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Essential Precalculus for Calculus (AP AB)


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We've been having our noses to the grindstone and now dd is just finishing Precalculus (one semester block using Foerster) in preparation for starting AP Calc AB in the next couple of days (for the test in May)...I realize this is a bit late for the question but perhaps it will help others be better prepared...

 

There's not really any way around it, but it seems she has a B which makes me worry about readiness (or should I not be?)...

 

But then I wonder what the 'body' of Precalc really is because in the recent past we had some long rabbit trails which turned out to be meaningless. Ie she spent a lot of time trying to figure out how to do problems, for which I couldn't find help in other books. Finally I realized, if it's not in the other Precalculus books, then it's probably not really an important concept/topic (at least for Calculus)! I don't know why this didn't hit me with ds2 who used the same book, but he seemed to adjust better.

 

Thinking she should at least have the bases covered, she'll do a quick Precalc review at the beginning of Calculus...

 

To get to the real question - which of all the things she studied are really necessary for Calculus? and are there any free online videos for Precalc review (I'll look at Khan)? 

 

Here is the TC for Foerster 2nd ed  ( I found Matoyshka's post about the contents - thank you Matroyshka!)

 

1. Functions and Mathematical Models                                                                      

2. Periodic Functions and Right Triangle Problems                                                    

3. Applications of Trig and Circular Functions                                                            

4. Trig Function  Properties, Identities, and Parametric Functions                           

5. Properties of Combined Sinusoids                                                                           

6. Triangle Trigonometry                                                                                             

7. Properties of Elementary Functions                                                                    

8. Fitting Functions to Data                                                                                                                                

9. Probability and Functions of a Random Variable                                                       

10. Three-Dimensional Vectors                                                                                   

11. Matrix Transformations and Fractal Figures                                                             

12. Analytic Geometry of Conic Sections and Quadric Surfaces                                               

13. Polar Coordinates, Complex Numbers, and Moving Objects                                 

14. Sequences and Series                                                                                              

15. Polynomial and Rational Functions, Limits, and Derivatives  

 

Thank you for any help!!

Joan

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To get to the real question - which of all the things she studied are really necessary for Calculus?

 

1. Functions and Mathematical Models                                                                      

2. Periodic Functions and Right Triangle Problems                                                    

3. Applications of Trig and Circular Functions                                                            

4. Trig Function  Properties, Identities, and Parametric Functions                           

5. Properties of Combined Sinusoids                                                                           

6. Triangle Trigonometry                                                                                             

7. Properties of Elementary Functions                                                                    

8. Fitting Functions to Data                                                                                                                                

9. Probability and Functions of a Random Variable                                                       

10. Three-Dimensional Vectors                                                                                   

11. Matrix Transformations and Fractal Figures                                                             

12. Analytic Geometry of Conic Sections and Quadric Surfaces                                               

13. Polar Coordinates, Complex Numbers, and Moving Objects                                 

14. Sequences and Series                                                                                              

15. Polynomial and Rational Functions, Limits, and Derivatives 

 

8-11 are not necessary for understanding single variable calculus.

 

12 may not be, depending on how deep they go.

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8-11 are not necessary for understanding single variable calculus.

 

12 may not be, depending on how deep they go.

 

Thank you regentrude!

 

I don't know the actual answer to your question, but ALEKS has a course that is specifically a review for calculus.

 

Thank you too Kai....we don't want to do a whole course just like a mini review of the chapters which regentrude has indicated are part of single variable calculus....Dd looked at a review DVD that goes with Larson but she found it over simplified (it was all in one half hour), so I am still looking around for something like a few hours summary video...I realize this is pretty vague! At least there are already fewer chapters to worry about....

 

Joan

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If she is only doing AP Calculus AB, chapters 13 and 14 aren't necessary because those topics go with BC not AB. But, they are necessary for single variable calculus, just not part of the AB curriculum. 

 

Slightly off topic, but I'm curious:

how do they start out with introducing the limit without doing sequences and series first?

 

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Thank you regentrude!

 

 

Thank you too Kai....we don't want to do a whole course just like a mini review of the chapters which regentrude has indicated are part of single variable calculus....

 

The thing about ALEKS is that if it is truly review for the student, it doesn't take very long.  It only requires practice for the things the student doesn't know.

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Slightly off topic, but I'm curious:

how do they start out with introducing the limit without doing sequences and series first?

 

 

Usually sequences are done informally just before limits and then formally in calc 2. The concept of limit in many calc 1 classes that are computationally focused can be summed up as "follow the graph with your finger and see where it's going" or "plug in numbers that are closer and closer on your calculator and see where it's going".

 

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Thank you all for discussing this!

 

Just thought I'd put in the chapter titles for Calculus AB for anyone else like me...

 

Limits and their properties

Differentiation

Applications of Differentiation

Integration

Applications of Integration

Logarithmic, Exponential, and other Transcendental Functions

Differential Equations

(optional) Integration techniques...

 

Joan

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