An Overview of our Calculus Materials

We divide our calculus material into two categories: The first is the everyday classroom activities. This includes teaching and testing.  The second is preparing for the AP exam.   While teachers are encouraged to incorporate AP exam prep in their everyday teaching, sometimes you have to have students do many mundane problems to nail down differentiation and integration techniques. These problems are covered in the everyday materials.

Everyday classroom materials:

• RU Ready for AP Calculus  This is a review of essential algebra and precalculus concepts that are necessary for students to have success in AP calculus. Best given as a summer assignment prior to students entering AB calculus.

• AB student manual and BC student manual.  These manuals, described below, are great for an everyday workbook for students. You teach directly from it. It effectively will replace the textbook.

• AB and BC exams and quizzes.  These are exams and quizzes that you give that will cover and entire topic. While some AP type problems are included, most of the exams are what you traditionally give to determine whether students have mastered a topic. (revision coming soon)

• Calculus Cache of Hidden Treasures. This is a huge catalog of multiple choice problems, both in AB and BC. The solution versions are editable in Microsoft Office allowing you to create your own quizzes, exams and worksheets.

• Calculus On the Wall - Powerpoint lessons. Each lesson has approximately 20 - 30 slides that are narrated or, if you wish unnarrated, but with a written script so you can teach it on your own.

AP Exam Preparation:

We divide AP exam preparation into 2 categories:

The Global Approach

On typical AP questions, many concepts can be addressed. A problem giving a function might a) ask for the equation of a tangent line to the function at a point as well as b) ask for the area under the curve. While students might be able to part a) in October, then cannot do part b) until they have studied integration which might be in February.  Still, these are realistic AP type problems, so we offer a good number of problems and examples with this approach.

• Demystifying the AP Exam - Revision available now

• Ripped From the Headlines - 38 free response type questions that use real-life type problems inspired from news articles from newspaper and the Internet.

• Review Topics for the exam - a series of phrases that students see on the AP exam. These focus on what to do rather than how to do them. For instance, if a student is asked to find a critical point, he must know what that means. These are in both written form and classroom slides.

The Individual Topic Approach

These problems use the approach that nothing is tested before it is taught. For example, problems involving differentiation techniques will not involve integrals or applications of differentiation. So it is a continually building processs. While students will be asked to problems in the global approach on the AP exam, this approach allows teachers to focus in on a specific calculus topic.

• Step-by-Step - free response questions in AP format - 9 points apiece

• Diving Into AP Calculus -  for each topic, there are 4 multiple choice problems (A,B,C,D) as well as a multi-part free response question.

Diving into the AP Exam BC - available now

Have some fun while reviewing for the AP exam with our very popular Clue Game and Jeopardy.

• Calculus Clue.  Based on the old Parkers Brothers game that most kids played when they were kids, solve a mystery of a buried treasure (who buried it, where it was buried, and what the treasure is) by a process of elimination. Students have to correctly solve 87 calculus problems to solve the mystery. The game can be played individually or in teams.

• Jeopardy. Play the popular game show with topics like Limits, Differentiation, What's my Area, and Taylor's World to name a few. There is a Jeopardy, Double Jeopardy, Triple Jeopardy, and BC Jeopardy and the answers and questions are also available in written form. This game uses a browser like Firefox or Chrome, and many others, but does not require an internet connection.

Evolution of the A.P. Calculus Manuals

I started teaching A.P. calculus AB in 1993 after years of teaching a college preparatory calculus course. The textbook was Larson and Hostetler, 3rd edition. It has been my experience that we buy expensive and heavy textbooks for the students but find that students simply have trouble learning from them. Students see the textbook as a source of problems, but not a teaching tool.

As is my practice, I developed worksheets that would lead students through certain types of problems. If a student was absent and wanted the work that we missed, I found it easier just to hand the student the worksheet rather than refer him to the text.

Since our periods were short, I also found that rather than assign many problems from the textbook, I would assign what I felt to be essential problems I needed to get through and simply added them to the worksheet. Over a period of six years, I developed worksheets for just about every topic in A.P. calculus.

However, I found myself spending most of free periods in front of the copy machine. One year, I got the brainstorm to put all of these worksheets together in one comprehensive manual so the reproducing could be done all at once and the students would receive the manual at the start of school. I did so, adding a table of contents, and explaining where the concepts taught in the manual were to be found in the textbook we were using.

Over a summer, I copied these 225 page manuals and put them together. I used them first in the 1999-2000 school year and had unbelievable testimonials from students. I have been using them ever since. A textbook is distributed at the beginning of the school year and students are encouraged to take it home and use it as a reference if they need more insight to a proof of a theorem or simply want more practice problems.

Taking over the BC calculus class in 2000, I spent the summer writing a BC manual and my students have used it for seven years as well. The reactions were even stronger.

My school moved to a copying service. At the start of the summer, I requested that these manuals be published. They came back to me in August, double sided, and with holes punched in them. They were given to the students on day one and we complete the entire manual. In using a text, we rarely complete half of it. The students are allowed to keep the manual at the end of the course. Many have told me that they have taken it to college with them and it remains a valuable source of review for them. If students are diligent and do all the classwork and homework in the appropriate places in the manual, they have a complete record of the entire AP calculus course.

Several years later, I decided to write an accompanying solution manual. I do not like answer keys as there is too much fumbling trying to find the correct page. My thought was to have a solution manual that was exactly like the manual I give the students, except that the solutions to the problems are written in the spaces. So the teacher can teach directly out of the solution manual and not have to handle two separate documents.

