Calculus Manuals - Overview
FREE! You can DOWNLOAD our entire Calculus Manuals AB and BC for FREE.
Click HERE for the FREE Calculus AB Manual
Click HERE for the FREE Calculus BC Manual
The answer keys are available for purchase: Click HERE
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 reproducung 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 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.
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.
|Topics for AB Calculus
1. Tangent Lines
2. Slopes of Secant and Tangent Lines
3. Graphical Approach to Limits
4. Finding Limits Algebraically
5. Definition of Derivative
6. Derivatives Using Technology
7. Techniques of Differentiation
8. Differentiation by the Chain Rule
9. Differentiation of Trig Functions
10. Implicit Differentiation
11. Continuity and Differentiation
12. Related Rates
13. Straight Line Motion
14. Rolle's and the Mean Value Theorem
15. Function Analysis
16. Finding Absolute Extrema
17. Newton's Method of Roots (*)
18. Approximation Using Differentials (*)
19. Optimization Problems
20. Economic Optimization Problems
21. Indefinite Integration
23. Sigma Notation
24. Area Under Curve
25. Riemann Sums
26. Exact Area Under a Curve (*)
27. Definite Integral as Area
28. Accumulation Function
29. Fundamental Theorem of Calculus
30. Definite Integration with u-Substitution
31. Straight Line Motion Revisited
32. Average Value/2nd Fundamental Theorem
33. Area of Region Between 2 Curves
34. Volume by Disks and Washers
35. Volume by Cylindrical Shells (*)
36. Review of Exponentials and Logarithms
37. Differentiation of the ln function
38. Integration and the ln function
39. Derivatives and Integrals with “e”
40. Inverse Trig Functions
41. Integration and Inverse Trig Functions
42. Derivatives of Inverse Functions
43. Differential Equations by Separation of Variables
44. Slope Fields
45. Exponential Growth
46. Exponential Growth Continuation
48. Taking "Impossible" integrals
49. L'Hopital‘s Rule for Indeterminate Forms (*)
(*) Not currently on the AB Calculus Exam
|Topics for BC Calculus
1. Symmetry, Transformations, Differentiability
2. Epsilon-Delta Definition of Limit
3. L'Hopital's Rule
4. Business/ Economic Applications
5. Newton's Method
7. Definite Integral as Area
8. Accumulation Function
9. Area Under Curve
10. Sigma Notation
11. Riemann Sums
12. Area by Simpson's Rule
13. Volume by Disks/Washers
14. Volume by Shells
15. Arc Length
16. Surface Area
17. Work Problems
18. Fluid Force
19. Center of Mass
20. Natural Logs and “e” Review
21. Differential Equations - Separation
22. Exponential growth & decay
23. Exponential growth Continuation
24. Integration by Parts
25. Powers of sines and cosines
26. Integration by Partial Fractions
27. Improper Integrals
28. Finding "Impossible" Integrals
29. Slope fields
30. Euler's Method
29. Logistic Growth
30. Inverse Trig functions
31. Integrations Involving Inverse Trig
32. Derivatives of Inverse Functions
33. Parametric equations
34. Calculus/Parametric equations
35. Polar equations & graphs
36. Area & arc in polar coordinates
37. Vectors in the plane
38. Vector valued functions
39. Velocity & acceleration of Vectors
40. Taylor Polynomial approximations
42. Infinite Series
43. Convergence - Integral and p-series
44. Comparison of series
45. Alternating series
46. Ratio and root tests
47. Power series
48. Function representation by power series
49. Taylor & Maclaurin series
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 between 2 to 14 pages with 6 the norm. 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'.
Click HERE to purchase the Answer Key.
Click here to email us: team@MasterMathMentor.com