Polar Coordinates Teacher Resources

Find Polar Coordinates lesson plans and worksheets
Showing 1 - 113 of 113 resources
31 Items in Collection
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Number and Quantity: High School Common Core Math

For Teachers 9th - 12th Standards
This collection has a resource for each standard in the Number and Quantity selection of the CCSS. While several of the resources cover multiple standards, the focus standard is listed in the notes section of each resource for easy viewing.
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Polar Coordinates

For Teachers 10th - 12th Standards
Graphing outside of the Cartesian plane is a unique challenge for many students, particularly the part where they need to convert (x, y) coordinates into polar form. Enter this lesson and corresponding worksheet covering the basics of...
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Introduction to Polar Coordinates

For Teachers 10th - 12th
High schoolers compare polar coordinates to that of rectangular coordinates. They locate points in a polar coordinate plane and convert that point to one on a rectangular coordinate plane, and vice versa.
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Polar Coordinates

For Students 11th - Higher Ed Standards
Polar opposites might not work together—but polar coordinates do! The interactive provides learners the opportunity to graph trigonometric and algebraic functions using polar coordinates. The program takes either individual data points...
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Worksheet 39 - Polar Coordinates

For Teachers Higher Ed
In this polar coordinates worksheet, pupils graph polar coordinates and determine the values of a given series. This one-page worksheet contains 14 multi-step problems.
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Introduction to Polar Coordinates - Concept

For Students 9th - 12th Standards
Learning polar coordinates does not require visiting the North Pole, though explaining igloos is much easier using polar coordinates. The lesson begins with a video explaining how to find coordinates on a spherical plane and how to...
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Introduction to Polar coordinates

For Teachers 11th - 12th Standards
The class practices plotting points in a Cartesian coordinate system and a Polar coordinate system. They convert from one system to the other to get coordinates to plot. Then they play a Tic-Tac-Toe or Connect Four game to have a...
1 In 1 Collection
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Unit 8 Review Packet: Polar Coordinates, Polar Graphs, and Vectors

For Teachers 10th - 12th Standards
Tying together an introductory unit on polar coordinates, graphs, and vectors is often a daunting task. So many nuanced math skills develop through these lessons that making sure an assessment hits them is difficult, to say the least....
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Plots of Polar Coordinates: Submarine Sonar

For Students 11th - Higher Ed Standards
Find the location of enemy submarines with a sonar display that doubles as a polar coordinate system. Pupils find polar coordinates that would be the same location of plotted submarines. They then determine multiple polar coordinates...
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Rectangular to Polar Form for Equations: Polar Coordinates

For Students 10th - 12th Standards
Plot points around a wheel. Pupils use an interactive tool to plot a point using polar coordinates with the aid of a wheel. Scholars use the interactive to answer five questions to finish the lesson. The resource provides background...
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Distance Between Two Polar Coordinates: Exploring Changes in Angle and Radius

For Students 10th - 12th Standards
Get straight answers on a curved grid. An interactive has learners apply the Law of Cosines to find the distance between two points on the polar coordinate plane. The pupils use the radii lengths and the angle between the two radii to...
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Polar Functions

For Teachers 9th - 12th
Explore the concept of polar functions and learn how to determine the length around a function using polar coordinates. High schoolers use their Ti-calculators to determine the length of a function that looks like a five-leaved rose....
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Polar and Cartesian Coordinates

For Teachers 11th - 12th
The class has a brief review of polar and Cartesian coordinates. Then they get to play battleship and discover polar coordinates in more depth. They get a lot of practice converting from polar to Cartesian coordinate points and vice...
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Space Shuttle's Heat Shield Problem

For Teachers 9th - 12th
Students participate in a role-play activity to determine how to replace heat shields on the space shuttle using polar coordinates.
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Complex Numbers: Plotting and Polar Form

For Teachers 9th - 12th Standards
Explore the concept of, and use the Ti-Nspire to, convert complex numbers into polar form. Then practice graphing complex numbers in the polar coordinate plane.
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Worksheet 31

For Students 11th - Higher Ed
In this math worksheet, learners investigate vectors and polar coordinates. They convert the paths of polar coordinates to Euclidian points.
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Worksheet 28 - Spring 1996

For Students 11th - Higher Ed
In this math learning exercise, students examine the graph in polar coordinates of r = f(θ). Then they sketch a graph of the modified functions indicated.
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Worksheet 36-Spring 1996