The manuals changed little over the years with the exception of correcting some errors. But I felt that the look of the manual, using much older technology, had become dated. Graphics were blocky and hard to understand. Because the manual used a much older version of Microsoft Word that was no longer supported, I ended up typing the manual again and it took more than 6 months to re-create it. But it is a huge improvement in terms of looks and content. Both manuals now cover all topics in the revised AB and BC curriculum for 2016-2017. Each manual has an Essentials section and a Non-Essential section that covers topics if you have more time to spend. The AB manual has a brief review of important precalculus topics and the BC manual has a review of essential AB topics. There is a Combination manual available as well for schools that teach AB/BC as one course.

Use of the A.P. Calculus Manuals

The manual is not a textbook. It is not intended to be one. It simply presents topics and walks students through a series of classwork problems. The teacher does the teaching of the problem. The students take notes in the space provided. There is little or no attempt to prove theorems. You can still do that on your own. The manual provides you and your students sample problems, which will touch upon every concept that is covered in the A.P. curriculum. (and some that has been eliminated from the curriculum as well). To reiterate, this manual still needs a good teacher - you. You cannot just hand the student the manual and expect him or her to read it and understand it.

There are also homework problems for every concept. Again, space is provided for students to complete them. There are enough challenging problems but the idea is to give students enough problems to test whether they understand a concept without overburdening them. I am not smart enough to write a math book. In coming up with sample problems and homework problems, I used a number of calculus textbooks for ideas. While one cannot copyright "take the derivative of 2x," there are word problems that I adapted from these sources. In most cases, I attempted to change the problem slightly by altering a given value or the context of the problem.

By downloading the free manuals (or purchasing paper copies), you have the right to make as many copies as you wish as long as you use them for face-to-face classroom use. They may not be placed on a school's website except by special permission. Solutions should never be placed on the Internet.

Calculus Manual Topics

 Topics for AB Calculus   I. Essentials 1. Introduction 2. Tangent Lines 3. Slopes of Secant and Tangent Lines 4. Graphical Approach to Limits 5. Finding Limits Algebraically 6. Definition of Derivative 7. Derivatives Using Technology 8. Techniques of Differentiation 9. Differentiation by the Chain Rule 10. Differentiation of Trig Functions 11. Implicit Differentiation 12. Derivatives/Transcendental Funct. 13. Derivatives of Inverse Functions 14. Linear Approximations 15. Continuity and Differentiation 16. Related Rates 17. Straight-Line Motion 18. Three Important Theorems 19. Function Analysis 20. Curve Sketching 21. Finding Absolute Extrema 22. Optimization Problems 23. Economic Optimization Problems 24. Indeterminates/L'Hospital's Rule 25. Indefinite Integration 26. u-Substitution 27. Riemann Sums 28. Definite Integrals 29. The Accumulation Function 30. Fundamental Theorem of Calculus 31. Def.Integration/u-Substitution 32. Transcendentals & Integration 33. Straight-Line Motion Revisited 34. Average Value/2nd FTC 35. Inverse Trig Functions 36. Area of Region Between 2 Curves 37. Volums of Revolution 38. Slope Fields 39. Deparable Differential Equations 40. Exponential Growth 41. Other Growth & Decay Models   II. Non-Essentials  1a. Introduction 12. Logarithmic Differentiation 14a. DIfferentials 24a. Newton's Method 26a. L'Hopital's Rule Advanced 29a. Exact Area Using Limits 37a. Volume Using Cylindrical Shells   III. Precalculus Review Eliminating Complex Fractions Inverses Exponentials & Logarithms Graphical Solutions Topics for BC Calculus   I. Essentials 1. Indeterminates/L'Hospital's Rule 2. Integration by Parts 3. Integration by Partial Fractions 4. Improper Integrals 5. Arc Length/Surface Area 6. Eule'rs Method 7. Logistic Growth 8. Curves Defined by Parametric Equations 9. Calculus and Parametric Equations 10. Polar Coordinates & Graphs 11. Polar Coordinates Area/Arc Length 12. Vectors in the Plane 13. Vector-Valued Functions 14. Velocity/Acceleration of Vectors 15. Taylor Polynomial approximations 16. Sequences 17. Infinite Series 18. Geometric and p-series 19. The Integral Test 20. Comparison of series 21. Alternating series 22. Ratio and root tests 23. Series Convergence Review 24. Power Series 25. Taylor & Maclaurin Series 26. Manipulation of Series   II. Non-Essentials 0a. Marginal Analysis/Demand Elasticity 1a. Epsilon Delta Definition of Limits 2a. Power of Sines & Cosines 3a. Partial Fractions Advances 5a. Simpson's Method 7a. Work 7b. Fluid Force 7c. Center of Mass 27. First Order Differential Equations   III. AB Review R1. Basic Differentiation R2. Linear Approximation R3. Limits/Continuity/Differentiation R4. Related Rates R5. Function Analysis R6. Integration Techniques R7. Definite Integral/Accumulation R8. Riemann Sums R9. Fundamental Theorem of Calculus R10. Straight-Line Motion R11. Area and Volume R12. Differential Equations/Growth & Decay

Pricing

We are happy to offer these manuals for no charge. Go to the Calc AB Manual or Calc BC Manual page to download any or all sections of either the AB or BC manual. Each section has approximately 5 topics. They are in PDF format.

The manual is also available in paper format as well as the solution manual for both AB and BC calculus. Go to the page on paper manual and solution manuals. These do have a cost associated with them. You can order them from the same pages. Go to Purchase Options to order them in combination for less money.

Every teacher needs an answer key.  You can either solve the problems in your own copy of the student manual, or purchase the answer key in paper format.  The answer key has the same page numbering as the student manual to make it easy to keep your students 'on the same page'.