# Suspended Objects in Calculus Class

This just in from Mrs. McCullagh:

Calculus students just turned in their projects for trimester two. Students were asked to design and model the solution for suspending an object of their choice from wherever they want, with the least amount of wire. Some of the interesting designs were for suspending: a Williston sign from the bridge, a jumbotron at the hockey rink, a tire from a tree, a tree in a planter from the roof over the patio at the Reed Campus Center, a North Carolina flag from an airplane, a car from a crane, among others. Students first needed to decide how far apart the hooks should be from which they would hang their object, and how far down they want the object to hang. Based on those dimensions they needed to minimize the amount of wire needed. All their calculations needed to be carefully displayed and they needed to produce a model of their solution.

# 2019 AP Calculus BC Free Response Questions & Answers!

A few days after each AP Calculus BC exam, the College Board releases the free response questions from the exam. They don’t release their very succinct answer keys for a few more weeks… so… I had my students make their own answer keys as well as screen recordings of their solutions!

Official 2019 answer keys will eventually go online right here, along with the ones from past years that have already been posted.

You can view the 2019 AP Calculus BC Free Response Questions right here.

All of the 2019 answer keys that my students created can be viewed right here.

All of their 2019 video solutions can be viewed right here.

You can check out this project from past years here (2018)here (2017), and here (2016).

Many more Williston student screencasts can be found online right here.

# 2018 AP Calculus BC Free Response Questions & Answers!

A few days after each AP Calculus BC exam, the College Board releases the free response questions from the exam. They don’t release their very succinct answer keys for a few more weeks… so… I had my students make their own answer keys as well as screen recordings of their solutions!

Official 2018 answer keys will eventually go online right here, along with the ones from past years that have already been posted.

Here are the answer keys and videos that my students created:

You can check out this project from past years here (2017) and here (2016).

Many more Williston student screencasts can be found online right here.

# Calculus Projects!

This just in from Mrs. McCullagh:

Calculus students displayed their work on a challenging optimization problem. They were asked to plan a design to hang “something” from “somewhere”, and then determine the least amount of rope or wire needed.
Some of the things they chose to hang included a Williston medallion from the Golden Gate Bridge, a disco ball from Eiffel Tower, a circus hoop from the circus tent, a tire swing from a tree, and a target in a hockey goal. They needed to plan how far apart the hangers would be and how far down their item would hang. They then used Calculus to find the minimum amount of rope or wire needed for the project. Their presentations needed to include all of their calculations and drawing to support their work and solutions. They also needed to build a model to represent their solution.

# 2017 AP Calculus BC Free Response Questions & Answers!

A few days after each AP Calculus BC exam, the College Board releases the free response questions from the exam. They don’t release their very succinct answer keys for a few more weeks… so… I had my students make their own answer keys as well as screen recordings of their solutions!

All 2017 released free response questions and answer keys are online right here. Questions and answers for past years can be found right here.

Here’s the direct link to the 2017 AP Calculus BC free response questions.

Here are the answer keys and videos that my students created:

Many more Williston student screencasts can be found online right here.

# Dispatch from Calculus

This just in from Mrs. McCullagh:

Teaching Calculus to seniors and a few juniors, I feel an obligation to help move them toward independence and self-sufficiency in their learning. I want them to learn to support themselves as learners and know how to reach out for assistance. I use two primary methods to this end.

First, I provide full solutions for all homework. Students are expected to use these solutions to check their work as they complete each problem to be sure they not only have the correct answer, but more importantly, that they have supported their work appropriately. The other way they can use these solutions is as a hint on how to start a problem if they just need a little help. No one should come to class with a blank homework saying they did not know how to do the work. With this, they know when they need help and are expected to ask for it.
My second strategy for student increased independence is to have all students at the boards at the same time to do problems together. By being visible, at the boards, they can and should look to others around them to confirm they are headed in the right direction. Each student becomes a source of information for everyone else. Students who might not take the lead sitting at their desks are now asked for help by their peers. Again, no one is left unable to start a problem. Help is all around.

# Solids of Revolution Project

This just in from Mrs. McCullagh:

For the last few days in Calculus, with help from Mr. Roe in the Art Department, my classes built models as part of a project exploring solids of revolution. Partners were assigned an equation, asked to sketch and graph that equation and then find the volume of the solid that would be created by revolving that graph around the x-axis. They needed to sketch and estimate the volume if filled with only four cylinders, then find the estimated volume if filled with eight cylinders using a computer generated model. Using Calculus they were able to find the actual volume and compare it with their estimates. Next they needed to create a three dimensional model of their solid using wire and foam core. On the last day of classes they presented their project to their classmates. The projects were on display in the Reed Center in time for graduation for their families to see.