definite Integral as Limit of Riemann Sum Video (Due 1/18)
Definite Integral as Limit of RS Self-Assess (Due 1/18)
Definite Integral Video (Due on 1/18)
Definite Integral Self-Assessment (Due on 1/18)
Integration by u-substitution Video (Due on 1/19)
Integration by u-substitution Self-Assessment (Due 1/19)
Week 21
Definite Integration using u-substitution Video (Due 1/24)
Definite Int using u-substitution Self-Assess (Due 1/24)
Unit 6 Integration Test (1/29)
Unit 7 - Differential Equations
Week 22

Writing Differential Equations Video (Due on 1/31)
Writing Differential Eq Self-Assessment (Due on 1/31)
Verifying Solutions of Diff Eq Video (Due on 2/1)
Verifying Solutions to Diff Eq Self-Assessment (Due 2/1)
Sketching Slope Fields Video (Due on 2/2)

Sketching Slope Fields Self-Assessment (Due on 2/2)
Unit 7 Differential Equations Quiz (2/5)
Week 23
Separable Differential Equations Video (Due on 2/7)
Separable Differential Eq Self-Assessment (Due on 2/7)
Finding Particular Solutions of Diff Eq Video (Due 2/8)
Finding Particular Solutions Self-Assessment (Due 2/8)
Unit 7 Differential Equations Quiz (2/12)
Week 24
Exponential Models with Diff Eq Video (Due 2/14)
Exponential Models with Diff Eq Self-Assess (Due 2/14)
Unit 7 Differential Equations Test (2/19)
Unit 8 - Applications of Integration
Week 25

Average Value of a Function Video (Due on 2/21)
Average Value of a Function Self-Assess (Due 2/21)
Motion with Integration Video (Due on 2/22)
Motion with Integration Self-Assess (Due 2/22)
Integrals in Context Video (Due on 2/23)

Integrals in Context Self-Assessment (Due on 2/23)
Unit 8 Applications of Integration Quiz (2/26)
Week 26
Area Between a Curve and x-axis Video (Due on 2/28)
Area Between a Curve and x-axis Self-Assessment (Due on 2/28)
Area Between Two Curves Video (Due 3/1)
Area Between Two Curves Self-Assessment (Due 3/1)
Horizontal Area Between Curves (Due 3/2)
Horizontal Area Between Curves Self-Assessment (Due 3/2)

Unit 8 Applications of Integration Quiz (3/5)
Week 27
Volume by Disc Method Video (Due on 3/7)
Volume by Disc Method Self-Assess (Due on 3/7)
Volume by Washer Method Video (Due on 3/8)
Volume by Washer Method Self-Assess (Due on 3/8)
Volume Around Other Axes Video (Due on 3/9)
Volume Around Other Axes Self-Assess (Due on 3/9)

Unit 8 Applications of Integration Quiz (3/12)
Spring Break
Week 28
Volumes with Cross-Sections (Squares and Rectangles) Video (Due on 3/22)
Volumes with Cross-Sections (Squares and Rectangles) Self-Assess (Due on 3/22)
Volumes with Cross-Sections (Triangles and Semicircles) Video (Due on 3/23)
Volumes with Cross-Sections (Triangles and Semicircles) Self-Assess (Due on 3/23)

Unit 8 Applications of Integration Test (3/26)
AP Calculus AB Review
Unit 1 Review - Limits and Continuity
Unit 2 Review - Differentiation: Definition and Basic Derivative Rules
Unit 3 Review - Differentiation: Composite, Implicit, and Inverse Functions
Unit 4 Review - Contextual Applications of Differentiation
Unit 5 Review - Analytical Apps of Differentiation
Unit 5 Calculus Review Video
Unit 5 Calculus Sample AP Problems Video
Unit 6 Review - Integration & Accum of Change
Unit 6 Calculus Review Video
Unit 6 Calculus Sample AP Problems Video
Unit 7 Review - Differential Equations
Unit 7 Calculus Review & Sample AP Problems Video
Unit 8 Review - Applications of Integration
Unit 8 Calculus Review & Sample AP Problems Video

2019 AP Calculus AB #1 (15 min)
2019 AP Calculus AB #1 Video
2019 AP Calculus AB #2 (15 min)
2019 AP Calculus AB #2 Video
2019 AP Calculus AB #3 (15 min)
2019 AP Calculus AB #3 Video
2019 AP Calculus AB #4 (15 min)
2019 AP Calculus AB #4 Video
2019 AP Calculus AB #6 (15 min)
2019 AP Calculus AB #6 Video