For Teachers Higher Ed
In this math worksheet, students sketch the regions that give rise to three integrals. They find the volume of a solid in the first octant bounded by a defined cylinder and a parabaloid. Students change a function to polar coordinates....
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Worksheet 38-Spring 1996

For Teachers Higher Ed
In this math worksheet, students determine if the definite integral of given functions exist. They use a Taylor polynomial to approximate given values. Students express the arc length of a graph on a polar coordinate system as an integral.
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Visualizing Vectors

For Teachers 9th - 12th Standards
Investigate vectors in standard positions and use the CellSheet application on the TI calculator to find the sum of two vectors. Convert from polar to rectangular coordinates and vice versa, and show graphs of the vectors.
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Direction on the Earth: Using a Compass

For Students 6th - 8th
Navigate the world of orienteering in an informative interactive. Earth science scholars learn practical direction skills, such as proper polar coordinates and pairing compasses with maps. The interactive map allows them to practice...
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A Second View of Polar Coordinates

For Teachers Higher Ed
In this polar coordinates worksheets, students change ordered pairs from rectangular form to polar form. They plot and label points and identify alternative coordinate pairs for given points. There are approximately 20 problems on this...
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Math Handbook: Trigonometry

For Students 9th - 12th Standards
You'll be spinning in unit circles once you read through this jumbo-sized resource of everything you need to know about trigonometry. Each page has color-coded examples with explicit directions that detail the problems and formulas. 
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Ellipses and Kepler's First Law

For Teachers 11th - 12th
The class examines graphs in the form r = F(¿¿) in polar coordinates (r, ¿¿), in particular with the circle, ellipse and other conic sections. They determine the nature of an ellipse by studying the role of the semimajor axis and...
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Trigonometric Form of Complex Numbers

For Teachers 11th - 12th Standards
This lesson is written from the perspective of a student teacher. A step by step lesson in which the class works on the trigonometric form of complex numbers. They convert between trigonometric and complex forms. They will also practice...
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PreCalculus: Final Examination

For Students 10th - 12th
In this final examination worksheet, students find the tangent function and sine function.  They graph problems on a polar coordinate.  Students describe trigonometric properties.  This twelve-page worksheet contains 80 problems.
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AP Calculus Practice Exam: BC Version - Part A

For Students 11th - 12th
In this calculus worksheet, students solve 28 multiple choice problems. Students find derivatives, volumes, limits, convergent series, etc.
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Complex Numbers

For Students 10th - 12th
A straightforward approach to teaching complex numbers, this lesson addresses the concepts of complex numbers, polar coordinates, Euler's formula, De moivres Theorem, and more. It includes a practice problems set with odd answers and a...
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Calculus Volume 3

For Students 11th - Higher Ed
See calculus to the end. The eBook is the last of a three-volume series covering college-level calculus topics. Scholars begin with parametric equations and polar coordinates before moving to vectors, finally ending with multi-variable...
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A comparison of Function, Polar, Parametric, and Implicit Plots

For Teachers 11th - 12th
Students explore different methods of graphing a function.   In this Pre-calculus/Calculus lesson, students compare the function mode, polar mode, parametric mode, and implicit plots as they use A TI-89 to graph the equation of a circle. 
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Architecture: CAD Design

For Teachers 10th - 12th
Students apply computer-assisted design programs to develop sketches and technical drawings for a three-bedroom house. Working together, they develop strategies for presenting their designs, investigate building codes, and hone skills...
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Representation of Complex Numbers

For Teachers 9th - 12th
Learners write complex numbers in standard form. They add, subtract, multiply and divide complex numbers correctly.
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Graphing Polar Coordinates

For Teachers 9th - 12th
Students engage in a lesson that is about the plotting of polar coordinates while graphing equations. They plot multiple points with the help of a graphing calculator and using coordinate graph paper. Students identify the pattern known...
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Intersections of Polar Curves

For Students 10th - 12th
Expand on your pupils' knowledge of polar graphs, systems, and trigonometry. An informative math lesson prompts learners to solve systems of polar equations. The polar coordinate solutions are referenced both algebraically and graphically. 
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Worksheet 26

For Students 11th - Higher Ed
In this math worksheet, learners use the polar coordinates to find the Euclidian coordinates. Then they compare points on the coordinate plane.
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Worksheet 38

For Students 11th - Higher Ed
In this math worksheet, students investigate different types of functions and coordinate systems. They review that when integrating a function over a region in the plane using polar coordinates, a “magical” factor of r appears in the...
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Cartesian Coordinates

