Enrichment

 

This page will focus on materials that teachers can use to enhance the learning of calculus and focus on more than the AP Calculus exam.

 

Right now, we have one enrichment document. Hopefully there will be more coming.

 

Ahead of the Curve

 

This 70-page manual focuses on 33 mathematical equations and their curves, different from what the student usually sees in a typical calculus course.  Curves with strange names like cissoids, lemniscates, quartics, nephroids, catenaries, ovals, foliums, conchoids, and devil curves, to name a few, are analyzed.

 

Ahead of the Curve Solutions:

Web Download Version

This purchase will provide you with the solution version of Ahead of the Curve in two downloadable files (PDF format - 17 mb).

Only $28.95

Ahead of the Curve Solutions:

Paper Format Version

This purchase will provide you with the entire solution version of Ahead of the Curve (including opening pages) in paper format mailed to you.

Only $35.95 plus $6 Shipping

 

 

 

Students are asked to use their implcit differentiation skills to find tangent lines including vertical and horizontal tangents, areas enclosed by the curves, volume when the curve is rotated about an axis, and for BC students, arc length of the curve. Formulas for the curves are given in Cartesian, parametric, and polar forms and students will see why these alternate forms make certain integration problems easier. They will also appreciate the mathematicians who first discovered these curves, all well before the age of calculators and computers.

 

The workbook encourages students to use computer graphing apps such as Grapher and Desmos, as many of the curves cannot be graphed on their calculators because they cannot easily be written in closed form (y as a function of x). Download links to view these curves in Mac Grapher and Desmos are given as well.

 

The calculus necessary for this workbook is no more advanced than what is used in AP calculus. But the algebra is more complicated and this workbook is terrific in enhancing the algebraic skills that sadly is missing in even the better calculus students. 

 

Teachers will enjoy having this collection of curves to challenge students. They are perfect as emergency lesson plans and teachers can distribute them as extra credit problems as well.

 

As usual, the student version of Ahead of the Curve is absolutely free.

 

Opening Pages/Contents

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4.1 meg

Closed Curves

   Witch of Agnesi, Catenary, Kappa Curve,

   Kamplye of Eudoxus, Lamé Curves,

   Astroid, Cissoid of Diocles, Figure Eight,

   Pear-shaped Quartic, Granville's Egg, Kiss Curve,

   Right Strophoid, Tschirnhausen's Cubic,

   Newton's Diverging Parabolas, Conchoid

   of de Sluze, Tricuspoid

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2.2 meg

Other Curves

   Bow Curve, Bean Curve, Knot Curve,

   Lemniscate of Bernoulli, Bifolium, Bicorn,

   Devil's Curve, Nephroid, Durer's Shell Curve,

   Spiric Sections, Cartesian Oval, Talbot's Curve,

   Fish Curve, Cochleoid, Tractrix, Cycloid,

   Heart Curve

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2.1 meg

Grapher and Desmos Links

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0.5 meg

 

Ahead of the Curve Solutions:

Web Download Version

This purchase will provide you with the solution version of Ahead of the Curve in two downloadable files (PDF format - 17 mb).

Only $28.95

Ahead of the Curve Solutions:

Paper Format Version

This purchase will provide you with the entire solution version of Ahead of the Curve (including opening pages) in paper format mailed to you.

Only $35.95 plus $6 Shipping