Handout
Wolfram Research

Wolfram Math World: Epicycloid

For Students 9th - 10th Standards
Shows how to graph them and also derives the polar equations from the parametric equation. The site then defines a few special Epiycloids. Includes a definition, formulas, graphs, video, and links to related topics.
Activity
Texas Instruments

Texas Instruments: Powers and Roots of Complex Numbers

For Teachers 9th - 10th Standards
Complex numbers can be represented graphically using parametric equations. The roots of complex numbers, including the roots of unity, can be represented graphically using De Moivre's theorem and parametric equations.
Activity
Texas Instruments

Texas Instruments: Visualizing Related Rates Problems

For Teachers 9th - 10th
This activity models related rates problems using parametric equations for simulation purposes.
Activity
Texas Instruments

Texas Instruments: Numb3 Rs: The Chase

For Teachers 9th - 10th
Based off of the hit television show NUMB3RS, this lesson has students develop the concept of pursuit curves, in which one object moves according to the movements of another object. This lesson is framed in the context of an officer...
Activity
Texas Instruments

Texas Instruments: Motion of Related Objects

For Teachers 9th - 10th
This activity introduces the concept of related rates with parametric equations using a projectile motion problem.
Handout
Johan Claeys

Math Abundance: The Parabola

For Students 9th - 10th Standards
Defines parabolas, their properties, gives parametric equations, tangent line in a point D of a parabola, etc.
Activity
Texas Instruments

Texas Instruments: Numb3 Rs Season 2 "Convergence" Where Is the Bullet?

For Teachers 9th - 10th
Charlie uses parametric equations of projectile motion to figure out where to look for a fired bullet in the "Convergence" episode of the show NUMB3RS. The lesson plan includes a student page complete with keystroke instructions for the...
Handout
Johan Claeys

Math Abundance: The Hyperbola

For Students 9th - 10th Standards
Great Site! Defines Hyperbola, gives the parametric equation, etc.
Handout
University of California

Ucla Calculus Problem: Symmetric Equation of a Line

For Students 9th - 10th Standards
This site explains the steps to finding the parametric and symmetric equations of a line given two points in three dimensions.
Activity
Texas Instruments

Texas Instruments: Conics in Standard and Parametric Form

For Teachers 9th - 10th Standards
This is a second learn check to use after completing the intro to changing from rectangular form to parametric form of the equations of conics.
Activity
Texas Instruments

Texas Instruments: Conics & Parametrics 1

For Teachers 9th - 10th Standards
This activity is a LearningCheck to quickly assess students' ability to identify conics from their equations in both rectangular and parametric form.
Interactive
Other

Gobierno De Navarra: Cicloides Y Trocoides

For Students 9th - 10th Standards
This unit shows the graph of a polar equation and gives several pretty graphed examples. It shows the difference in the graphs just by varying a constant value.
Unit Plan
Wolfram Research

Wolfram Math World: Sphere

For Students 9th - 10th
This webpage thoroughly discusses the math of spheres. Includes the equation for a sphere in Cartesian and spherical coordinates as well as parametrically. Surface Area, volume, and curvature are addressed at this extensive site.
Handout
Wolfram Research

Wolfram Math World: Cardioid

For Students 9th - 10th
The site opens with a visual representation of how a Cardoid, a one-cusped epicycloid, is made. The site then shows the parametric, Cartesian, and polar equation for the special epicycloid. The last half of the page gives more equations...
Graphic
University of St. Andrews (UK)

University of St. Andrews: Curves: Epicycloid

For Students 9th - 10th
Gives the parametric equation and a brief history.
Unit Plan
Interactive Mathematics

Interactive Mathematics: Curvilinear Motion

For Students 9th - 10th
Using parametric equations, velocity and acceleration values are determined for objects in curvilinear motion.
Handout
Wolfram Research

Wolfram Math World: Surface of Revolution

For Students 9th - 10th
This math site from MathWorld.com explains what a surface of revolution is, a formula for the surface area of such a surface, this site contains many relevant links, examples. A standard parametric formula is given, formulas for...
Website
Other

Xah Lee's Home Page: Ellipse

For Students 9th - 10th Standards
Good site with history, descriptions, properties, etc. of the Ellipse. This site gives the parmetric equation of an elipse and many interesting ways to find an ellipse in objects.
Graphic
University of St. Andrews (UK)

University of St. Andrews: Asteroid

For Students 9th - 10th
This site, which is provided for by the University of St. Andrews, shows the graph of an asteroid and gives the parametric and cartesian equations.
Activity
Other

Git: What Is the Slope Intercept Form of a Line?

For Students 9th - 10th
Not only does this site show what the slope-intercept form is, but it helps you find the slope and the intercept of a line. There is also additional information on parallel lines, parametric form, and the distance between two points.
Graphic
University of St. Andrews (UK)

University of St. Andrews: Lissajous Curves

For Students 9th - 10th Standards
Gives a brief history and lists the parametric cartesian equations.
Graphic
University of St. Andrews (UK)

University of St. Andrews: Cardioid

For Students 9th - 10th
This site, which is provided for by the University of St. Andrews, gives a brief history of the cardioid. Shows parametric and cartesian equations.
Activity
Ministry of Education and Universities of the Region of Murcia (Spain)

Ministerio De Educacion Y Ciencia: Curvas Y Superficies

For Students 9th - 10th
In Spanish. This unit extends the model of Cartesian representation to three dimensional. You will be able to study interactively some curves and surfaces in space, its parametric and implicit equations.
eBook
CK-12 Foundation

Ck 12: Precalculus Concepts 2.0

For Students 10th - 12th Standards
A complete high school Precalculus Concepts course. Includes 'Related Modalities' for each lesson that teach the same concept in different ways. The text materials follows Algebra II and comes before Calculus or Statistics. The content...

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