For Students 11th
In this Cartesian coordinates worksheet, 11th graders solve and complete 4 different multiple choice problems. First, they express each of the Cartesian coordinates provided as polar coordinates. Then, students find the Cartesian...
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Worksheet 20 - Derivatives

For Teachers Higher Ed
In this derivative worksheet, students solve functions, sketch the direction of the rate of change, and describe functions using polar coordinates. This two-page worksheet contains seven multi-step problems.
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Math 53 – Practice Midterm #1

For Teachers 9th - Higher Ed
In this math worksheet, students find the length of the curve given in the polar coordinates. They also evaluate the functions and simplify them.
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Trigonometric Form of Complex Numbers

For Students 11th - Higher Ed Standards
Represent complex numbers in two ways. Pupils use the interactive to convert polar and rectangular representations of complex numbers. The learners drag an overlay back and forth over the coordinate plane to reveal the polar coordinates...
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Trigonometry

For Teachers 9th - 12th Standards
This trigonometry textbook takes the learner from a basic understanding of angles and triangles through the use of polar coordinates on the complex plane. Written by a mathematician-engineer, examples and problems here are used to...
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Polar And Cartesian Coordinates

For Teachers 9th - 12th
Students engage in a lesson plan that is about the study of Cartesian and Polar Coordinates. They play a game of Battleship to create the context for the lesson plan. The examples in the lesson plan can be used as a guide for the...
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Polar Coordinates Game

For Students 10th - 11th
In this algebra game, students pair off to plot polar coordinates on a circular graph. They attempt to hit each other by guessing their opponents location on the graph. This is a great way to reinforce the concept of polar coordinates....
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Worksheet 25

For Teachers Higher Ed
In this math worksheet, students draw a graph of functions on a polar graphing system. They graph two functions by first plotting them on the vertical axis as a function of a given angle, then by plotting them at a radial distance from...
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Matrix Revolutions

For Teachers 10th - 12th Standards
Beginning with references to the pop culture phenomena of the Matrix movies, this activity moves quickly into the realm of math theory. Using matrices to manipulate polygons in the plane is the focus, with hints at extensions into deeper...
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PhyzJob: Composition Classics

For Students 10th - 12th
In this coordinates worksheet, students write displacement vectors given seven lines in a graph. They write them in rectangular form and then convert them to polar form.
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Worksheet 9 - Math 222 - Three-Dimensional Coordinate System

For Students 12th - Higher Ed
In this coordinate system worksheet, students compute the areas and lengths in polar coordinates, find unit vectors, work with the three-dimensional coordinate system, compute cross products, and compute dot product equations. This...
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Pre-Calculus Review Sheet

For Students 10th - 12th Standards
Pre-Calculus has some detailed formulas involved and here is a great resource that lumps then all together for you. Broken up into rectangular, polar, and parametric sections, the conics all include formulas and graphs. 
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Polar Graphs

For Teachers 10th - 12th Standards
The world of graphing polar graphs is filled with beautiful curves and patterns once a young mathematician masters a few basic techniques. This comprehensive resource covers many of these techniques and resulting shapes, from the basic...
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Review Sheets: Trigonometry

For Students 9th - 12th Standards
Review guide, practice test, homework packet? Yes, yes, and yes as it's all possible with a wonderful trigonometry packet. Every type of problem is there, starting from the unit circle and ending with conic sections. 
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Introduction To Coordinate Entry

For Teachers 9th - 12th
Students demonstrate industrial literacy. They conduct problem solving, graphing, note taking, and self management skills. They construct then plot, Absolute and Relative Cartesian Coordinates and Absolute and Relative Polar Coordinates.
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Worksheet 29 Spring 1999

For Students 12th - Higher Ed
In this math worksheet, learners describe in terms of reflections what happens to a point when (r, θ) in polar coordinates changes. They also discuss the concept of symmetry.
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Graphing Polar Coordinates

For Teachers 11th - 12th
Students define polar equations and learn to plot them. In this calculus lesson, students relate polar equations to real life scenarios such as plants and comic strips. They discuss and define the curves of polar equations.
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Introduction To Polar Coordinates

For Teachers 9th - 12th
Students investigate the polar coordinate system and practice plotting using Cartesian Coordinates. They find the angle and the radius and plot them while comprehending the ordered pairs using the x and y axis. The lesson includes...
1 In 1 Collection
EngageNY

