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Ms. Zhao's Home Page
AP Calculus AB
AP Calculus AB
AP Calculus BC
AP Calculus BC
AP Calculus Standards
AP Calculus Standards
AP Calculus Study Tips
AP Calculus Study Tips
AP Exam Information
AP Exam Information
Smart Board Class Notes
Smart Board Class Notes
Formulas and Theorems
Formulas and Theorems
Notes and Tutorials
Notes and Tutorials
My grade on skedula
My grade on skedula
AP Website Links
AP Website Links
Graphing Calculator
Graphing Calculator
Cooperative Learning
Cooperative Learning
Chapters Tests On Line
Chapters Tests On Line
Ms. Zhao's Schedule
Ms. Zhao's Schedule
AP Calculus Tutors
AP Calculus Tutors
My Message Board
My Message Board
Exam Book Solutions
Exam Book Solutions
AP Calculus Exam Review
AP Calculus Exam Review
2011 Letters to Future AP Calculus Students
2011 Letters to Future AP Calculus Students
FRQ PowerPoint
FRQ PowerPoint
Calculus as it relates to real world problems
Calculus as it relates to real world problems
Homework Sheet
Homework Sheet


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      Welcome to Ms. Zhao's AP Calculus Website    

Video Calculus AB/BC and Practice Problems

I. LIMITS

  1. Calculating limits intuitively.

  2. The definition of a limit.

  3. The arithmetic of limits; limits of sums, differences, products and quotients.

  4. Trigonometric limits.

  5. Continuity, including the Intermediate and Extreme Value Theorems.

II. DIFFERENTIATION

  1. Definition of the derivative; calculating derivatives using the definition; interpreting the derivative as the slope of the tangent line.

  2. Differentiation formulas; the power, product, reciprocal, and quotient rules.

  3. The chain rule.

  4. Differentiating trigonometric functions.

  5. Higher Order Derivatives.

  6. Implicit differentiation.

  7. Rates of change per unit time; related rates.

  8. Velocity and Acceleration.

  9. Differentials and Newton's method.

III. APPLICATIONS OF THE DERIVATIVE

  1. Rolle's Theorem and the Mean Value Theorem.

  2. Critical numbers and the first derivative test.

  3. Concavity and the second derivative test.

  4. Curve sketching.

  5. Extreme values on intervals.

  6. Optimization problems.

IV. THE DEFINITE INTEGRAL

  1. The definite integral; Riemann sums, area, and properties of the definite integral.

  2. The fundamental theorem of calculus.

  3. Anti-differentiation and indefinite integrals.

  4. Integration by substitution.

  5. Mean Value Theorem for integrals; average value.

V. APPLICATIONS OF THE DEFINITE INTEGRAL

  1. Area; area under a curve, area between two curves.

  2. Volume; volumes by slicing.

  3. Volumes of solids of revolutions; disks and washers, cylindrical shells.

  4. Center of mass of a rod and centroid of a planar region.

The following topics are BC Calculus Level:

VI. INTERATION TECHNIQUES, L'HOPITAL'S RULE AND IMPROPER INTEGRALS

  1. Integration by Parts
  2. Trig Powers and Trig Substitution
  3. Partial Fractions
  4. L'Hopital's Rule
  5. Improper Integrals

VII. SEQUENCES AND SERIES

  1. Sequences
  2. Series
  3. Alternating Series, Ratio and Root Tests
  4. Taylor Polynomials
  5. Power Series
  6. Taylor and Maclaurin Series

VIII. PARAMETRIC EQUATIONS AND POLAR COORDINATES

  1. Plane Curves and Parametrics
  2. Polar Coordinates and Graphs
  3. Area in Polar Coordinates

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This tutorial is designed with the student in mind. The topics selected are those that students will use in college algebra, college trigonometry, and freshman calculus. Special care has been given to selecting topics and examples that the student will be able to use in these courses. The TI-83 and TI-84 have identical key strokes for functions that are in common. Any small variations that occur are not major. The TI-84 has a number of built-in applications that are covered in a separate section. Any additional functions that the TI-84 has are included in the combined sections.

 

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General Resources

Use these general resource documents and activities to help increase your success in this course. Some content requires software plugins. Visit our Plugin Help Center for help with downloading plugins.