Complex Numbers and Transformations

For Teachers 9th - 12th Standards
Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...
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A Cardioid for Valentine’s Day

For Students 7th - 12th Standards
It's Valentine's Day in geometry class! Celebrate the day of love with a heart-themed activity in which young mathematicians create a cardioid on polar graph paper.
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The AP Calculus Problem Book

For Students 11th - Higher Ed Standards
Are you always looking for extra problem resources to incorporate in your classes?  A set of problems for a full AP Calculus course may be all you need! Each unit has a full set of questions and a sample test.
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Precalculus

For Students 11th - Higher Ed Standards
Take a step beyond Algebra 2. Learners use the eBook to learn concepts from the typical Precalculus course. Content starts off with a short review of functions in general and moves on to the basic functions, finishing up with more...
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College Algebra

For Students 9th - Higher Ed Standards
Is there more to college algebra than this? Even though the eBook is designed for a college algebra course, there are several topics that align to Algebra II or Pre-calculus courses. Topics begin with linear equation and inequalities,...
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Calculus - Early Transcendentals

For Teachers 9th - Higher Ed Standards
This textbook takes the learner from the basic definition of slope through derivatives, integrals, and vector multivariable calculus. Each section is composed primarily of examples, with theoretical introductions and explanations in...
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Discussion Sheet 4: Integrals

For Students Higher Ed
In this integral worksheet, students sketch solids in three dimensional space, determine the coordinates, evaluate the integrals and identify the moment of inertia. This one-page worksheet contains six multi-step problems.
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Polar and Cartesian Coordinates

For Teachers 11th - 12th
Students review polar coordinates, as well as translations and rotations in Cartesian Coordinates. They also watch a video on conics and write a summary of the video for a quiz grade. Students then find an equation after a...
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Complex Numbers in Polar Form; DeMoivre’s Theorem

For Teachers 10th - 12th Standards
The iconic links between trig functions and complex numbers are introduced in a lesson on the basic properties of complex numbers in polar form. Quickly progressing through the polarization of complex coordinates, a bulk of the worksheet...
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Multivariable Calculus: Curvilinear Coordinates

For Students Higher Ed
In this curvilinear coordinate learning exercise, students compute the Jacobian of standard transformations to Cartesian coordinates from polar, spherical and cylindrical coordinates. They identify the determinant of the Jacobian...
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Saxon Math: Algebra 2 (Section 10)

For Teachers 9th - 12th Standards
In this 10th of 12 Saxon math sections, the curriculum definitely has an end-of-course feel to it. Conic sections, polar graphing, rational equations, and exponential inequalities all work to stretch the young algebrist and prepare them...
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2013 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Apply the skills to problems to ace the AP test. Free-response questions require scholars to take calculus skills and apply them to situations. Pupils use the questions to see how those situations appear on an upcoming exam. Teacher use...
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2014 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
How much of the material is really important? Pupils use the free-response questions from the 2014 AP Calculus BC exam to see how the questions appear. With the supporting material, teachers understand the topics that appear on the test...
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2017 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Pupils use the six released free-response questions from an AP Calculus BC exam to prepare for their own exam. The questions cover a range of topics from the BC curriculum, with half of the items coming strictly from AB material and the...
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2007 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Provide a review for the exam so individuals don't tank. AP® provides the free-response questions for teachers to use to help their pupils prepare for the exam. The six BC questions from 2007 include regions bounded by functions, water...
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2018 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Don't just rely on the textbook. Released items from the AP Calculus BC provide pupils and teachers insight on how topics appear on the exam. The six items are divided into calculator and non-calculator sets with half of them also...
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The Mass of the Van Allen Radiation Belts

For Students 10th - 12th
In this van Allen Radiation Belts worksheet, students are given the formula for the field line of the Earth's inner magnetic field. Students use this equation to find the polar coordinates of a field line in the van Allen Belts. They...
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Independent and Dependent Systems

For Teachers 10th - 12th Standards
Learners practice their linear algebra skills with laser focus on the unique cases of independent and dependent systems in this short problem set and presentation. The pairing of the two concepts really brings into focus the difference...
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2003 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
There are shaded areas, particles, polar equations, oh my! Teachers use the materials to see how their pupils compare to the AP® Calculus BC exam expectations. Scholars use the released items to practice on several BC topics and become...
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2011 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
Take a second look. Form B of the AP® Calculus BC free-response questions allow pupils and teachers to see another set of items. The six questions expand the set of items from the 2011 free-response questions. Form B items include a...
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2009 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
Let them eat cake. The free-response questions from an AP® Calculus BC exam cover several topics that include finding the area under a curve within the context of creating a birthday cake. Calculus concepts include finding rates of...
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2005 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Differentiate between the exams. Using the Q&A document, teachers compare the free-response questions that BC test-takers see to those that AB test-takers see. The pupils see which questions come from AB content and also those that...
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Calculus Volume 2

For Students 11th - Higher Ed
Delve into the middle of calculus. The resource is the second eBook of three that covers the complete calculus content. Seven chapters begin with integrals and different methods of integration before moving on to differential equations....
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2003 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
Be integral to the learners in the classroom. Pupils use integrals, differentiation, and limits to solve the free-response questions from an AP® Calculus BC exam. Items cover topics such as area under a curve, particle motion, average...
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Worksheet 16: Area

For Students Higher Ed
In this area activity, students compute the area of a region bounded by graphs. They identify polar coordinates and sketch graphs of equations. This two-page activity contains approximately fifteen problems.
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Graphing Polar Equations

For Students 11th - Higher Ed
In this graphing polar equations worksheet, students solve and complete 10 various types of problems. First, they construct a table of values using the special angles and their multiples. Then, students plot the points in the table on a...
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A Critical Lab

For Teachers 9th - 12th
Physics lab groups finagle with laser lights to determine the critical angle of refraction for both water and Lucite. Because there are no detailed steps or an answer key for this enlightening exercise, an inexperienced physics...
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Vector Addition

For Students 9th - 12th Standards
Model vector addition graphically. A simple interactive has users add vectors and adjust the lengths and angles of the vectors. The interactive automatically updates the magnitude, angle, and components of the sum.
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Worksheet 4 - Math 126: Sketching Polar Equations

For Students 9th - 12th
In this sketching polar equations worksheet, high schoolers solve 5 short answer and graphing problems. Students describe a curve given the equation of the curve in polar form. High schoolers sketch a graph of the equation.
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Polar Graphs

For Teachers 9th - 12th Standards
High schoolers graph polar graphs. In this calculus lesson, students convert between polar and rectangular coordinates. They graph their solution on the TI calculator and make observations.
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Calculating Arc Lengths of Simple Functions-I

For Students 10th - Higher Ed
In this calculating arc lengths instructional activity, students are given 4 simple functions and they use the Pythagorean Theorem and the basic techniques of calculus to find the arc-length formula in order to find the arc-length.
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Promote Precalculus

For Teachers 10th - 12th
Use projects, real-world activities, and games to bring precalculus to life for students.
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Variational Calculus 3

For Students 12th - Higher Ed
In this methods of applied mathematics worksheet, students solve 5 various types of problems that relate to variational calculus equations. First, they determine a second order differential equation for the geodesic. Then, students write...
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Vector Addition and Dot Products

For Teachers 12th
Twelfth graders plot vectors on the coordinates and evaluate them. In this physics activity, 12th graders watch a video tutorial and complete assigned worksheet.
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Worksheet 35-Spring 1996

For Teachers Higher Ed
In this math worksheet, students sketch six integrals and rewrite the equations as double integrals with reversed integration orders. Students evaluate four integrals. They sketch all points on a coordinate plane when given complex...
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Worksheet 36

For Teachers Higher Ed
For this math worksheet students find the solution u(x,y) of Laplace's equation in a given rectangle with specified boundaries. Students use the chain rule to compute values for a function and relate this answer to Laplace's equation....
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Virus and Bacteriophage

For Teachers 5th - 6th
Learners examine the differences between a virus and a bacteriophage. They explore various websites, identify the parts of a virus and a bacteriophage, and construct a model of a virus or bacteriophage.
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The Solar System

For Teachers 9th - 12th
Students construct a sketch of the planets in our solar system using concentric circles and angles. For this solar system lesson plan, students plot the position of each planet on concentric circles using graph paper. The sun is included...
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The Dawn Mission: Ion Rockets and Spiral Orbits

For Students 11th - Higher Ed
In this ion rocket and orbits worksheet, students read about the spiral orbit the Dawn spacecraft took due to its ion rocket motor. Students solve 3 problems including finding the path taken by the spacecraft, determining the total path...
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The Ant and The Turntable-Frames of Reference