Bullet image Appendices
For Layout
Additional resource material related to calculus topics

Bullet image Calculus Labs
For Layout
These labs demonstrate real-world applications of the calculus concepts covered in the chapter that utilize computer algebra systems. Each lab includes an introduction with background information, observations, a statement of the purpose of the lab, and references for further investigation of the topic of the lab. Software specific data files, graphs and equations are available for each lab series.

Bullet image Algebra Review Summary
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Additional resources for review of algebra skills .

Bullet image Algebra Review Table
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Printable quick references from the book.

Bullet image Derivatives and Integrals
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Printable quick references from the book.

Bullet image Formulas from Geometry
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Printable quick references from the book.

Bullet image Trigonometry Review Table
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Printable quick references from the book.

Bullet image Graphing Calculator Programs
For Layout
The calculator programs referenced in the Graphing Calculator Guide can be downloaded from this page.

Bullet image Online Graphing Calculator

Bullet image Math Articles
For Layout
Link to download and print articles and abstracts referenced throughout the text.

Bullet image CalcChat
For Layout
With a subscription to CalcChat, you can access the following.
  • Step-by-step solutions to odd-numbered exercises
  • Chat rooms to talk about solutions with other students
  • Monitored chat rooms with a teaching assistant

Bullet image HM mathSpace Student CD: Updated Section 2.1 Try It 6
For Layout
For students using the HM mathSpace CD, we have provided an updated version of Section 2.1 The Derivative and the Tangent Line Problem. This electronic supplement provides opportunities for selfpaced review and practice.
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Hall of Fame

 

Our students have scored a 5 on the AP Calculus AB/BC Examination in 2011

 

             Name      

  AP Score  

AP Calculus AB/BC

1. Fazena Bacchus

5

BC/AB

2. Naralys K. Batista

5

BC/AB

3. Edward R. Garcia

5

BC/AB

4. Seong-Won Hwang

5

BC/AB

5. Yazhan Lin

5

BC/AB

6. Eve Pan

5

BC/AB

7. Kenneth Warren

5

BC/AB

8. Wendy Zhang

5

BC/AB

9. Ludy Fung

5

AB

10. Mei Lo

5

AB

11. Angela Qu

5

AB

12. Hillary Ramirez

5

AB

13. Cecily Vivas

5

AB

14. Siu Ka Wong

5

AB

15. Niki Xu

5

AB

16. Kenny Yang

5

AB

17. Kelvin Chew

5

AB

18. Grace Eckojojo

5

AB

19. Diana Eng

5

AB

20. Michael Golaszewski

5

AB

21. Liza Honorio

5

AB

22. Manuel Jara

5

AB

23. Karla Kirsch

5

AB

24. Nina Luksanapol

5

AB

25. Rebeca Otero

5

AB

26. Gerson Tejeda

5

AB

27. Andy Wen

5

AB

28. Gabriela Witek

5

AB

29. Zhiwei Zou

5

AB

30. Etjen Vincani

5

AB

 

Question: Is My AP Score Good Enough?

Answer: AP scores are much more straight-forward than SAT scores or ACT scores since the AP is graded on a simple 5-point scale. However, not every college treats AP scores the same way.

Students who take the AP exam will get a score ranging from 1 to 5. The College Board defines the numbers as follows:

·         5 - Extremely well qualified to receive college credit

·         4 - Well qualified to receive college credit

·         3 - Qualified to receive college credit

·         2 - Possibly qualified to receive college credit

·         1 - No recommendation to receive college credit

The five-point scale, probably not coincidentally, can also be thought of in terms of letter grades:

·         5 - "A"

·         4 - "B"

·         3 - "C"

·         2 - "D"

·         1 - "F"

·          

The average score on all AP exams is slightly below a 3. In 2008, of the nearly 3 million AP exams administered, the grades broke down as follows:

·         5 - 14% of test takers

·         4 - 19% of test takers

·         3 - 24% of test takers

·         2 - 22% of test takers

·         1 - 21% of test takers

Now for the bad news: Although the College Board defines a 2 as "possibly qualified" to receive college credit, almost no college will accept a score of 2. In fact, most selective colleges will not accept a 3 for college credit.

In the majority of cases, a student who scores a 4 or 5 will receive college credit. In rare cases, a school may require a 5. The exact guidelines vary from college to college, and they often vary from department to department within a college. At Hamilton College, for example, a student can receive credit for a 3 in Latin, but a 5 is required in Economics.

 

 

 





Ms. Zhao