For Students 11th - 12th
In this frames of reference worksheet, students solve 5 problems given the details of a journey an ant takes from the center of a CD ROM to its edge. Students draw a scaled sketch of the turntable showing the motion of the ant from...
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Construction an Eillipse ID: 9980

For Teachers 11th
Eleventh graders explore ellipses.  In this Algebra II lesson, 11th graders construct an ellipse using the Ti-nspire handheld and investigate the sum of the distance from a point on an ellipse to its foci.  Students use that information...
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Constructing an Ellipse ID: 9980

For Teachers 11th
Eleventh graders investigate ellipses.  In this Algebra II activity, 11th graders explore an ellipse from a geometric perspective.  Students derive the equation of an ellipse with the center at the origin. 
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Precalculus Exam

For Students 11th - 12th
In this precalc lesson, students write out definitions, identify functions, solve integrals and derivatives and graph trig functions as they relate to angles. This is a final exam for precalculus. There are 80 questions on this exam.
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Complex numbers in polar form

For Teachers 9th - 12th
Young scholars plot complex numbers in the polar plane. They convert complex numbers in polar form to rectangular form. Students plot coordinates in the polar plane. They plot complex numbers in the complex plane. Young scholars are...
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Complex Analysis: Polar & Exponential Forms

For Students Higher Ed
In this polar and exponential form worksheet, students use Euler's Formula to write complex numbers in exponential form. They write numbers in rectangular form. This two-page worksheet contains seven multi-step problems.
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Complex numbers in polar form

For Teachers 9th - 12th
Students plot complex numbers in the polar plane. They are asked to list what they believe are the five most famous numbers in mathematics. Students are explained that generally accepted that the five most famous numbers in mathematics...
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Worksheet 37

For Students 11th - Higher Ed
For this math worksheet, students sketch the regions that give rise to the integrals. Then rewrite them as double integrals with the integration order reversed.
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Math 222. Worksheet 8. Cartesian Coordinates

For Students Higher Ed
In this Cartesian coordinate instructional activity, students eliminate cross-product terms by a rotation of the axes, graph polar equations, and find the equation for a tangent line. This two-page instructional activity contains...
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Polar Equations

For Students Pre-K - Higher Ed
In this precalculus worksheet, students find the solutions to polar equations for the 3 detailed problems using the coordinates and graphing calculators.
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Beginning Lesson on Coordinate Grids: First Quadrant

For Teachers 3rd
Third graders play a game. In this plotting points lesson, 3rd graders discuss the number line and the coordinate plane. Students practice plotting points on a grid and play the simple maze game for more practice.
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Graphing Polar Equations

For Teachers 11th - 12th
Students work in groups to graph groups of polar equations and investigate questions about classic curves. They discuss the answers and develop equations that are answered given the graphs and classic curves. Then students analyze the...
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Vector Manipulation Unit

For Teachers 9th - 10th
Students are introduced to the concept/idea of a vector, what it represents and why they are used. They develop an understanding of what vectors are, how and why they are used.
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Worksheet 34

For Students 11th - Higher Ed
In this math worksheet, learners find the plane perpendicular to the path (t2, t, cos 2πt) at time t = 1/4. Then they determine the location in which the object is moving the fastest.
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Worksheet 27

For Students 11th - Higher Ed
In this math worksheet, students examine the equations for the planets of Mercury and Saturn. Then they find the distance of Saturn’s closest and farthest approach to the sun.
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Worksheet 29

For Students 11th - Higher Ed
In this math activity, students investigate how time is related to the concept of increasing or decreasing velocity. Then they consider times and answer the questions of whether the velocity is changing.
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Coordinates

For Teachers 9th - 12th
High schoolers use cartesian coordinates (x,y,z) in 3-dimensional space. [Optional: appreciate there exist two ways of defining the z axis, and which of them is used.] They become familiar with the tools and terms used by surveyors.
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Math 53 Worksheet

For Students Higher Ed
In this college level calculus worksheet, students sketch the graphs of polar equations.    The one page worksheet contains eight problems.  Answers are not included. 
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Ellipses And Kepler's First Law

For Teachers 9th - 12th
Students explain that planets actually orbit the center of gravity of the solar system, and that distant planets may be detected by motions of their central star around the centers of gravity of their planetary systems.
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Vectors Via the Calculator

For Teachers 8th
Eighth graders resolve vector problems without the knowledge of math.  In this vectors lesson students with poor math skills get a chance of passing the course. 

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Polar Coordinates